Room 14-0551 MITLibraries Document Services 77 Massachusetts Avenue Cambridge, MA 02139 Ph: 617.253.5668 Fax: 617.253.1690 Email: docs@mit.edu http://libraries.mit.edu/docs DISCLAIMER OF QUALITY Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort possible to provide you with the best copy available. If you are dissatisfied with this product and find it unusable, please contact Document Services as soon as possible. Thank you. Pages are missing from the original document. PAGES 85 THRU 88 ARE MISSING An Integrative System Dynamics Approach to Project Management by Thorarinn Sveinsson Civil Engineer, University of Iceland (1992) Submitted to the Department of Civil and Environmental Engineering in Partial Fulfillment of the Requirements for the Degree of Master of Science in Civil and Environmental Engineering at the Massachusetts Institute of Technology February 1995 © 1994 Thorarinn Sveinsson. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part. Signature of Author Department of Civil and Environmental Engineering August 11, 1994 Certified by Professor Jerome Connor Thesis Supervisor /I Accepted by- ;A a - Professor Joseph Sussman Departmental Committee on Graduate Studies ar;r Eai I .""I -' %I An Integrative System Dynamics Approach to Project Management by Thorarinn Sveinsson Submitted to the Department of Civil and Environmental Engineering on August 11, 1994 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Civil and Environmental Engineering Abstract Repeated schedule and cost overruns in the field of project management have indicated the inadequacy of today's standard project management support tools. This inadequacy takes various forms in the operation of a project, but one of the most disturbing issues is that schedule and cost overruns can often not been explained by standard tools. This indicates a need for a framework capable of simulating project management implementation in a realistic way, where causes are identified and solutions are arrived at through an improved understanding of the real behavior. The purpose of this research effort is to develop an improved understanding of the interacting forces in a project from a managerial perspective. In order to do so, the framework of system dynamics is utilized to provide a computer model of a generalized civil engineering design project where the subject of interest is constrained by a defined boundary. Critical aspects to success are identified while exploring the field of project management in general. In a more detailed manner, critical variables and processes in a civil engineering design project management are identified, and their formulation justified. This was done through interviews and questionnaires filled out by experienced people in the field of project management and system dynamics. Fifteen sectors located under five subsystems form an integrative system dynamics model developed from the identified variables and processes. The model is capable of simulating the behavior of interacting forces from the beginning of the design phase to the end of the project where a tender specification set has been developed and published. An example of the model output is demonstrated and discussed. The potential of several parameter changes is considered and effects of changes explored. Finally, the validity of the project model is discussed from a management consulting point of view. Acknowledgements My first acknowledgment goes to the people at ECECO, especially to Sveinn Thorarinsson for his assistance when a perspective was needed on various project managerial subjects. I would like to thank James H. Hines, Professor at the Sloan School of Management, who introduced me to the field of system dynamics and was always ready to share his knowledge with me. I would like to thank Asmundur Tordarson, M.A., for his hints about the English in this thesis. However, I am aware of that this acknowledgment is not neccessarily in favor of his future as a english consultant if some errors will be identified after the thesis has been handed in. In that case I would like to empahsize my responsibility. Finally, I would like to thank all the people at the Civil and Environmental Engineering Department, especially Jerome Connor for his supervision and support to my plans and David Ford which shared his knowledge of system dynamics and provided me with many useful ideas. 3 To my parents, Sveinn and Olof 4 Table of Contents Abstract.......................................................... Acknowledgements..............................................................................3 Table of Contents .......................................... 5 1 Introduction ................................................................................... 7 1.1 1.2 2 Overview of Project Management Concepts . 7....................................... 8 ...................................... 9 2.1 Introduction to Project Management ......... 2.2 Organizational Structures .......................................................... 2.2.1 Line Organization......... .................... 2.2.2 Line-Staff Organization...................................... 2.2.3 Product Organization...................................... ................. 2.2.4 Matrix Organization ..................................... System Dynamics and Organizational Structures . ................................. 2.3 2.4 2.5 3 Background . ..................................... Objectives ................................................................................ .................................... Project Scheduling..................................................................... 26 2.4.1 The Critical Path Method .................................................. 27 2.4.2 The Project Evaluation and Review Technique ........................... 29 System Dynamics and Project Scheduling.......................................... 30 Development of a Project Model ............................. 3.1 Introduction to System Dynamics Conventions .... 3.1.1 CausalLoop Diagrams...................................................... 3.1.2 Stocks and Flows Representation ......................................... 3.2 Smoothing of Information ............................................................ 3.3 The Scope of the Project Model . ..................................................... 3.3.1 Model Boundary............................................................. 3.3.2 Sources of Information ..................................................... 3.4 Model Overview ....................................................................... 3.5 Human Resource Management ...................................................... 3.6 3.7 33 .33 34 36 38 40 41 43 45 48 3.5.1 Staffing and Training ................................ 48 3.5.2 Overtime Policy and its Effects ........................................ 58 3.5.3 Workforce Allocation....................................................... 64 Project Planning ........................................................................ 70 3.6.1 Planned Workforce Allocation .............................. 70 3.6.2 Forecast of Workforce Needed ............................................ 74 Project 3.7.1 Controlling ............................ 82 Schedule Pressure ........................................................... 3.7.2 Scheduling ........................... 3.7.3 3.8 9 14 14......... 14 18 19 20 23 Project Database . 3.8.1 Development Productivity ......... 3.8.2 3.8.3 85 ............................................................ TenderSpecificationProduction......... .. Rework Productivity ........................... Learning Influence on Productivity . 5 82 ......... ......... 89 .... 91 91......... .............. 91 ........................... 98 .99 3.9 3.8.4 Quality.................... 3.8.5 ProgressIndicators......... ............. ......................................10 3 3.8.6 Rework Detection ......... .. ......... .................... 1 10 114 1....................14.... Environment...................................... 121 3.9.1 Initial Values ...................................... 3.10 Summary of Project Model Development .. 121 124 4 Model Testing ................................. 4.1 Human Resource Management.............................. 125 126 4.2 4.3 Project Planning .............................................. Project Controlling ................................................................... 133 136 4.4 Tender Specification Production .............................. 139 4.5 4.6 Schedule and Cost Overruns . ............................................ 149 151 Parameter Changes ....................................... ........................151 4.6.1 Effects of Increase in Productivity per Worker . .............................. 157 4.6.2 Effects of Changes in Additional Work 160 4.6.3 Effects of More Aggressive Hiring Strategy............................ 163 4.6.4 Effects of Over-Estimation in Project Size.............................. 167 Model Validity ........................................................................ 4.7 5 Sum mary . 5.1 5.2 ................................................................................... Conclusions ................................................................... Final Thoughts and Further Research .............................................. 170 70 171 6 Bibliography.......................................... 174 Appendix A: System Archetypes .......................................... 177 Appendix B: Model Documentation (Base Run).................................... 180 6 1 Introduction The purpose of this thesis is two-fold. Firstly, to develop an improved understanding of the interacting forces in a civil engineering project from a managerial perspective. Secondly, to construct a system dynamics project model capable of simulating the behavior of interacting forces from the beginning of the design phase of a civil engineering design project to the end of the project where a tender specification set has been developed and published. The forecasting capabilities of the model allow exploration of the effects of changes in structures, policies, and time factors that are institutionalized in the organizational structure. 1.1 Background Repeated schedule and cost overruns in the field of project management have indicated the inadequacy of today's standard project management support tools. This inadequacy takes various forms in the operation of a project, but one of the most disturbing issues is that schedule and cost overruns can often not been explained by standard tools. This indicates a need for a framework capable of simulating project management implementation in a realistic way, where causes are identified and soulutions are arrived at through an improved understanding of the real behavior. Several publications exist on this subject and the application of system dynamics. History of work in the area of project models , includes that of Roberts (1964 and 1978), 7 Cooper (1980 and 1993), Richardson and Pugh (1981), Abdel-Hamid (1984) and Sterman (1992) and more. 1.2 Objectives This thesis is undertaken to satisfy three primary objectives: * To gain insight into project management in general with a particular emphasize on civil engineering design and design implementation. * To use system dynamics to identify the systematic forces acting on a Project Management implementation. * To develop a generalized system dynamics project model with respect to information conducted through interviews and review on related research. Of a particular interest is also to consider the potential of several parameter changes and explore effects of changes. The theoretical foundations for this work are the fundamental concepts of system dynamics and traditional managerial concepts and frameworks. System dynamics incorporates the mental models of managers and employees and provides the key concept of traditional feedback theory adjusted for use in a business environment. 8 2 Overview of Project Management Concepts 2.1 Introduction to Project Management Project management (PM) is considered to be relatively young approach in its current form although it has undoubted been applied in one way or another for a very long time. Many of the remarkable and famous ancient achievements in construction, could not have been performed without appropriate project management approach. However, the PM approach has developed extensively. During past decades, managers have become increasingly aware of how success in project management is influenced by company's structure and control of resources. The project management approach is characterized by methods and tools which purpose is to obtain better control and use of existing resources. The role of project management and its approach develops further with changes in complexity and various environmental factors such as competition, quality requirements, more demanding time and cost goals etc. Today, many corporate problems are constructed from inappropriate control and usage of resources 1. Managers are becoming more and more aware of the advantages of applying the PM concepts to various situations, both in order to limit the number of responsible people and to structure organizational operations in a clear and simple way. PM is therefore a subject of interest to most organizations. Most projects involve a contract Kerzner, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 1 9 between two or more parties. Considering the five basic functions of business management, an overview definition of PM can be stated as follows 2: Project management involves the functions of staffing, planning a course of action, controlling of cost, schedule and performance, organizing company's resources and directing a project towards specific goals, objectives and completion. Project Management concepts are applied within various organizations and industries for various types of projects. Project management utilizes the systems approach to management by having finctional personnel (verticalhierarchy)assigned to a specific project (horizontal hierarchy)2 Various interactions and trade-offs exist between the constraints on a project, which are: * Time, * Cost, * Quality, * Scope, and * Good customer relations. 2 Kermer, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 4 10 Customer relations can either be directed towards a customer within the organization or outside of it. It is listed as a constraint because without good customer relations the project team will most likely not be assigned to additional work, which sometimes boosts up the profit, or a new project from the same customer. Quality is integrated into and between time, cost and scope constraints 3. Very few projects are completed within the original scope of the project. The scope constraint indicates that scope changes must be held within certain limits and those that are required must be approved by the project manager as well as the customer. Excessive scope changes can work out to be difficult to handle because of the project team's expertise and capabilities but they can also play an important role as a base of additional work and additional payments as a crucial part of the profit associated with the project. The role of the project manager is to build up and lead the project team to ensure project completion within all constraints. On the macro level, organization may be divided into at least two different types 4: * Non-project-driven organization, and * Project-driven organization. Non-project-driven organization measure profit and loss on functional (vertical) lines and projects exist merely to support the product lines or functional lines. Thus, functional management coordinates on repeated work of a similar nature by the same people. Informal project management appears most often in non-project-driven 3 Oberlender, Garold D. 1993. Project Management for Engineering and Construction. McGraw-Hill. New York. p. 4 4 Kerzner,H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 40 11 organization. A classical example of non-project-driven organization is i.e. low-cost manufacturing. In a project-driven organization, such as construction or design, all work is performed through projects, and each project has its own profit and loss statement. Winning new contracts is necessary for the operation of any project-oriented business. Company's technical capabilities and experience are developed towards future business growth, with each project. This includes systematic development of the project management expertise within a company. This paper focuses on project-driven organizations with particular emphasize on civil engineering design companies and the construction industry where each project has its own profit statement and clearly apparent start- and end-point. Bidding (or a fixed amount for a project) is becoming more and more common form in this sector as a way to lower cost for the owner (the purchaser of the service). Unfortunately, cost and schedule overruns appear quite frequently in the construction sector which makes it more challenging from the managerial point of view. Changes in the project problem definition, from the project team perspective, appear quite frequently and depend on various internal and external factors. Internally directed changes to the project team's problem definition often result from 5: * Insufficient quality which require rework, i Errors which require the pursuit of new approaches, and * Misjudgements by the management team of the complexity or scope of the project. 5 Hajek, Victor G. 1984. Management of Engineering Projects. McGraw-Hill. New York. p. 4 12 Externally directed changes to the project team's problem definition often result from 5: * Revision of design because of engineering problems, * Management redirection to take advantage of new technology or because of resource circumstances, and * Changes directed by customer. Cost because of changes directed by customer and revision of design because of engineering problems is usually paid by the customer and management redirection to take advantage of new technology or because of resource circumstances is in some cases paid by the customer. Externally directed changes are occasional and unpredictable in many cases. Internally directed changes, on the other hand, depend on how efficient and well suited the project team is and also on the nature of the project. It's possible to take them into account in many cases by working from previous experience or to reduce them by better control and other managerial functions. Excessive undesirable delays inbuilt in organizational structures along with lack of communication between organizational units are partly responsible for why project managers have not succeeded in dealing with internally directed changes. Also partly responsible are the standard tools for project managing, monitoring and planning which in complex projects are often inadequate. It appears quite frequently in the field of project management that large portions of project effort can not be described or explained by applying standard tools 6. The technique for scheduling doesn't capture effects of fundamental factors such as schedule pressure, rework, and changes in workforce which in many cases are critical to a project success. 6 Cooper, K.G. Feb 1993. The Rework Cycle: Why Projects Are Mismanaged. Project Management Journal. 13 2.2 Organizational Structures During the past ten years there has been a so-called hidden revolution in the introduction and development of new organizational structures 7. Organizational structures play an important role in success of companies. Construction companies with different projects in different environments, even in different countries often have to organize themselves in a different way for each project. Project manager will i.e. have to use different methods in Asian, African or Middle Eastern construction projects than in Scandinavian projects 8. Rules about import, monopoly of certain unions in certain areas and other constrains are all subject of interest that are not covered in this paper. Depending on circumstances, certain aspects of organization may outweigh others. Traditional line structure in comparison to matrix structure is a subject of key interest in PM. The project manager's functions, responsibilities and authority in a matrix structure differ significantly from those in the traditional line organization. 2.2.1 Line Organization The line organization is the oldest and most traditional type of organization and is widely used in today's companies. An engineer launching his own engineering consulting 7 Kerzner, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 97 8 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 33 14 office and employing people to do surveying, design, etc. would most likely select the line organization Figure 2.1 9. Traditional (line) organizational structure 10 A project organized along the traditional structure would have the project manager as an apex of the pyramid. Generally, this structure is successful in meeting the schedule, cost, and quality objectives if no major difficulties are encountered and if project revisions are not required. When difficulties appear and the project environment requires revisions of the project, the traditional structure may involve too slow response due to functional gaps (departmentation) and an additional lead time required for approval of decisions. There are always some management gaps between various levels of management in addition to functional gaps between working units of the organization. When management 9 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. 10 Hajek, Victor G. 1984. Management of Engineering Projects. McGraw-Hill. 15 p. 38 New York. p. 2 and functional gaps are added up, it results in operational islands with very limited information flow and support between each other. /\ a/ \ -! /ZII\ L7LIBZI\ / Management gaps Figure 2.2 Functional gaps Operational islands Gaps in organization and operational islands 11 It is the project manager's responsibility to get the operational islands to communicate and support each other cross-functionally towards specific goals, objectives and completion of a project. The traditional structure can work out very well in some situations but has however some characteristics that are not favourable to many of today's projects. Some important characteristics of the traditional (line) structure are 12,13: 11 Kermer, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 5 12 Kerzner, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 102-106 13 Hajek, Victor G. 1984. Management of Engineering Projects. McGraw-Hill. New York. p. 1-11 16 * Communication channels are well structured, because each person reports to only one individual. Budgeting and cost control structure is constructed in a very clear way as well. * Slow response to customer needs. The top management gets involved with the daily routine because all communication is channelled through upper level management which refers problems down through the vertical chain. The emphasis on various operating functions focuses attention on internal aspects and relations. * Lack of communication between divisions and difficulties in performing activities that cross functional lines. Line structure tends to breed isolation among different projects. * The strongest functional group dominates decisions and the functional managers tend to focus on their group rather than the total project. * Strong resistance to changes often develops within the functional organization. Long-term corporate planning tend to be superficial and infrequently updated, which often leads to over-staffing and inefficiency. The traditional line structure is very well suited for small projects and is therefore often selected by small companies which are building up their potential. When companies becomes larger and projects more complex the need for organizational changes becomes apparent. Company culture is however developed from the birth of a company and is very hard to change after it becomes stable. Therefore, in most cases, a lot of effort is needed in order to perform organizational changes. This is especially true when changing from the line structure. 17 2.2.2 Line-Staff Organization The line-staff organization has the project manager separated from controlling influences of functional managers in order to give the control of a project to personnel which first loyalty is directed towards the objectives of the project. The word staff in the line-staff organization refers to those who are appointed to assist the line by counseling, advising or other assistance Figure 2.3 14. In line staff organization the amount of authority given to the project manager often leads to serious problems 15 Often the line-staff organization doesn't succeed because department managers don't like to take directions from project managers in addition to directions from the division managers. Division managers often consider it as a threat to have to give up any of 14 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 38-40 15 Kerzer, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 102-112 18 their power. Line-staff project manager reports to his division head and doesn't have authority or control over those portions of the project performed in other divisions 15. 2.2.3 Product Organization Product organization is simply a division along the product lines and is common in manufacturing, wholesaling and retailing 16 Figure 2.4 Pure product organization 17 In pure product organization the product manager maintains complete line authority over the entire project. Reaction time is rapid but technology suffers because no single group exists for planning and integration. Duplication of effort and inefficient usage of facilities and personnel is common 17. 16 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 45 17 Kerzner, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 113-115 19 The product organization is not well suited for the civil engineering design industry, where technology often plays an important role in determining company's success. 2.2.4 Matrix Organization The matrix organization is a modern type of organization where a lateral project organization is superimposed over the traditional functional organization .18 ........... Assigned project team members Figure 2.5 General form of matrix project structure of an engineering department 19 In the matrix structure the project manager shares authority, over the project team members and discipline supervisors, with the functional manager. 18 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 42 19 Hajek, Victor G. 1984. Management of Engineering Projects. McGraw-Hill. New York. p. 5 20 Chief engineering manager Assistant eng. manager lI Chief eng. developm. Chief civil eng. design I I I Chief mech. eng. design Chief electrical eng. design Chief eng. for contracts & specifications i, Project manager X 1 IIJ Project manager Ur it Y _ Project managerL _ Z r Li .I Figure 2.6 l '" it l sl sl A.g ., Li Li l . AL Li " . .,g Li Matrix organization of an engineering department 20 The project managers have responsibility for the project's success and each of them represent a potential profit center. Their power and authority comes directly from the division head. When a company, organized with the matrix structure, grows in size and in number of projects, a position of chief of project management is often created. The chief of project management is responsible for all projects and program management. Functional departments have responsibility to maintain technical excellence on the projects. Organizational matrixes can be subdivided into two forms of operation, fixed matrix and shifting matrix 21. In fixed matrix, the same functional personnel remains responsible to the 20 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 43 21 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 42 21 same project managers, but in the shifting matrix functional personnel may work under different project managers according to the priority of projects. Some important characteristics of the matrix organization are listed below 22,23,24: * The "unity of command" principle is violated and personnel in the matrix organization have two superiors and even the possibility of more superiors in the shifting matrix organization. * More people than necessary are required, primarily administrative, and more effort and time is needed initially to define policies and procedures, compared to the line organization, but policies and procedures can easily be set up independently for each project. Too many people may be involved in decision making and during economic crunch the overhead may easily become too excessive. * Maximum project control is maintained through line managers over all resources, including cost and personnel and the functional organization exists primarily as a support for the projects. However, functional managers have their own set of priorities and the balance of power between project and functional organization must be watched. * Rapid development of specialists occurs and key people can be shared. Knowledge is available for all projects on equal basis. However, shifting people from project to project may interrupt the training process of employees. 22 Hajek, Victor G. 1984. Management of Engineering Projects. McGraw-Hill. New York. p. 1-11 23 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. p. 42-44 24 Kerzner, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. p. 115-127 22 * Each project operates independently and duplication of i.e. R&D efforts can occur. * Long-term plans may suffer from the requirements of temporary projects. Management goals are different from project goals. In short-term, a rapid response to changes is possible. The matrix organizational form is ideal for project-driven organization such as construction companies. Modem complex projects are generally very dynamic as far as revisions is concerned. Therefore, they require flexible management which cannot be realized with a line organization. In the pure product organization, technology is sacrificed and in pure functional organization, time and schedule are sacrificed. Matrix organization is a compromise attempted to create synergism through shared responsibility between project and functional management. 2.3 System Dynamics and Organizational Structures No two companies have exactly the same organizational design because no working environments are exactly the same. Unfortunately, many companies do not realize what organizational structure is appropriate at a time or/and respond too slowly to changes in the environment. Such environmental factors might i.e. include * Technology, * Consumer demands, and * Competition. 23 Changes in these factors require fast response which often is best reached through a matrix organisation. Complex projects, where some major difficulties can easily appear, are often not efficiently utilized in the traditional line-project organizations. In many cases, resource problems that are inherent in line organizations have been reduced or even eliminated in the matrix organisation. However no single organizational structure can be performed without problems and these problems are always going to be significant. In the matrix structure the principle of "unity of command" is violated and the overhead requires more people than actually necessary for the operation. System dynamics (SD) models have proven to help in making organizational pitfalls apparent, especially in the integration of flow of work and delay time between cause and effect 25. It also helps identifying what linkages between operational units needs to be improved and where new linkages need to be added. It is not possible to model every activity of a company in detail but system dynamics model has to include those aspects that are critical to the success of a company. "The significance of a model depends on how well it serves its purpose. The purposeof industrialdynamicsmodelsis to aid in designingbetter management systems." 26 When using system dynamics to simulate organizational behavior, one of the highest leverage points for improving performance is the minimisation of system delays 27. 25 Class notes from the "15.874 System Dynamics for Business Policy' class at MIT". Spring 1994. Both Peter Senge and Jay Forrester pointed out some examples concerning this subject in their speeches as guestspeakers in the 15.874 class. 26 Forrester, Jay W. 1961. Industrial Dynamics. Productivity Press. Cambridge MA. p. 115 27 Stata, R. 1989. Organizational Learning - The Key to Management Innovation. Sloan Management Review. Vol. 30, No. 3, p. 65 24 Input into a model from external resources can be varied easily and organizational behavior can be simulated for various sensitivity values that can be created within the organization. Various processes performed and time values required within the organization can thus be changed and experienced without the cost of real world experience. Inappropriate response (too slow, too fast or oscillating etc.) from certain sectors within an organization often become apparent in such simulations. The system dynamics usefulness in optimizing response time to changes in environment is especially well suited to explore organizational pitfalls in the traditional line structure where time and schedule is often sacrificed for technology and simply constructed communication system. Various time factors such as time to plan workforce, time to detect rework and time to perceive productivity etc. depends on the organizational structure of a project. Interactions between time factors, cost and long run creativity exist in many cases. Organizational structures that are better suited for completing projects on time and schedule, than the traditional line structure, may involve crucial disadvantages in some cases. Therefore, a well grounded knowledge and awareness of the characteristics of various types of organizational structures is critical. Methods for coordinating flow of work between functional units without modification to existing organizational structure may be sufficient in some cases but the need for a focal point for the project to ensure integration of activities will never be doubted. In project management, the organizational learning through shared insights, knowledge, and mental models along with organizational memory should be integrated into the structure of a company 28. It's especially important in the field of project management to find ways to learn from mistakes and overruns in scheduled time and cost because similar mistakes seems to repeat themselves. 28 Stata, R. 1989. Organizational Learning - The Key to Management Innovation. Sloan Management Review. Vol. 30, No. 3, p. 64 25 "Industrialdynamics is the investigation of the information character of industrial systems and the use of models for the design of improved organizationalformand guidingpolicy."29 In the project-planning process the choice of appropriate organizational structure depends on various factors. Organizational structure may differ from project to project within the same company and system dynamics modeling of a project in the planning process is an essential tool to identify weaknesses in organizational structures when applied to the project circumstances and possible paths of progress. Formal organization to manage a project has to be applied from the beginning of a project but not only from the beginning of the actual working phase. 2.4 Project Scheduling Unfortunately, overruns in schedule and cost, are rather rule than exception in the field of project management 30. In projects where the project completion is on schedule it may be important to explore organizational structure and policies in order to improve the company success further. On the other hand, research in that direction may sound weightless when dealing with the fact that the traditional science of complex development project management is a failure with enormous consequences in terms of losses both in the 29 Forrester, Jay W. 1961. Industrial Dynamics. Productivity Press. Cambridge MA. p. 13 30 Sterman, John D. 1992. "System Dynamics Modelling for Project Management". Working paper available from John Sterman. MIT Sloan School of Management. Cambridge, MA, p. 2 26 construction industry and other businesses 3 1. However the organizational structure is very important from the learning perspective and proper organizational learning and memory has to be integrated into an organization. Due to the complex and uncertain nature of many factors critical to the accuracy of today's planning, some project end up with huge schedule and cost overruns which have even more than doubled the initial estimations in many cases. Of course, performance like that is unacceptable, but the worst thing is that we have made rather little progress in learning how to manage large projects and we still get surprised again and again even in projects that can't be considered unique in any sense 3. Project managers are equipped with standard tools for project managing, monitoring and planning which in complex projects are often inadequate and large portions of project effort can not be described or explained by applying standard tools 31. As a standard project management tool, the Critical Path Method (CPM) and the Program Evaluation and Review Technique (PERT) are both very powerful. Knowledge of how to apply them is widespread all over the world. They are unique in the sense that no other methodology seems to be able to cover their ability to represent detailed project planning in such a clear and readable way as they do. 2.4.1 The Critical Path Method CPM (Critical Path Method) grew out of a joint effort by Remington Rand Univac and the DuPont Company, initiated in 1957.32 31 Cooper, K.G., Feb. 1993, "The Rework Cycle: Why Projects Are Mismanaged", Project Management Journal, p. 5 32 Moder, Joseph J., and Cecil R. Phillips. 1970. Project management with CPM and PERT. Van Nostrand Reinhold Company. New York. p. 6. 27 The CPM method provides a framework in which the linkages between, and the duration of individual tasks can be planned. The critical time-path lies through a certain sequence of tasks which only includes tasks that can not be delayed without delaying the entire project 33. Critical path networks fall broadly into two main classes, generally known as arrow (activity on arrow) and precedence (activity in node). These classes are recognizable from their diagram notation. Unlike the precedence diagram approach, which puts tasks into boxes, the activity on arrow approach places the tasks on the arrows that connect events (generally circled) 34.The arrow diagram is more commonly used but some popular softwares allow the user to use both classes. The CPM and PERT methods have for long time dominated among techniques for project planning and forms the basis of all popular project management software offered. These methods provide an excellent means of communicating what is to be done in the project to those that are involved and is extremely useful planning tool when properly constructed and updated. However, CPM scheduling has its limits and has been criticised for its inadequacy as a project planning tool. There is nothing inherently wrong in either the CPM concept or the subsequent schedules resulted from its analysis, the fault lies in the way it is applied in practice 35 Most people with some experience in project management have experienced when the time-plan in the critical path goes out of control. Most managers response by updating the CPM schedule from a new time-point during the project. In other words the feedback 33 Cooper, K.G. Feb 1993. The Rework Cycle: Why Projects Are Mismanaged. Project Management Journal. p. 6 3 4 Oberlender, Garold D. 1993. Project Management for Engineering and Construction. McGraw-Hill. New York. p. 71 3 5 Jaafari, Ali. June 1984. Criticism of CPM for project planning analysis. Journal of Construction Engineering and Management. Vol. 110, No 2. 28 control is all managed by a human hand, resulting in slow responses and often rather expensive project supervision compared to the cash flow associated with the project. When a CPM plan fails it doesn't only affect the project itself and involving tasks. It can also affect other projects that interact with the one that went out of control. This is true when the projects share resources such as manpower, equipments etc. Changes in scheduled completion date, of tasks or projects, also affects the scheduled cashflow and other things which depend on the accuracy of the project plan. CPM plan is often required and always accepted technique for project planning but on the other hand it is also inadequate model for managing complex projects. 2.4.2 The Project Evaluation and Review Technique The development of PERT began in 1958 36, when the US Navy was faced with the challenge of the Polaris Weapons System program. A research team evolved the PERT system considering techniques such as Line-of-balance, Gnatt charts, and milestone reporting systems. The PERT technique is an arrow diagram system that is similar in many respects to CPM. The main difference is that in PERT the planner specifies three different durations for each activity. These durations are 37: * tm = the most likely duration · tp = the most pessimistic duration estimate · to = the most optimistic duration estimate 36 Moder, Joseph J., and Cecil R. Phillips. 1970. Project management with CPM and PERT. Van Nostrand Reinhold Company. New York. p. 6. 3 7 Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. 29 p. 461 In the original PERT method the expected duration for each activity was formulated as: to + 4 tm + tp te = - 6 This formula has been modified in various ways, usually to weight the result towards the pessimistic value. 2.5 System Dynamics and Project Scheduling In today's standard project scheduling each task is portrayed as having definable beginning and end without taking the quality of the work done, into account. The amount of rework required is often a significant percentage of the total work done in a project but very few companies actually put effort into modeling it properly 38. Sometimes several rounds are needed on a task to complete it. I.e. engineering design of a house may involve several iterations of the same tasks before completed. System dynamics is known to be an effective analytical tool in wide variety of situations. Critical feedback loops affecting completion day may easily be modelled by making use of the system dynamics technique. SD models have been used to manage projects more effectively and make it possible to asses the magnitude and sources of cost and schedule overruns in a clear logistic way. First built for a ship design project at Litton 39, the 'Rework Cycle' model has since been applied accurately and successfully to over 38 Cooper, K.G. Feb 1993. The Rework Cycle: Why Projects Are Mismanaged. Project Management Journal. 39 Cooper, K.G. Dec 1980. Naval Ship Production: A Claim Settled and a Framework Built. Interfaces. Vol. 10, No. 6. 30 sixty different projects 40. By keeping track of critical factors affecting each task and each project, companies may also be able to forecast these factors for special kinds of tasks and projects. They can make use of data from their previous experience of similar or even same type of tasks and projects in order to bring the effects of critical feedback loops into their modeling procedure. In small projects, contractors actually tend to build on their previous experience in their scheduling procedure, sometimes with acceptable results and sometimes not. They know from their experience what to expect in terms of causal effects involved in each activity and they take it into consideration by including it in their estimation of completion day for each task, often by a flat percentage. But when projects are very big and complicated this technique often fails because of the complexity involved. It becomes too complex to estimate effects of varied quality because of schedule pressure, undiscovered rework, changes in workforce etc. During the project it even becomes complex to estimate difference between perceived progress and real progress and that brings inaccuracy into the system when schedule updating procedure is applied. Some companies have developed rule of thumbs for certain types of project to count for rework I.e. the author recalls when he was working for an engineering consulting office, some years ago, that certain scale factors were in development there for certain type of projects for each project manager within the company. The person in charge of a project claimed a certain number of workers for the project for certain amount of time, which he estimated from his experience. The initial schedule was simply multiplied by these factors in order to get some idea of what time was actually needed i.e. for complete engineering design of a house. The accuracy of the scheduled time for each project was very important to the company because of future allocations of workforce. In many companies, estimation 40 Cooper, K.G. Feb 1993. The Rework Cycle: Why Projects Are Mismanaged. Project Management Journal. 31 of rework and additional work, is crucial to their success and a high need exists for technique which recognizes the rework cycle, simulates it and helps managing its weight in the total project. Application of system dynamics provides a framework where projects are treated as flows of work where multiple rework cycles exists rather than as a simplified sum or sequence of discrete tasks, as in the standard CPM/PERT scheduling techniques 41. The author consider SD models as an interesting support tool to today's standard PM tools. CPM diagrams are excellent for scheduling a detailed layout of how various tasks depend on each other, while SD models are excellent for simulating a dynamic behavior that can't be explained by traditional tools. 41 Cooper, K.G. Feb 1993. The Rework Cycle: Why Projects Are Mismanaged. Project Management Journal. 32 3 Development of a Project Model 3.1 Introduction to System Dynamics Conventions When modeling a structure according to the system dynamics representation, the first priority is to consider some feedback loops that seem important in determining behavior of a system. The concept of information-feedback systems is the most important foundation for system dynamics and such systems are indeed fundamental to all individual, industrial, and social actions. An information-feedback system exists whenever the environment leads to a decision that results in action which affects the environment and thereby influencesfuture decisions 42 Control systems are classified into two general categories: open loop and closed loop systems. The control action, which activates the system to produce an output, determines whether a system is an open loop or a closed loop system 43. 42 Forrester, Jay W. 1961. Industrial Dynamics. Productivity Press. Cambridge MA. p. 14. 43 Richardson, G.P., and A.L. Pugh. 1981. Introduction to System Dynamics Modeling with DYNAMO. Productivity Press. Cambridge MA. p. 3-6 33 * Closed loop: Control action depends on the output and feedback is the characteristics of closed loop control which distinguishes them from open loop systems. Feedback exist when a closed sequence of cause and effect relations exist. * Open loop: Control action is independent of the output and action is planned and then executed without any feedback. A loop which is open isn't really a loop and the term "open loop" implies that something is missing. An interconnected set of feedback loops is a feedback system. Diagram of a feedback loop as a closed sequence of causes and effects is generally referred to as feedback loop or causal loop diagrams in the field of system dynamics. 3.1.1 Causal Loop Diagrams Single causal loops are classified into balancing (negative) loops and reinforcing (positive) loops. The number of minus-signs distinguish between negative and positive loops. Loop is negative if it has an odd number of minus-signs but positive otherwise. A Figure 3.1 - A causal loop diagram of a balancing (negative) loop. When A increases, it causes increase in B which causes decrease in A. 34 The classification of a causal loop into negative or positive loop is identified by a minus or a plus sign within a circular arrow inside the loop. A - B Figure 3.2 A causal loop diagram of a reinforcing (positive) loop. When A increases, it causes decrease in B which causes increase in A. Some interconnections of causal loops have appeared to be more common than others and they have been classified into System Archetypes. In "The Fifth Discipline", Mr. Peter Senge has identified ten System Archetypes: * Balancing Process with Delay, * Limit to Growth, * Shifting the Burden, * Shifting the Burden to the Intervenor, * Eroding Goals, * Escalation, * Success to the Successful, * Tragedy of the Commons, * Fixes that Fail, and * Growth and Underinvestment. 44 44 Senge, Peter M. 1990. The Fifth Discipline: The Art and Practice of the Learning Organization. Doubleday. New York. p. 378-390. 35 The system archetypes are those loops that have been identified as common loops which can serve as building blocks in complex causal dynamics. The majority of these archetypes are illustrated in Appendix A along with guide-lines of possible intervention strategies. Generic intervention strategies have been developed for each archetype and an archetype template may serve as a helping tool for managers to identify archetypes operating in their environment. 3.1.2 Stocks and Flows Representation From the system dynamics perspective all systems can be represented by interconnected networks of "stocks" and "flows" variables, and "converters" as a supporting variables and functions. "iThink" is a computer simulation language, which will be used in this paper to create a system representing the project management scenario. All graphical representation will thus be based on the layout provided by "iThink". A stock is signified by rectangle and it is a accumulation, or integration, of flows which serve as input and output of the stock. Accumulations in feedback systems are variously called stocks, state variables, or levels. The flows increasing and decreasing a level are variously called rates or flows. R O- Stock Output Rate Figure 3.3 Input Rate Simple flow diagram, showing conventional symbols for stocks and flows Flows will always originate somewhere and terminate somewhere.The little cloud symbols, appearing in figure 3.3. represent sources and sinks. Sources and sinks are 36 used when the origin or destination of the flow is treated as outside of the model concern. Mathematical equations for the structure in figure 3.3 would be represented as follows: Stock(t) = Stock(t - dt) + (Input_Rate - Output_Rate) * dt INIT Stock = 1 INFLOWS: Input_Rate = 2 OUTFLOWS: Output_Rate = 1 In the equation-set for the structure in figure 3.3, some arbitrary values have been chosen for the flows and also for the initial value of the stock. Flows can be formulated as functions which may take negative values. In such cases flows can be mapped as "biflows" which allows them to input or output negative values and therefore serve in opposite direction. When representing flow as a function of some variables, the variables could be connected to the flow in the form of converters. Converters convert inputs into outputs and unlike stocks, they do not accumulate. Converters can be formulated as constants or as mathematical or graphical functions. Change in Price -- 8 (~n~~ j Total Price with Taxes Price Taxes DeliveryDelay Target Price Time to Adjust Price Figure 3.4 Margin Simple flow diagram, showing conventional symbols for a biflow and a graphical function, where Margin is graphed as a function of Delivery Delay The graphical function is a special type of convertor which allows a creation of custom graphs where one variable is graphed as a function of another. The converter symbol for 37 graphical functions is distinguished from other converters by a special symbol within the converter circle. Figure 3.4 shows conventional symbols for biflows and graphical functions. Although the iThink software doesn't offer unit checking, its important to document units for each variable in order to clarify its meaning. In figure 3.4, change in price, could have units of $/time unit, while the price stock would have the unit of $. Several feature variations exist between system dynamics softwares but general graphical expression for stocks, rates and converters is standardized as box for stocks, valve for rates and circle for converters. 3.2 Smoothing of Information Smoothing and averaging processes are fundamental to a proper treatment of system dynamics and are essential for filtering out short-period of noise. Exponential smoothing processes formed by exponential delays serve as primary building blocks of system dynamics models. Such smoothing process doesn't have any cutoff time. In exponential smoothing, data points are given less weight, exponentially, as they become older and more recent informations take over 45. Stock Exponentialsmoothingtime Figure 3.5 Target Stock Schematic layout of exponential smoothing of first-order 45 Forrester, Jay W. 1961. Industrial Dynamics. Productivity Press. Cambridge MA. p. 408. 38 The first-order exponential smoothing process, which an example of is shown in figure 3.5, is widely used in the following project model. In iThink the rate and stock formulation of the structure in figure 3.5, would be represented as follows: Stock(t) = Stock(t - dt) + (- Rate) * dt INIT Stock = Initial Stock Value Rate = (Stock-TargetStock)/Exponential_smoothingtime In' more conventional representation we have, d(Stock(t)) = Rate(t) = - (Stock-Target_Stock)/Exponential dt smoothing_time Using more convenient names for variables the equation looks as: dS(T) S(r) - TS(T) dT T Solving the linear differential equation with initial value at t=O yields, S(t) = S(O) * e- t/T + e-t/T T (TS(T) * eT/T)dT Thus, if the Target Stock, TS, is constant we get, S(t) = TS + (S(O) - TS) * e-t/ r In terms of the variable names given in figure 3.5, the equation now looks as, Stock(t) = Target Stock + (Stock(O)-Target_Stock) * e- t/ 39 The graphical behavior of this equation is illustrated in figure 3.6, where the Target Stock is introduced to the system at t--O,and it remains constant throughout the simulation. Stock(time) 1: TargetStock= TS InitialStock 2: Stock- S T = Exponential smoothingtime D = InitialStock-TargetStock TargetStock )18 0 T 2T 3T 4T time Figure 3.6 First Order Exponential smoothing of the Stock variable, which in this example is subject to constant input of Target Stock and an exponential time constant T Exponential smoothing processes are sometimes constructed in such a way that the variable which is smoothed by first order exponential smoothing, is then smoothed again with another exponential time constant, which turns the process into second order exponential smoothing. Such smoothing processes of higher order than one, often appear in system dynamics models, although the first order exponential smoothing, is by far the most frequent one. 3.3 The Scope of the Project Model Excessive review on literature concerned with project management along with the experience of the author, as designer, engineering consultant and project manager in civil 40 engineering design companies forms the basis of how subjects of concern were selected for the project model. 3.3.1 Model Boundary The objective of the project model provided in this paper is to simulate a small to medium sized civil engineering design project, where the project is supposed to be started with data gathering and preliminary design and where the output of the project is a cost estimation and a complete set of tender specifications where all necessary information including drawings and specifications is provided. As indicated above the model handles one project and doesn't include any linkages to other projects in execution except for hiring and departure of workforce which may be considered to interact with workforce input and output of other projects. The purpose of the model is to develop understanding of and insight into the process of how civil engineering design projects are managed and developed. This includes: * Identification of variables influencing the success of civil engineering design projects, * Identification of what kind of managerial structures and processes are present in such projects, and * To provide a framework capable of simulating the actual recorded history of projects, and thus provide a tool with forecasting capabilities allowing exploration of the effects of changes in structures, policies and time factors institutionalized into the organizational structure. 41 The underlying purpose is also to provide the author with a computer simulation framework of this process which may be developed further in a Ph.D. thesis. The importance of the identification of managerial structures and processes should not be underestimated because such identifications may serve as an important preliminary work for a reengineering process. The model's boundary extends from the beginning of preliminary design and preliminary cost estimation of the engineering team and the definition phase of project's goals and objectives is supposed to be over and is excluded from our model. Any interactions with other organizations which in some cases may be working on the same project, are also excluded. All delays because of dependency on other development activities outside of the modelled organization are therefore excluded. The objective is to look at the decisions and actions within a civil engineering design development project and all activities because of discovered rework and additional work are within our model's boundary. The model boundary was very broad in the beginning, and was updated several times during the modeling process. In its final version, the model had more sectors and more variables than expected in the beginning. By disaggregating the model into relatively small sectors, its structure became more clear and easier to understand. The question of what to include and what to exclude in the model was, as expected, more difficult in the beginning of the modeling process than in later stages. As the model matured it became more apparent which processes were actually needed to express behavior of a design project in the field of civil engineering. However, most expansions were made in order to simplify the data gathering process and make the model's input and variables easier to understand. 42 3.3.2 Sources of Information Informations about critical aspects or about data that usually is accessible and available were collected through several sources: * Review on literature, * Review on related research within MIT, * Interviews, were critical processes were considered and several time factors and shape of curves were estimated. Various project management books were reviewed in order to identify critical aspects of project management. In the review on related research within MIT, several thesis written by MIT students were reviewed and also various texts from the Organizational Learning Center and the System Dynamics Group. Handouts and texts from System Dynamics classes at MIT also made an important contribution to the project model and some critical building blocks, covered in class, form the basis of some of the building blocks in the project model. In the interview process all the interviewees filled out a questionnaire about practical variables (custom graphs and time values). Because of confidentiality the filled out questionnaires are not accessible. However, the reader is notified whether a value of custom variable was based on interviews or other sources. In addition to the thesis supervisor the following people were interviewed during the modeling process. Sveinn Thorarinsson, president of the East Coast Engineering Consulting Office in Iceland. 43 David Ford, Ph.D student at civil engineering department in MIT. Ford is working on a system dynamics approach of the effects of coordination on product development. The purpose of the interviews was mainly to * select important building blocks and to get a perspective on how these blocks could be constructed in order to give a fair representation of a project behavior, and to * get estimation of, and perspective on, shape of various custom graphs and values of a number of time factors critical to the model behavior. Most of the practical time delays were gathered from the East Coast Engineering Consulting Office, ECECO, in Iceland, but the author worked there for several years before he came to study at MIT. Mr. Thorarinsson supervised the process of estimating time factors, shape of custom graphs and other critical factors within ECECO. ECECO has been responsible for several small and medium sized design projects including design of all houses for new college in Egilsstadir, which was the project we concentrated on when estimating values considered to vary significantly among projects. During the modeling process the model behavior was overviewed by ECECO in order to ensure that the graphical output of the model would match a behavior that they could expect from a real project. ECECO didn't have any available concrete data of a historic project's effort distribution into development of new tasks, rework and additional work although they had some data available about the fractional overruns in man-weeksand cost experienced from several projects. However, they had some idea of how these effort distribution output 44 could be shaped in a real project and therefore it was felt to be important to get their input on the behavior of the project model output from time to time during the modeling process. In addition to the sources at ECECO, the author felt it was important to get perspective from a person who's field was system dynamics modeling of processes similar to what the model contains. David Ford was very helpful in pointing out interesting variables influencing productivity and quality etc. and he also filled out the questionnaire which originally was constructed for the ECECO employees. 3.4 Model Overview The model was disaggregated into several sectors and all these sectors were located under five main fields, namely, * Environment, * Human Resource Management, * Project Controlling, * Project Planning, and * Tender Specification Production. The project model contains 15 sectors which are located under the five main fields in the following manner. * Environment - Initial values * Human Resource Management 45 - Staffing and training - Overtime policy and overtime worked - Workforce allocation Project Controlling - Scheduling - Project database - Schedule pressure * Project Planning - Forecast of workforce needed - Planned workforce allocation * Tender Specification Production - Progress indicators - Quality - Rework detection - Learning influence on productivity - Development productivity - Rework productivity The managerial functions of project planning, project controlling and human resource management serve as support activities to the tender specification production sector, which contains all the core variables for progress indicators and productivity. In the allocation of human resources it was decided to disaggregate the workforce into tender specification development team and support teams which include workforce to training, workforce to quality assurance, workforce rework and workforce to polishing and publishing. The tender specification development team is the team working on all cost estimation, design, drawings and specification tasks. Although, only one team is allocated 46 for these activities I considered possible layout of the disaggregation of the development team. According to the Engineering Association of Iceland 4 6 the total amount for a project, which goal is to provide complete tender specification set, can be divided approximately into four main fields as shown in figure 3.7. 70/n El Preliminary design and preliminary cost estimation 35% m Detailed design U Detailed drawings 03Specifications and material list Figure 3.7 Total amount for a civil engineering design project, disaggregated into specific tasks. The final product is a complete tender specification set. In many cases the most expensive processes (detailed design and drawings) overlaps greatly during the project. It depends on the nature of the design project how significant these overlaps are. In our model, these processes were considered to overlap somewhat, but in a rather clear way as shown in figure 3.8. However, our project model doesn't allocate workforce specially into these tasks but rather in a specific team working on the tender specification development itself and then specific teams working on rework, quality assurance and training at a time. The workforce allocated to the tender specification development is thus assumed to be working on new tasks and the other teams are considered for support activities. This ensures certain simplification and also that the 46 The Engineering Association of Iceland. 1986. Charging for engineering work". Reykjavik, Iceland. The Engineering Association of Iceland. 47 accuracy of the way in which figure 3.8 divides the entire development of new tasks is not overvalued. Thus, figure 3.8 serve more as a example of possible layout of the development team allocation, which can be considered and referenced to when creating custom graphs which may depend on it. Figure 3.8 Example of possible layout of the development team allocation, where the development team is the team working on new tasks. The rate of error generation, and other critical factors, may be a function of which tasks the development team is mainly concentrating on at that time. I.e. in the design process the error generation (where errors are measured as unworked rework) is in most cases at higher rate than in the detailed drawing process, and discovery rate of both rework and additional work, not counted for in the initial schedule, may become apparent at a different rate depending on what process the development team is mainly concentrating on. 3.5 3.5.1 Human Resource Management Staffing and Training The structure of the staffing and training sector is demonstrated graphically in figure 3.9. As the figure indicates, the total workforce of the project is composed of three workforce levels: 48 * "Inexperienced Workforce", * "Experienced Workforce", and * "Permanent Workforce". Hires NeededInsteadof Departures Time to Hire WorkersInsteadof DepartedA Figure 3.9 Human Resource Management - Staffing and Training 49 "Experienced Workforce" and "Permanent Workforce" are aggregated into the "Total Experienced Workforce" variable. The reason why total experienced workforce is represented by these two stocks is that in a civil engineering design projects the turnover rate out of the "Experienced Workforce" stock represents a true behavior where employees with special expertise are assigned to the project team for certain tasks and certain time and then departed through the "Departure Rate" variable. Thus, the stock of experienced workforce represent those workers that are fully trained but may depart because of their special expertise, which may not be needed throughout the project. However, in most projects a special stock of permanent workers also exist where the "Permanent Workforce" level represent those experienced workers who work on the project from the beginning to the end and are not subject to departure rate like the stock of "Experienced Workforce". The only stock of workforce which is subject to quits, which means that workers leave the organization permanently, is the "Permanent Workforce" stock. In other words it is assumed that "Experienced Workforce" and "Inexperienced Workforce" are not subject to any permanent quits once they have been assigned to the project team. This seems fair because it seems unlikely that workers will quit before they have finished their role in a project which does not last for a very long time. The rate of quits is formulated as a function of the average employment time of permanent workforce, "AvEmplTime of PW", which has a value conducted from the interviews and is set to 780 weeks (15 years). "Experienced Workforce" is transferred to the "Permanent Workforce" by the "Transfer Rate" flow, which in the model is set equal to "Quits". This ensures that the project will have certain and steady level of permanent workforce which is committed to the project until it is completed. "Permanent Workforce" can be considered to include the management team necessary and also other workers who are needed continuously throughout the entire project. 50 The stock of "Inexperienced Workforce" indicates those workers that are in the training and assimilation process. It is necessary to disaggregate the "Total Workforce" into "Inexperienced Workforce" and "Total Experienced Workforce" because the number of inexperienced workforce governs how much manpower is needed into training and the productivity of inexperienced workers may also be somewhat lower than of those that are fully trained and considered to be experienced. In the model a certain amount of manpower per week is needed to complete a task. A task is a custom unit of the work that has to be done and it doesn't have any absolute meaning except that a certain base productivity per worker is defined in the model in terms of tasks per worker per week. Thus, the project needs certain amount of workers per week to ensure the appropriate productivity rate of tasks per week. The "Departure Rate" flow out of the "Experienced Workforce" stock, outputs the workers who's special expertise is not needed any more in the project. It is desired to hire new workers, with other special expertise, instead of those who depart as soon as possible and the number of these new workers is already authorized except if the management team desires cuts in workforce. It is assumed that all departures are planned. However, it may take some time to hire the new workers needed. This represents the true behavior in projects where the desired special experts, which are supposed to come in at the time when other workers depart, are not available and may be busy finishing their role in other projects etc. These workers are then subject to the model's hiring delay for workers who come instead of those who departed. "Time to Hire Workers Instead of Departed Workers" represents the waiting time until workers, within or outside of the organization, are available to the project. "Time to Hire Workers Instead of Departed Workers" is set equal to 2 weeks. If it becomes apparent during the project that additional workers are needed in order to boost up the overall productivity, then more time is normally needed for hirings because they were not planned in the beginning. "Time for Hiring" represents the average 51 time it takes to hire new people from recruiting procedures or wait until workers, within the organization, are ready to start working on the project. Workers can be hired both from sources within the organization as well as from sources outside of the organization. The time for hiring is set to 8 weeks, which is a value conducted from the interviews. By considering in a short cut what it means that workers, needed instead of those that depart, are subject to "Time to Hire Workers Instead of Departed Workers", we see that a very high departure rate may cause excessive overruns in both schedule and cost compared to a scenario where the departure rate is low. This may happen both because of inadequate workforce level and less productive workforce due to continuously high level of workforce in assimilation or training process. All new members of the project team are not necessarily recruited outside of the organization. New members may be experienced engineers within the organization, transferred from other projects, but they may also be newly graduated engineers with no experience at all. However, all newly assigned employees need some period of time to sense the project's plan of work and its speciality. The inexperienced workforce is assimilated to experienced workforce by the flow of "Training Rate". "Average Training Time" is formulated as a first order exponential delay, meaning that the training rate is formulated as a first order exponential smoothing function. The average training time is set equal to 16 weeks, which is a value compromised from the interviews. The correction of workforce is a function of the difference between authorized workforce and total workforce, which is divided by a time delay for hirings or lay-offs depending on the sign of the difference. Thus the equation for the "Correction to WF" variable is formulated as: Correction_to_WF = (Authorized_WF-Total_Workforce)/ 52 (IF((Authorized_WF-Total_Workforce)>O) THEN(Time_forhiring) ELSE(Time_for_layoffs)) If "Correction to WF" has a negative value then its value goes into "Layoffs" but otherwise it goes into "Hiring Rate". Thus, lay-offs represent a negative value of correction to workforce. "Time for layoffs" is set to 1 week, which may represent the time needed for paper work etc. When the project is overstaffed and lay-offs are needed then the inexperienced workforce is laid off prior to experienced workers. However, if the stock of inexperienced workforce does not contain enough workers to fulfil the desired lay-offs then experienced workers are laid off. If the stock of experienced workers doesn't contain enough workers then finally permanent workers are laid off. It is quite unlikely that so intense lay-offs will be desired during the project, except if the number of workers that can work together on the project is somehow restricted. Such restriction are sometimes experienced in the end of projects where some narrowly focused but time consuming tasks may be the only thing left to do. The authorized workforce, which influences correction to workforce, is conducted from a variable named "Desired WF". Desired workforce indicates the number of workers that the management team perceive required to complete the project on scheduled time. Authorization of desired workforce level has normally an inbuilt time delay, which is needed to plan workforce. Such a delay for authorization also stabilizes the staffing process. The perceived desired workforce may change rapidly from time to time and therefore a time delay for authorization is present in most projects although the actual planning phase may be quick and simple. Authorized workforce is formulated as a stock which value is influenced by a flow named, "Chg in AWF", change in authorized 53 workforce 47.The "Chg in AWF" variable smooths the authorized workforce towards the value of desired workforce with a smoothing delay named "Time to plan WF" but is also influenced by certain limitations, namely, the value of authorized workforce can never be greater than the ceiling on total workforce, which is equal to the value of "Total Experienced WF" multiplied by 1 plus the maximum number of inexperienced workers that each experienced worker can handle. The "Max No of Inexp Workers that each Exp Worker can handle" variable is set to 2 workers, which is a value derived from the interviews, when the "Chg in AWF" has a positive value, it is multiplied by a variable named "Will to new hires", willingness to new hires. "Will to new hires" can take values between 0 and 1. The value, 0, indicates no willingness to new hires but the value, 1, indicates that perceived indicator for workforce level needed will rule without any effects of willingness. The time to plan workforce is formulated as first order exponental delay and is set to 4 weeks, which is a value conducted from the interviews. The willingness to new hires represents the scenario where willingness to new hires drops because of little time left of the project and also where it increases because of the danger of passing the maximum completion time, which indicates restrictions in time overruns. Restrictions in time overruns are supposed to be present in such a form that it may be desired to sacrifice cost for time when the perceived time needed to complete the project goes too close to the maximum time available. In the model the variable of "Max 47 The way in which the structure of 'Athorized Workforce" is modelled was partly based on class notes from 15.874, System Dynamics for Business Policy, MIT. 54 Completion Time" is set to 70 weeks while our "Initial Scheduled Completion Time" is set to 50 weeks. Willingness to new hires is a function of two variables and is formulated as: Will_tonew_hires = MAX(WilltoNH_becof_F_of_ IMSS_used, Will_to_NH_bec_of_STR_and_PH&AT) where * "Will to NH bec of F of IMSS used" represents the willingness to new hires because of fraction of the initial maximum scheduled time-slack needed, and * "Will to NH bec of STR and PH&AT" represents the willingness to new hires because of scheduled time remaining and perceived average time needed for hiring and adjustment of a worker T. Abdel-Hamid suggested this way of formulating willingness to new hirings in his Ph.D. thesis at MIT 1984 48. In a collaboration with the interviewees, it was felt that both these variables governing willingness to new hires would be best expressed by custom graphs. The interviewees made sketches of what they felt a fair shape of both these variables and our custom graphs express a compromise of these sketches. The "Will to NH bec of F of IMSS needed" was thus, formulated as a graphical function of the fraction of initial max scheduled time-slack needed which means that the willingness is expressed by the y-values on the graph illustrated in figure 3.10. 48 Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Mangement. Ph.D. Thesis at MIT. 55 iThink does, as mentioned before in this paper, provide an environment where custom graphs can be created and modified. Such graphs are used extensively in System Dynamics and are very useful, especially when making functions, which would be difficult to express mathematically. U. I- 0 U O .0 z 0 O.,m -. 1 4 e0 0 0.8 Co 0.6 0.4 0.2 O , 0.0 I t 0.2 JI I 0.4 I- -- U =. -- I I 0.6 0.8 1. 0 Frac of initial max sch slack needed Figure 3.10 "Will to NH bec of F of IMSS needed" formulated as a graphical function of "Fraction of Initial Maximum Slack needed". The shape of the curve in figure 3.10 seems reasonable because when a rather low fraction of initial maximum slack is perceived needed, the managers feel rather calm about the progress and are not willing to sacrifice cost for time. After a certain fraction is reached the management team becomes increasingly worried about how close to the maximum completion time their perceived progress is directing the project. After a certain level is reached they don't want to take any changes of overrunning the maximum completion time and the willingness takes a constant value 1, which means they are completely willing to hire additional workforce although the project is near completion. Therefore, the curve has 56 equilibrium at both ends and the S-shape of the curve becomes apparent when connecting the horizontal lines at the ends. The variable of "Will to NH bec of STR and PH&AT" was formulated in a similar fashion but as a function of "STR over PH&AT". The "STR over PH&AT" variable is calculated as "Scheduled Time Remaining" over "Perceived Hiring and Assimilation Time". This formulation of "STR over PH&AT" ensures that the time needed to hire and assimilate workers is indeed compared to the scheduled time remaining before new hirings are authorized. The value of this comparison measured as a proportion of these variables then governs the willingness. The ECECO employees felt that this formulation expressed well how willingness to new hires changes in later stages of a project and the compromised final graph is illustrated in figure 3.11. o0 X 0.8 or ./ 0.6 0.4 o 'X 0.2 0." 0.0 /,/ " I_. 0.5 I 1.0 ! 1.5 2.0 STR over PH&AT Figure 3.11 "Will to NH because of STR and PH&AT" formulated as a graphical function of "STR over PH&AT" Similar to the curve in figure 3.10, the curve in figure 3.11 must have equilibrium at ends representing full willingness and no willingness. The S-shape of the curve becomes 57 apparent when the equilibrium lines at the ends are connected. If hires are needed and the hiring and assimilation period is just 50% of the scheduled time left, then the willingness starts to drop and when the project is very near completion, absolutely no willingness to new hirings exist except for the willingness formulated in figure 3.10. This formulation of the starting and ending points of the S-shape curve was compiled from the interviews. However, there was a considerable difference between interviewees, in their estimation of the location of these points. All stocks in the staffing and training sector are initialized by values given in the "Initial Values" sector. The initial total workforce was set to 4 workers, from which 25 % goes to initial experienced workforce, 70% to permanent workforce and the rest to inexperienced workforce. The choices of all initial values will be justified and discussed later in this paper. 3.5.2 Overtime Policy and its Effects In the modeling process of the project's overtime policy it was decided to model overtime in the form of multiplier to normal work-week, where normal work-week is 40 hours per week. The defined base productivity was set to 1 task per worker per week as discussed before and the multiplier to normal work-week therefore serves as a multiplier to productivity but in addition another multiplier was also identified to be influenced by the overtime worked and that is the productivity multiplier due to manpower's burnout. Burnout represents how tired or how exhausted the average worker feels. The structure of the sector of overtime policy and its effects is illustrated in figure 3.12. 58 Prd mpldue to BO PrdM Mplto soughtOT Soughtmplto NWW Figure 3.12 Human Resource Management - Overtime Policy and its Effects. As illustrated in figure 3.12 the sought multiplier to normal work-week, named "Sought mpl to NWW" indicates the overtime sought by the project management team and is a function of Schedule Pressure. Schedule Pressure will be defined later, but it simply takes a value of 0 if no pressure because of time schedule is present, a positive value if the project is behind schedule and a negative value if the perceived time needed is less than what remains according to time schedule. I.e. if a time perceived still needed is 20 weeks but the time schedule indicates 15 weeks left then the schedule pressure is (2015)/15=5/15=0.33. A clear and simple way to model the effects of schedule pressure on the sought multiplier to normal work week is to formulate "Sought mpl to NWW" as custom graph influenced directly by the schedule pressure. The interviewees were asked to estimate how 59 such a graph should be shaped and a compromise of their estimates is illustrated in figure 3.13. · 1.5 / 1.4 Z 0 1 .3 1.2 E 1.1 E 0 8 0.71 I -0.5 . . I -0.3 -0.1 0.1 I I 0.3 0.5 Schedule Pressure Figure 3.13 "Sought mpl to NWW" formulated as a graphical function of "Schedule Pressure" As seen in Figure 3.13 the sought multiplier to normal work-week has a rather steep increase once it has been discovered that the project is behind schedule. This steepness represents the willingness to get the project back on track rather quickly before further time overruns are experienced. The multiplier sought takes also lower values than 1 when the project is experienced well within schedule. According to the ECECO the minimum workweek will hardly ever be less than 32 hours per week on average, which equals 80% of the normal work-week. Maximum work-week will also hardly ever be greater than 60 hours on average, which would represent a value of 1.5 of the multiplier. Burnout was defined in the model in terms of dimensionless values between 0 and 1. Burnout equal to 0 indicates that the workers are not tired at all because of overtime worked. Burnout equal to 1 indicates that the workers are exhausted because of excessive 60 overtime worked for past several weeks. Burnout is formulated as a stock with a biflow input, which means that the input flow can serve as an output if its values are negative. The input flow was formulated as an exponentially smoothed variable. The smoothing time, namely, "Time to feel Exhausted", was set equal to 4 weeks which is a conducted value from ECECO. Due to the nature of the first order exponential smoothing process, this indicates 12 weeks period of maximum workweek resistance before 95% exhaustion is reached. The input flow into the "Burnout due to Overtime" stock was formulated as a function of "Time to feel Exhausted" and "Effect of Overtime on Burnout". It was decided to represent the effect of overtime on burnout by a custom graph, which is a function of the actual multiplier to normal work-week. The custom graph for effect of overtime on burnout is illustrated in figure 3.14. c o 1- / 0.8 0.6 / 0.4 .; Z0.2 W 0.5 0.75 1 1.25 1.5 1.75 Act mpl to NWW Figure 3.14 "Effect of Overtime on MP Burnout" formulated as a graphical function of "Act mpl to NWW" As shown in figure 3.14 the burnout due to overtime is never going to reach the value 1 because the actual multiplier to normal work-week is never going to be greater that 1.5, which is the maximum value the management team will seek for. It was felt that more 61 research was needed on this formulation of effects on burnout and estimations of the ECECO employees of this graph differed significantly. The graph in 3.14 is however a compromise of their estimations. It seems reasonable to shape the curve steeper as the overtime increases because workers tend to feel physiological exhaustion in addition to psychological exhaustion when their tolerance for worked overtime is stretched further and further. In our model the actual multiplier to normal work-week is formulated as a function of the multiplier sought by the management team and also the multiplier to overtime sought, which represents the willingness to work overtime. The multiplier to the overtime sought is a function of the average level of burnout. It became apparent in the interviews with ECECO that if workers feel very tired, because of excessive overtime worked for past several weeks, then their willingness to work overtime drops. When worker's willingness to work overtime drops then a overtime worked immediately drops according to our interviews with ECECO. This indicates that at ECECO, workers are not pushed to work overtime unless they are willing to do so. In terms of this behavior ECECO may in someone's opinion seem a little bit loosely managed, compared to the experience that some people have from a classical prescriptive management. However, it became apparent in the formulation of multiplier to overtime sought, that in the ECECO's projects, employees seem to be very willing to work overtime if needed, although, they have been working long work weeks for several weeks. The multiplier to overtime sought is formulated as a function of burnout, namely, Mpl_to_sought_OT = 1-Burnout_due_to_Overtime 62 Thus, the equation is formulated in a linear manner. It means that the burnout can be thought as simply expressing the unwillingness to work overtime, which makes the meaning of it clearer. The productivity multiplier due to burnout, which was mentioned before, is formulated as custom graph and is simply a function of the "Burnout due to Overtime" stock. The graph is illustrated in figure 3.15. 1 o 0.8 . 0.6 0.4 E 0.2 a. 0 · 0.0 I I I I I 0.2 0.4 0.6 0.8 1.0 Burnout due to Overtime Figure 3.15 "Prd mpl due to BO" formulated as a graphical function of "Burnout due to Overtime" As shown in figure 3.15, it was felt that productivity would decrease with a steeper rate as burnout increases. This seems fair because it seems reasonable that a worker could get a little bit tired, i.e. 20% burnout, but still be producing at a similar rate as if not tired at all. Also it seems very unlikely that a very exhausted person could reach any kind of well defined equilibrium where from productivity would not decrease further, except for when zero productivity is reached. Zero productivity indicates that the exhausted person is taking some time off in order to recapture former energy. 63 Finally, the productivity multiplier due to overtime is formulated as the "Prd mpl due to BO" multiplied by "Act mpl to NWW". This overall multiplier from our overtime sector is multiplied directly to nominal productivity which then yields gross productivity, in the development productivity sector. 3.5.3 Workforce Allocation As mentioned before, when the scope of the project model was discussed, the total workforce is allocated into: * Workforce to design and tender specification development, * Workforce to Rework, * Workforce to training, * Workforce to quality assurance, and * Workforce to polishing and publishing. In the project model these variables, which represent the actually allocated workforce at a time, are named as: * WF to D&TS Dev, * WF to RW, * WF to Training, * WF to QA, and * WF to P&P 64 However, it is assumed that the same type of workers are working all these jobs. The total weekly manpower available to the project is simply equal to the total workforce, which was calculated in the staffing and training sector. In many organizations, employees may be assigned to more than one project at a time. It is assumed in the project model that the number of workers represent the total full-time manpower allocated to the project each week. Thus, if every worker is on average spending 50% of their time on the project and the actual total number of workers is 20 workers per week, then in fact 10 full-time workers are working on the project. It was decided to use simply the number of full-time worker equivalents in the model. Therefore, it does not matter what the actual number of part-time employees are assigned to the project. The design and tender specification development team is the team working on new tasks. Other teams serve as support activities to the development work. The team allocated for polishing and publishing is of size 0 workers throughout the project except in the end where it increases in the publication phase of the complete tender specification set. According to ECECO this represents the scenario in the end of a project where all previous work is organized and integrated into the complete tender specification set and generally some details are also added and the overall picture polished. Workforce to training is calculated from the stock of inexperienced workforce and a parameter representing the trainers needed per inexperienced workers. Other inputs into the workforce allocation sector are produced mainly in two sectors which are located under the project planning field. These sectors are: * "Forecast of Workforce Needed" , and * the "Planned Workforce Allocation" sector. 65 The perceived workforce needed for rework is calculated in the "Forecast of Workforce Needed" sector, but workforce to both P&P and QA is planned for in the "Planned Workforce Allocation" sector. The structure of the workforce allocation sector is illustrated in figure 3.16. QAFracof WF needed forNorm DetectRate srict moothng procedure Proj PerceivedSize of RW TeamNeeded Figure 3.16 Human Resource Management - Workforce Allocation The planned level of workforce to quality assurance forms the base for the actually allocated QA workforce. However, the planned level is influenced by a reduction factor, namely, the "Multiplier to Fraction to QA because of SP". This parameter represents the 66 reduction in manpower allocated to QA because of schedule pressure. According to ECECO, more emphasize is generally put into the development work than in quality assurance when schedule pressure becomes high. Thus, the workforce allocated to QA may be decreased down to a certain level, but the project manager is not likely to reduce the workforce to QA beyond what is perceived as a minimum level. Therefore, the multiplier would have an S-shape where it goes from certain level down to another level as a function of schedule pressure. The multiplier is formulated as a custom graph in the model. The shape of the graph was compromised from the interviewee's estimations. c 1 _ P O U. 0.8- _.1~ I ._ *-M o 0' 0.6z 0.4. . a .. 0 . -o 0.2i 0 0 0.2 . . 0.4 0.6 . 0.8 1 Schedule Pressure Figure 3.17 "Multiplier to Fraction to QA because of SP" formulated as a function of "Schedule Pressure" According to available information, QA is generally allocated as some fraction of the total manpower spent on the project at a time. The QA may be in the form of weekly meetings and detailed reviews of already completed tasks. I.e. after an engineer has supervised a completion of a drawing, it is generally put into inspection, where another engineer reviews the design process and its drawing implementation, and then certifies the drawing by signing it. 67 In the model it is assumed that certain fraction of total manpower is needed to ensure normal detection rate of rework, where rework represents the work, measured in tasks, that has to be performed because of errors generated. In modeling of the rework detection a certain base detection rate is therefore influenced by the "Multiplier to Nominal Detection of RW because of All WF to QA" variable, which is a function of what fraction of the needed QA workforce for normal detection rate, is actually allocated. The multiplier is simply formulated as: Fractionof Tot_WFto_Quality_Assurance/ QAFracof WF_needed_for_Norm_Detect_Rate "WF to QA" is formulated as: Fraction_of Tot_WF_to_Quality_Assurance*Total_Workforce After, workforce has been allocated to both QA and training, the workforce level left is captured through the "Avail WF to D&TS Dev & RW & PP" variable. The desired workforce for P&P takes the value of the planned P&P workforce, which formulation will be discussed later in this paper. The actual workforce allocated to P&P is represented as a stock in the model and its smoothing factor is named "P&P alloc time" and represents the time it takes to allocate the P&P workforce from what is desired. "P&P alloc time" is set to 1 week in the model. According to ECECO the number of workers that can work on certain parts of the project may be restricted because of the nature of the tasks left. If the workforce to RW and D&TS development is somewhat restricted in the end of a project and the "Time for layoffs" delay causes us to have extra workforce assigned to the project, then this extra workforce is allocated to P&P. By allocating extra workforce to P&P a behavior is 68 captured that often is experienced in the end of projects. If workers, that are not needed, are still assigned to a project and do not have any other place to go immediately or have not been laid off yet, then these workers are often allocated into some polishing or organizing work at project's final stages. Restrictions of workforce to D&TS development are captured through the "Base for Max Allowed WF to D&TS Dev in End of Proj" variable, which is formulated in the "Planned Workforce Allocation" sector. After, workforce has been allocated to QA, Training and P&P, the "WF to RW" is subtracted from the available workforce. The "Perceived Size of RW Team Needed" is calculated in the "Forecast of Workforce Needed" sector. The perceived size is smoothed into the "WF to RW" stock by an allocation smoothing time, which is set to 1 week in the model. This process is smoothed because full and immediate action is seldom taken on a change of incoming information such as perceived size of workforce needed for rework. Finally, the workforce left is allocated to D&TS development, which is the team working on new tasks. The reason for this formulation is that in most cases it is desired to finish necessary rework within a short period, from the time it is detected. By finishing the rework necessary shortly after it is detected, it is ensured that known errors will not cause generation of new errors in following tasks. Therefore, rework has priority over development in the model. Scheduling is done from the progress and perceived future productivity of D&TS development. If high fraction of the workforce available to RW and D&TS development, is allocated to RW then the D&TS development suffers. The perceived future productivity, measured in tasks per man-week, represents the development rate of new tasks per worker per week. Perceived future productivity is expressed in tasks per man-week from total workforce. Therefore, when fraction to RW rises, the perceived future productivity drops after some time-lag depending on the time it takes to perceive: 69 3.6 3.6.1 Project Planning Planned Workforce Allocation The structure of the "Planned workforce allocation" sector is illustrated in figure 3.18. AverageHist D&TS DevWF PlannedP&PWF Planned Fractionof Total WF for QA Initially PlannedFracof Ave D&TS Dev WF for P&P Plannedmpl to QAFNFNDR Perc Frac of D&TS Dev Completed r Actual Frac of D&TS Dev Completed QA Frac of WF needed for Norm DetectRate Scheduled D&TS Dev CompletionTime i O mpl to PlannedP&PWF Basefor Max AllowedWF to D&TS I)ev in Endof Proi Initial ScheduledCompletionTime >.. DesiredD&TS Dev WF ev Completed WF to D&TS Dev Frac of D&TS Dev to start th Fractionof RestrictedTasks in the End out of Total Work Size Figure 3.18 Project Planning - Planned Workforce Allocation. 70 The "Planned Workforce Allocation" sector has three outputs, which all serve as input into the "Workforce Allocation" sector. These output variables are: "Planned Fraction of Total WF to QA", "Planned P&P WF", and "Base for Max Allowed WF to D&TS Dev in End of Proj". The planned fraction of total workforce to QA has a constant value equal to the "QA Frac of WF Needed for Norm Detect Rate" throughout the project. The fraction to QA needed for normal detection rate is in the model set to 0.10, which is a value within the range given by the interviewees. Their estimation of this fraction ranged from 0.05 up to 0.20, so our value is probably in the lower range of what is usual. "Planned P&P WF" is formulated as a custom graph. It is expressed as a fraction of average D&TS development workforce and is a function of the perceived fraction of D&TS development completed. The custom graph is illustrated in figure 3.19. .n u 0.5 O 0.3 <i. >, .o 0.2 0 > .- - L ./ "0· ,-- " ·I 0.8 0.85 0.9 I I 0.95 1 Perc Frac of D&TS Dev Completed Figure 3.19 "Initially Planned Frac of Ave D&TS Dev WF to P&P" formulated as a graphical function of "Perc Frac of D&TS Dev Completed" 71 The ECECO employees supported the way in which the fraction to P&P ends in an equilibrium in the project's final stage. The fraction to P&P also must start from an equilibrium, because it doesn't take off until in the end of the project, and has the value of 0 before that. Therefore, the curve of planned P&P workforce, becomes S-shaped. The planned fraction to P&P is calculated from the average historic D&TS development workforce, measured in workers per week. The planned P&P workforce is influenced by one multiplier, which counts for the time spent on the project. The multiplier is formulated as equal to: Scheduled_D&TS_Dev_Completion_Time/ Initial_Scheduled_Completion_Time and is multiplied directly to initially planned fraction to P&P. Thus, if the scheduled completion time has not changed, then the multiplier has neutral effect. The "Base for Max Allowed WF to D&TS Dev in End of Proj" was formulated in order to capture possible restrictions to the number of workers that are able work at the same time on the D&TS development in the end of the project. In the project model no severe restrictions were formulated, but it was decided to identify and make an example of how such restrictions could be incorporated into the model. The "Desired D&TS Dev WF" variable, which was calculated in the "Forecast of Workforce Needed" sector serves as the value used as the restricted value in this paper. However, in the model the desired D&TS workforce is simply a function of the scheduled time left and the perceived productivity per D&TS development man-week. Therefore, if number of workers in D&TS development has to be restricted in a simulation, an easy way to incorporate such restrictions is to formulate them as a custom graph and make the "Desired D&TS Dev WF" variable also a function of the custom graph representing the restrictions. This could be done by simply 72 assigning the minimum value of desired workforce due to schedule, which already exists in the model, and desired workforce due to restrictions, to the "Desired D&TS Dev WF" variable. The "Base for Max Allowed WF to D&TS Dev in End of Proj" is represented as a stock in the model. This process is smoothed because full and immediate action is seldom taken on a change of incoming information such as restrictions, which are often not planned in the beginning of a project. In the planning process, before the project is started, the management team makes an attempt to plan the project in such a way that restrictions to workforce will be minimum. The reason is that it is not feasible to have to keep workers waiting for a certain task to be completed, before they can start working on their next task and schedule can easily suffer from restrictions. In the structure of "Base for Max Allowed WF to D&TS Dev in End of Proj" variable, it is assumed that restrictions to workforce may be experienced in the end of the project and this variable takes the value of "WF to D&TS Dev" throughout the project until restrictions start to influence the workforce allocations. In the model, restrictions start at certain fraction of the total work completed. "WF to D&TS Dev" may be increasing rather steeply in the project's end because of cuts in workforce to RW, while the "Desired D&TS WF" may be decreasing rather steeply from certain time point, because of restrictions. In order to make a smooth curve when changing to the "Desired D&TS WF", the smoothing process is formulated as a function of both these variables for a certain amount of time, before entirely switching to the "Desired D&TS WF" variable. To ensure a smooth change in the curve, the "Smoothing Time for ADWF" is therefore formulated as custom graph, which allows assigning a longer smoothing time in the beginning of the switching process, when the changes in the curve's slope occur more rapidly because of more difference in the slopes of these two variables. The "Smoothing Time for ADWF" as a function of "Actual Frac of D&TS Dev Completed" is illustrated in figure 3.20. 73 20 L. c E ijua 15 10 U o 5 E 0 0 cO * 0.88~~~~IIi 0.9 0.92 .86 a·---I ·- M I 0.94 . 0.96 0.98 1 Actual Frac of D&TS Dev Completed Figure 3.20 "Smoothing Time for ADWF" formulated as a graphical function of "Actual Frac of D&TS Dev Completed" In the formulation, the smoothing, towards the restricted value of workers, starts before it takes over. Thus, a rapid cut in workforce and rapid change in trend over a very short period of time, is avoided. Such rapid changes in trends are usually rare in design development projects and the workforce level usually smooths down to the restricted value in few weeks. Note, that values for "Fraction of Restricted Tasks in the End out of Total Work Size" and "Frac of D&TS Dev to start the smoothing procedure" are not based on any data gathering process and the purpose of this structure is mainly to identify and provide an example of how restrictions to workforce may be incorporated into the model. 3.6.2 Forecast of Workforce Needed The structure of the "Forecast of Workforce Needed" sector is illustrated in figure 3.21. "Forecasted Future D&TS Dev Prod per ManWeek from Tot WF" represents the forecasted productivity of new tasks per each man-week provided by a worker out of total 74 workforce. In this paper I distinguish between productivity in terms of development rate of new tasks per "man-week from total workforce" or per "D&TS development man-week". The reason for this is that the productivity is calculated as the overall development rate of new task by the entire workforce divided by either total workforce per week or D&TS development workforce per week, which is the number of workers that actually perform the development of new tasks. According to ECECO, the overall productivity of new tasks per worker out of the entire workforce, generally forms the basis of what is perceived as the overall productivity or progress, and those are the values that the management team normally judges the status of the project from. It was felt convenient to measure productivity in terms of overall development rate of new task per worker, regardless of where the worker is allocated. When i.e. workforce allocated to rework increases, the actual trend in development rate of new tasks per worker slows down because of less number of workers allocated to D&TS development. According to ECECO, a general way to measure productivity is to estimate productivity per man-week based on historic data, if available. However, in the beginning of a project, an attempt to perceive the development productivity rate from time to time, often provides a value which weight is dominant at earlier stages of a project. Both these productivity indicators mentioned above are captured in the model. The "Forecasted Future D&TS Dev Prod per ManWeek from Tot WF" variable is a function of "Assumed Hidden Prod Loss", two productivity indicators and also a factor representing the weight of these indicators. These productivity indicators are: * "Perc Historic D&TS Dev Prod per ManWeek from Tot WF", and * "Estimated Current D&TS Dev Prod per ManWeek from Tot WF", which represents productivity estimations from time to time. 75 "Assumed Hidden Prod Loss" represents the fractional loss that is estimated to be hidden in the beginning of the project. The assumed hidden productivity loss influences the forecast for future productivity because no rework is present in the beginning and undiscovered additional work may also be counted for as loss in productivity. On the other hand some potential productivity gains because of overtime and motivation may not be present in the beginning. The assumed hidden productivity loss ensures that the project is not perceived overstaffed (understaffed) in the beginning, although estimated week to week productivity rate may seem higher (lower) than needed. If needed, the graph should be shaped to ensure match in the initial values of the model so the initial authorized workforce multiplied by initial forecasted productivity will yield scheduled completion day. It should be noted that if the project is started with a sufficient level of authorized workforce then no overtime will be worked in the beginning of the project. That is the case in the initialation of this version of the model and therefore no potential productivity gains, because of motivation and overtime etc., are present in the beginning of the simulation. An average productivity loss of 40% was assumed while an average multiplier to productivity due to motivation and overtime was assumed to equal 1.40. These values yield an average number of 8.9 workers which appears to be very similar to the desired level in the beginning of the simulation. No overtime is desired in the beginning of the project but a variety of other factors such as communication, motivation etc. also influences the level of desired workforce in the beginning. Because of the match in desired and authorized workforce level in the beginning of the simulation, the graph of assumed hidden productivity loss takes values of zero throughout the simulation. The factor representing the weight of our productivity indicators, namely "Weight of Historic D&TS Prod", is formulated as equal to "Actual Frac of D&TS Dev Completed". 76 PercHistoricD&TSDevProdperManWeek :e His Tot WF Prod JWF Timeto PercProdof D&TSDevManWeek CurrentD&TSProdper D&TSDevworker VFNeeded K) Smoothing Time Cha in PRTN eworkto do 'S DevCompletec irk per Worker ActualFracof D&TSDevCompleted Figure 3.21 Project Planning - Forecast of Workforce Needed. The "Perc Historic D&TS Dev Prod per ManWeek from Tot WF" variable is formulated simply as "Historic D&TS Dev Productivity per ManWeek from Tot WF" 77 smoothed over a smoothing time named "Time to perc Historic prod", which represents the time it takes to perceive historic productivity. "Historic D&TS Dev Productivity per ManWeek from Tot WF" is calculated as cumulative D&TS tasks already developed over cumulative total man-weeks already spent on D&TS development and support activities. Thus, the "Historic D&TS Dev Productivity per ManWeek from Tot WF" represents the average productivity rate from the beginning of the project. The "Time to perc Historic prod" is set to 8 weeks in the model, which is a compromised value of what was felt reasonable by the ECECO employees. The "Estimated Current D&TS Dev Prod per ManWeek from Tot WF" variable is formulated as a projected productivity per man-week from "Perc Prod per D&TS Dev ManWeek". The "Perc Prod per D&TS Dev ManWeek" variable is represented as a stock, which contains values from "Current D&TS Prod per D&TS Dev worker" smoothed by "Time to Perc Prod of D&TS'Dev ManWeek". The value of the smoothing time is set to 6 weeks, which is a value compromised from the interviews. ECECO employees, certified the way in which both these productivity indicators were modelled. However, it was considered that in the future development of the project model it might be reasonable to add some additional functions to the model, influencing both these indicators. Such additional functions may i.e. represent inaccuracy in estimations of the status of the project, from time to time, because of: * Complexity of the project and variations in difficulties in perceiving the status of the project, * The likelihood of too much dependency of the management team on engineering professionals and their beliefs of their progress, and 78 The likelihood of inaccuracy in reporting because of tendency to hide embarrassing situations. All these factors depend on the nature of the project and the quality and experience of both the management team and other employees. They may also vary somewhat during the project. After some thoughts about how these factors could be incorporated into the simulation it was decided to avoid making the model more complicated, but it was also decided to identify them in this paper as a contribution to possible future development of the project model. After calculating the "Forecasted D&TS Dev Future Prod per ManWeek from Tot WF" variable the perceived total workforce needed can be calculated by dividing it into the "Desired D&TS Dev Prod Rate" variable, which is calculated in the "Scheduling" sector. Because full and immediate action is seldom taken on a change of incoming information such as perceived workforce needed, the "Perc Total WF needed" is smoothed into the "Desired Workforce" stock with a smoothing time which value is set to 4 weeks. The smoothing time ensures certain level of stability in desired workforce level and it also takes into account the time needed to report values, of perceived total workforce needed, to the management team. The "Perceived Size of RW Team Needed" is also calculated in the forecast sector. "Desired Rework Rate" is calculated by dividing "Desired Time to Finish Rework" into "Discovered Rework to do". According to the interviewees, the "Desired Time to Finish Rework" may differ somewhat throughout the project. Therefore, it is formulated as a graphical function of "Perc Frac of D&TS Dev Completed", which represents the fraction of design and tender specification development perceived completed. However, in this version of the project model, the values of the custom graph are set to constant value of "Desired Time to Finish Rework" equal to 2 weeks. Such a low value for "Desired Time to 79 Finish Rework" represents the willingness to correct already detected errors before they produce others. The "Actual Size of Rework Team Needed" is calculated as: Desired Rework Rate/ Gross_Rework_Productivity_Rate_per_Worker The "Actual Size of Rework Team Needed" is smoothed into the stock of "Perceived Size of RW Team Needed" by a smoothing time factor named, "Time to perceive Size of RTN". Thereby, capturing the fact that the management team does not perceive such information until after some delay. According to ECECO, the rework cycles, in the end of a design development project, are generally of simpler and more predictable nature than rework cycles in the design phase. This is normally the case, except for rare cases, where something is fundamentally wrong in the performance of the project team and significant amount of time is spent in the end, reworking fundamental errors from earlier stages in the design phase. Such fundamental errors from earlier stages of the design phase, not reworked until in the end of the project, may have served as a basis for a significant amount of work and therefore had serious effects on following tasks. It is more general that in the end of a project, some small design details, not influencing other parts of the project in a very severe way, have to be reworked. The typical late rework is often redoing material lists, redoing cost estimation, redoing specification and polishing drawings and the way individual pieces build on and interact with each other. Therefore, all estimations of the actual rework needed, and workforce needed for rework are normally more accurate in the end of a D&TS development project than in earlier stages. This simpler and more predictable nature of 80 rework cycles in the end of a design project, normally increases accuracy in estimations of the rework productivity per worker. In order to capture this behavior the "Time to perceive Size of RTN", time to perceive size of rework team needed, is modelled as a graphical function of "Actual Frac of D&TS Dev Completed". This allows reducing the "Time to perceive Size of RTN" in the end of the project and therefore move "Perceived Size of RW Team Needed" closer to the "Actual Size of Rework Team Needed", which should be the trend if the nature of late rework is simpler than rework at earlier stages. The custom graph for "Time to perceive Size of RTN" is illustrated in figure 3.22. U'4 > 1 X) CC 10 *-* :0 ° oN 5 - 1 L- O 0 ",I- I~~~~ 0 i~i ~ '-.-'- 0.5 1 Actual Frac of D&TS Dev Completed Figure 3.22 "Time to perceive Size of RTN" formulated as a graphical function of "Actual Frac of D&TS Dev Completed" The graph of "Time to perceive Size of RTN" was estimated by ECECO. However, they notified difficulty in estimating this variable, but they also notified that the perceived value for workforce needed for rework is often built on previous experience from the development of new tasks where errors are actually generated. Because of the willingness 81 to finish rework within a short amount of time and also because of previous experience from the development phase of tasks that have to go through a rework phase, the management team is generally able to perceive size of rework team needed in a rather accurate manner. Therefore, the "Time to perceive Size of RTN" has rather low values throughout the project, and lower values in the end, when the nature of rework needed becomes simpler and more predictable. 3.7 3.7.1 Project Controlling Schedule Pressure Schedule pressure has crucial effects on various aspects in the model. Not only, does it affect the amount of overtime worked and the efforts assigned to the project from time to time, but it also affects the generation rate of errors and the way in which workforce is allocated. Various causal loops exist in an execution of a project. Changes in schedule pressure, arising from mismatch between schedule goals and perceived cumulative progress, has effects on aspects crucial to the success of the project as mentioned before. In most cases the output of progress and rework, which may depend on the schedule pressure, do not control schedule goals or staffing functions until after some problems have been measured or perceived and then a strategy is revised. Thus, loops for schedule pressure have to be illustrated as closed loops but on the other hand, inputs and outputs of the system are not monitored continuously and excessive delays may be involved before a strategy is revised. Basic causal loops for schedule pressure are illustrated in figure 3.23. 82 The time needed to perceive problems depends on various things inbuilt in the organization and also on factors such as ability and time needed to measure productivity and detect undiscovered rework. These factors may depend on what fraction of the project is already completed or when some tasks, having the uncompleted one as a prerequisite, are indeed executed. Rework Progress needed +Schedule Pressure Fraction Schedule Pressure Satisfactory + Quality Figure 3.23 ' + m /' Gross Productivity Overtime and Efforts Causal loops for schedule pressure. A typical "Limits to Success" scenario. As structured in figure 3.23, the effects of schedule pressure on overtime and efforts indicate how schedule pressure may influence the overtime worked, the way in which workforce is allocated and other possible changes in efforts assigned to the project, i.e. in terms of number of workers on the entire project team. Schedule pressure is modelled as a stock in the model, because it will always take some time to adjust it into the project's organizational structure. The structure of the "Schedule Pressure" sector is illustrated in figure 3.24. 83 Schedule Pressure Schedule Pressure Adj Ti eduled Time Remaining c Time Req to Finish D&TS Dev Gap in Required and S Figure 3.24 Project Controlling - Schedule Pressure "Schedule Pressure" is a function of "Gap in Required and Scheduled time left" and "Scheduled Time Remaining". It is smoothed by a smoothing time named "Schedule Pressure Adj Time", which represents the time it takes to adjust the "Schedule Pressure" into the project's organizational structure. The "Chg in SP" is formulated as equal to: (Gapin_Required_and_Scheduled_timeleftl Scheduled_Time_Remaining-Schedule_Pressure)/ Schedule_Pressure_Adj_Time where "Gap in Required and Scheduled time left" is formulated as equal to: Perc_Time_Req_to_Finish_T&DS_Dev-Scheduled_Time_Remaining Thus, the schedule pressure simply takes value of zero when the project is exactly on time according to schedule, a positive value if the project is behind schedule and a negative value if the perceived time needed is less than what remains according to time schedule. 84 PAGES (S) MISSING FROM ORIGINAL PAGES 85 thru 88 ARE MISSING willingness to new hires in the "Staffing and Training" sector, because new hires in the end of a project are normally not desired except if the management team feels uncomfortable because of the maximum completion time. The maximum completion time may be present because of interactions to other organisations, which role may be built on the tender specification set provided by our project team. Also the tender specification set has to be completed in advance of scheduled events such as opening of biddings. 3.7.3 Project Database The "Project Database" sector serves as a data collector and it ensures collection of historic data of expended man-weeks, of both the total workforce and sub-teams. Data is collected by conducting flows, measured by workers per week, into stock variables, which serve as accumulators. Some values, serving as inputs for forecasting and planning, are also calculated in this sector. The structure of the "Project Database" sector is illustrated in figure 3.26. The "Average Hist D&TS Dev WF" represents the average expended man-weeks to D&TS development from the beginning of the project and it influences allocation of workforce to P&P in the "Workforce Allocation" sector. It is simply calculated as "D&TS Cum ManWeeks" over "Current Time". "Hist RW Productivity per ManWeek", historic rework productivity per man-week, is identified and calculated in this sector although it doesn't influence any processes in the model. It might be used to influence the perceived size of rework team needed in later versions of the model, but in this version the perceived size was simply modelled as a function of the actual size of rework team needed. 89 Q Inc in C.AMVtMnoAT I AverageHist D&TS Dev WF / I . _ -A urrent rime i ReworkWorked W oductivityper ManWeekfrom RW WF WF to Rework Inc in CMWtoQA ACum ManWeeks IWtQo A _. Acl Ad:t mpl to NWW WF to QA ks Developed im Tot WF Inexperienced Workforce CumulativeMplto NWW = AverageMpI to NWW i·'-' / .. Act mplto NWW Figure 3.26 Mplto NWW Project Controlling - Project Database 90 Current Time Finally, the "Historic D&TS Dev Productivity per ManWeek from Tot WF" is calculated as cumulative D&TS development tasks already developed over cumulative total man-weeks already spent on D&TS development and support activities. It influences the estimated future productivity per worker in the "Forecast of Workforce Needed" sector. P&P, which appears only in the end of the project, is not considered as a support activity when productivity of total workforce is calculated. Therefore, cumulative man-weeks to P&P are subtracted from the total man-weeks expended, in our formulation of "Historic D&TS Dev Productivity per ManWeek from Tot WF". 3.8 3.8.1 Tender Specification Production Development Productivity Figure 3.27 depicts the development productivity for the D&TS development of new tasks. As mentioned before, the project is defined in terms of tasks and therefore, overall development productivity is measured in tasks per week. In principle, a "task" can be any arbitrary unit, by which a coordinate frame for measuring the project's size is provided. The initial productivity per worker is defined as 1 task per worker per week. "Defined Nominal Productivity per Worker", which is defined in the "Initial Values" sector, represents nominal productivity before any effects of learning, workforce mix, communication, motivation, and overtime are applied. 91 I·_ Mpl to Prodbec Inexr T Total WF to D&TSDev Perceived RemainingNew Tasks Figure 3.27 Tender Specification Production - Development Productivity "Potential Base Productivity per Worker" represents productivity per worker without any effects of schedule pressure, overtime and number of workers. The "Potential Base Productivity per Worker" variable is formulated as "Defined Nominal Productivity per Worker" multiplied by productivity multipliers due to: 92 * Learning curve of the organization, depending on the company's experience in performing projects similar to the current one, * Project familiarity, depending on what fraction of the project is already completed * Workforce mix, depending on what fraction of the total workforce is inexperienced T. Abdel-Hamid suggested the project familiarity and workforce mix productivity multipliers in his Ph.D. thesis at MIT 1984 50. Multipliers due to learning curve and project familiarity are calculated in the "Learning Influence on Productivity" sector, which will be discussed later. As mentioned before, the stock of inexperienced workers represents newly hired workers, from which some workers are newly graduated and some are experienced in terms of previous work although they are considered inexperienced in terms of familiarity to the project's work plan and scope. The multiplier due to workforce mix, is calculated from the inexperienced fraction of total workforce and a variable named "Prod of Inexp WF as a Fraction of Prod of Exp WF". The variable of "Prod of Inexp WF as a Fraction of Prod of Exp WF" represents how productive inexperienced workers are in comparison to experienced, on a fractional basis. "Prod of Inexp WF as a Fraction of Prod of Exp WF" is set equal to 0.8. "Basic D&TS Dev productivity per Worker" is calculated as "Potential Base Productivity per Worker" multiplied with productivity multipliers due to: 50 Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Mangement. Ph.D. Thesis at MIT. 93 * Motivation, depending on schedule pressure, and Communication overhead, depending on the total number of workers T. Abdel-Hamid suggested both these productivity multipliers in his Ph.D. thesis at MIT 1984 51. These factors may both be formulated in a different way or integrated into other variables in the model. The motivation effect represents how workers become more productive when under a time pressure. However, error generation rate also increases with schedule pressure as formulated in the "Quality" sector. The reason why motivation because of schedule pressure influences productivity is that when under time pressure, workers start to limit the time they spend in coffee breaks, non-productive communication, and ineffective polishing of details that do not matter very much to the project's success etc. The ECECO employees made attempt to estimate what they thought could be a reasonable behavior of the motivation multiplier. It was decided to formulate "Mpl to Prod bec of Motivation" as a graphical function of "Schedule Pressure". The custom graph of "Mpl to Prod bec of Motivation" is S-shaped, with both lower and upper limits. The reason is that motivation effect can only increase average productivity per worker up to certain limit because after certain time pressure is reached, workers are not able to improve their efficiency more by being well targeted and planned and willing to sacrifice their coffee breaks and non-productive communication. However, motivation has also a lower limit, because when the time perceived required to finish is less than the scheduled time remaining, the managers do not allow workers to show average productivity below certain limit and some competition between workers also exist and pushes the average worker to act responsible and perform tasks with some minimum productivity. The custom graph for "Mpl to Prod bec of Motivation" is illustrated in figure 3.28. 51 Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Mangement. Ph.D. Thesis at MIT. 94 1 1 1.4 o a0. c0 1.2 1. E.---E-0-00 0 0.8" 0.6 -0.5 0 0.5 Schedule Pressure Figure 3.28 "Mpl to Prod bec of Motivation" formulated as a graphical function of ·"Schedule Pressure" "Frac of Tot WF to Comm OH" represents the fraction of potential productivity, per average worker, which goes into team communication. This variable was therefore formulated as overhead 5 2 although it also influences productivity in another way. Good and effective communication is undoubtedly a very important contribution to the project's success. However, the definition of communication as a overhead is based on the assumption that average productivity per worker does not decrease when number of workers increases except for those decreases measured in the fractional efforts to communication overhead. Communication includes any additional workload due to interfaces, such as verbal communication, documentation, and reporting etc. The 52 Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Mangement. Ph.D. Thesis at MIT. 95 employees at ECECO estimated how the variable of communication overhead could be shaped. However, they noted that this kind of informations are not available within their company and has never been researched. It is believed by many managers that communication overhead increases proportional to the number of workers in power of 2 53. However, it is apparent that such general statements may be too simple in many cases and fractional efforts to communication overhead are most likely influenced by a variety of factors. Therefore, the subject may be expanded to how fractional efforts to communication overhead changes with factors like: * Email usage * Technical capabilities, such as how computerized the company is in terms of hardware equipments, cad and design systems etc. * Level of efficiency of communication efforts due to how communication efforts are planned, if it is in a systematic manner or not. * The nature of the project i.e. complexity and level of dependency and interactions between tasks etc. The factors above were discussed with David Ford, which was very helpful in pointing them out or in giving a comment leading to their identification. In our formulation of the efforts to communication overhead we decided to keep the model simple and leave more detailed approach to future development. However, it was felt reasonable to identify and formulate the "Frac of Tot WF to Comm OH" variable. It was assumed that the slope of a curve, representing fraction to communication, would increase with increasing number of workers. The reason is how interfaces increases with number of workers if a interface is 53 Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Mangement. Ph.D. Thesis at MIT. 96 assumed between every two workers. Such assumption yields equation for number of interfaces, which may be formed as: F = -N2 -_ 2 2 where "N" represents the number of workers and "F" represents the number of interfaces. The custom graph was therefore formulated with a increasing slope as number of workers increases. Although the graph has increasing slope, it was decided that the curve for "Frac of Tot WF to Comm OH" should not have as steep increase in slope as the formula for number of interfaces indicates because it was felt that interface between every two workers would not be needed except for a very low workforce level. The ECECO employees also estimated that if 15 workers were working on a design project, it would be fair to allocate c.a. 20% of their efforts into communication. Therefore, the curve is shaped as illustrated in figure 3.29. 0. LL 3OI 0.4 0 0.3 ' E 0.2 0.1 LL 0 0 5 10 Total Figure 3.29 15 20 25 Workforce "Frac of Tot WF to Comm OH" formulated as a graphical function of "Total Workforce" Finally the "Basic D&TS Dev productivity" variable represents the overall development productivity before overtime effects. It is simply calculated by multiplying 97 "WF to D&TS Dev" to "Basic D&TS Dev productivity per worker". Bringing in the productivity multiplier due to overtime then yields the gross D&TS development productivity rate, which determines the development progress of new tasks when accumulated. 3.8.2 Rework Productivity The rework productivity determines the rate of which errors are reworked. Errors are measured in tasks, and it was decided to refer to errors by the word "rework", which can both be undiscovered or discovered etc. depending on rework detection. Rework generation will be discussed later in the "Quality" sector. Rework is generated as a fraction of development rate of new tasks or as bad fixes and therefore it was felt convenient to measure it in tasks to keep the consistency in units for progress indicators. rs Prd Mpl due Gross Rate Rework perProductivity Worker Gross Rework Productivity Rate per Worker Figure 3.30 Basic D&TS Dev productivity per Worker Tender Specification Production - Rework Productivity 98 According to ECECO, the difficulty in correcting errors may cause the rework productivity per worker, measured in tasks per worker per week, to be lower than development productivity of new tasks per worker. Instead of formulating rework productivity as equal to the D&TS development productivity, we decided to capture the correction difficulty through the "Multiplier to Rework Prod" variable. This multiplier is calculated as Difficulty_in_Correcting_Errors/Base_Difficulty "Base Difficulty" serves as a reference frame to difficulty and is set equal to 1 in the model. Although, the "Difficulty in Correcting Errors" may range over a large interval, it was decided to set it equal to 1.5, which is value felt reasonable by the ECECO employees. Reworking design errors involves generally more complexity than rework in the end of a project, which may include remaking of material lists and other tasks that normally do not involve any complexity beyond the original development. Thus, the difficulty in correcting errors represents an average value in the model, but may also be modelled as a custom graph with varied values of difficulty. Multiplying "Basic D&TS Dev Productivity per Worker", from the "Development Productivity" sector, by the "Multiplier to Rework Prod" yields "Basic RW prod per Worker". Finally, the overall gross rework rate is calculated by bringing in WF to RW and the productivity multiplier due to overtime. 3.8.3 Learning Influence on Productivity The "Learning Influence on Productivity" sector includes two factors influencing productivity, namely, 99 * learning curve of the organization, depending on the company's experience in performing projects similar to the current one, * project familiarity, depending on what fraction of the project is already completed As project proceeds, the workers learn their job better and the project becomes more familiar to them. Therefore, both factors because of learning influence on productivity, indicate the rate of improvement and are formulated as multipliers to productivity. The structure of the "Learning Influence on Productivity" sector is illustrated in figure 3.31. Initial Cumulative Production Cumulative Production Production Rate of Learning Curve Fractional Productivity Increase per Doubling Gross D&TS Dev Prod Rate Actual Frac of D&TS Dev Completed I" ae . Mpl to Prod bec of Project Familiarity 9-,,,,0 Figure 3.31 Tender Specification Production - Learning Influence on Productivity The multiplier due to project familiarity, is formulated as a custom graph in the model. This factor depends on company's previous experience of similar projects although 100 it is not modelled as a function of cumulative experience. The reason is that if the company has a lot of experience from similar projects then the total increase in productivity, because of familiarity, is not going to be as much as if it was a unique project with no similarity to previous projects. Therefore, in order to keep the model consistent, the graph representing multiplier due to project familiarity has to be altered manually if changes are made to other parts of the model, which may influence project familiarity. A significant previous experience from similar projects is assumed in this version of the model because of the experience and speciality of ECECO, which has rather well defined focus. The improvement in productivity due to project familiarity does generally only change slightly in the end of a project and it seems reasonable to assume that the improvement rate will be fastest once all preliminary work is finished and the main core of the project is reached. Therefore, the curve for project familiarity is S-shaped and the "Mpl to Prod bec of Project Familiarity" is formulated as a graphical function of "Actual Frac of D&TS Dev Completed" as illustrated in figure 3.32. >, 1.15 ue 9~ 'E / 1.1- ./ o ,, 1.05 X *I 0 I*1 0.2 Actual Figure 3.32 I I I I 0.4 0.6 0.8 1 Frac of D&TS Completed "Mpl to Prod bec of Project Familiarity" formulated as a graphical function of "Actual Frac of D&TS Completed" 101 The learning curve due to company's previous experience from similar projects is formulated mathematically as the classical learning curve. In the classical learning curve, each doubling of the curve produces a constant fractional increase in productivity 54 . If we start with productivity of Po and a constant fractional increase f, then after one doubling, productivity rate will be P1 = Po *(1 + f) and after n doublings the productivity rate will be (1) Pn = Po *(1 + f)n After n doublings the cumulative productivity will be CPn = CPo * 2 n Dividing by initial productivity at both sides yields CPn = 2n CPo This equation solved for n can serve as substitute for n in equation (1) which was derived before. Taking a natural logarithm of both sides, we find that LN(CPo = n LN(2) Substituting this equation into equation (1), yields LN (CP0 Pn = Po 0 *(1 + f) LN(2) 54 Hines, James H. "Formulating The Learning Curve", distributed in the '15.874 System Dynamics for Business Policy' class at MIT. 102 Therefore, we formulate our "Mpl to Productivity due to Learning Curve" as ( +Fractional_Productivity_Increase_per_Doubling)A(LOGN( Cumulative_Production/Initial_Cumulative_Production)/ LOGN(2)) Where the fractional productivity increase per doubling is set equal to 0.1. The learning curve has very conservative influence in our model because a significant previous experience of similar tasks was assumed. Thus, "Initial Cumulative Production" is set equal to 12000 tasks while our real project size is set equal to 500 tasks. The value of "Cumulative Production" is calculated by a stock which accumulates the values of "Gross D&TS Dev Prod Rate" from week to week. 3.8.4 Quality The quality sector provides us with values of rework generation rate and real production rate. As mentioned before, real production rate represents the rate at which satisfactory tasks are generated. Several authors have suggested ways to formulate rework and influenced the way in which the approach is constructed in this model 55,56,57.The generation of undiscovered rework represents the rate at which errors, detectable during the design project or construction, are generated. This definition provides a link with the real 55 Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Mangement. Ph.D. Thesis at MIT. 56 Cooper, K.G. Feb 1993. The Rework Cycle: How it Really Works .. And Reworks ... Project Management Journal. p. 25-28 57 Richardson, G.P., and A.L. Pugh. 1981. Introduction to System Dynamics Modeling with DYNAMO. Productivity Press. Cambridge MA. 103 world in such a way that data about rework generation can be collected after construction is finished because, by our definition of rework, all errors, in the tender specification set, have already been detected at that time. As in the real world, some of the errors in the design project are not going to be detected until in the construction phase and therefore the design project will have some amount of undiscovered rework left at the time it is completed. Rework detection will be discussed later in the "Rework Detection" sector. The "Quality" sector includes four factors influencing the satisfactory fraction of developed new tasks, namely, * Fraction satisfactory due to the fraction of workers considered inexperienced, * Fraction satisfactory because of schedule pressure, * Fraction satisfactory because of active errors that have not been detected and can therefore produce new errors, and * Nominal fraction satisfactory representing the fraction satisfactory before effects from the three factors mentioned previously Since, the model's focus is on the managerial subjects in tender specification production rather than on technical issues of design development, errors are neither disaggregated into types of errors nor given any special weight depending on in what stage of the project they are generated. However, the example of a possible layout of the development team allocation, illustrated in figure 3.8, was considered when formulating the fraction satisfactory and the detection rate. The structure of the "Quality" sector is illustrated in figure 3.33. 104 InexperiencedWorkforce' discoveredRework Schedule Pressure s D&TS Dev Prod Rate FS due to Schedule ; Real ProductionRate Cum D&TS New Tasks Developed\. Undisc PotentiallyActive ReworkI ,TS prodper Worker Aclual rra oTLJ I . uev complete Figure 3.33 BasicD&TS Dev productivityper Worker Tender Specification Production - Quality In the formulation of "Nominal Fraction Satisfactory", the example of a possible layout of the development team allocation, which was illustrated in figure 3.8, was considered. Figure 3.34 Example of possible layout of the development team allocation, where the development team is the team working on new tasks. (This graph was previously illustrated in figure 3.8) 105 As mentioned before the allocation layout example, illustrated in figure 3.34, does not represent an actual project but serves as a example of how the efforts of the development team may be shifted between certain phases, which nature is different in terms of complexity etc. Design errors are normally created at higher rate and will normally be harder to detect than errors created in later stages of the project. Therefore, rework, measured in tasks, is generated at higher rate in the beginning of the project. In the end where a significant efforts are allocated into performing detailed drawings and specification work, rework is generated at much lower rate than in the beginning. This behavior of rework generation is captured through the "Nominal Fraction Satisfactory" variable, which is formulated as a graphical function of "Actual Frac of D&TS Dev Completed". The custom graph for "Nominal Fraction Satisfactory" is illustrated in figure 3.35. 4 M-E 0.9- MI o 0.8o - 0.7 I, X o. 0.6 mm 0.5- 'c .2 0.4- 'E <Cn, 0. 3- zo 0.20.1 O . I 0 I I 0.2 0.4 0.6 I 0.8 ] 1 Actual Frac of D&TS Dev Completed Figure 3.35 "Nominal Fraction Satisfactory" formulated as a graphical function of "Actual Frac of D&TS Completed" 106 The "Nominal Fraction Satisfactory" reflects the assumption of relative error generation rate for the project model. The graph can easily be reshaped to reflect actual data, if available. During the training or assimilation period, workers are normally more likely to produce errors than if experienced. The fraction satisfactory, due to the fraction of workers considered inexperienced, is also formulated as a custom graph. Fraction satisfactory normally drops with higher fraction of inexperienced workers out of total workforce. It was felt reasonable to let the curve drop at a steeper rate as the fraction of inexperienced workers increases because then the fraction of experienced advisers decreases and errors than normally could have been avoided are more likely to be produced. When the workforce is comprised of only experienced workers, the multiplier is set equal to 1, which indicates neutral effect on the nominal fraction satisfactory. Thus, the graph of "FS due to Frac Inexp" is shaped as illustrated in figure 3.36. x1 1IWww °04 0.8 u 0 0.5 1 WF fraction Inexperienced Figure 3.36 "FS due to Frac Inexp" formulated as a graphical function of "WF fraction Inexperienced" fraction Inexperienced" 107 It should be noted that although the graph in 3.36 can provide values for workforce comprised of only inexperienced staff, such situation is avoided by the ceiling of new hires formulated in the "Staffing and Training" sector. As workers become more worried about time schedule, they do not only work more overtime but also tend to make more errors. The reason for this behavior can be inappropriate overlapping of activities and also inadequate cooperation with other workers because of their busyness. It is assumed that the schedule pressure does not affect error generation rate significantly until it reaches certain limit. It is also assumed that after a certain drop in fraction satisfactory, this factor will stabilize and that increase in schedule pressure above 0.5-0.6 will not cause further decrease of any significance. Thus, the custom graph is shaped as illustrated in figure 3.37. , o C) 0.8 =r 0.6 0.4 X 0.2 I I 0 0.2 0.4 I 0.6 I 0.8 I 1 Schedule Pressure Figure 3.37 "FS due to Schedule Pressure" formulated as a graphical function of "Schedule Pressure" 108 Error generation because of active errors, which have not been detected and can therefore produce new errors, is formulated mathematically in the model. The value of undiscovered potentially active rework is conducted from the "Rework Detection" sector, where it is represented by a stock, named "Undisc Potentially Active Rework". The fraction of already completed tasks, which are a prerequisite to tasks in execution, defines what fraction of the proportion of active rework over cumulative tasks already developed, contributes to the error generation rate. Thus, the "FS due to Act RW" is formulated as: (1-Fraction of_tasks_that_are_a_Prerequisite* Undisc_Potentially_Active_Rework/ Cum_D&TS_New_Tasks_Developed) After, multiplying all the "FS" multipliers together, the variable of overall fraction satisfactory defines what fraction of "Gross D&TS Dev Prod Rate" has to be reworked during the design project or during construction. Thus, "Generation of Undiscovered Rework" is formulated as equal to Gross_D&TS_Dev_Prod_Rate*(1-Fraction_Satisfactory) In a similar fashion the "Gross Real D&TS Dev Prod Rate" variable is formulated as equal to Fraction_Satisfactory*Gross_D&TS_Dev_Prod_Rate It should be noted that this indicator of real productivity can not be measured by the management team during the project. However, it allows monitoring the underlying real 109 behavior during the simulation and it can be compared to variables visible to the management team in order to help identifying and understanding problematic behavior. 3.8.5 Progress Indicators Figure 3.38 illustrates the progress indicators for D&TS. As mentioned before some variables such as gross real productivity rate and actual fraction completed etc. are not visible to the management team. In the model, the word "perceived" refers to visibility and the words "actual" or "real" indicate invisibility in most cases. Generation of UndiscoveredRework CumulativeUndisc RW From New Tasks Gross D&TSReal Production Rate ForecastedFuture D&TSDev Prod per ManWeekfrom Tot WF Figure 3.38 Perceived Fracof RW completeO 1 STOP RU PAUSE TO STOP RUI Tender Specification Production - Progress Indicators The cumulative number of new tasks already developed, contains all new tasks that have been developed, despite of whether they include errors or not. Already developed 110 tasks, which include errors, are reworked by the "WF to RW" team but not by the "WF to D&TS" team. Therefore, the "Cumulative D&TS Tasks Developed" variable is formulated as: Cum_Real_Progress+Cumulative_Undisc_RW_From_New_Tasks The "Cum Real Progress" is formulated in the "Quality" sector and it simply excludes the fraction of tasks that are unsatisfactory from the total number of new tasks developed. Unsatisfactory tasks, produced in the development phase of new tasks, are collected into "Cumulative Undisc RW From New Tasks". Therefore, the formulation above adds the undiscovered rework to the variable, which it was excluded from before. The reason for this approach, is simply that we wanted to make it clear what the "Cum D&TS New Tasks Developed" variable, consisted of and we also wanted to keep track of the cumulative real progress, although, it is normally not known by the management team, even not in the end of the project. "Cumulative Undisc RW from New Tasks" is formulated as stock, which input is the flow named, "Gen of Undiscovered RW". "Gen of Undiscovered RW" represents the error generation rate from new tasks. "Cum Real Progress" is formulated in a similar manner and accumulates the flow of "Gross Real Prod Rate". The real size of the project, measured in new tasks, is defined in the "Initial Values" sector. Normally, in complex development projects, the real project size is not known in the beginning of the project. As discussed in chapter 2, changes to the project team's problem definition of new tasks, often results from: * Misjudgements by the management team of the complexity or scope of the project, * Revision of design because of engineering problems, and * Changes directed by customer 111 The perceived project size of new tasks is in most cases different from the real project size. This is captured in the model through the stock, named "Undiscovered New Tasks". The stock of "Undiscovered New Tasks" is initialized by multiplying the real project size by "Initial Undiscovered Fraction of Project Size", which is defined in the "Initial Values" sector. The value of "Undiscovered New Tasks" is smoothed into the stock of "Perc Proj Size" by a flow named "Disc Rate", which is formulated as: Frac_Discovered_per_week*Undiscovered_New_Tasks where "Frac Discovered per week" is formulated as a graphical function of "Perc Frac of D&TS Dev Completed". The graph is constructed in such a way that it ensures that all undiscovered new tasks are smoothed into "Perc Proj Size" before the project is perceived completed. The custom graph is illustrated in figure 3.39. a. 1 0.8 0 , 0.6 0.4 a 0.2 ou 0 0.2 0.4 0.6 0.8 1 Perc Frac of D&TS Dev Completed Figure 3.39 "Frac Discovered per Week" formulated as a graphical function of "Perc Frac of D&TS Dev Completed" By dividing "Perc Proj Size" into "Cum D&TS New Tasks Developed" we can now determine the "Perc Frac of D&TS Dev Completed". In a similar fashion the "Actual Frac of D&TS Dev Completed" is calculated by using "Real Project Size" as a nominator. 112 Subtracting "Cum D&TS New Tasks Developed" from "Perc Proj Size" then determines the "Perceived Remaining New Tasks" variable. Finally "Perceived time Req to Finish D&TS Dev" is formulated as equal to Perceived_Remaining_New_Tasks/(Assumed_Workforce* Forecasted_Future_D&TS_Dev_Prod_per_ManWeek_from_ Tot_WF) where the forecasted productivity is conducted from the "Forecast of Workforce Needed" sector and assumed workforce is formulated as: Authorized_WF*Weightof_Auth_WF+ Total_Workforce*( 1-Weight_of_Auth_WF) where the weight of authorized workforce represents the manager's perception of what compromise of authorized workforce and already assigned workforce is going to determine the overall D&TS productivity. The assumed workforce is formulated as graphical function of "Perc Frac of D&TS Dev Completed". 1_ = 0.8 . 0.6 o 0.4 ·= 0.2 0I 0 0.5 1 Perc Frac of D&TS Dev Completed Figure 3.40 "Weight of Auth WF" formulated as a graphical function of "Perc Frac of D&TS Dev Completed" 113 At earlier stages of the project, the authorised workforce is normally assumed to determine the average workforce for the rest of the project. In later stages, the already assigned workforce has more weight and in the end it is apparent to the management team that the time it takes to hire new workers will cause a little increase in assigned workforce although some difference exist between already assigned workforce and authorized workforce. Therefore the custom graph of "Weight of Auth WF" is shaped as illustrated in figure 3.40. 3.8.6 Rework Detection The "Rework Detection" sector includes all processes determining how generated rework escapes from inspection and also how rework is detected and reworked. The stock of "Undisc & Uninspect Rework" represents rework that has not been inspected and discovered yet. This stock has two input flows, namely, * Generation rate of undiscovered rework, and * Bad fixes generation rate The "Generation of Undiscovered Rework" has already been discussed in the "Quality" sector. The "Bad Fixes Gen Rate" represents errors created in the reworking process. The stock of "Undisc & Uninspect Rework" has also two output flows, namely, * Discovery rate of RW in normal inspection, and * Escape rate The escape rate, represents the rate at which errors escape from normal inspection performed by the quality assurance team. The term "normal inspection" represents a systematically performed quality assurance, which may i.e. be in the form of regular 114 meetings, careful examinations, and reviews. Once errors have escaped normal inspection, they become active and are normally not detected until in late reviews of tasks that serve as a prerequisite to tasks in execution. The structure of the "Rework Detection" sector is illustrated in figure 3.41. DiscoveredReworkto do I <• Actual Fracof D&TS Dev Completed ByNominal EscapeFraction Nominal Detection Frac Multiplierto Nominal Detectionof RW bec of All WF to QA Figure 3.41 Tender Specification Production - Rework Detection 115 The "Disc Rate of RW in Norm Inspection" variable is formulated as a first order exponential smoothing function with a smoothing time named "Inspection Delay". Once rework has been detected it is stored in the stock of "Discovered Rework to do" until it is reworked. In a similar manner the "Escape Rate" is formulated with the same smoothing time. The "Inspection Delay" is formulated as a graphical function of "Perc Frac of D&TS Dev Completed" in order to be able to show lesser time for inspection in the end of the project. The graph for inspection delay is illustrated in figure 3.42. D6-I c a 4 0. Qs 2CL u, ., 0 c C 0 U 0 E~I `1 0.5 % 1 Perc Frac of D&TS Dev Completed Figure 3.42 "Inspection Delay" formulated as a graphical function of "Perc Frac of D&TS Dev Completed" "Fraction Detected" determines what fraction of the "Undisc & Uninspect Rework" is detected and the rest is considered to escape until later. Therefore, the "Escape Fraction" variable is simply formulated as equal to I-Fraction_Detected 116 where "Fraction Detected" is formulated as equal to Nominal_Detection_Frac*Multiplier_to_Nominal_Detection_of_ RW_becof All_WF_to_QA "Multiplier to Nominal Detection of RW bec All WF to QA" was explained in detail in the "Workforce Allocation" sector and will not be discussed further here. The nominal detection fraction is formulated as: 1-Nominal_Escape_Fraction and "Nominal Escape Fraction" is the variable we felt most comfortable to express in a custom graph. The graph is illustrated in figure 3.43. The mid part or late mid part of a design project is the part of the project where serious design errors often come apparent. Errors, measured in tasks, normally escape at a higher rate in the design phase than in the detailed drawings phase because of more complexity and difficulty involved in detection of design errors. In the end of a project, errors escape at relatively low rate. The reason is that execution of tasks in the end of a project is normally much simpler and more straight forward than of tasks executed in earlier stages both because of familiarity to the project and relatively simpler nature of drawing or specification related tasks than design tasks. Therefore, the custom graph for "Nominal Escape Fraction" is shaped as illustrated in figure 3.43. 117 1 0 CU o w C I -- 0.8 c0 0.6 o, ILL E 0.4 0.2 0 Z al I 0 I l 0.5 1 Actual Frac of D&TS Dev Completed Figure 3.43 "Nominal Escape Fraction" formulated as a graphical function of "Actual Frac of D&TS Dev Completed" After normal inspection, the rework which escaped detection flows into the "Undisc Potentially Active Rework" stock, which we made use of in the "Quality" sector when formulating how active errors cause generation of new errors. The "Undisc Potentially Active Rework" stock has one outflow, namely "Rate of Late Detection", which serves as a inflow in the stock of "Discovered Rework to do". The "Rate of Late Detection" flow is influenced by several factors, such as: * The fraction of already completed tasks that are a prerequisite to the tasks in execution * Multiplier to late detection because of fraction of cumulative escaped errors left * Multiplier to nominal detection of rework because of allocated workforce to quality assurance When previously worked tasks are a prerequisite to tasks in execution, some reviewing processes are in most cases performed in order to ensure quality and integration. 118 These reviews may allow the project team to detect errors, which were not detected in normal inspection and therefore became active. The nominal detection fraction is formulated as the "Fraction of Completed Tasks that are a Prerequisite" multiplied by a constant named "Frac Detected in Reviewing Process", which represent what fraction will be detected out of those tasks that are a prerequisite to tasks in execution. The "Fraction of Completed Tasks that are a Prerequisite" represents the fraction of already completed tasks, which are a prerequisite to the tasks in execution.It is formulated as a graphical function of "Perc Frac of D&TS Dev Completed". The graph is illustrated in figure 3.44. . ' 0.8 m X 0.6 0.4 O o X 0.2 o LL I 0 I 0.5 1 Perc Frac of D&TS Dev Completed Figure 3.44 "Fraction of Completed Tasks that is a Prerequisite" formulated as a graphical function of "Perc Frac of D&TS Dev Completed" As mentioned before, the "Rate of Late Detection" flow is multiplied by the "Multiplier to Nominal Detection of RW bec of All WF to QA", which was formulated in the "Workforce Allocation" sector. This multiplier represents how schedule pressure causes 119 the project team to put less emphasize into QA when under time pressure. Schedule pressure will also influence the rate of late detection and therefore the multiplier is also applied here but not only in the detection rate because of normal inspection. The last factor influencing the rate of late detection of rework is the "Mpl to LD bec of Frac of Esc Err left" variable. This factor takes into account how many errors out of cumulative escaped errors are left in the stock of "Undisc Potentially Active Rework". It is assumed here that it will become exponentially more difficult to find these errors as the fraction of escaped errors left decreases. Therefore, the "Mpl to LD bec of Frac of Esc Err left" is formulated as equal to EXP( 1- /Fracof Esc_Errors_Left) where "Frac of Esc Errors Left" is formulated as equal to Undisc_Potentially_Active_Rework/Cum_Esc_Errors Thus, the nominal detection fraction serves as the rate of late detection before density of escaped errors left and multiplier because of allocated workforce to quality assurance are taken into account. Finally, the outflow of the stock of "Discovered Rework to do" goes into the "Rework Worked" stock. This flow is named "Rework Rate" and is simply equal to "Gross Rework Rate" which was formulated in the "Rework Productivity" sector. Certain fraction of the rework rate, because of unsatisfactory work, determines the rate at which the "Bad Fixes Gen Rate" flow, contributes to the stock of "Undisc & Uninspect Rework". The "Unsatisfactory Frac of Worked RW" is set equal to 0.1 in our model. The "Perceived 120 Frac of RW complete", calculated as "Rework Worked" over "Discovered Rework to do" finally determines what fraction of necessary rework has already been worked. 3.9 Environment 3.9.1 Initial Values The "Initial Values" sector includes initial values of some variables that have been explained in other sectors but were considered to be influenced by the project's environment as it appears in the beginning of the project. The variables in the "Initial Values" sector are illustrated in figure 3.45. O Real Project Size O Initial Undiscovered Fraction of Project Size ZI IInitial ExperiencedWorkforce Initial Permanent Workforce Initial Workforce Wh initial Inexperienced Workforce Initial Scheduled Completion Time Initial Frac of MCT in max slack Max Completion Time O Initial Cumulative Production O Defined Nominal Productivity per Worker Figure 3.45 Environment - Initial Values 121 The real project size is set equal to 500 tasks and the "Initial Undiscovered Fraction of Project Size" is set equal to 0.25. Thus, the project team perceives the project size to be 375 tasks in the beginning of the project. The "Defined Nominal Productivity per Worker" is set equal to 1 task per worker per week. The "Initial Scheduled Completion Time" is set equal to 50 weeks, while the "Max Completion Time" is set equal to 70 weeks. The values presented so far allow the management team to estimate the average number of workers needed. Some efforts will be needed for training, QA and reworking. Some productivity losses may also be present because of necessary turnover in workforce, extra efforts needed for additional tasks and other losses. Assume average 40% loss in productivity and a average productivity multiplier of 1.40 because of overtime, motivation and experience gains. Then the total effort needed may be estimated as Effort needed = 375 {tasks} / [1 {task/worker/ week} I / (0.6*1.4) = 446 man-weeks Thus, the number of workers needed for 50 weeks will be 446/50 = 8.9 workers on average. However, the total initial workforce is only 4 workers, which from 70% are permanent workers, 25% are experienced and the rest is inexperienced. Therefore, in the beginning the project has 4/8.9=45% of the perceived average workforce needed for 50 weeks. 122 These calculations of workforce needed could represent a rough estimation before the project is started. Such estimates are often conducted from previous experience of similar projects. In many cases it is very hard to estimate the efforts needed for a small or medium sized design project and approaches similar to this one are widely used. The management team would most likely estimate the cost from the value of 446 man-weeks needed. Average worker per normal work-week might i.e. cost about 50 $/hour * 40 hours/week = $ 2000 per worker per week Assume a multiplier to normal work-week equal to 1.30, which indicates 12 overtime hours per week and therefore a value of 446*1.30 = 580 normal work-week equivalents is perceived needed to complete the project. The total salary cost of the project can be estimated as 580 * 2000 =$ 1,160,000 It is apparent that a markup of about 20-30% is most likely included in this value. It is becoming more popular to use the bidding form when hiring a company to perform design development. If the company is very aggressive in getting the project, the cost estimate can in many cases be compared to publicly available final cost of similar projects. If the management team perceives that their cost estimate may be too high compared to other bidders, they may even consider to lower their markup, which makes smallest overruns more dangerous than otherwise. 123 3.10 Summary of Project Model Development The fallowing subjects have been covered in chapter 3: * System Dynamics schematic conventions, * Definition of the model's boundary, * Sources of information, * Overall description of how the model was organized, and * Detailed description of the structure of the model where one sector was presented at a time. All time factors and custom graphs may be changed later on in a future development of the model. However, all graphical functions and time values have been justified and explained in detail. They should not be changed without justifying the changes properly and considering the influence they may have on other variables. 124 4 Model Testing As mentioned in chapter 3, the main purpose of the project model development was to identify variables and processes, influencing the success of civil engineering design projects. The identification of these variables and processes is covered in detail in chapter 3. Some variables and processes were identified in chapter 3 but not included in the model. These variables can be considered further in the future development of the project model. In addition to the identification process, the purpose was also to provide a framework capable of simulating the actual recorded history of projects, and thus provide a tool with forecasting capabilities where the effects of changes in structures, policies and various factors institutionalized into the organizational structure can be experienced. The system dynamics modeling process is iterative and the model has already went through many iterations, yielding changes in processes and policies and increasingly detailed model. Although, no further efforts will be allocated into further development of the project model in this paper, a detailed illustration of how the model works in its current version is going to be presented in this chapter. The current version of the model simulates a civil engineering design project, which consist of 500 tasks. These 500 tasks are scheduled to be finished in 50 weeks. The absolute maximum time for completion of the project is 70 weeks. It is assumed that if the execution time of the project exceeds 70 weeks, it will result in some very serious andcostly situation, such as back payments for every week exceeding the initially scheduled 50 weeks in addition to some basic penalty payments for each of these weeks. Therefore an attempt to avoid such situation was made through the "Will to new hires" and other variables influencing schedule overruns. The "Reported Time Req to Finish D&TS Dev" 125 variable, is i.e. formulated as a function of "Absorbed Time Excess" and ensures a reluctance to make schedule adjustments although the project may fall behind schedule. Instead it is assumed that excess time can be absorbed to certain level by increasing overtime worked and the size of the project team. Therefore, time overruns are kept relatively low compared to the cost overruns that can be experienced. The initial workforce is set equal to 4 workers and the defined initial productivity per worker is 1 task per worker per week. 4.1 Human Resource Management The sectors located under the "Human Resource Management" sub-system were listed in chapter 3 as: - Staffing and training - Overtime policy and overtime worked - Workforce allocation The main output variables out of these sectors are going to be covered here but some variables from the workforce allocation sector are also going to be discussed further when considering the "Project Planning" sector, which includes both the initial planning of workforce and the forecast of workforce needed from time to time. "Authorized Workforce" is initialized by the initial estimation of 8.9 workers needed on average throughout 50 weeks. Relatively low initial estimates of productivity losses because of rework, additional work, communication etc. yields overruns both in schedule and cost in the current version of the model. 126 In its current version, carefully justified in chapter 3, the model yields completion time of 59.8 weeks, which means 19.6% overrun in time when compared to the initially scheduled 50 weeks. 1:DesiredWorkforce Inn 2: AuthorizedWF 3: Ceilingon TotalWorkforce _r 21 31 2i 3 2 2 3 Weeks Figure 4.1 Behavior of authorized workforce level for the entire project team. As seen in figure 4.1 the level of authorized workforce rises significantly from it's initial value of 8.9 workers. As explained before, the authorized workforce is influenced by the willingness to new hires. The reason is that it was felt that authorization should not be granted without willingness to complete hires. Therefore, authorized workforce fallows the curve of desired workforce until in week 35. After that the authorized workforce remains at a similar level throughout the project. As shown in figure 4.2 the willingness to new hires drops as the project comes near completion. 127 1. Will to new hires 1: . . ...... I... . - 1 . . . . . . .. . .. .. 11 1 1: ,. 0 tn I u./U ).00 I 20.00 I 60.00 40.00 I 80.00 Weeks Figure 4.2 Grap iical expression of the willingness to new hires As shown in figure 4.1. the initial estimation of average workforce needed, which was the initial number of authorized workers, didn't match the level of authorized workers in the end. As mentioned before, the reason is that the initial estimation of productivity losses, were too low and also that the project was started with a mismatch in authorized and assigned workforce, and mismatch in perceived and actual project size. The behavior of "Authorized WF" and "Total Workforce" is illustrated in figure 4.3. 1: AuthorizedWF 1] OU.UU - 2: Total Workforce .-..-........... ................................. .---.------------- -------. ........... .......... ---...---...--...---.............. ----. --. --....... ...... 25.00- ............................... ... . . . . . I.. . . . . .. Z- ......... ...................... - 1 I--, V. V - l 0.00 l -- 20.00 40.00 60.00 80.00 Weeks Figure 4.3 Authorized workforce in comparison with the total workforce working on the project. 128 The total workforce takes a lower value than authorized workforce throughout the simulation but reaches it in the end. The reason for why it doesn't respond quicker has two aspects. The first one is the departure rate of experienced workers. Hirings because of workers that depart are subject to a delay of 2 weeks, which means that although these departures are normally carefully planned, the new workers that are supposed to come in when other depart, are not necessarily available because of schedule changes in interacting projects in execution within the organization. The second aspect is the 8 week hiring delay involved when additional workers are hired because of the need to increase productivity beyond what was planned in the beginning. 1: WF to Rework 2: WFto D&TSDev 3: WF to Training 4: WF to P&P 5: WF to QA 21 3 4j 21 4 4' Weeks Figure 4.4 Disaggregation of total workforce into sub-teams. As shown in figure 4.4, the number of workers in the end is not restricted. However, the structure for restrictions in the end was incorporated in the model and an example of how to add a graph of maximum workforce in the end was discussed in chapter 3. 129 In addition to disaggregation of total workforce into sub-teams it was also disaggregated into inexperienced, experienced and permanent workforce. 1: Experenced Workforce .uu O 11 21 .................. 2: Inexperienced Workforoe 3: Permanent Workforce ......... ............................................................ , . . . ....... 2'I ................. - ..................... 10. ncowu 0.00 20.00 40.00 60.00 ___ I 80.00 Weeks Figure 4.5 Disaggregation of total workforce in terms of experience. As mentioned before, the fraction of inexperienced workers out of total workforce influences productivity. These influences are incorporated into the model by the productivity multiplier named "Mpl to BP because of WF Mix". 1:Mplto BP becauseofWF mix 1: 1.00 1: 0.95 1: 0.90 Weeks Figure 4.6 Multiplier to base productivity because of workforce mix. 130 The multiplier to productivity because of overtime was also modelled in the human resource management sub-system. Sought multiplier to normal work week yields actual multiplier to NWW after the level of burnout has been taken into account. The reason for this approach is that the willingness to work overtime is formulated as a function of burnout. As seen in figure 4.7 the sought and actual multiplier almost take the same values in the beginning. When burnout builds up, the difference between them increases. Actual multiplier to NWW yields the productivity multiplier due to overtime, after the effect of burnout on productivity has been taken into account. 1:Prd Mpl due to OT 2: Soughtmpl to NWW 3:Act mpl to NWW 1.50 d3 1.25 d3 1.00 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.7 Multiplier to productivity because of overtime. The high level of "Sought Mpl to NWW" in the end indicates higher schedule pressure than in earlier stages of the project. High schedule pressure influences also how workforce is allocated into quality assurance. When schedule pressure rises the workforce 131 into QA is allocated at lower level than planned. Figure 4.8 shows the effect of this formulation. 1: PlannedQA WF 11 2: WF to QA 5.00 ............................................................................................................................ 2j 2 .50 ......................................................... 5.00: 2.50. .......................................................................... 0.00...i 0.00 20.00 40.00 80.00 80.00 Weeks Figure 4.8 Allocation of workforce into quality assurance. Allocated workforce to quality assurance as a fraction of planned workforce to QA influences the nominal detection rate of errors. The multiplier to nominal detection rate because of allocated workforce to QA is illustrated in figure4.9. 1: Multiplierto Nominal Detectionof RW bec of All WF to QA 1: 1: I: 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.9 Multiplier to normal error detection rate because of the number of workers allocated into quality assurance. 132 The reason why the multiplier goes to zero in the end lies in the way the workforce to QA was planned. It was assumed that it would be planned as zero workers at the time the project is completed. Thus, the planned WF to QA was formulated to decrease rather steeply in the end. When the allocated WF to QA reaches zero, no error detection takes place. Therefore, it was felt convenient to formulate the multiplier to nominal detection in such a way that it would take a value of zero in the end and thereby ensure detection rate of zero. 4.2 Project Planning The sectors located under the project planning sub-system were listed in chapter 3 as: - Forecast of workforce needed - Planned workforce allocation Some important variables showing planned and forecasted workforce have already been expressed graphically in chapter 4.1. Those, which were not expressed in chapter 4.1 will be illustrated here and compared to values from the workforce allocation sector. The forecasted future productivity, which drives all forecasts of workforce needed, will also be illustrated in comparison to perceived historic productivity and estimated current productivity. The graph for planned workforce to quality assurance in comparison to the actually allocated workforce to QA was illustrated in figure 4.8 in the discussion of the "Human 133 Resource Management" sector. Workforce into P&P was also planned in similar fashion in the "Project Planning" sector. As mentioned before it appears in the end of the project and represents the workers needed for polishing and publishing. The planned P&P workforce was allocated with a small allocation delay of I week. Therefore, the curves for planned and allocated workforce do not match perfectly although the difference between them appears to be very small. 2: WFto P&P 1: Planned P&P WF zu.W - I........ I........ ............. ................ ... .... .... ... .... ... .... .... .... .I ... . . . .. .. . . .. . . .. 10.00 j .............................. .................................... 0.00- 1 1-2 0.00 i 1-2lmi 20.00 1 -2 40.00 h ................................. i! 60.00 o.oo0 Weeks Figure 4.10 Planned P&P workforce in comparison to allocated workforce to P&P. The variable of desired workforce, which was illustrated graphically in figure 4.1, was calculated in the "Project Planning" sub-system. As explained in chapter 3, it makes use of the forecasted future productivity which is calculated as a function of estimated current productivity, perceived historic productivity and assumed hidden productivity loss. Assumed hidden productivity loss was set to zero in this simulation and therefore it doesn't affect the forecasted future productivity here. 134 1. ForecastedFutureD&TS De . ii 1.00- I . ....... .. 2. EstimatedCurrentD&TS De . . ... . .. - - .... 3. Perc Historic D&TS Dev Pr .. ... .. .. ..... .......... . 21 31 ..... ..................................... '1,-'.- .............. .. .... .. .. .... .. .. . .. .. .. .. ... Z7 050- ............................... - - ....- ... I 0.00 I 0v.vv00 · I 20.00 40.00 . . 60.00 80.00 Weeks Figure 4.11 Forecasted future productivity, in tasks per worker per week, in comparison to estimated current productivity and historic productivity. Thus, the forecasted future productivity takes the value of estimated current productivity in the beginning. In the end it depends only on the historic productivity. In addition to the desired workforce, the estimation of the rework team needed is also influenced by the forecasted future productivity. 1: Perceived Size of RW Team Needed 2: WF to Rework 20.00............................................................................................................................... 10.00' ............................................................. ... ....... 0.00 · ...... ... .... .... .... ...... .... .. .. .... . . .. . .. .. ... . ..... .. 111ti .... :... 11 ........................ . "l . . . ; 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.12 Allocated workforce to rework in comparison to what is perceived as needed. 135 As shown in figure 4.12, the allocated workforce to rework follows the perceived size of rework team needed with a time lag due to a allocation time inbuilt in the model. 4.3 Project Controlling The sectors located under the "Project Controlling" sub-system were listed in chapter 3 as: - Scheduling - Project database - Schedule pressure The "Project Controlling" sub-system contains information about schedule and the historic data that has been collected during the project. The curve for cumulative expanded man-weeks for the total workforce is illustrated in figure 4.13. It is also illustrated how it divides into inexperienced and experienced workforce. 21 1:CurmTotalManWeeks 1500.0o 2: Cumulative ExpManWeeks 3: CumInexManWeeks 1 2 3 32 750.00 0.00 Weeks Figure 4.13 Cumulative expanded man-weekson the project divided into levels of experience. 136 Figure 4.14 shows how cumulative total workforce was divided into certain activities during the simulation. It should be noted here that all numbers for cumulative man-weeks are expressed in terms of normal work-weeks, which is assumed to be 40 hours. Thus, if workers work 60 hours per week, it is considered as 1.5 man-week in the calculations of cumulative man-weeks. 11 21 1: D&TSCum ManWeeks 2:P&P Cum ManWeeks 3:QA Cum ManWeeks 4: RW CumManWeeks 800.00 ---------------------..............-..------------------------------ 4i 1 2 3 4 ii 40( 11 Weeks Figure 4.14 Cumulative expanded man-weeks divided into specific type of tasks. Schedule pressure and schedule changes are also located under the project controlling sub-system. Figure 4.15 shows how the scheduled completion time changed during the simulation. 137 1- Scheduled Time Remamning 2: ScheduledD&TS Dev CompletionTime 2: 1 1· 2- 1: 2: 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.15 Changes in scheduled completion time. During the project, the management team constantly attempts to estimate if the project is on schedule or not. These estimations by the management team are expressed as schedule pressure in the model. The behavior of the perceived schedule pressure is illustrated in figure 4.16. 1: 1: SchedulePressure 0.50 1: 0.25 1: 0.00 Weeks Figure 4.16 Schedule pressure. As explained in chapter 3, the schedule pressure takes a value of zero when the project is exactly on time according to schedule, a positive value if the project is behind schedule and 138 a negative value if the perceived time needed is less than what remains according to time schedule. 4.4 Tender Specification Production The sectors located under the "Tender specification production" sub-system were listed in chapter 3 as: - Progress indicators - Quality - Rework detection - Learning influence on productivity - Development productivity - Rework productivity The "Tender Specification Production" sub-system contains all actual productivity indicators and actual and perceived progress indicators. 1:Acdual Fracof D&TSDevCompleted 2: PercFracof D&TSDevCompleted 2] 21 Weeks Figure 4.17 Perceived fraction completed in comparison to actual fraction completed in the development of new tasks. 139 As seen in figure 4.17, the difference between actual and perceived progress in new task development is very significant until in week 40-50 and the two curves take almost identical values after week 50. The perceived project size is partly responsible for the behavior in figure 4.17. Initially, 25% of the real project size, measured in new tasks, is not known. These additional tasks are discovered at a rather rapid rate during the mid-part of the project and in week 50 the real project size is known by the management team. The way in which new tasks are discovered depends on what fraction of new tasks is perceived completed. 1: Perc Proj Size I: OUU.UU - ................................,,,,, ,,,,,,,..,,..,,,,,,,,.......... ......... ............ I -1 .1 ~ ... .... ............................. '..-'' - - .''.---'-V.-.-- .......... ........ .- 1 I..... .............................. : ........ ..... ... ... .. ........ ..... .. ... .. 1: 250.00 - ................................I................................................................ .......................... 1: 0.00' 0.00 ................................. ................................ ............................... 20.00 40.00 60.00 80.00 Weeks Figure 4.18 Perceived project size measured in new tasks. Although, the project team's progress is perceived at higher level than it actually is, the time required to finish is perceived higher than the scheduled time left throughout the entire project. 140 1:PercTimeReqto FinishD&TSDev 2: Scheduled Time Remaining Weeks Figure 4.19 Perceived time required to finish in comparison to scheduled time require to finish. Unfortunately, this kind of behavior often appears in project management. However, during the project, the management team may perceive that the project will be on schedule after a certain amount of time if it is possible to keep the same productivity in D&TS development of new tasks during that time. As seen in figure 4.19 the project seems to be getting on track in week 10. But in weeks 10-15 an increase in rework needed causes drop in the production rate of new tasks. When the project seems to be getting on schedule again shortly after week 30, a new increase in discovered rework appears. The effects are again excessive increase in efforts to rework and the perceived time left moves further away from the scheduled time remaining. The rate at which rework is discovered is represented by the variables of "Disc Rate of RW in Norm Ins" and "Rate of Late Detection". These variables along with the generation rate of undiscovered rework are shown in figure 4.20. 141 1 Disc Rate of RW in Norm Ins.. 2: Gen of Undisc Rework 3. Rate of Late Detection 10 00 - ...... .. ...............I. .. ... ......... . ............................ ..... ------21 31 ........................... ............... 5.00 nnf 31 I I 1 - 0.00 , 20.00 I so.oo 40.00 I Bo.oo Weeks Figure 4.20 Detection of rework in comparison to generation rate of undiscovered rework. The total detection rate of rework can be obtained by adding late detection rate to discovery rate of RW in normal inspection. Rework is disaggregated into several levels in the project model depending on if it has been inspected and discovered, if it has not been inspected or if it has escaped normal inspection and turned active. The sum of uninspected rework and active rework determines what amount of rework is left when the design project is completed in week 60. The difference between cumulative undiscovered rework from new tasks and rework left has already been discovered and reworked when the project is perceived completed. 1:CumulativeUndiscRWFrom... 2: Undisc&Uninspect Rework 3: UndiscPotentiallyActiveR... 300.00 11 3 150.00.................. 2 . 13 .. .............................. ................................. 2 131 . 0.00 1 1 0.00 IC 20.00 40.00 60.00 , 80.00 Weeks Figure 4.21 Rework disaggregated into levels of uninspected rework and active rework. 142 The rework left at the completion date of the design project will be discovered and reworked during the construction phase of the project. During the design project, the stock of "Discovered Rework to do" doesn't build up significantly because of the attempt to rework errors in a very short period of time once they have been discovered. Figure 4.22 shows the stock of "Rework Worked" in comparison to cumulative rework generated from new tasks. It should be notified that a small portion of total cumulative undiscovered rework is generated by the bad fixes generation rate, which is not included in the curves of cumulative rework generated from new tasks shown in figures 4.21 and 4.22. 1:CumulativeUndiscRW From... 2: ReworkWorked 1.1 2 3: DiscoveredReworkto do 300.00 . ................................................................ ................................................................. 3 2 3 2 3 0.00 10, . . 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.22 Rework worked in comparison to cumulative rework generated from new tasks. As explained in chapter 3, the generation of rework is influenced by various factors, namely, * Fraction satisfactory due to the fraction of workers considered inexperienced, * Fraction satisfactory because of schedule pressure, 143 · Fraction satisfactory because of active errors that have not been detected and can therefore produce new errors, and * Nominal fraction satisfactory representing the fraction satisfactory before effects from the three factors mentioned previously All these factors are formulated as multipliers and multiplied together they determine the overall fraction satisfactory from the development of new tasks. 1: FS due to Act RW 2: FS due to Frac Inexp 1.00 - 3: FS dueto Schedule... ......... 4: NominalFractionSe... .......................................................... ....... 4I x a. 21 31 ........ 0.75 ................................................................................. 4, 0 50 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.23 Multipliers determining overall fraction satisfactory. 1: FractionSatisfactory 1: 1.wuI ............................................................... I............................... ...............................I.............................................................................................. 0.75' ........I...................... k .:....... ........................ ....... '~"~"~'~~"' ~ ............................. 1~ 1 ................................ 1 ' 0.50 0.00 20.00 II 40.00 Weeks Figure 4.24 Overall fraction satisfactory. 144 60.00 I 80.00 Therefore, the variable of "Mpl to Prod bec of Learning Curve" has almost negligible effect on productivity. It takes a value just above 1.0 in the end of the project as shown in figure 4.26. 1:Mplto Prod becof ProjectFamiliarity 2: Mplto Prodbecof LearningCurve Weeks Figure 4.26 Multipliers to productivity because of learning. Project familiarity was assumed to have more significant effect on productivity and the multiplier rises from 1 to 1.15 during the project. The effect of project familiarity may undoubtedly be much greater when dealing with a project which is unique in the sense that no previous experience exists from similar projects. As explained before, the schedule pressure influences productivity through the multiplier due to overtime. It also influences the level of motivation which influences productivity. As explained in chapter 3, the level of motivation may affect the time spent into coffee brakes, personal time off etc. The multiplier to productivity because of motivation is illustrated in figure 4.27. 146 1 Mplto Prodbec of Motivation . 1: 1: Weeks Figure 4.27 Multipliers to productivity because of motivation. High level of communication is undoubtedly crucial to the project's success as mentioned before. However, the time for communication was considered as a loss in productivity in the the project model. Thereby, it has been assumed that the level of efficiency in communication will remain the same throughout the project and its effect on productivity will only be present in the form of the time that has to be spent on it. 1: Mplto Prodbec of CommOH 1: .UU - .. , .. .. .. .. .. .. .. .. .. I .. .. .. . .. .. .. 1 .... .. .. .. .- .. i .................I............: ................................... . .. .. .. .. .. . .. .. .. .. .. .. . .. .... .. .. .. . Z I ....... ·- ·· ·- · · · · · · · ·- · ·· · · · · · ·- · · · · · ··-I I 0.50" I.............................. ............................... :............................. ............................... ....... ............I......... .. . . . . . . .. . . . . . . . 1: 0.\.Vfl/\AA 1.00 . 20.00 I 40.00 . -- -- 60.00 - l 80.00 Weeks Figure 4.28 Multiplier to productivity because of communication overhead. 147 It was assumed in the formulation of "Mpl to Prod bec of Comm OH" that the loss in productivity because of communication overhead would increase with increasing number of workers. Because of continuous increase in number of workers during the project, the multiplier because of communication overhead decreases throughout the project. The gross productivity for development is calculated by multiplying all multipliers to productivity together with the initial productivity per worker, which was set to 1 task/worker/week. 1: Current D&TS Prod per D&TS Dev worker 4s "'o"_ 2I I.- a .... ....... .... ... .... ... 2: Gross Rework Productivity Rate per Worker ---------------------.... . . .... ... . .. .. ... .: -------------- -- ... X,, -, e 4 1 ........I................................................................I..................... ................................. r- 0.60- 2- _, 2--"--." ............................... ........................... .................................... --------- ....................... : : ................................ 0.00 ^^ :................................ I I 'IIIII[111 ................................ ................................. : I /I"l! fll! ~4,11Ill! Uf~ I'ttl Weeks Figure 4.29 Gross development productivity of new tasks in comparison to gross rework productivity. Finally the rework productivity per worker was formulated as equal to the development productivity rate multiplied by a factor representing difficulty in reworking errors. Therefore, it takes lower values than the development productivity throughout the simulation. 148 4.5 Schedule and Cost Overruns The "iThink" software supports both graphical and table output for variables. Table outputs are very useful when seeking exact numbers from the simulated model. The base simulation discussed in this paper yields the following values for execution time, overtime and total expanded normal man-weeks. Total expended normal man-weeks Total time needed to complete the project Average multiplier to normal work-week Table 4.1 1,054 man-weeks 59.8 weeks 1.30 Data for cost and time from the base run. Thus, the actual total man-weeks worked can be calculated as Actual total man-weeks = 1054/1.30 = 811 and the overtime worked per week equals 40 {hours per normal work-week} * (1.30-1) = 12 {hours} The initial estimate of actual total man-weeks needed to complete the project was 580 normal man-weeks. By assuming a fixed cost of worker per normal work-week equivalents the actual overrun in salary cost can be calculated as Overrun in salary cost = (1054-580)/580 = 81.7% 149 Thus, the salary cost of the project appeared to be 81.7% higher than in the initial estimate. It was desired to keep time overruns within certain limits because of the maximum completion time and assumed penalty payments for each week exceeding 50 weeks. The simulation yields a completion time well within the maximum completion time although the project is not completed on the initial scheduled completion date. The overrun in schedule equals Overrun in schedule = (59.8-50)/50 = 19.6% Thus, the time needed to complete the project appeared to be 19.6% more than was initially estimated. The current version of the project model yields significantoverruns in both schedule and salary cost. Schedule overrun 19.6% Overrun in salary cost 81.7% Table 4.2 Overruns from the base run. A severe misjudgement of the real size of the project along with much more rework than was expected, are undoubtedly the most significant underlying causes of this behavior. However, it is also apparent that a low workforce level in the beginning of the project causes slower progress than desired in the beginning and that leads to increase in desired overall productivity rate. Although the ECECO employees agreed that the simulation could represent a real behavior of project's variables they notified that the simulation resulted in a rather extreme 150 case of overruns. In such extreme cases, the customer is normally partly responsible because of changes directed by his representatives. 4.6 Parameter Changes The project model is essential for exploring how changes in various factors may result in a different behavior of variables critical to the project success. The effects of potential changes in variables such as productivity per worker may be explored in order to evaluate investments. In a similar fashion all critical processes and time factors may be altered and changed in order to evaluate potential structural changes within the organization. 4.6.1 Effects of Increase in Productivity per Worker The ECECO employees have notified that in addition to be interested in the identification of variables and processes crucial to the success of civil engineering design projects, they are also interested in how changes in various factors within the organization may result in a different behavior of specified projects. An example of such changes might i.e. be an average 15% increase in productivity per worker. Such average increase in productivity per worker might i.e. be reached through a new cad-system with integrated design capabilities. The value, 15%, might have been reported by a similar company which has already moved from ECECO's current cad environment into the new one, or it might have been estimated from some other sources. The question is how will such an increase in productivity per worker affect the output of the simulation. 151 A new run was performed to experience the effects of increased productivity per worker. The defined basic productivity per worker was increased from 1.00 to 1.15 and initial value of authorized workforce was decreased from 8.9 to 8.9*0.85=7.56 {workers} to ensure that the authorized workforce level would match the desired workforce in the beginning. As expected, the change in productivity resulted in a quite different behavior from the previous one. Total expended normal man-weeks Total time needed to complete the project Average multiplier to normal work-week Table 4.3 855 man-weeks 58.0 weeks 1.29 Data for time and salary cost from a run where productivity per worker is increased from 1.00 to 1.15 and the initial authorized workforce level was decreased from 9.3 to 7.91. The actual total man-weeks worked can be calculated as Actual total man-weeks = 855/1.29 = 663 An average multiplier to normal work-week of 1.29 indicates that the average actual work- week consists of 40*1.29=51.6 hours. However, it is convenient to do cost calculations from values expressed by total expended normal man-week equivalents. The reason is that the normal work-week represents a 40 hours work-week and by calculating the expended man-weeks in normal work-week equivalents it is ensured that all cost comparison is made from the same reference point. Therefore, it was decided to assume a fixed cost for each normal work-week equivalent spent on the project which indicates that no distinguishes is done between a salary per a day-time hour and an overtime hour. The base run yielded 152 Total expended man-weeks = 1054 normal work-weeks Thus, the 15% increase in productivity per worker yields (1054-855)/1054 = 18.9% reduction in cost. The reason for this behavior is not only less loss in productivity because of higher fraction of experienced workers but also less efforts per worker spent into communication and lower error generation rate. As explained in chapter 3, the productivity loss because of communication increases with increased number of workers and fraction satisfactory due to workforce mix increases with higher fraction of experienced workers. The authorized workforce level takes lower values throughout the project compared to the base run. The authorized workforce level illustrated in figure 4.30 can be compared to figure 4.1, which represents the values from the base run. 1: DesiredWorkforce And- _ 2: AuthorizedWF 3: Ceilingon TotalWorkforce . 2: 3 2:. 3. 1. 2: 3 Weeks Figure 4.30 Behavior of desired and authorized workforce. The defined nominal productivity was set equal to 1.15. The graph can be compared to figure 4.1 where defined nominal productivity was set equal to 1.00. 153 Similar to the behavior in the base run, the total workforce level responds rather slowly to the authorized level. The total workforce level illustrated in figure 4.31 can be compared to figure 4.3, which represents the values from the base run. 1: AuthorizedWF 11 2: TotalWorkforce .............................. ........................... ,............................................. ............................................... oU.uu I- ........... ........................................... ............................. . .............. ........ ............................................................................ 25.00- ............................................................................ -1............................................... -2== .... 0.00 ; 0.00 20.00 40.00 I 60.00 80.00 Weeks Figure 4.31 Authorized workforce in comparison to the total workforce. The defined nominal productivity per worker was set equal to 1.15. The graph can be compared to figure 4.3 where defined nominal productivity per worker was set equal to 1.00. The way in which workforce is divided into certain activities changes also compared to the base run although the shape of the workforce curves appears to be similar in terms of extreme points. The workforce disaggregation illustrated in figure 4.32 can be compared to figure 4.4, which represents the values from the base run. 154 1: WF to Rework 2: WF to D&TS Dev 3: WF to Traininq 4: WF to P&P 5: WF to QA ,,,, ZUUU 2 3 4 13 10.00 4 5 1 3 4 Dr A1 u.uu I'll . 0.00 . , . 20.00 _ 40.00 60.00 . .~~~~ 80.00 Weeks Figure 4.32 Disaggregation of total workforce into sub-teams. The 15% increase in the defined nominal productivity per worker results in 15% increase in rework productivity per worker because of the way in which rework productivity was formulated as a function of defined nominal productivity. Therefore, the cumulative efforts spent into rework become significantly less than in the base run. Sensitivity analysis are commonly used in the field of system dynamics when exploring how changes in input variables affect behavior of a model. "iThink" supports sensitivity analysis in such a way that calculations for multiple set of input values can be performed in one simulation. Output values from a sensitivity analysis for different values of defined nominal productivity per worker, are presented in table 4.4. In order to ensure initial match in authorized and desired workforce, the initial value of authorized workforce was also changed. 155 Defined nominal productivity per worker Initial value of authorized workforce 1.05 tasks/worker/week 8.45 workers Total expanded normal man-weeks 978 NMW Average multiplier to normal work-week 1.29 Actual expanded man-weeks 758 MW Total time needed to complete the project Decrease in execution time Decrease in salary cost with respect to the base run 59.0 weeks 1.3% 7.2% Defined nominal productivity per worker Initial value of authorized workforce 1.10 tasks/worker/week 8.01 workers Total expanded normal man-weeks 917 NMW Average multiplier to normal work-week 1.29 Actual expanded man-weeks 711 MW Total time needed to complete the project Decrease in execution time Decrease in salary cost with respect to the base run 58.6 weeks 2.0% 13.0% Definednominal productivity per worker Initial value of authorized workforce 1.15 tasks/worker/week 7.56 workers Total expanded normal man-weeks 855 NMW Average multiplier to normal work-week 1.29 Actual expanded man-weeks 663 MW Total time needed to complete the project Decrease in execution time Decrease in salary cost with respect to the base run 58.0 weeks 3.0% 18.9% Defined nominal productivity per worker Initial value of authorized workforce 1.20 tasks/worker/week 7.12 workers Total expanded normal man-weeks 806 NMW Average multiplier to normal work-week 1.29 Actual expanded man-weeks 625 MW Total time needed to complete the project 57.8 weeks Decrease in execution time 3.3% Decrease in salary cost with respect to the base run 23.5% Table 4.4 Sensitivity analysis where effects of changes in productivity per worker were explored. Cost is compared with the base run by assuming fixed cost per normal work-week equivalents. As seen in table 4.4, the salary cost was compared to the base run where the defined nominal productivity per worker was set equal to 1.00. Increase in productivity per worker doesn't only yield more fractional decrease in cost than can be explained by the fractional increase in productivity but it also decreases execution time and may therefore reduce problems because of off-schedule projects within the organization. 156 An investment in technology such as a new cad system with integrated design capabilities may be supposed to yield certain increase in productivity per worker. But, by using the "what if' capabilities of the project model for a certain project, the management team can explore cost decrease for a specific range of defined nominal productivity per worker in order to make an estimate of the potentially most pessimistic and most optimistic cost benefits. 4.6.2 Effects of Changes in Additional Work As mentioned before, a customer directed changes in the project's size or scope are generally considered as additional work. The customer makes additional payments in most cases for such additional work. Payments for additional work can be higher than payments for identical work in the initial project definition, often because of better contractual position of the contractor once the project has been started. It may be desirable for the contractor to know how the success of a project is influenced by additional work. The total size of the project is defined in the project model by the "Real Project Size" variable, which was set equal to 500 tasks in the base run. It was assumed in the base run that a fraction of 25% of the real project size, measured in new tasks, was undiscovered when the project was started. Thus, the initial perceived project size was 500*0.75 = 375 tasks. Assuming that additional work counts for 10% of the real project size the real project size without the additional work can be calculated as 500*0.9 = 450 tasks. Thus, the variable of "Initial Undiscovered fraction of Project Size" without additional work takes the value of (450-375)/450 = 0.167. By running the model without the additional work, we can experience how (500-450)/450 = 11% increase in the project size because of additional work, influences the cost of the project if the additional work has to be done within the initially scheduled time for completion. 157 Real Project Size Initial Undiscovered Fraction of Project Size Table 4.5 450 tasks 0.167 Values without additional work of 50 tasks. The simulation without additional work yields the values presented in table 4.6. Compared to the output data from the base run, the cost increase because of additional work appears to be greater than the fractional increase in tasks. An 11% increase in project size yields (1054-923)/923 = 14.2% increase in cost if assuming a fixed cost per normal man-week equivalent. Real Project Size Initial Undiscovered Fraction of Project Size Total expanded normal man-weeks Average multiplier to normal work-week 450 tasks 0.167 923 NMW 1.29 Actual expanded man-weeks 716 MW Total time needed to complete the project 55.8 weeks 11% increase in project size because of additional work yields Increase in execution time 7.2% Increase in salary cost with respect to the base run 14.2% Table 4.6 Values from a simulation where additional work of 50 tasks was excluded. Salary cost was compared to the base run by assuming fixed cost per NWW. The exclusion of additional work results in lower values of both desired and authorized workforce than in the base run except for in the beginning. The behavior of the desired and authorized workforce levels is illustrated in figure 4.33, which can be compared to figure 4.1 from the base run. 158 1: Desired Workforce 2: AuthorizedWF 3: Celling on Total Workforce ..... 5 2 3 2 3i 3 Weeks Figure 4.33 Behavior of desired and authorized workforce level for the entire project team when additional work of 50 tasks is excluded. The graph can be compared to figure 4.1 from the base run. The way in which workforce is divided into certain activities changes compared to the base run although the shape of the workforce curves appears to be similar in terms of extreme points as in all the runs performed in this paper so far. The workforce disaggregation illustrated in figure 4.34 can be compared to figure 4.4, which represents the values from the base run. 1: WF to Rework II 21 31 41 51 u. UU 2: WF to D&TS Dev 3: WF to Training .,,.,,,,. ,.,,,,,,.,,,,,.,,,,,,,,,, - .,, ,,- 4: WF to P&P ............................................................. ............................. 5: WF to QA ,.. .,.,,.-- ... ,-, .. , - ..... . 'I V'vv~~~~~~~~~~~~~~~~ u.oU 20.00 40.00 -- 60.00 Weeks Figure 4.34 Disaggregation of workforce into sub-teams. 159 I 80.00 It should be noted here that the assumed requirement of completing the additional work within the initially scheduled time for completion is the underlying cause for why the fractional increase in cost because of additional work becomes higher than the fractional increase in tasks. Such requirements are normally not made except when a project is very seriously constrained by time. The contractor would generally be provided with some additional time for additional work. However, it became apparent that if the contractor is required to complete additional work within the initially scheduled time frame, the dynamic of cost determining variables associated with the additional work should be considered carefully. 4.6.3 Effects of More Aggressive Hiring Strategy As explained in chapter 3, the model has inbuilt time factors for both hirings and lay-offs. The time for hiring is currently set to 8 weeks while time for lay-offs is set to 1 week. As illustrated in figure 4.3, the base run yields very slow response to the level of authorized workforce when the total workforce is increasing. Therefore, it may be desired to decrease the time for hiring if possible. However, the time for hiring is not the only reason for this slow response. The departure rate is also a drag on the response when the size of the project team has to be increased. As explained before, all hirings because of workers that depart are subject to a delay of 2 weeks, which means that although these departures are normally carefully planned, the new workers that are supposed to come in when other depart, are not necessarily available because of schedule changes in interacting projects in execution within the organization. In other words, their expertise is so badly needed in other projects that they have to delay their appearance in the project modelled in this paper. Many projects are 160 generally in execution within the organization at the same time. Some of these projects are very small and do not allow any delay in the scheduled time of completion and are therefore considered more important than projects that do not have to be completed until after a significant amount of time. It is of course desirable to lower the time needed to hire workers instead of those that depart but in this sub-chapter the subject of interest is the 8 week hiring delay which is involved when additional workers are hired because of the need to increase productivity beyond what was planned in the beginning. More aggressive hiring strategy, designed to decrease the 8 week hiring delay, can potentially be reached through factors such as * Wage and salary system, * Different qualification requirements, * Recruiting efforts, * Promotion, * Facilities, * Career planning system, and * Possible sharing of manpower with other companies. Assume that the time for hiring can potentially be decreased from 8 weeks down to 4 weeks. Some cost is most likely associated with a more aggressive hiring strategy. Therefore, it is interesting to explore how it affects the execution time and salary cost of the project. Such information can be helpful when evaluating the feasibility of more aggressive hiring strategy. Running the model with time for hiring set equal to 4 weeks yields the values presented in table 4.7. 161 4 weeks 1109 NMW 1.29 860 MW 56.8 weeks 5.0% Time for hiring Total expanded normal man-weeks Average multiplier to normal work-week Actual expanded man-weeks Total time needed to complete the project Decrease in execution time Decrease in salary cost with respect to the base run Table 4.7 - 4.1% Values from a simulation where time for hiring was set to 4 weeks compared to 8 weeks in the base run. Salary cost was compared to the base run by assuming fixed cost per NWW. As seen in table 4.7, a decrease in time for hiring yields decrease in execution time but an increase in salary cost. Cost is therefore sacrificed for time. The reason for the cost increase is that more training and communication efforts are associated with steeper increase in workforce. 1: Authorized WF 11 2: TotalWorkforce ,50.00 .............................. ............................................................................................. ........ .. .... . .. .. ................................................. ........... 21 25.00 .. . . ... .. . . . .. . . .. . . .. . . . .. . . .. . . . ~~52- ......... ... .. ... .. ... .. .. ... . . . . . .. . . - ..... ! . .. ...... .... .. .. .. .. .. . 0.00 0.00 20.00 40.00 60.00 80.00 Weeks Figure 4.35 Authorized workforce in comparison to total workforce. As seen when comparing figure 4.35 to figure 4.3 from the base run, the authorized workforce takes a little bit higher value in the end in figure 4.35 than in figure 4.3. Because of higher level of total workforce and thus higher productivity losses due to communication 162 and training, the management team perceives lower productivity per worker which results in higher level of authorized workforce. No specific value of penalty payments have been assumed in this paper for each week excessing the initially scheduled 50 weeks. However, such payments may be of significant value and each additional week overrunning 50 week can also be costly in terms resource problems in other projects which may be experienced when one project goes off schedule. The management team would therefore have to consider various factors when estimating the benefits of more aggressive hiring strategy. 4.6.4 Effects of Over-Estimation in Project Size The project model can also handle a situation where a project is overstaffed. It responds to such situation by decreasing scheduled completion time and firing workers. In order to show these capabilities of the model it was decided to set the variable of "Initial Undiscovered Fraction of Project Size" equal to -0.25 which indicates that the size of the project is perceived 25 % larger than it actually is. The initialation from the base run was not changed because the initial perceived project size remains the same or equal to 375 tasks while the real project size changes to 300 tasks. Two runs were made, other with minimum scheduled completion time of 50 weeks but the other with no constraints on reduction in scheduled completion time. In some cases the management team might want to keep the initial scheduled completion time of 50 weeks because of possible interaction with subcontractors. By allowing only positive change in scheduled completion day the behavior in figure 4.36 was experienced for the authorized and desired workforce. The run yielded a completion time of 50 weeks. 163 1:DesiredWorkforce 2: AuthorizedWF 3{- .................. Wu.U .. . ..... .......... ............ ...... .... .... ....... .............. .......... ........... 3: Ceilingon TotalWorklor-e .......... ............................ ............................. ......... .. .............................. ...I. ......................... ...... ........... .. . ............. ................................... 25.00- ................................. il ...2 ,,,, ..... I_I ................ - . i1 2: -Ia.~ 31 1 2: 3 0.00 | E1 l I nn ----- I 40.00 20.00 -liv , , .................................. I l 80.00 80.00 Weeks Figure 4.36 Authorized workforce in comparison to desired workforce. As explained before the actual total workforce shows slow response when increasing but because of a time for lay-offs equal to only 1 week, the curve of total workforce follows authorized workforce very closely when declining. 1: AuthorizedWF 50.00 2: TotalWorktorce .. . .. . .. .. .. . .. .. .. . .. . ... . .. . . ... .. . . .. ... . .. . ... . .. . . ... .. . . ... .. . . ... .. . . 25.00 ............................................................. I... ............................... ......... .... ..... .... .... 0.00 . 0.00 ...... ......4_4........... - 11 ........................ 20.00 i 40.00 60.00 80.00 Weeks Figure 4.37 Authorized workforce in comparison to total workforce. 164 Figure 4.38 shows how the total workforce was disaggregated into sub-teams. The level of workforce into D&TS development appears to be more steady than in the base run mainly because of smoother behavior of allocated workforce into other activities which have priority over D&TS development. 1 WFto Rework 3: WF to Training ........................................................................................ --- 10.00 - .............................. 21 3, 41 11 2: WF to D&TSDev Ju.w . . 5 WFtoQA ................. . ... ...... 4: WF to P&P . .................................. .. . .. .. .. . .. .. - -.... ------... ..... 4t f· 21 41 3~~3~~-~--C~' 0.001 II 000 __ Figure 4.38 1 _. 20.00 - 1 ~ 40.00 Weeks ·----- I - I 60.00 80.00 Disaggregation of total workforce into sub-teams. The behavior of the perceived project size is illustrated in figure 4.39. 1: Perc ProiSize 1: 375.00 1: 337.50 1 . . 300 ___. 00 _ I nno .uu u.=uu 'n. . eu. . Un M.WWeeks 80.00 Weeks Figure 4.39 Authorized workforce in comparison to total workforce. 165 By releasing constraints on the scheduled completion time the execution time appeared to be 49 weeks. As seen in figure 4.40, the schedule adjustments causes less decrease in authorized workforce in the end of the simulation than in the previous run. 1: Desiired Workforce 2: Authaorized WF 3: Ceiling on Total Wadorce 50.00 ................................................................................................................. 3I"I 2 33 2 .00 5.00 ....................... ........................ ............................ ... ... .. ... .. 0.00 u.uu n AA AA z:.uw ^^ AX ^^ 40.00 . . .. ..... ....................... OA AA eo.oo AA AA~~~~~~~~~~~~~~~~~~~~~~~~~~: 80.00 Weeks Figure 4.40 Authorized workforce in comparison to total workforce. Initial Undiscovered Fraction of Project Size -0.25 Real project size Total expanded normal man-weeks 300 tasks 576 NMW Average multiplier to normal work-week 1.13 Actual expanded man-weeks 510 MW 49.0 weeks Total time needed to complete the project Decrease in execution time Decrease in salary cost with respect to the base run Table 4.8 45.4% 18.1% Values from a simulation where "Initial Undiscovered Fraction of Project Size" was set equal to -0.25 compared to 0.25 in the base run. The real project size was set to 300 tasks compared to 500 tasks in the base run. Thus, the workforce initialation was the same as for the base run. Salary cost was compared to the base runby assuming fixed cost per NWW. As seen in table 4.8 the 25% over-estimation of the project's size yielded 45.4% decrease in salary cost compared to the base run where the project's size was underestimated with a fraction counting for 25% of the project size. Thus, the (500-300)/500--40% decrease in the project size yielded 45.4% decrease in salary cost. 166 4.7 Model Validity The question of validity of system dynamics models should always be considered carefully. The validity of recommendation based on a model's behavior is influenced by various factors. One thing is to get a truthful generalized behavior from a model where input variables have been estimated from experience. A whole another thing is to model processes where each input variable has been developed based on high quality data collection. Such precise modelling is in many cases best accomplished by concentrating on the behavior of isolated processes rather than on a total picture where a number of processes interact in various ways as in the project model provided in this paper. In this paper the final goal is mainly to get an insight into a real world problem and identify interacting forces within the management scope of a project. The model contains a number of processes and the behavior of many input variables is estimated from experience and they are often constrained by logically derived equilibrium, data points or mathematical equations. The model behavior was not supposed to yield an actually recorded history. In the discussion of the model's boundary the purpose was rather to provide a framework which may be capable of simulating recorded history and to identify what kind of information would have to be conducted from a real world project in order to make such simulation possible. Although, the model's trend in behavior towards changes can serve as a base for recommendations given in full confident, all precise output values such as the precise percentage for decrease in salary and execution time due to certain changes should not be considered as a base for recommendations without an additional development performed to simulate actually recorded history of a project with acceptable accuracy. After such additional development the model validity would have to be reconsidered. 167 In addition to the runs made in the discussion of parameter changes, several runs were also made for extreme cases in order to make sure that the modelling structure would also perform properly in such situations. The model passed all such tests and has been proved to work properly for overstaffed projects as well as understaffed projects. However, it is apparent that a situations where a project is perceived overstaffed are rarely experienced within ECECO because the company is generally understaffed and the top management wants to keep it that way according to my sources. Most processes within the model need to be developed further aligned with a organized data collection in future projects within ECECO. Such development doesn't only yield more accuracy in the model but it also exploits an excellent tool for storing information from historic projects. When performing parameter changes and comparison of salary cost and execution time to the base run, no thoughts were given to the level of undiscovered rework left in the end of the design project. Such rework will not been discovered and reworked until in the construction phase but does however contributes to the final cost of the project. The rework left in the end of the design project is an example of an indirect cost determining variable that should be considered when comparing changes in salary cost and execution time due to changes in factors within the model. Other examples are i.e. the number of workers in the end of the project, level of burnout in the end, level of inexperienced workers in the end etc. Finally, the author would like to express his perception of the forecast capabilities of system dynamics models of a size similar to the size of the model provided in this paper. It is the author's perception that the forecasting capabilities of such models should not be overrated. Although, it may be useful to experience how policies and processes may respond to changes in input variables, the actual generation of i.e. rework or additional work can only be simulated based on past experience. Such historic behavior doesn't 168 necessarily repeat itself although in may give an idea of what to expect, especially not if some changes have been made due to past experience. However, such changes may be explored in the model in order to gain general understanding of their effects. 169 5 Summary 5.1 Conclusions This thesis was undertaken to satisfy three primary overall objectives. · To gain insight into project management in general with a particular emphasize on civil engineering design and design implementation. * To use system dynamics to identify the systematic forces acting on a Project Management implementation. * To develop a generalized system dynamics project model with respect to information conducted through interviews and review on related research. All objectives were achieved with notable results. In addition the original thesis objectives, generic discussion and analysis of organizational structures and project scheduling was performed. Problems associated with traditional organizational structures and project scheduling contributed to the project model when identifying potential problematic behavior. System Dynamics aided greatly in the process of gaining insight into Project Management implementation because it forced the author to consider underlying causes for a specific behavior in a logistic and systematic manner. Aligned with informations conducted from interviews and review on related research, this ultimately allowed the author to identify and formulate variables in the project model. A variety of critical aspects was also identified for future development. 170 Most time factors and graphical variables were constructed with respect to questionnaires which were filled out be the interviewees. The model behavior was also confirmed with the employees at ECECO by presenting examples of its output in order to ensure that the system structures which had been identified were valid. Once the model was completed after a number of iterative processes and testing runs, it's output was finally illustrated for the base run which values and graphs were explained and justified in detail in the chapter on model development. Several parameter changes were made in order to determine the trend of behavior in the project model in comparison to the base run. These parameter changes serve as examples of possible use of the project model. 5.2 Final Thoughts and Further Research The author learned through the interviewing and modelling process, that some crucial data for variables such as error detection rate, error generation rate, amount of rework worked, efforts into communication, efforts into training etc. are often not available. Factors such as efforts into communication and training were estimated by our interviewees in the form of graphical functions and such estimations were considered sufficient for the generalized project model provided in this thesis. It passed the author's mind during the development phase of the project model that the framework provided by the system dynamics field is in fact essential for identifying interesting research areas in a very rapid manner. Various relationships such as efforts into communication as a function of workforce, efforts into training as a function of experienced and inexperienced workforce, effects of overtime on productivity etc. are all interesting areas on the softer side of the project management field and furthermore it may 171 be real fun to investigate these factors for a specified company or even specified businesses. All variables concerning error generation and amount of rework worked were formulated by the author which then sought for a perspective on the resulting behavior. Historic data for rework worked did not exists within ECECO. The main interest of the author was on managerial aspects rather that on professional aspects in civil engineering design and therefore it was decided to avoid bringing in additional complexity due to specified types of errors where errors could be defined in terms of error characteristics as well as in terms of the characteristics of the environment they were created or detected in. However, these thoughts indicate the need for a some kind of system where insufficient work can be measured and located in a systematic manner. It is not an easy task to develop such system within a organization both because of varied tendency to hide or justify rework and also because of how errors or rework can be defined in various ways. However, it is undoubtedly very important to provide companies with some reference frame which allows comparison between projects in a consistent manner and thus more understanding of critical behavior. It is apparent that various rework cycles are greatly responsible for misjudgement in the project's progress and various misperceptions that exist in a execution of a project. Therefore, rework has to be acknowledged, measured and even prevented if possible in order to limit the amount of unforeseen cost and unexpected delays in future projects. The thing is however that in most organization this implies changes in organizational cultures, monitoring logic and critical aspects to managerial support systems. Further research to support extension of the project model needs to be performed. Two sets of model extensions are proposed. 172 * Extend the model so it can handle multiple projects in a parallel manner. Such extension would incorporate the interactions that generally exist between projects that are executed parallel to each other. Outputs from the current model such as departure rate of workers and lay-offs would serve as an input into parallel projects if needed and inputs such as hiring rate would be partly conducted from departure rate from other projects. The project model could allow sharing of fixed cost between projects and some extensions to allow sharing of manpower could be incorporated in order to control schedule pressure and overtime worked in such a way that no single project would experience pressure far beyond what is experienced in other projects. This environment would provide a framework where influences of various allocation and schedule pressure control policies could be experienced. * Extending the project model so it can handle the entire project from the starting point of preliminary design to the end of the construction phase. Such extension would i.e. address the cost associated with the amount of rework left in the end of the design and tender specification development project. As explained in previous chapters the total amount of unsatisfactory work was defined from the point of view that it represented errors which would be reworked during either the design and tender specification phase or the construction phase of the project. Finally, the project model can also be extended within its current framework with or without the sets of extensions mentioned previously. Variables, identified in the chapter on model development, but not included in the current version of the project model may serve as an excellent starting point for such extensions. The End 173 6 Bibliography Abdel-Hamid, K. Jan 1984. The Dynamics of Software Development Project Management. Ph.D. Thesis at MIT. Balz, W.P., and S.R. Garderberg. Jan 1993. A System Dynamics Analysis of Total Quality Management Implementation. M.S. Thesis at MIT. Cooper K.G. Feb 1993. The Rework Cycle: How it Really Works .. And Reworks ... Project Management Journal. Cooper, K.G. December 1980. Naval Ship Production: A Claim Settled and a Framework Built. Interfaces. Vol. 10, No. 6. Cooper, K.G. February 1993. The Rework Cycle: Why Projects Are Mismanaged. Project Management Journal. Forrester, Jay W. 1961. Industrial Dynamics. Productivity Press. Cambridge MA. Forrester, Jay W. September 1964. Common foundations underlying engineering and management. IEEE Spectrum. Forrester, Jay W. 1965. A New Corporate Design. Industrial Management Review. Vol. 7., No. 1. Forrester, Jay W., and Peter M. Senge. 1980. Tests for Building Confidence in System Dynamics Models. TIMS Studies in Management Science. 14, p. 209-228. Hajek, Victor G. 1984. Management of Engineering Projects. McGraw-Hill. New York. Hines, J. H. 1994. "Formulating The Learning Curve". Working paper distributed in the "15.874 System Dynamics for Business Policy" class at MIT. Hines, J.H. 1994. Class notes from the "15.874 System Dynamics for Business Policy" class at MIT. Hogarth, R.M., and S. Makridakis. February 1981. Forecasting and Planning: an Evaluation. Management Science. Vol. 27, No 2. Jaafari, Ali. June 1984. Criticism of CPM for project planning analysis. Journal of Construction Engineering and Management. Vol. 110, No 2. Kerzner, H. 1989. Project Management. A Systematic Approach to Planning Scheduling and Controlling. Van Nostrand Reinhold. Lock, D. 1993. Handbook of Engineering Management. Butterworth-Heinemann. 174 Moder, Joseph J., and Cecil R. Phillips. 1970. Project Management with CPM and PERT. Van Nostrand Reinhold Company. New York. Morecroft, John D.W. 1988. System dynamics and microworlds for policymakers. European Journal of Operational Research. 35. Oberlender, Garold D. 1993. Project Management for Engineering and Construction. McGraw-Hill. New York. Peterson, J.T., and T.H. Lim. Jan 1993. A System Dynamics Analysis of Total Quality Management Implementation False Starts. M.S. Thesis at MIT. Richardson, G.P., and A.L. Pugh. 1981. Introduction to System Dynamics Modeling with DYNAMO. Productivity Press. Cambridge MA. Risch, J.D., and L. Troyano-Bermudez. Jan 1993. Strategic Application of System Dynamics Methodology. M.S. Thesis at MIT. Ritz, George.J. 1990. Total Engineering Project Management. McGraw-Hill. New York. Roberts, E.B. 1964. A Simple Model of R&D Project Dynamics. In: Managerial Applications of System Dynamics, ed. E.B. Roberts. Cambridge, Mass., Productivity Press. Roberts, E.B. 1978. The Dynamics of Research and Development. Productivity Press. New York. Roman, D.D. 1986. Managing Projects: A System Approach.Washington D.C. Elsevier Science Publishing Co. Senge, Peter M. 1990. The Fifth Discipline; The Art and Practice of the Learning Organization. Doubleday. New York. Senge, Peter M. 1993. Transforming the Practice of Management. Quarterly. Vol. 4, No. 1. Shannon, Robert.E. 1980. Engineering Management. John Wiley & Sons. New York. Spinner, Pete M. 1989. Improving Project Management Skills and Techniques. PrenticeHall. New Jersey. Stata, R. 1989. Organizational Learning - The Key to Management Innovation. Sloan Management Review. Vol. 30, No. 3. Sterman, John D. 1992. "System Dynamics Modelling for Project Management". Working paper available from John Sterman. MIT Sloan School of Management. Cambridge, MA. The Engineering Association of Iceland. 1986. "Charging for engineering work". Reykjavik Iceland. The Engineering Association of Iceland. 175 Weil, Henry B., and Rayford L. Etherton. 1990. "System Dynamics in Dispute Resolution, in Andersen, D., Richardson, G., & Sterman, J." System Dynamics '90 Proceedings of the 1990 International System Dynamics Conference, p. 1311-1324. 176 Appendix A: System Archetypess8 58 Kim, Daniel. H. 1992. System Archetypes. Toolbox Reprint Series. p. 5-6. 177 Archetype Drifting Description Goals In a "Drifting Goals" archetype, L_ c~,J-O -/ Escalation A'Ra I B'a Ral L £ stq4 \ s B2 A,,,' -'R o / flh, A s, \ / ; w A Fixes that o Si Fail t1 c.u and resulting in more threatening actions by A. The reinforcing loop is traced - What are the significant delays in the system tha may distort the true B < i out by following the outline of the nawreofthethreat? figure-8 produced by the two I balancing loops. (See Toolbox, I November 1991). · What are the deep-rooted assumptions that lie beneath the actions taken in response to the threat? problem symptom rurns to its S previous level or becomes worse. , Underinvestment 1 To break an escalation srucure. ask the following questions: * What is the relative measure that pits one party against the other and can you change it? In a "Fixes that Fail" situation, a problem symptom cries out for resolution. A solution is quickly implemented that alleviates the ! symptom (B1), but the uruntended I consequeces of the "fix" exacerbate s the problem (R1). Over time, the I Com' Growth In the "Escalation" archetype, one party (A) takes actions that are perceived by the other as a threat. The i other party (B) responds in a simnilar manner. increasing the threat to A and I FUi \ I \ · Drifting performance figures are usually indicators that the "Drifting Goals" archetype is at work and that real corrective actions are not being taken. * A critical aspect of avoiding a potential "Drifting Goals" scenario is to. determine what drives the seting of the goals. * Goals located outside the system will be less susceptible to drifng goals pressures. a gap between the goal and current reality can be resolved by taking corrective action (B 1) or lowering the goal (B2). The critical difference is : that lowering the goal immediately closes the gap, whereas corrective actions usually take time. (See Too/box, October 1990). -2 c Gc Guidelines Psmain ' swwu Pouved lN.d -w"I solution will help ensure that you don't j get I (See Toolbox. November 1990). In a "Growth and Underi investment" archetype, growth I approaches a limit that can be elimiInated or pushed into the future if capacity investments are made. i Instead. performance standards are I lowered to justify underinvestment, i leading to lower performance which further justifies underinvesmenL ,M8 l · Breaking a "Fixes that Fail" cycle iusually requires two actions: acknowledging that the fix is merely alleviating a symptom,. and making a commitment to I solve the real problem now. * A two-pronged altrac of applying I the fix and planning out the fundamental I (See Toolbox, June/July 1992). 178 caught in a perpetual cycle of solving yesterdays "solutions." I * Dig into the assumptions which I drive capacity investment decisions. If I past performance dominates as a consideration, try to balance that perspective with a fresh look at demand and the factors that drive its growth. * If there s a potential for growth, build capacity in anticipation of future Idemand. Archetype Description to Success Limits In a "Limits to Success" scenario, continued efforts initially lead to improved performance. Over time, however, the system encounters a limit which causes the performance to slow down or even decline (BI), even as efforts continue to rise. (See Toolbox, December 1990/January 1991). coami Efac l Mc A Guidelines · The archetype is most helpful when it is used well in advance of any problems, to see how the cumulative effects of continued success might lead to future problems. * Use the archetype to explore questions such as "What kinds of pressures are building up in the organuzanim as a result of the growth?" Look for ways to relieve pressures or remove limits before an organizational gasket blows. Shifting the Burden/Addiction Symptomanc: In a "Shifting the Burden" archetype, a problem is "solved" by applying a symptomatic solution (B 1) which diverts attention away from more fundamental solutions (R ). (See Toolbox, September 1990). In : an "Addiction" structure, a "Shifting the Burden" degrades into an addictive pattern in which the side-effect gets so entrenched that it overwhelms, the original problem symptom. (See I Toolbox, April 1992). · Problem symptoms are usually easier to recognize than the other elements of the st'ucture. * If the side-effect has becne the problem, you may be dealing with an "Addiction" structure. · Whether a solution is "symptomatic" or "fuindamental" often depends on one's perspective. Explore the problem from differing perspectives in order to come to a mone comprehensive understanding of what the fundamental solution may be. I Success to the Successful -_ot A AUocon to ^A of A Sccss .. B s Instadof Rcsou oA ^ / I to B, Racm In a "Success to the Successful" archetype, if one person or group (A) is given more resources, it has a higher likelihood of succeeding than B (assuming they are equally capable). The iniial success justifies devoting more resources to A than B (RI). As B gets less resources, its success diminishes, further justifying more resource allocauons to A. (See Toolbox, March 1992). * Look for reasons why the system was set up to create just one "winner." * Chop off one half of the archetype by focusing efforts and resources on one group, ather than creating a "winnertake-all" competition. * Find ways to make teams collaboratots rather than competurs. Tragedy of the Commons G&w NeMa RI' tac s A A'sAM, a Rmm \ -,= - B1 Toal _-. Md I u ° , AACU.A uApy B2 B s Amv \ l r In a "Tragedy of the Commons" structure, each person pursues actions which are individually beneficial (RI and R2). If the amount of activity grows too large for the system to support, however, the "commons" becomes overloaded and everyone experiences diminishing benefits (BI and B2). (See Toolbox, August 1991). / o5ts -~~~~~~ 179 * Effective solutions for a Tragedy of the Commons" scenario never lie at the individual level. - Ask questions such as: "What are the incentives for individuals to persist in their actions?" and "Can the !long-term collective loss be made more real and immediate to the individual actors?" * Find ways to reconcile short-term individual rewards with long-term cumulative consequences. Appendix B: Model Documentation (Base Run) 180 Environment - Initial Values Initial_Experienced_Workforce(t) = Initial_Experienced_Workforce(t - dt) INIT Initial_ExperiencedWorkforce = 0.25*Initial_Workforce Initial_lnexperienced_Workforce(t) = Initial_Inexperienced_Workforce(t - dt) INIT Initial_Inexpenrienced Workforce = Initial_Workforce-lnitial_Experienced_WorkforceInitial_Permanent_Workforce Initial_Permanent_Workforce(t)= Initial_Permanent_Workforce(t- dt) INIT Initial_Permanent_Workforce= 0.7*InitialWorkforce Defined_Nominal_Productivityper Worker = 1 Initial_Cumulative_Production = 12000 Initial_Frac_of_MCT_in_max_slack = (Max_Completion_TimeInitial_ScheduledCompletion_Time)/Max_Completion_Time Initial_Scheduled_Completion_Time = 50 Initial_Undiscovered_Fraction_of_Project_Size= 0.25 Initial_Workforce = 4 Max_Completion_Time = 70 RealProject_Size = 500 Human Resource Management - Overtime Policy and its Effects Burnout_due_to_Overtime(t) = Burnout_due_to_Overtime(t - dt) + (Chgin Frac_MP_Burnout) *dt INIT Burnout_due_toOvertime = 0 INFLOWS: Chg_inFrac MP_Burnout = (Effect_of_Overtime_on_MP_BurnoutBurnoutdue to Overtime)/Time_to_feel_Exhausted Act mplto_NWW = IF(Sought_mpl_to_NWW> 1)THEN(1+(Sought_mpl_to_NWWI)*Mpl_to_sought_OT)ELSE(Sought_mpl_to NWW) Mpl_to_sought_OT = -Bumout_duetoOvertime PrdMpldueto_OT = Prd_mpl_due_to_BO*Act_mpl_to_NWW Time to_feelExhausted = 4 Effect_of_Overtime_onMP_Burnout = GRAPH(Act_.mpl_to_NWW) (0.8, 0.00), (0.895, 0.00), (0.99, 0.00), (1.08, 0.02), (1.18, 0.055), (1.27, 0.11), (1.37, 0.185), (1.46, 0.3), (1.56, 0.455), (1.65, 0.675), (1.75, 1.00) Prd_mpl_due_to_BO = GRAPH(Burnout_due_to_Overtime) (0.00, 1.00), (0.1, 0.975), (0.2, 0.925), (0.3, 0.86), (0.4, 0.79), (0.5, 0.715), (0.6, 0.64), (0.7, 0.56), (0.8, 0.475), (0.9, 0.38), (1, 0.285) Sought_mpl_to_NWW = GRAPH(Schedule_Pressure) (-0.5, 0.8), (-0.4, 0.8), (-0.3, 0.8), (-0.2, 0.814), (-0.1, 0.852), (-3.33e-17, 1.00), (0.1, 1.36), (0.2, 1.47), (0.3, 1.50), (0.4, 1.50), (0.5, 1.50) Human Resource Management - Staffing and Training Authorized_WF(t) = Authorized_WF(t - dt) + (Chg_in.AWF) * dt INIT Authorized_WF = 8.9 INFLOWS: Chg_in_AWF = IF((Desired_WFAuthorizedWF)>0)THEN(IF(Authorized-WF<CeilingonTota-Workforce)THEN(Willtonewhires)EL SE(O))ELSE(I)*(DesiredWF-Authorized_WF)/Timeto-planWF Experenced_Workforce(t)= Experenced_Workforce(t - dt) + (Training - Transfer_Rate - EW_layoffs Departure_Rate) * dt INIT Experenced_Workforce= InitialExperiencedlWorkforce 181 INFLOWS: Training = Inexperienced_Workforce/Average_TrainingTime OUTFLOWS: Transfer_Rate = Quits EW_layoffs = IF(TotExp_layoffs>0O)THEN(MIN(Tot_Exp_layoffs,Experenced_Workforce))ELSE(O) Departure_Rate= Experenced_Workforce/AverageEmploymentTime Hires_Needed_Insteadof Departures(t) = Hires_Needed_lnsteadof Departures(t - dt) + (DR - Hirings_becof Departures)* dt INIT Hires_Needed_Instead_of Departures = 0 INFLOWS: DR = Departure_Rate OUTFLOWS: Hirings_becof Departures = Hires_Needed_Itead of Depof_ Departures/TimetoHireWorkersnsteadtedWorkers imetonstead_ Inexperienced_Workforce(t)= Inexperienced_Workforce(t- dt) + (Hiring_Rate - Training - IW_layoffs)* dt INIT Inexperienced_Workforce = Initial_Inexperienced_Workforce INFLOWS: HiringRate = Hirings_bec_of_Departures+Hirings OUTFLOWS: Training = InexperiencedWorkforce/AverageTraining Time lW_layoffs = IF(Layoffs>0)THEN(MIN(Layoffs,InexperiencedWorkforce))ELSE(0) PermanentWorkforce(t) = Permanent_Workforce(t - dt) + (Transfer_Rate - Quits - PW_layoffs) * dt INIT Permanent_Workforce = Initial_Permanent_Workforce INFLOWS: Transfer_Rate = Quits OUTFLOWS: Quits = Permanent_Workforce/AvEmplTime_of_PW PW_layoffs = MIN(TotExp_layoffs-EW_layoffs,Permanent_Workforce) AvEmplTimeof_PW = 780 Average_Employment_Time = 50 Average_TrainingTime = 16 Ceiling_on_New_Hires = Total_Experienced_WF*Max_No_of Inexp_ Workers that_ each_Exp Worker_can_handle CeilingonTotal_Workforce = Ceiling_on_New_Hires+Total_Experienced_WF Correction_to_WF = (Authorized_WF-Total_Workforce)/(IF((Authorized_WFTotal_Workforce)>0)THEN(Time_for_hiring)ELSE(Time_for_layoffs)) Desired_WF = Desired_Workforce Hirings = IF(Correction_to_WF>0)THEN(Correction_to_W)ELSE(0) Layoffs = IF(Correction_to_WF<0)THEN(-Correctionto WF)ELSE(0) Max_No_of InexpWorkers that_each_Exp_Worker_can_handle =2 STR_over_PH&AT = Scheduled_Time_Remaining/(Time_forhiring+Average_Training_Time) Time_for_hiring = 8 Time_tor_layoffs = 1 Time_to_Hire_Workers_Instead_of_ Departed_Workers= 2 Time_to_planWF = 4 Total_Experienced_WF= Experenced_Workforce+Permanent_ Workforce Total_Workforce= ExperencedWorkforce+lnexperienced_Workforce+PermanentWorkforce Tot_Exp_layoffs = IF(Layoffs>0)THEN(MAX(Layoffs-IW_layoffs,0))ELSE(0) Will_to_new_hires = MAX(WilltoNH_becof F ofIMSS_needed,Will_to_NH_becof_STR_and_PH&AT) Will_to_NH_bec_of_Fof_IMSS_needed = GRAPH(Frac_of_initial_max_sch_slack_needed) (0.00, 0.00), (0.1, 0.00), (0.2, 0.00), (0.3, 0.00), (0.4, 0.00), (0.5, 0.00), (0.6, 0.00), (0.7, 0.08), (0.8, 0.62), (0.9, 1.00), (1, 1.00) 182 Will_to_NH_bec_ofSTR_and_PH&AT = GRAPH(STR_over_PH&AT) (0.00, 0.00), (0.2, 0.00), (0.4, 0.05), (0.6, 0.19), (0.8, 0.51), (1, 0.77), (1.20, 0.925), (1.40, 0.975), (1.60, 0.985), (1.80, 0.995), (2.00, 1.00) IIuman Resource Management - Workforce Allocation WF toP&P(t) = WFto_P&P(t - dt) + (AP&PWF_chg) * dt INIT WFtoP&P = 0 INFLOWS: AP&PWF_chg = (MAX(Desired_P&P_W F,Avail_Extra_WFin theend)-WF_to_P&P)/P&Palloc_time WF_to_Rework(t) = WF toRework(t - dt) + (Chg_in_Alloc_RW_team) * dt INIT WFtoRework = 0 INFLOWS: Chgin_Alloc_RW_team = (MIN(Perceived_Size_of_RW_Team_Needed,MAX_WFtoRW)WF_to_Rework)/Allocation_smoothingTime Actual_QA_WF_as Fraction_of_planned = Fraction_ofTot_WF_to_Quality_Assurance/Planned_Fraction_of_Total_WF_forQA Allocation_smoothing_Time = 2 Available_WF toRW_and_D&TS = Avail_WF toD&TS_Dev & RW & PP-WF toP&P Avail_Extra_WF in the_end = Available_WF to RW_and_D&TS-WF toD&TS_Dev-WF toRework Avail_WF_to_D&TS_Dev_&_RW_&_PP = Total_Workforce-WF_to_QA_and_Training Desired_P&P_WF = MIN(Avail_WF_to_D&TS_Dev_&_RW_&_PP,Planned_P&P_WF) Fraction_of_Tot_WF_to_Design_and_Making_ofTenderSpec = WF_to_D&TS_Dev/Total_Workforce Fraction_of_Tot_WF_to_Quality_Assuranc e = Planned_Fraction_of Total_WF_for_QA*Multiplier_to_Fraction_to_QA_because_of_SP MAX_Allowed_Dev_WFin endofproject_duetoRestrict = IF(Actual_Fracof_D&TS_Dev_Completed>Frac of D&TS_Dev_to_start_thesmoothingprocedure)TH EN(Base_for_Max_Allowed_WF _to_D&TS_Dev_inEndof Proj)ELSE(9999) MAX_WF toRW = Available_WF toRW_and_D&TS Multiplier toNominal_Detection_of RW_bec_of AI_WF_to_QA = Fraction_ofTot_WF_to_Quality_Assurance/QA_Fracof WF_needed_f orm_Detect_Rate P&P_alloc time = 1 Tot_WF_Fraction_to_'rraining_Overhead = Inexperienced_Workforce*Trainers_from_TWF_neededperInexp_worker/(TotalExperiencedWF+Inexperi enced_Workforce) Trainers_from_TWF_needed_per_Inexp_worker= 0. 15 WF_to_D&TS_Dev= IF(Actual_Frac_of D&TS_Dev_Completed>0.9999)THEN(0)ELSE(MIN(Available_WF_to_RW_and_D& TS-WF_to_Rework,MAX_Allowed_Dev_WF _in_endofproject_due_to Restrict)) WF_to_QA = Fraction_ofTot_WF_to_Quality_AssurancTototal_Workforce WF_to_QA_and_Training = WF_to_QA+WF_to_Training WF_to_Training = Tot_WF_Fraction_to Training_Overhead*Total_Workforce MultipliertoFraction_to_QA_because_of SP= GRAPH(Schedule_Pressure) (0.00, 1.00), (0.1, 0.965), (0.2, 0.89), (0.3, 0.77), (0.4, 0.665), (0.5, 0.605), (0.6, 0.58), (0.7, 0.57), (0.8, 0.57), (0.9, 0.57), (1, 0.57) Production - Development Productivity Basic_D&TS_Dev_productivity= Basic_D&TS_Dev_productivity_per_Worker*WFtoD&TS_Dev Basic_D&TS_Dev_productivity_per_Worker= Poten.tial_Base_Productivity_per_Worker*Mpl_to_Prod_bec_ofComm_OH*Mpl_to_Prod_becof Motivat ion Gross D&TSDev Prod Rate = MIN(Prd_Mpl_due to_OT*Basic_D&TS_Dev_productivity,Perceived_Remaining_New_Tasks/DT) Mpl_to_BP_because ofWF_mix = (Total_ExperiencedWF+Inexperienced_Workforce*Prod_ofInexp_WFas a Fraction_ofProd_of Exp_W F)/(Inexperienced_Workforce+Total_ExperiencedWF) 183 Mpl_to_Prod_becofComn_OH = (1-Frac_ofTot_WF_to_Comm_OH) Potential_Base_Prodxluctivity_perWorker = Defined_Noinal_Productivity_perWorker*Mpl_to_BP_becauseofWF_mix*Mpl_to_Prod_becof Learn ingCurve*Mpl_to_Prod_becof Project_Familiarity Prod ofInexp_WF as_a_Fraction_ofProd of Exp_WF = 0.8 FOTWFTCOH_OLD = GRAPH(Total_Workforce) (0.00, 0.00), (2.50, 0.015), (5.00, 0.035), (7.50, 0.06), (10.0, 0.085), (12.5, 0.115), (15.0, 0.15), (17.5, 0.19), (20.0, 0.23), (22.5, 0.28), (25.0, 0.33) Frac_ofTot_WF_to_Comm_OH = GRAPH(Total_Workforce) (0.00, 0.00), (2.50, 0.015), (5.00, 0.04), (7.50, 0.07), (10.0, 0.105), (12.5, 0.145), (15.0, 0.19), (17.5, 0.235), (20.0, 0.28), (22.5, 0.33), (25.0, 0.38) Mpl_to_Prod_becof Motivation = GRAPH(SchedulePressure) (-0.5, 0.8), (-0.4, 0.8), (-0.3, 0.815), (-0.2, 0.845), (-0.1, 0.895), (-3.33e-17, 1.00), (0.1, 1.07), (0.2, 1.10), (0.3, 1.11), (0.4, 1.11), (0.5, 1.11) Production - Rework Productivity Base_Difficulty = I BasicRW_prod_perWorker = Basic_D&TS_DevproductivityperWorker*MultiplierjtoRework_Prod Difficulty_in_CorrectingErrors = 1.5 Gross_Rework_Productivity_Rate_perWorker = Prd_Mpl_dueto OT*Basic_RW_prod_per_Worker 'Gross_Rework_Rate= WF_to_Rework*Basic_RW_prodper_ Worker*Prd_Mpldue toOT Multiplier toReworkProd = Base_Difficulty/Difficulty_in_Correcting_Errors Project Controlling - Project Database Cumulative_Mpl_to_NWW(t) = Cumulative_Mpl_to_NWW(t - dt) + (Mpl_to_NWW) * dt [NIT Cumulative_Mplto_NWW =0 INFLOWS: MpIto_NWW = Act__mpl_to_NWW CumInex_ManWeeks(t) = Cum_Inex_ManWeeks(t - dt) + (Inc in CIMW) * dt [NIT Cum_Inex_ManWeeks =0 INFLOWS: linc_in_CIMW= Inexperienced_Workforce*Act pl_to_NWW Cum_Total_ManWeeks(t) = Cum_Total_ManWeeks(t - dt) + (Inc_in_CTMW) * dt [NIT Cum_Total_ManWeeks = 0.00001 INFLOWS: Inc_in_CTMW = Total._Workforce*Act_mpl_to_NWW D&TS_Cum_ManWeeks(t) = D&TS_Cum_ManWeeks(t - dt) + (Inc in CMWtoD&TS) * dt [NIT D&TS_Cum_ManWeeks = 0.00001 INFLOWS: Inc_in_CMWtoD&TS = WF_to_D&TS_Dev*Act_mpl_to_ NWW P&P_Cum_ManWeeks(t) = P&PCum_ManWeeks(t - dt) + (Inc_in_CMWtoP&P) * dt [NIT P&P_Cum_ManWeeks = 0 INFLOWS: Ilnc_in_CMWtoP&P = WF_to_P&P*Actmpl_to_NWW QA_Cum_ManWeeks(t) = QA_Cum_ManWeeks(t - dt) + (Inc in CMWtoQA) * dt I[NIT QA_Cum_ManWeeks = O0 INFLOWS: *[ncinCMWtoQA = WF_to_QA*Actmpl_to_NWW RW_Cum_ManWeeks(t) = RW_Cum_ManWeeks(t - dt) + (Inc inCMWtoRW) * dt I[NIT RW_Cum_ManWeeks = 0.00001 184 INFLOWS: Inc_in_CMWtoRW = WF_toRework*Actmpl_toNWW Train_Cum_ManWeeks(t) = Train_Cum_ManWeeks(t - dt) + (Incin_CMWtoT) * dt INIT Train_Cum_ManWeeks = 0 INFLOWS: Inc_in_CMWtoT = WF_to_Training*Act_mpl_to_NWW Average_Hist_D&TS_Dev_WF = D&TS_Cum_ManWeeks/(Current_Time+0. 1) Average_Mpl_to_NWW = Cumulative_Mpl_to_NWW/(Current_Time+0.01) Cumulative_Exp_ManWeeks = Cum_Total_ManWeeks-Cum_lnex_ManWeeks Historic_D&TS_Productivity_per_ManWeek_from_Tot_WF = Cum_D&TS_New_Tasks_Developed/(Cum_Total_ManWeeks-P&P_Cum_ManWeeks) Hist_RW_Productivity_per_ManWeek_from_RW_WF= Rework_Worked/RW_Cum_ManWeeks Project Controlling - Schedule Pressure Schedule_Pressure(t) = Schedule_Pressure(t - dt) + (Change_in_SP) * dt INIT Schedule_Pressure = 0 INFLOWS: Changein_SP = (Gap_in_Required_and_Scheduled_timeleft/(ScheduledTime_Remaining+ 1)SchedulePressure)/Schedule_Pressure_Adj_Time Gapin_ Required_and_Scheduled_time_left= Perc_Time-Req_to_Finish_D&TS_DevScheduled_Time_Remaining Schedule_Pressure_Adj_Time= 2 Project Controlling - Scheduling Scheduled_D&TS_Dev_Completion_Time(t) = Scheduled_D&TS_Dev_CompletionTime(t - dt) + (Changes_inSchedule) * dt INIT Scheduled_D&TS_Dev_Completion_Time= Initial_Scheduled_Completion_Time INFLOWS: Changes_in_Schedule = (Current_Time+Reported_Time_Req_to_Finish_D&TS_DevScheduled_D&TS_Dev_Completion_Time)/Schedule_Adjustment_Time Absorbed_Time_Excess= IF(Assumed_Max_Absorption_Fraction_of_PTReq>TE_as_Frac_of PTR_to_F_T&DS_Dev)THEN(Time_ Excess)ELSE(Assumed_Max_Absorption_Fraction_of_P TReq*Perc_Time_Req_to_Finish_D&TS_Dev) Assumed_Max_Absorption_Fraction_ofPTReq = 0.20 Current_Time = TIME Desired_D&TS_Dev_Prod_Rate= IF(Scheduled-Time_Remaining>0)THEN(MAX(0,Perceived-Remaining_New-Tasks/(Scheduled_Time_Re maining+0.1)))ELSE(0) Frac_of_initial_max_sch_slack_needed= (1-Max_Completion_Time*(lInitial_Frac_of_MCT_in_maxslack)/Scheduled_D&TS_Dev_CompletionTime)/Initial_Frac_of_MCT_in _max_slack Reported_Time_Req_to_Finish_D&TS_Dev = Perc_Time_Req_to_Finish_D&TS_DevAbsorbed_Time_Excess Scheduled_Time_Remaining = MAX(Scheduled_D&TS_Dev_Completion_Time-Current_Time,0.001) TE_as_Frac_of_PTR_to_F T&DS_Dev = Time_Excess/Perc_Time_Req_to_Finish_D&TS_Dev Time_Excess = MAX(Perc-Time-Req_to_Finish_D&TS_-Dev-Scheduled_Time_Remaining,0) Schedule_Adjustment_Time = GRAPH(Actual_Frac_of_D&TS_Dev_Completed) (0.00, 1.00), (0.1, 1.00), (0.2, 1.00), (0.3, 1.00), (0.4, 1.00), (0.5, 1.00), (0.6, 1.00), (0.7, 1.00), (0.8, 1.00), (0.9, 1.00), (1, 1.00) Project Planning - Forecast of Workforce Needed Desired_Workforce(t)= Desired_Workforce(t - dt) + (Chgjin Desired_WF) * dt INIT Desired_Workforce = Authorized_WF 185 INFLOWS: Chg_in_Desiredl_WF = (Perc_Total_WF_Needed-Desired_Workforce)/Smoothing_Tinme Perceivedl_Size_of_RW_Team_ Needed(t) = Perceived_Size_ofRW_Team_Needed(t - dt) + (Chg_in_PRTN) * dt INIT Perceived_Size_of RW_Team_Needed = 0 INFLOWS: Chg_inPRTN = (Actual_Size_of_Rework_Team_Needed- Needed)/TimetoperceiveSize ofRTN Perceived_Size_of_RW_Team_ Perc_Historic_D&TS_Dev_Prod_per_ManWeek(t)= Perc_Historic_D&TS_Dev_Prodper_ManWeek(t - dt) + (Chg_PHP) * dt INIT Perc_Historic_D&TS_Dev_Prod_per_ManWeek = Current_D&TS_ProdperD&TS_Dev_worker*WF_to_D&TS_Dev/Total_Workforce INFLOWS: Chg_PHP = (Historic D&TS_Productivity_per_ManWeek_from_Tot_WF- Perc_Historic_D&TS_Dev_ProderManWeek)/Timeto_percHistoricprod Perc_Prod per_D&TS_Dev_ManWeek(t) = Perc_Prod_per_D&TS_Dev_ManWeek(t - dt) + (Chg_in_PCP) * dt INIT Perc_Prod_per_D&TS_Dev_ManWeek= Current_D&TS_Prod_per_D&TS_Dev_worker INFLOWS: Chgin_PCP = (Current_D&TS_Prod_per_D&TS_Dev_workerPerc_Prod_per_D&TS_Dev_ManWeek)/Timeto..Perc_Prod_of_D&TS_Dev_ManWeek Actual_Size_ofRework_Team Needed = Desired_ReworkRate/GrossRework_Rate/GroductivityRateperWorker Current_D&TS_Prod_per_D&TS_Dev_worker = Gross_D&TS_Dev_Prod_RateIWF_to-_D&TSev Desired_D&TS_WF = Desired_D&TS_Dev_Prod_Rate/Perc ProdperD&TS_Dev_ManWeek Desired_Rework_Rate= DiscoveredRework_to_do/Desired_Time to Finish_Rework Estimated_Current_D&TS_Dev_Prod.perrManWeek_from_Tot_WF = Perc_Prod_per_D&TS_Dev_ManWeek*WF_to_D&TS_Dev/Total_Workforce Forecasted_Future_ D&TS_Dev_Prod_per_ ManWeek_from_Tot_WF = (Perc_Historic_D&TSDev-Pr&odper_ManWeek*Weight-ofHistoricD&TS-Prod+EstimatedCurrentD &TS_Dev_Prod_per_ManWeek_from TotWF*(1-Weightof_Historic_D&TS_Prod) )*(1Assumed_Hidden_Prod_Loss) Perc Total WF Needed = Desired_D&TS_Dev_Prod-Rate/Forecasted-FutureD&TS-Dev-Prode-r Smoothing_Time = 4 ManWeek-from_Tot-WF Time_to_percHistoric_prod=8 Time_to_Perc_Prod_of_D&TS_Dev_ManWeek= 6 Weight_ofHistoric_D&TS_Prod = Actual_Frac_of-D&TS_Dev_Completed Assumed_Hidden_Prod_Loss = GRAPH(Actual_Frac_of_D&TS_Dev_Completed) (0.00, 0.00), (0.1, 0.00), (0.2, 0.00), (0.3, 0.00), (0.4, 0.00), (0.5, 0.00), (0.6, 0.00), (0.7, 0.00), (0.8, 0.00), (0.9, 0.00), (1.00, 0.00) Desired_Time_to_Finish_Rework = GRAPH(Perc_Frac_ofD&TS_Dev_Completed) (0.00, 2.00), (0.1, 2.00), (0.2, 2.00), (0.3, 2.00), (0.4, 2.00), (0.5, 2.00), (0.6, 2.00), (0.7, 2.00), (0.8, 2.00), (0.9, 2.00), (1, 2.00) Time_to-perceive_Size_of RTN = GRAPH(Actual_Frac_of_D&TSDev_Completed) (0.00, 8.00), (0.1, 8.00), (0.2, 8.00), (0.3, 8.00), (0.4, 8.00), (0.5, 8.00), (0.6, 7.70), (0.7, 6.70), (0.8, 5.20), (0.9, 2.50), (1, 1.00) Project Planning - Planned Workforce Allocation Base_for_Max_Allowed_WFto_D&TS_Dev_in_End_of_Proj(t) = Base_for_Max_Allowed_WF_to_D&TS_Dev_inEnd_of_ Proj(t - dt) + (CADWF) * dt INIT Base_for_Max_Allowed_WF_to-D&TS_Dev_in_End_of Proj = Initial_Workforce*(1Planned_Fractionof Total_WF_for_QA) 186 INFLOWS: CADWF = IF(Frac_of D&TS_Dev_to_start_the _smoothing_procedure<Actual_Frac_of_D&TS_Dev_Completed)TH EN((Desired_D&TS_WF- Base_for_Max_Allowed_WF_to_D&TS_Dev_in_End of Proj)/Smoothing_Time_for_ADWF)ELSE((WFt o_D&TS_Dev-Base_for_Max_Allowed_WFtoD&TS_Devin_End_of Proj)/DT) Total_Work_Size = 0.1 Fractionof Restricted_Tasksinthe_End_outof Frac_of D&TS_Dev_tostart_the_smoothingprocedure = 1(0.04 t Fraction_of Restricted_Tasks_in_the_End_out_of Total_Work_Size) mpl_to_Planned_P&P_W F = Scheduled_D&TS_Dev_CompletionTime/Initial_Scheduled_Completion_Time Planned_Fraction_of_Total_WFfor_QA = QA_Frac_ofWF_needed_for_Norm_Detect_Rate*Planned_mpl_to_QAFNFNDR Planned_P&P_WF = Average_Hist_D&TS_Dev_WF*Initially_Planned_Frac of_Ave_D&TS_Dev_WF for_P&P*mpl_to_Plan ned_P&P_WF Planned_QA_WF = Planned_Fraction_of Total_WF_forQA*Total_Workforce QA_EracofWF_needed_for_Norm_Detect_Rate Initially_Planned_Frac_of Ave_D&TS_Dev_WF = 0.1 for_P&P = GRAPH(Perc_Frac_of D&TS_Dev_Completed) (0.8, 0.00), (0.82, 0.00), (0.84, 0.00), (0.86, 0.00), (0.88, 0.00), (0.9, 0.05), (0.92, 0.145), (0.94, 0.32), (0.96., 0.435), (0.98, 0.465), (1.00, 0.465) Planned_mpl_to_QAFNFNDR = GRAPH(Actual_Frac_ofD&TS_Dev_Completed) (0.00, 1.00), (0.1, 1.00), (0.2, 1.00), (0.3, 1.00), (0.4, 1.00), (0.5, 1.00), (0.6, 1.00), (0.7, 1.00), (0.8, 1.00), (0.9, 1.00), (1, 0.00) Smoothing_Time_for_ADWF = GRAPH(ActualFrac of D&TS_Dev_Completed) (0.86., 19.4), (0.87, 17.6), (0.88, 14.3), (0.89, 7.40), (0.9, 2.90), (0.91, 1.60), (0.92, 1.00), (0.93, 1.00), (0.94!, 1.00), (0.95, 1.00), (0.96, 1.00), (0.97, 1.00), (0.98, 1.00), (0.99, 1.00), (1.00, 1.00) Tender Spec Production - Learning influence on productivity Cumulative_Production(t) = Cumulative_Production(t - dt) + (Production_Rate) * dt INIT Cumulative_Production = Initial_Cumulative_Production .[NFLOWS: Production_Rate = Gross_D&TS_Dev_Prod_Rate = 0.1 ,Fractional_Productivity_Increaseper_Doubling = Mpl_to_Prod_bec_of_Learning_Curve (LOGN(Cumulative_Production/Initial_Cumulative_Pr (II +Fractional_Productivity_Increase_per_Doubling) oduction)/LOGN(2)) Mpl_to_Prod_bec of Project_Familiarity = GRAPH(Actual_Frac_of D&TS_Dev_Completed) (0.00, 1.00), (0.1, 1.01), (0.2, 1.01), (0.3, 1.03), (0.4, 1.04), (0.5, 1.07), (0.6, 1.10), (0.7, 1.12), (0.8, 1.14), (0.9, 1.14), (1, 1.15) Tender Specification Production - Progress Indicators Cumulative_Undisc_RW_From_New_Tasks(t) = Cumulative_Undisc_RW_From_New_Tasks(t - dt) + (GenofUndiscovered RW) * dt I[NIT Cumulative_Undisc_RW_From_New_Tasks =0 ][INFLOWS: Gen of Undiscovered_RW = Generationof Undiscovered_Rework Cum Real_Progress(t) = Cum_Real_Progress(t - dt) + (Gross_Real_Prod_Rate) * dt INIT Cum_Real_Progress = 0 INFLOWS: Gross_Real_Prod_Rate = Gross_D&TS_Real_Production_Rate Perc_Proj_Size(t) = Perc_Proj_Size(t - dt) + (Disc_Rate) * dt INIT Perc_Proj_Size = Real_Project_Size*(1-Initial_Undiscovered_Fraction 187 of Project_Size) INFLOWS: Disc_Rate = Frac_Discovered_perWeek*Undiscovered_New_ Tasks Undiscovered_New_Tasks(t)= Undiscovered_New_Tasks(t- dt) + (- Disc_Rate) * dt INIT Undiscovered_New_Tasks= Real_ProjectSize*InitialUndiscovered_Fraction_of_ProjectSize OUTFLOWS: Disc_Rate = Frac_Discoveredper_Week*Undiscovered_New_Tasks Actual_Frac_ofD&TS_Dev_Completed = Cum_D&TS_New_Tasks_Developed/RealProject_Size Actual_Remaining_Work = Real_Project_Size-Cnm_D&TS_New_Tasks_Developed Assumed_Workforce = Authorized_WF*Weight_ofAuth_WF+Total_Workforce*( l-WeighLofAuth_WF) Cum_D&TS_New_Tasks_Developed = Cum_Real_Progress+Cumulative_Undisc_RW_From_New_Tasks PAUSE_TO_STOP_RUN = IF(Actual_Frac_of_D&TS_Dev_Comp leted<0.999)OR(Perceived_Frac_of_RW_complete<0.999)THEN(0)E LSE(PAUSE) Perceived_Remaining_New_Tasks= MAX(Perc_Proj_Size-Cum_D&TS_New_Tasks_Developed,0) Perc_Frac_of_D&TS_Dev_Completed= Cum_D&TS_New_Tasks_Developed/Perc_Proj_Size Perc_Time_Req_to_Finish_D&TS_Dev = Perceived_RemainingNewTasks/(Assumed_Workforce*Forecasted_Future_D&TS_DevProd_per_ManWe ek_from_Tot_WF) Frac_Discovered_per_Week = GRAPH(Perc_Frac_of_D&TS_Dev_Completed) (0.00, 0.00), (0.1, 0.00), (0.2, 0.01), (0.3, 0.02), (0.4, 0.04), (0.5, 0.07), (0.6, 0.11), (0.7, 0.185), (0.8, 0.335), (0.9, 0.595), (1, 1.00) Weight_of_Auth_WF = GRAPH(Perc_Frac_of_D&TS_Dev_Completed) (0.00, 1.00), (0.1, 1.00), (0.2, 1.00), (0.3, 0.995), (0.4, 0.985), (0.5, 0.965), (0.6, 0.935), (0.7, 0.875), (0.8, 0.775), (0.9, 0.61), (1, 0.00) Tender Specification Production - Quality Basic_Real_D&TS_prod_per_Worker= Fraction_Satisfactory*Basic_D&TS_Dev_productivityper_Worker Fraction_Satisfactory = Nominal_Fraction_Satisfactory*FS_due_to_Schedule_Pressure*FS_due_to_FracInexp*FS_due_to_Act_R W FS_due_to_Act_RW =(1Fraction_of_Completed-Tasks-that-are-a-Prerequisite*Undisc-Potentially-Active-Rework/MAX(0. 1,Cum _D&TS_New_Tasks_Developed)) Generation_of_Undiscovered_Rework= Gross_D&TS_Dev_Prod_Rate*(l-Fraction_Satisfactory) Gross_D&TS_Real_Production_Rate = Fraction_Satisfactory*Gross_D&TS_Dev_Prod_Rate WF_fraction_Inexperienced= Inexperienced_Workforce/TotalWorkforce FS_due_to_Frac_Inexp = GRAPH(WF_fraction_Inexperienced) (0.00, 1.00), (0.1, 0.975), (0.2, 0.943), (0.3, 0.905), (0.4, 0.858), (0.5, 0.802), (0.6, 0.745), (0.7, 0.682), (0.8, 0.623), (0.9, 0.56), (1, 0.5) FS_due_to_SchedulePressure = GRAPH(Schedule_Pressure) (0.00, 1.00), (0.1, 1.00), (0.2, 0.984), (0.3, 0.942), (0.4, 0.84), (0.5, 0.756), (0.6, 0.714), (0.7, 0.7), (0.8, 0.7), (0.9, 0.7), (1, 0.7) Nominal_Fraction_Satisfactory = GRAPH(Actual_Frac_of_D&TS_Dev_Completed) (0.00, 0.7), (0.1, 0.7), (0.2, 0.7), (0.3, 0.7), (0.4, 0.705), (0.5, 0.725), (0.6, 0.775), (0.7, 0.85), (0.8, 0.91), (0.9, 0.95), (1, 0.965) Tender Specification Production - Rework Detection Cum_Esc_Errors(t) = Cum_Esc_Errors(t - dt) + (Esc_Rate) * dt INIT Cum_Esc_Errors = 0 INFLOWS: Esc_Rate = Escape_Rate Discovered_Rework_to_do(t)= DiscoveredRework to do(t - dt) + (Disc_Rate_of_RW_in_Norm_Inspection + Rate_of_Late_Detection - Rework_Rate) * dt [NIT Discovered_Reworkto_do =0 188 INFLOWS: Disc_Rate_of_RWin_Normnspection = Undisc&Uninspect_Rework*Fraction_Detected/InspectionDelay Rate_of_Late_Detection = Mpl_to_LD_bec_of_FracofEsc_Err_left*Undisc_Potentially_ActiveRework*Multiplier_to_Nominal_De tectionRW_bec_ofRWbecof_All_WF_to_QA*Nom Detection_Fraction OUTFLOWS: Rework Rate = Gross Rework Rate Rework_Worked(t) = Rework_Worked(t INIT Rework_Worked = 0 - dt) + (Rework_Rate) * dt INFLOWS: Rework_ Rate = Gross_Rework Rate Undisc&Uninspect_Rework(t) = Undisc&Uninspect_Rework(t - dt) + (Gen_ofUndisc_Rework + Bad_Fixes_Gen_Rate - Disc_Rate_of_RW_in_Norm_nspection - Escape_Rate) * dt INIT Undisc&Uninspect_Rework = 0 INFLOWS: Gen_of_Undisc_Rework= Generation_of_Undiscovered_Rework Bad_Fixes GenRate = Bad_Fixes OUTFLOWS: Disc_Rate_of_RW_in_NormInspection = Undisc&Uninspect_Rework*Fraction_Detected/InspectionDelay Escape_Rate = Undisc&Uninspect_Rework*Escape_Fraction/lnspectionDelay Undisc_Potentially.Active_Rework(t) = Undisc_Potentially.Active_Rework(t - dt) + (Escape_Rate Rate_of_Late_Detection) * dt INIT Undisc_Potentially_Active_Rework = 0 INFLOWS: Escape_Rate = Undisc&UninspectRework*EscapeFraction/InspectionDelay OUTFLOWS: Rate_of_Late_Detection = Mplto_LD_bec_of Frac_ofEsc_Err_left*Undisc_Potentially-Active-Rework*MultipliertoNominalDe tection_of_RW_bec_of_All_WF_to_QA*Nom_DetectionFraction Bad_Fixes = Gross_Rework_Rate*Unsatisfactory_Frac_of Worked_RW Density_of_Esc_Errors = Undisc_Poten tially_veRework/MAX(CumD&TSNew_TasksDeveloped,0.001 ) Escape_Fraction = l-Fraction_Detected Fractional_Cum_Esc_Errors_out_of_Cum_New Tasks_Dev = Cum_Esc_Errors/MAX(Cum_D&TS_New_Tasks_Developed,0.00 1) Fraction_Detected= Nominal_Detection_Frac*Multiplierto_Nominal_Detection_of_RW_bec_of_All_WFtoQA Frac_Detected_in_ReviewingProcess = 0.8 Frac of Esc_Errors_Left = (Density_ofEsc_Errors/MAX(Fractional_CumEsc_Errorsout_of_Cum_New_TasksDev,0.001)) Mpl_to_LDbec_of_Frac_of_Esc_Errleft = EXP(l-l/Frac_ofEsc_Errors_Left) Nominal_Detection_Frac = -Nominal_Escape_Fraction Nom_Detection_Fraction = Fraction_of Completed_Tasks_that_are_a_Prerequisite*Frac Detected_inReviewing_Process Perceived_Frac_of_RW_complete= ReworkWorked/MAX(DiscoveredRework_to_do+ReworkWorked,1) Unsatisfactory_Frac_of_Worked_RW= 0.1 Fraction_of_Completed_Tasks_that_are_a_Prerequisite= GRAPH(Actual_Fracof_D&TS_Dev_Completed) (0.00, 0.00), (0.1, 0.045), (0.2, 0.15), (0.3, 0.345), (0.4, 0.51), (0.5, 0.65), (0.6, 0.76), (0.7, 0.865), (0.8, 0.935), (0.9, 0.98), (1, 0.985) Inspection_Delay = GRAPH(Perc_Frac_of D&TS_Dev_Completed) (0.00, 4.00), (10.0, 4.00), (20.0, 4.00), (30.0, 4.00), (40.0, 4.00), (50.0, 4.00), (60.0, 4.00), (70.0, 4.00), (80.0, 3.00), (90.0, 2.00), (100, 1.00) Nominal_Escape_Fraction = GRAPH(Actual_Frac_of_D&TS_Dev_Completed) 189 (0.00, 0.945), (0.1, 0.935), (0.2, 0.92), (0.3, 0.88), (0.4, 0.81), (0.5, 0.705), (0.6, 0.545), (0.7, 0.345), (0.8, 0.215), (0.9, 0.16), (1, 0.15) 190