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Operations Research Models and Methods
Models Section
What is Operations Research?
The Operations Research Process

The goal of operations research is to provide a framework for constructing models of decision-making problems, finding the best solutions with respect to a given measure of merit, and implementing the solutions in an attempt to solve the problems. On this page we review the steps of the OR Process that leads from a problem to a solution. The problem is a situation arising in an organization that requires some solution. The decision maker is the individual or group responsible for making decisions regarding the solution. The individual or group called upon to aid the decision maker in the problem solving process is the analyst.

Recognize the Problem

Decision making begins with a situation in which a problem is recognized. The problem may be actual or abstract, it may involve current operations or proposed expansions or contractions due to expected market shifts, it may become apparent through consumer complaints or through employee suggestions, it may be a conscious effort to improve efficiency or a response to an unexpected crisis. It is impossible to circumscribe the breadth of circumstances that might be appropriate for this discussion, for indeed problem situations that are amenable to objective analysis arise in every area of human activity.

The figure shows the situation with vague outlines because most problems are poorly defined in their original conception. Historical data describing organizational operations and performance may be present in various forms. The data may be immediately relevant to the situation or investigations may reveal the need for additional data collection.

Formulate the Problem

The first analytical step of the solution process is to formulate the problem in more precise terms.

At the formulation stage, statements of objectives, constraints on solutions, appropriate assumptions, descriptions of processes, data requirements, alternatives for action and metrics for measuring progress are introduced. Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. The analyst is usually not the decision maker and may not be part of the organization, so care must be taken to get agreement on the exact character of the problem to be solved from those who perceive it. There is little value to either a poor solution to a correctly formulated problem or a good solution to one that has been incorrectly formulated.

We show an arc from the statement directly back to situation because careful examination of a problem often leads to solutions without complex mathematics. For complex situations or for problems involving uncertainty, the OR process usually continues to the next step.

Construct a Model

In the above figure we show the problem statement with more definition than the situation; however, greater simplification is still necessary before a computer-based analysis can be performed. This is achieved by constructing a model.

A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. Although the analyst would hope to study the broad implications of the problem using a systems approach, a model cannot include every aspect of a situation. A model is always an abstraction that is, by necessity, simpler than the reality. Elements that are irrelevant or unimportant to the problem are to be ignored, hopefully leaving sufficient detail so that the solution obtained with the model has value with regard to the original problem. The statements of the abstractions introduced in the construction of the model are called the assumptions. It is important to observe that assumptions are not necessarily statements of belief, but are descriptions of the abstractions used to arrive at a model. The appropriateness of the assumptions can be determined only by subsequent testing of the model’s validity. Models must be both tractable -- capable of being solved, and valid -- representative of the true situation. These dual goals are often contradictory and are not always attainable. We have intentionally represented the model with well-defined boundaries to indicate its relative simplicity.

Find a Solution

The next step in the process is to solve the model to obtain a solution to the problem. It is generally true that the most powerful solution methods can be applied to the simplest, or most abstract, model.

Here tools available to the analyst are used to obtain a solution to the mathematical model. Some methods can prescribe optimal solutions while other only evaluate candidates, thus requiring a trial and error approach to finding an acceptable course of action. To carry out this task the analyst must have a broad knowledge of available solution methodologies. It may be necessary to develop new techniques specifically tailored to the problem at hand. A model that is impossible to solve may have been formulated incorrectly or burdened with too much detail. Such a case signals the return to the previous step for simplification or perhaps the postponement of the study if no acceptable, tractable model can be found.

Of course, the solution provided by the computer is only a proposal. An analysis does not promise a solution but only guidance to the decision maker. Choosing a solution to implement is the responsibility of the decision maker and not the analyst. The decision maker may modify the solution to incorporate practical or intangible considerations not reflected in the model.

Establish the Procedure

Once a solution is accepted a procedure must be designed to retain control of the implementation effort. Problems are usually ongoing rather than unique. Solutions are implemented as procedures to be used repeatedly in an almost automatic fashion under perhaps changing conditions. Control may be achieved with a set of operating rules, a job description, laws or regulations promulgated by a government body, or computer programs that accept current data and prescribe actions.

Once a procedure is established (and implemented), the analyst and perhaps the decision maker are ready to tackle new problems, leaving the procedure to handle the required tasks. But what if the situation changes? An unfortunate result of many analyses is a remnant procedure designed to solve a problem that no longer exists or which places restrictions on an organization that are limiting and no longer appropriate. Therefore, it is important to establish controls that recognize a changing situation and signal the need to modify or update the solution.

Implement the Solution

A solution to a problem usually implies changes for some individuals in the organization. Because resistance to change is common, the implementation of solutions is perhaps the most difficult part of a problem solving exercise. Some say it is the most important part. Although not strictly the responsibility of the analyst, the solution process itself can be designed to smooth the way for implementation. The persons who are likely to be affected by the changes brought about by a solution should take part, or at least be consulted, during the various stages involving problem formulation, solution testing, and the establishment of the procedure.

The OR Process

Combining the steps we obtain the complete OR process. In practice, the process may not be well defined and the steps may not be executed in a strict order. Rather there are many loops in the process, with experimentation and observation at each step suggesting modifications to decisions made earlier. The process rarely terminates with all the loose ends tied up. Work continues after a solution is proposed and implemented. Parameters and conditions change over time requiring a constant review of the solution and a continuing repetition of portions of the process.

It is particularly important to test the validity of the model and the solution obtained. Are the computations being performed correctly? Does the model have relevance to the original problem? Do the assumptions used to obtain a tractable model render the solution useless? These questions must be answered before the solution is implemented in the field.

There are a number of ways to to test a solution. The simplest determines whether the solution makes sense to the decision maker. Solutions obtained by quantitative studies may not be predictable but they are often not too surprising. Other testing procedures include sensitivity analysis, the use of the model under a variety of conjectured conditions including a range of parameter values, and the use of the model with historical data.

If the testing determines that the solution or model is inappropriate, the process may return to the formulation step to derive a more complex model embodying details of the problem formerly eliminated through abstractions. This may, of course, render the model intractable, and it may be necessary to conclude that an acceptable quantitative analysis is out of reach. It may also be possible to construct a less abstract model and accept less powerful solution methods. In many cases, finding a good or an acceptable solution is almost as satisfactory as obtaining an optimal one. This is particularly true when the quality of the input data is low or when important parameters cannot be specified with certainty.

Different organizations have different ways of approaching a problem, and many do not admit quantitative techniques or analysts as part of the process. It is important to note, however, that in today’s world problems do arise and decisions are made (even inaction is a decision made by default). Many problems are solved in the first step of our process, but there will be cases when complexity, variability or uncertainty suggest that further analysis is necessary. In these cases, the Operations Research process will assist problem solving and decision making.

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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved