CPU- BUSINESS AND INFORMATION TECHNOLOGY COLLEGE ANALYTICAL DECISION MODELING FOR BUSINESS DECISION CHAPTER ONE : INTRODUCTION BY ; Shewayirga Assalf ( Asst. Prof.) April,2022 Chapter One: Introduction Origin and Development of OR The term Operations Research, was first coined in 1940 by McClosky and Trefthen in a small town, Bowdsey, of the United Kingdom. This new science came into existence in military context. Its concept was derived from the fact that “Unity is strength”. Why unity is strength? Because, when there is calamity to the nation, citizens of all shades join their opinions together to do their might to solve the problem. How this came to be proved? It was proved during World War II. Two blocks took part in the Second World War, namely, Axes Forces and Allied Forces. Axes forces included Nazi German, Italy and Japan in one block. Contrarily, the allied forces included America, Great Britain and Russia. Contd… During World War II, there was a natural calamity/disaster to Great Britain from Nazi German Forces. Superior weapons and strategy of Germans became a real threat to Allied Forces. Consequently, Allied Forces were threatened on land, sea and air by Axes forces, using superior weapons such as submarines, Uboats and air crafts. Being challenged by this serious situation, the Government of Great Britain appealed to the people and requested talents from all walks of life to join together and find a solution to the problem in order to overcome the threatening situation. Cont… Based on an appeal made by Government of Great Britain, military management called on scientists from various disciplines and organized them into teams to assist in solving strategic and tactical problems, i.e., to discuss, evolve and suggest ways and means to improve the execution of various military projects. Accordingly, scientists reported to the military management and they were grouped into various teams and each team is given strategic problem to come up with the possible solution. Contd… These combined efforts produced fantastic results. By their joint efforts, experience and deliberations, they suggested certain approaches that showed remarkable progress. Based on suggestions provided by teams of scientists, Allied forces defeated Axes forces. This signaled to the birth of Operations Research as a separate discipline. This new approach to systematic and scientific study of operations of the systems was called the Operations Research (abbreviated as O.R.) Cont.. Following the end of World War II, the success of military teams attracted the attention of industrial managers who were seeking solutions to their complex executive type problems. During the year 1950, O.R. achieved recognition as a subject worthy of academic study in the Universities Since then, the subject has been gaining more and more importance for the students of Economics, Management, Public Administration, Behavioral Sciences, Work, Mathematics, Commerce and Engineering Contd… With a view to increasing the impact of O.R. and establish in rapport between all its serious students and users, the Operations Research society of America was formed in 1950. Other countries followed suit, and in 1957 the International Federation of O.R. Societies was established. O.R. is, therefore, a systematic method consisting of stating the problem in clear terms, collecting facts and data, analyzing them, and reaching certain conclusions in the form of solutions to the problem. The ultimate aim of it is to find out an optimum solution which is most appropriate under the given circumstances. Meaning The term operations research consists of two terms, namely, operations and research. Literally, the operations may be defined as some action that we apply to some problems or hypotheses and the word research is an organized process of seeking out facts about the same. Dictionary meaning of research is “a careful investigation or inquiry especially through search for new facts”. It also means “systematized effort to gain new knowledge”. Thus, Operations Research could be thought of as a “systematized efforts to solve a given problem through careful investigation”. OR is the application of scientific methods, techniques and tools to problems involving the operations of a system. It is a scientific approach to problem solving for executive management . Defination • As far as the definition of O.R. is concerned, there is no single universally accepted definition. The following definition is proposed for this study to be used in common. Operations Research is a systematic analysis of a problem through scientific methods, carried out by appropriate specialists, working together as a team, constituted at the instance of management for the purpose of finding an optimum and the most appropriate solution, to meet the given objective under a given set of constraints. According to the definition given by operational research society, UK, Operations Research is the application of the methods of science to complex problems in the direction and management of large systems of men, machines, materials and money in industry, business, government and defense Contd…. The distinctive approach is to develop a scientific model of the system incorporating measurements of factors such as chance and risk, with which to predict and compare the outcomes of alternative decisions, strategies or controls. The purpose is to help management in determining its policy and actions scientifically. According to the definition given by operational research society, America, operations research is concerned with scientifically deciding how to best design and operate man-machine system usually requiring allocation of scarce resources. According to Daellenbach and George 1978, “Operations Research is the systematic application of quantitative methods, techniques and tools to the analysis of problems involving the operation of systems.” Contd…. According to S L Cook 1977, Operations Research has been described as a method, an approach, a set of techniques, a team activity, a combination of many disciplines, an extension of particular disciplines (mathematics, engineering, economics, etc.) a new discipline, a vocation, even a religion. It is perhaps some of all these things. Here are many more definitions as various authors have defined the term differently. As it has been written by many authors, discussing all the definitions exhaustively is very impossible. Definitions contd…. Meaning of O.R. is evident from the concept given in the definitions here above. However, some more aspects of O.R. are given here under to get better insight into it. 1. O.R is the application of scientific methods, techniques and tools to the problem to find out an answer. 2. O.R. is a management tool, in the hands of a manager, to take a decision. 3. O.R. is a scientific approach to the decision-making process 4. O.R. is an “Applied Research” which aims at finding a solution for immediate problem facing a society, industry or a business enterprise. It is not fundamental research. 5. O.R. is a decision-oriented research, which provides quantitative basis to managers of the organization for taking decisions. Nature and characteristics of OR Some significant features of O.R. are given here under as follows: i) Decision-making. Primarily O.R. is addressed to managerial decision-making or problem-solving. A major premise of O.R. is decision-making. ii) Scientific approach. O.R. employs scientific methods for the purpose of solving problems. It is a formalized process of reasoning. iii) Objective. O.R. attempts to locate the best or optimal solution to the problem under Prepared by consideration. For this purpose, it is necessary that a measure of effectiveness is defined based on the goals of organization. This measure is then used as the basis to compare the alternative courses of action. Contd….. iv) Inter-disciplinary team approach. O.R. is interdisciplinary in nature and requires a team approach to arriving at a solution of the problem. Managerial problems have economic, physical, psychological, biological, sociological and engineering aspects. This requires a blend of people with expertise in the areas of mathematics, statistics, engineering, economics, management, computer science and so on. v) Digital computer. Use of a digital computer has become an integral part of the O.R. approach to decision-making. The computer may be required due to the complexity of the model, volume of data required and the computations to be made. vi) Methodological Approach. O.R. is the application of scientific methods, techniques and tools to problems involving the operations of systems so as to provide optimum solutions to the problems. Contd…. The scientific method consists of observing and finding the problem; formulating and testing the hypothesis; and analyzing the results of the test. The data so obtained is then used to decide whether the hypothesis should be accepted or not. If the hypothesis is accepted, the results should be implemented. Otherwise, an alternative hypothesis has to be accepted. vii) Wholistic Approach. While arriving at a decision,An operations research team examines the relative importance of all conflicting and multiple objectives and the validity of claims of various departments of the organization from the perspective of the whole organization. Contd…. It is not so easy to exhaustively list down the features of O.R. as the matter of fact that it constitutes very broad area. However, the following features can also be mentioned in addition to those already listed here above. Existence of a problem. Intention to solve the problem. Application of system concept and system analysis to problem. Scientific approach to solving the existing problem. Assists the management to take decision. Role is that of recommendatory nature. Existence of a number of solutions to the problem. Solution must be optimum. Solution must be most appropriate. Solution must meet the objectives within the constraints. Solution must be given in quantifiable terms. Solution must be practical, application specific and result-oriented. APPLICATIONS OF OPERATIONS RESEARCH Operation Research is mainly concerned with the techniques of applying scientific knowledge, besides the development of science. It provides an understanding which gives the expert/manager new insights and capabilities to determine better solutions in his decision making problems, with great speed, competence and confidence. In recent years, O.R. has successfully entered many different areas of research in Defence, Government, Service Organizations and Industry. Some applications of O.R. in the functional areas of management are briefly presented here under: Finance, Budgeting, and Investment i) Cash flow analysis, long range capital requirements, dividend policies, investment portfolios. ii) Credit policies, credit risks and adequate account procedures. iii) Claim and complaint procedure. Contd…. Marketing i) Product selection, timing, comparative actions. ii) Advertising media with respect to cost and time. iii) Number of salesmen, frequency of calling of account, etc. iv) Effectiveness of market research. Physical Distribution i) Location and size of warehouses, distribution centers, retail outlets, etc. ii) Distribution policy. Purchasing, Procurement and Exploration i) Rules of buying. ii) Determine the quality and timing of purchase. iii)Bidding policies and vendor analysis. iv) Equipment replacement policies. Contd…. Personnel i) Forecasting the manpower requirement, recruitment policies and job assignments. ii) Selection of suitable personnel with due consideration for age and skills, etc. iii)Determination of optimum number of persons for each service center. Production i) Scheduling and sequencing the production run by proper allocation of machines. ii) Calculating the optimum product mix. iii) Selection, location and design of sites for the production plant. Contd…. Production i) Scheduling and sequencing the production run by proper allocation of machines. ii) Calculating the optimum product mix. iii) Selection, location and design of sites for theproduction plant. Research and Development i) Reliability and evaluation of alternative designs. ii) Control of developed projects. iii)Co-ordination of multiple research projects. iv) Determination of time and cost requirements. Besides the above mentioned applications of O.R. in the context of modern management, its use has now extended to a wide range of problems, such as the problems of communication and information, socio-economic fields and national planning. Models and Model Building A model is a selective abstraction of reality. Model is a representation of real objects/situations It is a simplified and often idealized representation of real world problems. A good model should capture the important details of reality without including minor details Thus, it is important to carefully decide which aspects of reality to include in a model. The classification of models is a subjective problem. Contd…. They may be distinguished as follows: 1. Models by Function: These models consist of : a. Descriptive Models: describe and predict facts and relationships among the various activities of the problem. These models do not have an objective function as a part of the model to evaluate decision alternatives. In this model, it is possible to get information as to how one or more factors change as a result of changes in other factors. b. Normative or Optimization Models: they are prescriptive in nature and develop objective decision-rule for optimum solutions. Model contd… Models by Structure and Abstraction : a. Physical (icon) model This is the representation of the situation, problem or object. It is also called Static Model. It is a representation of the real object. ◦ Example: Model of an airplane Photograph of a machine Layout drawing of a factory Contd…. b. Analogue Models: These are abstract models mostly showing inter and intra relationships between two or more parameters. For example: ◦ It may show the relationship between an independent variable (input) with that of a dependent variable (output). ◦ For instance; histogram, frequency table, cause-effect diagram, flow charts, Gantt charts, price-demand graph and others. Contd….. c. Mathematical models This is also an abstract model. Here a set of relations is represented in the form of mathematical equations, using symbols to represent various parameters. Example: 1. (x + y)2=x2+2xy+y2 2. Max.Z=3000x1 +2500x2 Subject to: 2x1+x2 < 40 x1+3x2 < 45 x1 < 12 x1, x2 > 0 x1 and x2 are decision variables Contd… 3. Models by Nature of an Environment : a. Depending on the degree of uncertainty we have about a problem, we can classify models as Deterministic and Probabilistic /Stochastic models. Deterministic models: represent problems of decision making under conditions of certainty. That is to say, we use deterministic models when we know all the numerical values in the model certainly. In deterministic models, all uncontrollable inputs to a model are known and cannot vary. Contd… b. Probabilistic/stochastic models: deal with problems of decision making under uncertainty or risk and the probabilities of the alternative states of nature are known. Unlike the deterministic models; here, any of the uncontrollable inputs are uncertain and subject to variation. 4. Models by Extent of Generality : These models can be categorized in to: a. Specific Models: when a model presents a system at some specific time it is known as a specific model. b. General Models: are models applicable to all situations without time bound. Simulation and Heuristic models fall under this category. Chapter Two: Linear Programming Contd… LP is a method for choosing the best alternative from a set of feasible alternatives. To apply LP, the following conditions must be satisfied: a. Objective Function :Is the goal or objective of a management, stated as an intent to maximize or to minimize some important quantity such as profits or costs. b. Constraints : Are limitations or restrictions imposed by the problems. And constraints include: 1. Resourse constraints Are restrictions that should be clearly identifiable and measurable in quantitative terms, which arise from limitation of available resources. Contd… Examples of limited resources: Plant capacity, Raw materials availability Labor power Market demand, etc. 2. Non-negativity constraints: Are constraints that require the decision variables not to take on negative values c. Linearity The Objective Function and the constraints must be linear in nature in order to have a Linear Programming Problems (LPP) d. Feasible alternative There should be a series of feasible alternative course of action available to the decision-making determined by resource constraints. Thus, we have to choose the best alternative Linear Programming Problems can be solved by using: i. The Geometric method called” Graphical Method” ii. The Algebraic method called” Simplex Method” Contd… 2.2. GRAPHICAL SOLUTION To use the graphic method, the following steps are needed: 1. Identify the problem i.e:The decision variables, the objective function and the constraints 2. Draw a graph including all the constraints and identify the feasible region 3. Obtain a point on the feasible region that optimizes the objective functionOptimal solution 4. Interprete the results Graphical LP is a two-dimensional model. A. Maximization Problem ==>Maximize Z with inequalities of constraints in < form Example: Consider two models of color TV sets; Model A and B, are produced by a company to maximize profit. The profit realized is $300 from A and $250 from set B.The limitations are a. availability of only 40hrs of labor each day in the production department. b. a daily availability of only 45 hrs on machine time c. ability to sale 12 set of model A.
