Chapter 2 Overview of the Operations Research Modeling Approach

The usual phases of an OR study is the following: u Define the problem of interest and gather relevant data. u Formulate a mathematical model to represent the problem. u Develop a computer-based procedure for deriving solutions to the problem from the model. u Test the model and refine it as needed. u Prepare for the ongoing application of the model as prescribed by management. u Implement

2.1 Defining the Problem and Gathering Data u Most practical problems are described in a vague, imprecise way. uTuThe appropriate objectives ucuconstraints uiuinterrelationships of the organization upupossible alternative courses of action ututime limits u…u…... We must determine

Problem definition u How to ascertain appropriate objectives u Identify the members of management who actually will be making the decisions and probe into this individual’s thinking regarding the pertinent objectives. u Concern with the entire organization rather than that of only certain of ins components

For Example: u For profit-making organizations: the objective may be: u In actual practice, a number of U.S. Corporations tends to adopt the goal of satisfied profits, combine with other objectives. But profit maximization. What?

The owners (stockholder, etc.): desire profits The employees: desire steady employment at reasonable wages The customers: a reliable product at a reasonable price The suppliers: integrity and a reasonable selling price for their goods The government and the nation: payment of fair taxes and consideration of the national interest The business firm: satisfied profits

Gathering Relevant Data about the Problem Because: u to gain an accurate understanding of the problem u to provide the needed input for the mathematical model u To install a computer- based management information system to collect the necessary data on an ongoing basis and in the needed form. u To enlist the assistance of individuals in the organization to track down all the vital data. u To spend considerable time to improve the precision of the data. Why?How

Discussion 1: u An OR study done for the San Francisco Police Department, resulted in the development of a computerized system for optimally scheduling and deploying police patrol officers. The new system provided annual savings of $11 million, an annual $3 million increase in traffic citation revenues, and a 20 percent improvement in response times.

Objects In assessing the appropriate objectives for this study, three fundamental objectives were identified: u 1. Maintain a high level of citizen safety. u 2. Maintain a high level of officer morale. u 3. Minimize the cost of operations.

Solution: u To satisfy the first objective, the police department and city government jointly established a desired level of protection. The mathematical model then imposed the requirement that this level of protection be achieved. Similarly, the model imposed the requirement of balancing the workload equitably among officers in order to work toward the second objective. Finally, the third objective was incorporated by adopting the long-term goal of minimizing the number of officers needed to meet the first two objectives.

Discussion 2: The Citgo Petroleum Corporation, optimized both refinery operations and the supply, distribution, and marketing of its products, thereby achieving a profit improvement of approximately $70 million per year.

u Initially, the preloader generated a log of error messages 1 inch thick! Eventually, the number of error and warning messages (indicating bad or questionable numbers) was reduced to less than 10 for each new run.

2.2 Formulating A Mathematical Model u Why? uRuRepresent the essence of the problem in mathematical model u…u…... We must u What is model ? Such as uMuModel of the atoms uMuModels of genetic structure uMuModel of airplane/portraits/global u…u…...

2.2 Constructing a Mathematical model u How to construct a model? u Expressed in terms of mathematical symbols and expressions that describe the essence of the problem. ……… u Some important terms: – Decision variables – Objective function – Constrains

2.2 Constructing a Mathematical model u Mine Cost per day ($’1000) Production (tons/day) u High Medium Low u X u Y u How many days per week should each mine be operated to fulfil the smelting plant contract?

2.2 Constructing a Mathematical model u Objective function Minimize Z = 180x + 160y subject to: 6x + y >= 12 3x + y >= 8 4x + 6y >= 24 x = 0 u Constrains u Decision variables

2.2 For Example: u An OR study done for Monsanto Corp. was concerned with optimizing production operations in Monsanto’s chemical plants to minimize the cost of meeting the target for the amount of a certain chemical product to be produced in a given month. The decision to be made are the dial setting for each of the catalytic( 接触 ) reactors used to produce this products, where the setting determines both the amount produced and the cost of operating the reactor. u How to create the mathematical model?

2.2 For Example: Formulating the model u For profit-making organizations: the objective may be: Cost Minimization What? u Minimize u Subject to For i=1,2,…,r C ij = cost of reactor i at setting j P ij = production of reactor i at setting j T= production target R= number of reactors S = number of settings Where If reactor i is operated at setting j Otherwise

u How to deriving the solution ? u You might think it is very difficult, but ………it is very simple with the help of software packages.. u Many algorithms help us to do it u We will discuss it later in details u What is optimizing? u What is satisficing? u …… 2.3 Deriving solution from the model

u What is satisficing ? Maybe you cannot find the word in dictionary? - satisficing = satisfactory + optimizing = good enough (Simon ) u Who is Simon? Nobel Laureate and Eminent management scientist in economics. Herbert Simon. u What is the distinction of optimizing and satisficing? -Reflect the difference between theory and the realities. According to the Samuel Eilon : - Optimizing is the science of the ultimate; satisficing is the art of the feasible… 2.3 Deriving solution from the model

post optimality analysis u What is post optimality analysis ? - It is a very important tool of OR research. - Because the optimal solution for the original model may far from ideal for the really problem, so additional analysis is needed. u What kind of methods should be used? - What-if analysis widely used for this kind problem. 2.3 Deriving solution from the model

sensitivity analysis u What is sensitivity analysis ? u Post optimality involves conducting sensitivity analysis to determine which parameters of the model are most critical in determining the solution. For example: - For a mathematical model with specified values for all its’ parameters, the model’s sensitivity parameters are the parameters whose value cannot be changed without changing the optimal solution. 2.3 Deriving solution from the model

sensitivity parameters u How to identify the sensitivity parameters ? - in order to avoid distorting the output of the model we should assign the value of sensitivity parameters, or at least its range of likely values. u We need to estimate the values. 2.3 Deriving solution from the model

2.4 Testing the model u Why? uDuDeveloping a large mathematical model, which is analogous （类 似） in some ways to developing a large computer program, it inevitably contains many bugs, so…... We haveWe should uTuTry to find the bugs before we really use it for the work

u How to test the model? u Model validation u Use the retrospective test u Documentation u ……… 2.4 Testing the model

2.5 Prepare to apply the model u What shall we do in this phase? What happens after the testing phase has been completed and an acceptable model has been developed? -If the model is to be used repeatedly, the next step is to install a well documented system for applying the model as prescribed by management. This system will include the model, solution procedure (including post optimality analysis), and operating procedures for implementation. - Then, even as personnel changes, the system can be called on at regular intervals to provide a specific numerical solution.

2.5 Prepare to apply the model u What is the “documented System”? -This system usually is computer-based. In fact, a considerable number of compute programs often need to be used and integrated. Databases and management information systems may provide up-to-date input for the model each time it is used, in which case interface programs are needed. In other cases, an interactive computer-based system called a decision support system is installed to help managers use data and models to support (rather than replace) their decision making as needed. Another program may generate managerial reports (in the language of management) that interpret the output of the model and its implications for application

2.6 IMPLEMENTATION u What shall we do in the last phase: IMPLEMENTATION? This phase is a critical one because it is here, and only here, that the benefits of the study are reaped. Therefore, it is important for the OR team to participate in launching this phase, both to make sure that model solutions are accurately translated to an operating procedure and to rectify any flaws in the solutions that are then uncovered.

2.6 IMPLEMENTATION u How to make it successful? u The success of the implementation phase depends a great deal upon the support of both top management and operating management. The OR team is much more likely to gain this support if it has kept management well informed and encouraged management's active guidance throughout the course of the study, Good communications help to ensure that the study accomplishes what management wanted and so deserves implementation. They also give management a greater sense of ownership of the study, which encourages their support for implementation.

2.6 IMPLEMENTATION u What are the steps of implementation? u The implementation phase involves several steps. First, the OR team gives operating management a careful explanation of the new system to be adopted and how it relates to operating realities. Next, these two parties share the responsibility for developing the procedures required to put this system into operation. Operating management then sees that a detailed indoctrination is given to the personnel involved, and the new course of action is initiated. If successful, the new system may be used for years to come. With this in mind, the OR team monitors the initial experience with the course of action taken and seeks to identify any modifications that should be made in the future.

2.6 IMPLEMENTATION u The last step is : obtain feedback u Throughout the entire period during which the new system is being used, it is important to continue to obtain feedback on how well the system is working and whether the assumptions of the model continue to be satisfied. u When significant deviations from the original assumptions occur, the model should be revisited to determine if any modifications should be made in the system. The post optimality analysis done earlier can be helpful in guiding this review process.

2.7 CONCLUSION u Although the remainder of this book focuses primarily on constructing and solving mathematical models, in this chapter we have tried to emphasize that this constitutes only a portion of the overall process involved in conducting a typical OR study. The other phases described here also are very important to the success of the study. Try to keep in perspective the role of the model and the solution procedure in the overall process as you move through the subsequent chapters. Then, after gaining a deeper understanding of mathematical models, you are suggested that you plan to return to review this chapter again in order to further sharpen this perspective.

2.7 CONCLUSION u OR is intertwined with the use of computers closely. In the early years, these generally were mainframe computers, but now personal computers and workstations are being widely used to solve OR models. u In concluding this discussion of the major phases of an OR study, it should be emphasized that there ale many exceptions to the "rules" prescribed in this chapter. By its very nature, OR requires considerable ingenuity and innovation, so it is impossible to write down any standard procedure that should always be followed by OR teams. Rather, the preceding description may be viewed as a model that roughly represents how successful OR studies are conducted. The end of chapter 2.