operation research

The bulk of this blog from the Hamdy’s book is devoted to the mathematical methods of operations research (OR). This is quite appropriate because these quantitative techniques form the main part of what is known about OR. However, it does not imply that practical OR studies are primarily mathematical exercises. As a matter of fact, the mathematical analysis often represents only a relatively small part of the total effort required. The purpose of this chapter is to place
things into better perspective by describing all the major phases of a typical OR study. One way of summarizing the usual (overlapping) phases of an OR study is the following:
1. Define the problem of interest and gather relevant data.
2. Formulate a mathematical model to represent the problem.
3. Develop a computer-based procedure for deriving solutions to the problem from the
model.
4. Test the model and refine it as needed.
5. Prepare for the ongoing application of the model as prescribed by management.
6. Implement.
Each of these phases will be discussed in turn in the following sections. Most of the award-winning OR studies introduced in Table 1.1 provide excellent ex- amples of how to execute these phases well. We will intersperse snippets from these ex- amples throughout the chapter, with references to invite your further reading.

DEFINING THE PROBLEM AND GATHERING DATA
In contrast to textblog examples, most practical problems encountered by OR teams are initially described to them in a vague, imprecise way. Therefore, the first order of busi- ness is to study the relevant system and develop a well-defined statement of the problem to be considered. This includes determining such things as the appropriate objectives, constraints on what can be done, interrelationships between the area to be studied and other areas of the organization, possible alternative courses of action, time limits for making a decision, and so on. This process of problem definition is a crucial one because it greatly affects how relevant the conclusions of the study will be. It is difficult to extract a "right" answer from the "wrong" problem! The first thing to recognize is that an OR team is normally working in an advisory capacity. The team members are not just given a problem and told to solve it however they see fit. Instead, they are advising management (often one key decision maker). The team performs a detailed technical analysis of the problem and then presents recommendations to management. Frequently, the report to management will identify a number of alternatives that are particularly attractive under different assumptions or over a different range of values of some policy parameter that can be evaluated only by management (e.g., the trade off between cost and benefits). Management evaluates the study and its recommendations,
takes into account a variety of intangible factors, and makes the final decision based on its best judgment. Consequently, it is vital for the OR team to get on the same wavelength as management, including identifying the "right" problem from management's viewpoint, and to build the support of management for the course that the study is taking. Ascertaining the appropriate objectives is a very important aspect of problem definition. To do this, it is necessary first to identify the member (or members) of management who actually will be making the decisions concerning the system under study and then to probe into this individual's thinking regarding the pertinent objectives. (Involving the decision maker from the outset also is essential to build her or his support for the imple-
mentation of the study.) By its nature, OR is concerned with the welfare of the entire organization rather than
that of only certain of its components. An OR study seeks solutions that are optimal for the overall organization rather than suboptimal solutions that are best for only one component. Therefore, the objectives that are formulated ideally should be those of the entire organization. However, this is not always convenient. Many problems primarily concern only a portion of the organization, so the analysis would become unwieldy if the stated objectives were too general and if explicit consideration were given to all side effects on the rest of the organization. Instead, the objectives used in the study should be as specific as they can be while still encompassing the main goals of the decision maker and maintain ing a reasonable degree of consistency with the higher-level objectives of the organization. For profit-making organizations, one possible approach to ircumventing the problem of suboptimization is to use long-run profit maximization (considering the time value of money) as the sole objective. The adjective long-run indicates that this objective provides the flexibility to consider activities that do not translate into profits immediately (e.g., research and development projects) but need to do so eventually in order to be worthwhile. This approach has considerable merit. This objective is specific enough to be used conveniently, and yet it seems to be broad enough to encompass the basic goal of profit making organizations. In fact, some people believe that all other legitimate objectives can be translated into this one.
However, in actual practice, many profit-making organizations do not use this approach. A number of studies of U.S. corporations have found that management tends to adopt the goal of satisfactory profits, combined with other objectives, instead of focusing on long-run profit maximization. Typically, some of these other objectives might be to maintain stable profits, increase (or maintain) one's share of the market, provide for product diversification, maintain stable prices, improve worker morale, maintain family control of the business, and increase company prestige. Fulfilling these objectives might achieve long-run profit maximization, but the elationship may be sufficiently obscure that it may not be convenient to incorporate them all into this one objective.

ancing the workload tive. 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. Furthermore, there are additional considerations involving social responsibilities that are distinct from the profit motive. The five parties generally affected by a business firm located in a single country are (1) the owners (stockholders, etc.), who desire profits (div-
idends, stock appreciation, and so on); (2) the employees, who desire steady employment at reasonable wages; (3) the customers, who desire a reliable product at a reasonable price; (4) the suppliers, who desire integrity and a reasonable selling price for their goods; and (5) the government and hence the nation, which desire payment of fair taxes and consideration of the national interest. All five parties make essential contributions to the firm, and the firm should not be viewed as the exclusive servant of any one party for the exploitation of others. By the same token, international corporations acquire additional obligations to follow socially responsible practices. Therefore, while granting that manage ment's prime responsibility is to make profits (which ultimately benefits all five parties),
we note that its broader social responsibilities also must be recognized. OR teams typically spend a surprisingly large amount of time gathering relevant data about the problem. Much data usually are needed both to gain an accurate understanding of the problem and to provide the needed input for the mathematical model being formu-
lated in the next phase of study. Frequently, much of the needed data will not be available when the study begins, either because the information never has been kept or because what was kept is outdated or in the wrong form. Therefore, it often is necessary to install a new computer-based management information system to collect the necessary data on an on going basis and in the needed form. The OR team normally needs to enlist the assistance
of various other key individuals in the organization to track down all the vital data. Even with this effort, much of the data may be quite "soft," i.e., rough estimates based only on educated guesses. Typically, an OR team will spend considerable time trying to improve the precision of the data and then will make do with the best that can be obtained.
Examples. 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 mil-
lion increase in traffic citation revenues, and a 20 percent improvement in response times.
In assessing the appropriate objectives for this study, three fundamental objectives were identified:
1. Maintain a high level of citizen safety.
2. Maintain a high level of officer morale.
3. Minimize the cost of operations.
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 balequitably among officers in order to work toward the second objec sign an effective needle exchange program to combat the spread of the virus that causes AIDS (HIV), and succeeded in reducing the HIV infection rate among program clients by 33 percent. The key part of this study was an innovative data collection program to obtain the needed input for mathematical models of HIV transmission. This program
involved complete tracking of each needle (and syringe), including the identity, location, and date for each person receiving the needle and each person returning the needle during an exchange, as well as testing whether the returned needle was HIV- positive or HIV-negative.
An OR study done for 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. Data collection also played a key role in this study. The OR team held data requirement meetings with top Citgo management to ensure the eventual and continual quality of data. A state-of-the-art management database system was developed and installed on a mainframe computer. In cases where needed data did not exist, LOTUS 1-2-3 screens were created to help operations personnel input the data, and then the data from the personal computers (PCs) were uploaded to the mainframe computer. Before data was inputted to the mathematical model, a preloader program was used to check for data errors and inconsistencies. Initially, the preloader generated a paper 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.