GWALIOR INSTITUTE OF INFORMATION TECHNOLOGY (GIIT) MAHARAJ PURA NEAR MILITARY AREA GWALIOR (M.P) CE-802-: construction planning & mangement- Prepared by: Er. Satish kumar ahirwar Mob. 9584834411 Email.: satish0946@gmail.com Unit -1 Modern management techniques- CPM/PERT with network analysis :Que.1 Discuss the historical background of CPM & PERT ? Ans.1 Cpm & Pert techniques have their origin from (1958 to 1960) in two parrallel but different problems of planning and controlling projects in U.S.A. CPM/PERT or Network Analysis as the technique is sometimes called, developed along two parallel streams, one industrial and the other military. CPM was the discovery of M.R.Walker of E.I.Du Pont de Nemours & Co. and J.E.Kelly of Remington Rand, circa 1957. The computation was designed for the UNIVAC-I computer. The first test was made in 1958, when CPM was applied to the construction of a new chemical plant. In March 1959, the method was applied to a maintenance shut-down at the Du Pont works in Louisville, Kentucky. Unproductive time was reduced from 125 to 93 hours. PERT was devised in 1958 for the POLARIS missile program by the Program Evaluation Branch of the Special Projects office of the U.S.Navy, helped by the Lockheed Missile Systems division and the Consultant firm of Booz-Allen & Hamilton. The calculations were so arranged so that they could be carried out on the IBM Naval Ordinance Research Computer (NORC) at Dahlgren, Virginia. Que.2 Discuss planning ,scheduling & controll ? Ans.2 Planning, Scheduling (or organising) and Control are considered to be basic Managerial functions, and CPM/PERT has been rightfully accorded due importance in the literature on Operations Research and Quantitative Analysis. Far more than the technical benefits, it was found that PERT/CPM provided a focus around which managers could brain-storm and put their ideas together. It proved to be a great communication medium by which thinkers and planners at one level could communicate their ideas, their doubts and fears to another level. Most important, it became a useful tool for evaluating the performance of individuals and teams. There are many variations of CPM/PERT which have been useful in planning costs, scheduling manpower and machine time. CPM/PERT can answer the following important questions: How long will the entire project take to be completed? What are the risks involved? Which are the critical activities or tasks in the project which could delay the entire project if they were not completed on time? Is the project on schedule, behind schedule or ahead of schedule? If the project has to be finished earlier than planned, what is the best way to do this at the least cost? Que.3 Advantages & Limitations of CPM & PERT network ? Ans.3 following are the advantages and limitation of CPM & PERT given below : Ø Advantages of PERT/CPM 1. Especially useful when scheduling and controlling large projects 2. Straightforward concept and not mathematically complex 3. Graphical networks help to perceive relationships among project activities 4. Critical path and slack time analyses help pinpoint activities that need to be closely watched 5. Project documentation and graphics point out who is responsible for various activities 6. Applicable to a wide variety of projects 7. Useful in monitoring not only schedules but costs as well Ø Limitations of PERT/CPM 1. Project activities have to be clearly defined, independent, and stable in their relationships 2. Precedence relationships must be specified and networked together 3. Time estimates tend to be subjective and are subject to fudging by managers 4. There is an inherent danger of too much emphasis being placed on the longest or critical path Que.4 Define and discuss various elements of network ? Ans. 4 the element of networks areas follows :1. Activity:- an activity is the performance of a specific task such as bending of reinforcement , placing of concrete,. Etc. it requires time & resourses for its completion & is represented by an arrows. ‘‘Concreting’’ 2. Event:- event (is also called ‘nodes’) represent instant in time when certain activity has been started or completed . in other words ‘Event describes start or completion of task. Or it is represented by an circle . ‘ Activity’ i- node j- node 3. Dummy:- a dummy is an artificial activity represented on the arrow dig. By dotted arrow . it doesn’t requires any time or resourses. A b c dummy 4. Network :- this is an arrow dig. Consisting only arrow and circle drawn to represent the inter relationship and sequences of all the required construction activity of a project . Network analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects. node Activity 5. Node :- A node is represented by a circle Que .5 what do you mean by the PERT event & also predecessor events and successor events ? Ans .5 PERT event: a point that marks the start or completion of one or more activities. It consumes no time and uses no resources. When it marks the completion of one or more activities, it is not "reached" (does not occur) until all of the activities leading to that event have been completed. predecessor event: an event that immediately precedes some other event without any other events intervening. An event can have multiple predecessor events and can be the predecessor of multiple events. successor event: an event that immediately follows some other event without any other intervening events. An event can have multiple successor events and can be the successor of multiple events. Que.6 what are the operation of concrete technology ? Ans.6 there are 2 operation of concrete technology following given below: a. formwork - Complete system of temporary structure built to contain fresh concrete so as to form it to the required shape and dimensions and to support it until it hardens sufficiently to become self-supporting. Formwork includes the surface in contact with the concrete and all necessary supporting structure. b. Centering - It is a temporary supporting structure to a soffit. It is the specialized formwork used in the construction of arches, shells space structure where the entire false-work is (struck or decentred) as a unit to avoid introducing injurious stress in any part of structure formwork requirement for ideal formwork : material used for formwork :- timber , ply wood, hard board, steel etc. removal of formwork:1. wall,column,& vertical side of beams – 24 to 48 hrs 2. slabs (props left under)- 3 days 3. beams soffits (props left under)-7 day 4. removal of props to slabs – spanning upto 4.5m :- 7days spanning over 4.5m :-44 days 5. removal of props to beams and arches- spanning upto 6 m :- 7 days spanning over 6m :- 21 days concreting ‘‘centering’’ 1.storing – a. storing of cement , aggeregates ,& water 2.batching- a.batching of cement, aggeregates,& water 3.mixing- a.hand mixing & machine mixing 4.handling and transporting 5.placing and compacting 6.finishing 7.curing 8.formwork removal Que.7 Discuss the PERT & its 3 estimates ? Ans .7 Discuss the pert & its three estimates Before any activity begins related to the work of a project, every project requires an advanced, accurate time estimate. Without an accurate estimate, no project can be completed within the budget and the target completion date. Developing an estimate is a complex task. If the project is large and has many stakeholders, things can be more complex. Therefore, there have been many initiatives to come up with different techniques for estimation phase of the project in order to make the estimation more accurate. The PERT (Probabilistic) Approach So far we have talked about projects, where there is high certainty about the outcomes of activities. In other words, the cause-effect logic is well known. This is particularly the case in Engineering projects. However, in Research & Development projects, or in Social Projects which are defined as "Process Projects", where learning is an important outcome, the cause-effect relationship is not so well established. In such situations, the PERT approach is useful, because it can accommodate the variation in event completion times, based on an expert’s or an expert committee’s estimates. For each activity, three time estimates are taken The Most Optimistic The Most Likely The Most Pessimistic The Duration of an activity is calculated using the following formula: Where te is the Expected time, to is the Optimistic time, tm is the most probable activity time and tp is the Pessimistic time. It is not necessary to go into the theory behind the formula. It is enough to know that the weights are based on an approximation of the Beta distribution. The Standard Deviation, which is a good measure of the variability of each activity is calculated by the rather simplified formula: The Variance is the Square of the Standard Deviation. Or PERT (Program Evaluation and Review Technique) is one of the successful and proven methods among the many other techniques, such as, CPM, Function Point Counting, Top-Down Estimating, WAVE, etc. PERT was initially created by the US Navy in the late 1950s. The pilot project was for developing Ballistic Missiles and there have been thousands of contractors involved. After PERT methodology was employed for this project, it actually ended two years ahead of its initial schedule. The PERT Basics At the core, PERT is all about management probabilities. Therefore, PERT involves in many simple statistical methods as well. Sometimes, people categorize and put PERT and CPM together. Although CPM (Critical Path Method) shares some characteristics with PERT, PERT has a different focus. Same as most of other estimation techniques, PERT also breaks down the tasks into detailed activities. Then, a Gantt chart will be prepared illustrating the interdependencies among the activities. Then, a network of activities and their interdependencies are drawn in an illustrative manner. In this map, a node represents each event. The activities are represented as arrows and they are drawn from one event to another, based on the sequence. Next, the Earliest Time (TE) and the Latest Time (TL) are figured for each activity and identify the slack time for each activity. When it comes to deriving the estimates, the PERT model takes a statistical route to do that. We will cover more on this in the next two sections. Following is an example PERT chart: The Three Chances There are three estimation times involved in PERT; Optimistic Time Estimate (TOPT), Most Likely Time Estimate (TLIKELY), and Pessimistic Time Estimate (TPESS). In PERT, these three estimate times are derived for each activity. This way, a range of time is given for each activity with the most probable value, TLIKELY. Following are further details on each estimate: 1. TOPT This is the fastest time an activity can be completed. For this, the assumption is made that all the necessary resources are available and all predecessor activities are completed as planned. 2. TLIKELY Most of the times, project managers are asked only to submit one estimate. In that case, this is the estimate that goes to the upper management. 3. TPESS This is the maximum time required to complete an activity. In this case, it is assumed that many things go wrong related to the activity. A lot of rework and resource unavailability are assumed when this estimation is derived. The PERT Mathematics BETA probability distribution is what works behind PERT. The expected completion time (E) is calculated as below: E = (TOPT + 4 x TLIEKLY + TPESS) / 6 At the same time, the possible variance (V) of the estimate is calculated as below: V = (TPESS - TOPT)^2 / 6^2 Now, following is the process we follow with the two values: For every activity in the critical path, E and V are calculated. Then, the total of all Es are taken. This is the overall expected completion time for the project. Now, the corresponding V is added to each activity of the critical path. This is the variance for the entire project. This is done only for the activities in the critical path as only the critical path activities can accelerate or delay the project duration. Then, standard deviation of the project is calculated. This equals to the square root of the variance (V). Now, the normal probability distribution is used for calculating the project completion time with the desired probability. Conclusion The best thing about PERT is its ability to integrate the uncertainty in project times estimations into its methodology. It also makes use of many assumption that can accelerate or delay the project progress. Using PERT, project managers can have an idea of the possible time variation for the deliveries and offer delivery dates to the client in a safer manner Que.8 Discuss the difference b/w CPM & PERT ? Ans 8 PERT vs CPM CPM and PERT (Program Evaluation and Review Technique) are most commonly used methods for project management. There are some similarities and differences between PERT and CPM. PERT can be applied to any field requiring planned, controlled and integrated work efforts to accomplish defined objectives. On the other hand, CPM (Critical Path Method) is the method of project planning consisting of a number of well defined and clearly recognizable activities. PERT/CPM – Differences between PERT and CPM Though PERT and CPM both are used for project management, there are differences between CPM and PERT. The relative table for PERT vs CPM is shown below. CPM PERT CPM uses activity oriented network. PERT uses event oriented Network. Durations of activity may be estimated with a fair degree of accuracy. Estimate of time for activities are not so accurate and definite. It is used extensively in construction projects. It is used mostly in research and development projects, particularly projects of non-repetitive nature. Deterministic concept is used. Probabilistic model concept is used. CPM can control both time and cost when planning. PERT is basically a tool for planning. In CPM, cost optimization is given prime importance. The time for the completion of the project depends upon cost optimization. The cost is not directly proportioned to time. Thus, cost is the controlling factor. In PERT, it is assumed that cost varies directly with time. Attention is therefore given to minimize the time so that minimum cost results. Thus in PERT, time is the controlling factor. Relationship :- Pert is the general case where the activity time is descrived by three time estimates , measuring the uncertanity by standard daviation and variance, Where as the CPM is the particular case when all the time estimate coincide with one value and the standard daviation and variance disapear Que.9 what is planning, scheduling and controlling ? Ans .9 Planning, Scheduling (or organising) and Control are considered to be basic Managerial functions, and CPM/PERT has been rightfully accorded due importance in the literature on Operations Research and Quantitative Analysis. Far more than the technical benefits, it was found that PERT/CPM provided a focus around which managers could brain-storm and put their ideas together. It proved to be a great communication medium by which thinkers and planners at one level could communicate their ideas, their doubts and fears to another level. Most important, it became a useful tool for evaluating the performance of individuals and teams. There are many variations of CPM/PERT which have been useful in planning costs, scheduling manpower and machine time. Project Planning In the process of planning , alternatives are examined and the best alternative is chosen. The goal of planning is to minimize resource use (cost) while satisfactorily completing the task . Efficient use of equipments , material , labor and ensuring coordinated effort are the basic aim . The outcome of planning is predetermined course of action.Thus, the planning creates an orderly sequence of events, defines strategies to be followed in carrying forth the plan and describes ultimate disposition of the result. Putting the various activity of the project in the sequence on the time frame is the process of scheduling . Scheduling is required for continuous checking of the project (control), for resource mobilization , to minimize the cost and use of resources optimally. Various scheduling techniques have been employed to plan the activity in sequence in project management . In construction project , bar chart and critical path method (CPM) have been widely used . During the planning process , a manager builds the facilities on paper , thus identities each of the various tasks and time .During construction , these predetermined course of action form the basis for monitoring and the checking the progress of the work . Following steps are followed during planning , scheduling and control . Que. 10 what is scheduling , uses , advantages, classification & method ? Ans .10 Defination construction scheduling is a graphical representation which shows the phasing rate of construction activities with the starting and completion dates and the squential relationship among the various activities or operation in a project is that work can be carried out in an orderly and effective manner Uses 1. It gives the qquantity of works. 2. the actual progress of the work. 3.the project can be carried out in a symmetric manner using Scheduling . Advantages 1. By studying the scheduling of any kind of work and the many alternative method of execution, we can choose the best one. 2. it gives the clear idea regarding the reqquired men, material, and equipment at different stage of the work. 3. resourses utilization is optimized. 4. actual progress of the work is monitored with the actual plan. 5. total duration of the complete project is known. Classification of scheduling it is classified into different types of requirement such as :- 1. 2. 3. 4. Material scheduling Labour scheduling Equipment scheduling Financial scheduling and other types. Method of scheduling Scheduling can be done by different methods depending on the size of the project . the methods used are : 1. Bar chart or Gantt charts 2. Milestones chart 3. Network analysis. Scheduling of Activities Using a Gantt Chart Once the activities are laid out along a Gantt Chart (Please see chart below), the concepts of Earliest Start & Finish, Latest Start & Finish and Float will become very obvious. Activities 1-3 and 2-4 have total float of 1 week each, represented by the solid timeline which begins at the latest start and ends at the latest finish. The difference is the float, which gives us the flexibility to schedule the activity. For example, we might send the staff on leave during that one week or give them some other work to do. Or we may choose to start the activity slightly later than planned, knowing that we have a week’s float in hand. We might even break the activity in the middle (if this is permitted) for a week and divert the staff for some other work, or declare a National or Festival holiday as required under the National and Festival Holidays Act. These are some of the examples of the use of float to schedule an activity. Once all the activities that can be scheduled are scheduled to the convenience of the project, normally reflecting resource optimisation measures, we can say that the project has been scheduled. Que.11 what is Sequencing Activities ? Ans .11 Sequencing Activities Sequencing is the process of identifying and documenting relationship among the project activities. Activities are ordered based on their logical relationships and all but the first and the last are linked to at least one predecessor and one successor. Sequencing Basics Sequencing can be affected by • Product Description, characteristics or layout • Necessary Dependencies • Discretionary Dependencies • External dependencies Sequencing Techniques There are several commonly discussed networks including PERT/CPM and PDM. The Precedence Diagramming Method (PDM) is the one most frequently used for illustrating the dependent relationships among project activities and, consequently, the follow of work from start to end of the project. Characteristics of the PDM are: • Activities are shown as geometric shapes. • Arrows between activities identify only relationships – they do not represent work. • An arrow from one activity to another means that the successor activity cannot start until the predecessor activity is complete. • If the activity has more than one predecessor, it cannot start until all predecessors are complete. Project Activity Characteristics • Work is performed and described in terms of a verb, adjective, and noun – there is action performed. • A single person or organization is responsible for the work – more than one resource may be assigned to an activity, but one person is in charge of delivering the output. If this is not the case, the items need further decomposition or joint responsibilities clarified. • It has a defined starting point – there is a specific action that can be identified that marks the start of an activity or a predecessor activity that must be completed. • There is a tangible output or product at completion (usually) – projects occasionally have level-of-effort activities or support activities without clearly defined outputs; however, the primary activities have defined and measurable outputs. The point at which an activity is completed is determined by the availability of an output product that is used as input by a successor activity. • It fits logically under an existing WBS element – if it does not, then either the activity is not part of the project, the WBS needs modification, or the activity is ambiguous and needs redefinition. • It is of a size and duration that is sufficient for control – activities that are too long do not provide sufficient time for corrective action if problems arise, and too many activities that are too short can make the cost of the control more expensive than a problem that may arise; however, using a rolling wave concept where the nearterm activities are relatively short and those many months in the future are larger Que.12 calculation of time estimates in cpm ? Ans .12 Calculation of Time Estimates in CPM In the project network given in figure below, activities and their durations are specified at the activities. Find the critical path and the project duration. Calculations in Network Analysis The following calculations are required in network analysis in order to prepare a schedule of the project. a. Total completion time of the project b. Earliest time when each activity can start (i.e. earlist start time) c. Earliest time when each activity can finish (i.e. earlist finished time) d. Latest time when each activity can be started without delaying the project (i.e. latest start time) e. Latest time when each activity can be finished without delaying the project (i.e. latest finish time) f. Float on each activity (i.e. time by which the completion of an activity can be delayed without delaying the project) g. Critical activity and critical path The symbols used in the calculations are shown in table below. Symbol Description Ei Earliest occurance time of event i Lj Latest allowable occurance time of event j tEi-j Estimated completion time of activity (i,j) (EST)ij Earliest starting time of activity (i,j) (EFT)ij Earliest finishing time of activity (i,j) (LST)ij Latest starting time of activity (i,j) (LFT)ij Latest finishing time of activity (i,j) The computations are made in following steps. (a) Forward Pass Computations : (b) Backward Pass Computations : (c) Calculation of Slack: Event slack is defined as the difference between the latest event and earlist event times. Slack for head event = Lj - Ej Slack for tail event = Li - Ei The calculations for the above taken example network are summarised below in the table. S(i) Predecessor Successor tEi-j Event i Event j (EST)ij 5 10 7 0 7 0 7 0 5 15 12 0 12 7 19 - 5 20 17 0 17 5 22 - (EFT)ij (LST)ij (LFT)ij Slack 10 20 15 7 22 7 22 0 10 25 9 7 16 21 30 - 15 30 11 12 23 19 30 7 20 25 5 22 27 25 30 - 20 30 8 22 30 22 30 0 25 35 10 27 37 30 40 3 25 45 15 27 42 35 50 - 30 35 10 30 40 30 40 0 30 40 8 30 38 35 43 - 35 45 10 40 50 40 50 0 40 45 7 38 45 43 50 5 (d) Determination of Critical Path: The sequance of critical activities in a network is called the critical path. The activities with zero slack of head event and zero slack for tail event, are called as crititcal activities. In the taken network, the following activities are critical activities: 5 - 10, 10 - 20, 20 - 30, 30 - 35, 35 - 45. Thus the critical path is A - E - G - K - M. Critical path duration is 7 + 15 + 8 + 10 + 10 = 50. Calculation of Expected Time and Variance of a Path in PERT The Expected Time of a chain of activities in series, is the sum of their expected times. Similarly the variance of the path, is the sum of variances of activities on the path. In Figure below, three activities A,B and C are connected in series, (i.e. form a path). Their time estimates to-tm-tpare given along the activity arrows. The expected time of the path 1-2-3-4 is calculated as: As the length of the path ,that is the number of activies connected in series increases,the variance of the path and hence the uncertainty of meeting the expected time also increases. An Example In the network of figure below, the PERT time estimates of the activities are written along the activity arrows in the order to-tm-tp. Compute the expected time and variance for each activity. Also compute the expected duration and standard deviation for the following paths of the network. (a) 10-20-50-80-90 (b) 10-30-50-70-90 (c) 10-40-60-80-90 The computation of expected times and variances for different activities are carried in a table given below. Activity i Time Estimates j to tm Expected Time Variance tp tE σ2 10 20 6 9 12 9.00 1.00 10 30 3 5 9 5.33 1.00 10 40 10 14 18 14.00 1.78 20 50 7 10 13 10.00 1.00 20 70 3 4 8 4.5 0.69 30 50 4 10 12 9.33 1.78 40 50 8 11 14 11.00 1.00 40 60 5 10 15 10.00 2.78 50 70 3 4 5 4.00 0.11 50 80 11 15 14.67 1.00 60 80 7 9 12 9.17 0.69 70 90 4 8 10 7.67 1.00 80 90 6 7 9 7.17 0.25 17 Que .13 define the pert calculation ? Ans .13. PERT Calculations for the Social Project In our Social Project, the Project Manager is now not so certain that each activity will be completed on the basis of the single estimate he gave. There are many assumptions involved in each estimate, and these assumptions are illustrated in the three-time estimate he would prefer to give to each activity. In Activity 1-3, the time estimates are 3,12 and 21. Using our PERT formula, we get: The Standard Deviation (s.d.) for this activity is also calculated using the PERT formula We calculate the PERT event times and other details as below for each activity: Event to tm tp te ES EF LS LF TF s.d. Var. 1-3 3 12 21 12 0 12 0 12 0 3 9 3-5 6 15 30 16 12 28 12 28 0 4 16 1-2 2 5 14 6 0 6 5 11 5 2 4 2-4 5 14 17 13 6 19 11 24 5 2 4 3-4 2 5 8 5 12 17 19 24 7 1 1 4-5 1 4 7 4 19 23 24 28 5 1 1 Que .14 what is job lay out or site layout ? Ans .14 . Construction site or job layout involves identifying, sizing, and placing temporary facilities (TFs) within the boundaries of construction site. These temporary facilities range from simple laydown areas to warehouses, fabrication shops, maintenance shops, batch plant, and residence facilities. Required temporary facilities and their areas are depending in many factors including project type, scale, design, location, and organization of construction work. Site planning in particular, has been the most neglected aspect in the construction industry and the attitude of the engineers has been that it will be done as the project progress. It is important to realize that the site planning will be the conditions that site personnel will live with for the total duration of the construction period. Thus the careful pre-planning is imperative. Site Layout Planning Elements A well planned site including all temporary facilities and utilities lead to: increasing productivity and safety, 2) reducing area(s) needed for temporary construction, and 3) maximizing utilization. The following points should be considered in good site layout. 1. Safety 2. Site Accessibility 3. Information Signs 4. Security 5. Accommodation 6. Offices 7. Water Supply and Sanitation 8. Material Handling 9. Storage and site cleaning 10.Craft Change-Houses 11.Batch plant and Fabrication Shops Temporary Facilities Characteristics It is important to understand the characteristics of the temporary facilities before planning the site layout. Six generic temporary facility characteristics are discussed in this section. 1. Satisfying environmental and safety regulations: All temporary facilities should satisfy environmental and safety regulations. 2. Availability of diverse solutions for the same problem: There are many arrangements that can be made to establish a temporary facility. For example, if a warehouse is required, the planner can build a warehouse on the site, use existing facilities on the site, rent a building near the site, or plan a just in time delivery. 3. Relatively short life span of a specific location: The life span of temporary facility depends on the duration of the project. In general, it must be removed as soon as the project is completed. 4. Reutilization with a minimum loss for the same or modified function at another location: Due to the shorter life span of temporary facility on site, planners consider reutilization of the temporary facilities. This can result in saving the cost of construction. 5. Easy of assembly, dismantling, and exploitation: temporary facilities structures which are easy to assemble and dismantle will reduce both assembly and disassembly time. 6. Standardization of design: Standardization of design and construction of temporary facilities can increase the frequency of reutilization and reduce the work-hours and cost required for construction the facilities 8. Examples of Site Layout Planning Example 1 Figure 2 illustrates the layout of building materials and access roads for the purposes of servicing two hoists for the erection of a low-rise building. Comment on and criticize the present layout in relation to the positioning of both the materials and hoists. Que. 1Explain clearly the difference between an activity and an event. Ans. 1 Activity - Activity stands for the time consuming part of a project. It represents a job.Activities are denoted by arrows. Event - The event (also called node) is either the beginning or end of a job. Events aredenoted by circles. Event does not consume time.When all activities and events in a project are connected logically and sequentially, they forma network. Que.2 In what ways does a CPM network differ from Pert network ? Ans .2 PERT (Programme Evaluation & Review Technique) is event oriented whereas CPM(Critical Path Method) is activity oriented. In CPM based network analysis no allowance is made for the uncertainties in theduration of time involved. In CPM, times are related to costs. Que.3. Define, (i) predecessor event (ii) successor event Ans .3 Event or events that immediately come before another event are called predecessor events tothat event. Event or events that immediately follow another event are called successor eventsto that event. Que .4Draw a PERT network of opening a new office. Assume that following events take place insome sequence. Event 1: Location of site started Event 2: Location of site completed Event 3: Building for office selected Event 4: Cleaning of the office building started Event 5: Interior decorator starts work Event 6: Interior decorator finishes work Event 7: Opening of new office advertised or announced Event 8: List of invitees for the opening day prepared Event 9: Invitations sent Event 10: Office opened Ans .4 see fig.