This is hardly a matter of surprise when one considers that they both share many of the same objectives, techniques and application areas. Most of the O. During the next thirty or so years the pace of development of fundamentally new O. However, there has been a rapid expansion in 1 the breadth of problem areas to which O.
Today, operations research is a mature, well-developed field with a sophisticated array of techniques that are used routinely to solve problems in a wide range of application areas. This chapter will provide an overview of O. A brief review of its historical origins is first provided. This is followed by a detailed discussion of the basic philosophy behind O. Broadly speaking, an O. The emphasis of this chapter is on the first and third steps.
The second step typically involves specific methodologies or techniques, which could be quite sophisticated and require significant mathematical development. Several important methods are overviewed elsewhere in this handbook.
The reader who has an interest in learning more about these topics is referred to one of the many excellent texts on O.
While there is no clear date that marks the birth of O. The impetus for its origin was the development of radar defense systems for the Royal Air Force, and the first recorded use of the term Operations Research is attributed to a British Air Ministry official named A. Rowe who constituted teams to do "operational researches" on the communication system and the control room at a British radar station. The studies had to do with improving the operational efficiency of systems an objective which is still one of the cornerstones of modern O.
This new approach of picking an "operational" system and conducting "research" on how to make it run more efficiently soon started to expand into other arenas of the war.
Perhaps the most famous of the groups involved in this effort was the one led by a physicist named P. Blackett which included physiologists, mathematicians, astrophysicists, and even a surveyor.
This multifunctional team focus of an operations research project group is one that has carried forward to this day. Its first presence in the U. Like Blackett in Britain, Morse is widely regarded as the "father" of O. These ranged from short-term problems such as scheduling and inventory control to long-term problems such as strategic planning and resource allocation. George Dantzig, who in developed the simplex algorithm for Linear Programming LP , provided the single most important impetus for this growth.
To this day, LP remains one of the most widely used of all O. The second major impetus for the growth of O. The simplex method was implemented on a computer for the first time in , and by such implementations could solve problems with about constraints. Today, implementations on powerful workstations can routinely solve problems with hundreds of thousands of variables and constraints. Moreover, the large volumes of data required for such problems can be stored and manipulated very efficiently.
Once the simplex method had been invented and used, the development of other methods followed at a rapid pace. The next twenty years witnessed the development of most of the O. The scientists who developed these methods came from many fields, most notably mathematics, engineering and economics. It is interesting that the theoretical bases for many of these techniques had been known for years, e. However, the period from to was when these were formally unified into what is considered the standard toolkit for an operations research analyst and successfully applied to problems of industrial significance.
The following section describes the approach taken by operations research in order to solve problems and explores how all of these methodologies fit into the O. A common misconception held by many is that O. While it is true that it uses a variety of mathematical techniques, operations research has a much broader scope. It is in fact a systematic approach to solving problems, which uses one or more analytical tools in the process of analysis. Perhaps the single biggest problem with O.
This is an unfortunate consequence of the fact that the name that A. Rowe is credited with first assigning to the field was somehow never altered to something that is more indicative of the things that O. Sometimes O.
Compounding this issue is the fact that there is no clear consensus on a formal definition for O. For instance, C. Churchman who is considered one of the pioneers of O. This is indeed a rather comprehensive definition, but there are many others who tend to go over to the other extreme and define operations research to be that which operations researchers do a definition that seems to be most often attributed to E.
Regardless of the exact words used, it is probably safe to say that the moniker "operations research" is here to stay and it is therefore important to understand that in essence, O. The key here is that O. However, O. One should thus view O. However, the final decision is always left to the human being who has knowledge that cannot be exactly quantified, and who can temper the results of the analysis to arrive at a sensible decision. Given that O. To achieve this, the so-called O.
Tying each of these steps together is a mechanism for continuous feedback; Figure 1 shows this schematically. While most of the academic emphasis has been on Steps 4, 5 and 6, the reader should bear in mind the fact that the other steps are equally important from a practical perspective. Indeed, insufficient attention to these steps has been the reason why O. Each of these steps is now discussed in further detail.
To illustrate how the steps might be applied, consider a typical scenario where a manufacturing company is planning production for the upcoming month. The company makes use of numerous resources such as labor, production machinery, raw materials, capital, data processing, storage space, and material handling equipment to make a number of different products which compete for these resources.
The products have differing profit margins and require different amounts of each resource. Many of the resources are limited in their availability. Additionally, there are other complicating factors such as uncertainty in the demand for the products, random machine breakdowns, and union agreements that restrict how the labor force can be used. Given this complex operating environment, the overall objective is to plan next month's production so that the company can realize the maximum profit possible while simultaneously ending up in a good position for the following month s.
As an illustration of how one might conduct an operations research study to address this situation, consider a highly simplified instance of a production planning problem where there are two main product lines widgets and gizmos, say and three major limiting resources A, B and C, say for which each of the products compete. Each product requires varying amounts of each of the resources and the company incurs different costs labor, raw materials etc.
The objective of the O. Typically, the team will have a leader and be constituted of members from various functional areas or departments that will be affected by or have an effect upon the problem at hand. In the orientation phase, the team typically meets several times to discuss all of the issues involved and to arrive at a focus on the critical ones.
This phase also involves a study of documents and literature relevant to the problem in order to determine if others have encountered the same or similar problem in the past, and if so, to determine and evaluate what was done to address the problem.
This is a point that often tends to be ignored, but in order to get a timely solution it is critical that one does not reinvent the wheel.
In many O. The aim of the orientation phase is to obtain a clear understanding of the problem and its relationship to different operational aspects of the system, and to arrive at a consensus on what should be the primary focus of the project. In addition, the team should also have an appreciation for what if anything has been done elsewhere to solve the same or similar problem. In our hypothetical production planning example, the project team might comprise members from engineering to provide information about the process and technology used for production , production planning to provide information on machining times, labor, inventory and other resources , sales and marketing to provide input on demand for the products , accounting to provide information on costs and revenues , and information systems to provide computerized data.
Of course, industrial engineers work in all of these areas. In addition, the team might also have shopfloor personnel such as a foreman or a shift supervisor and would probably be led by a mid-level manager who has relationships with several of the functional areas listed above. At the end of the orientation phase, the team might decide that its specific objective is to maximize profits from its two products over the next month.
It may also specify additional things that are desirable, such as some minimum inventory levels for the two products at the beginning of the next month, stable workforce levels, or some desired level of machine utilization.
A clear definition of the problem has three broad components to it. The first is the statement of an unambiguous objective. Along with a specification of the objective it is also important to define its scope, i. While a complete system level solution is always desirable, this may often be unrealistic when the system is very large or complex and in many cases one must then focus on a portion of the system that can be effectively isolated and analyzed.
In such instances it is important to keep in mind that the scope of the solutions derived will also be bounded. Some examples of appropriate objectives might be 1 "to maximize profits over the next quarter from the sales of our products," 2 "to minimize the average downtime at workcenter X," 3 "to minimize total production costs at Plant Y," or 4 "to minimize the average number of late shipments per month to customers.
The second component of problem definition is a specification of factors that will affect the objective. These must further be classified into alternative courses of action that are under the control of the decision maker and uncontrollable factors over which he or she has no control.
For example, in a production environment, the planned production rates can be controlled but the actual market demand may be unpredictable although it may be possible to scientifically forecast these with reasonable accuracy. The idea here is to form a comprehensive list of all the alternative actions that can be taken by the decision maker and that will then have an effect on the stated objective.
Eventually, the O. The third and final component of problem definition is a specification of the constraints on the courses of action, i. As an example, in a production environment, the availability of resources may set limits on what levels of production can be achieved.
This is one activity where the multifunctional team focus of O. In general, it is a good idea to start with a long list of all possible constraints and then narrow this down to the ones that clearly have an effect on the courses of action that can be selected.
The aim is to be comprehensive yet parsimonious when specifying constraints. Continuing with our hypothetical illustration, the objective might be to maximize profits from the sales of the two products. The alternative courses of action would be the quantities of each product to produce next month, and the alternatives might be constrained by the fact that the amounts of each of the three resources required to meet the planned production must not exceed the expected availability of these resources.
An assumption that might be made here is that all of the units produced can be sold. Note that at this point the entire problem is stated in words ; later on the O. One of the major driving forces behind the growth of O. This has been a great boon, in that O. Simultaneously, this has also made things difficult because many companies find themselves in the situation of being data-rich but information-poor. In other words, even though the data is all present "somewhere" and in "some form," extracting useful information from these sources is often very difficult.
This is one of the reasons why information systems specialists are invaluable to teams involved in any nontrivial O. Data collection can have an important effect on the previous step of problem definition as well as on the following step of model formulation. Finally, based upon prior commitments and historical data on resource availability, it might be determined that in the next month there will be units of resource 1, units of resource 2 and units of resource 3 available for use in producing the two products.
It should be emphasized that this is only a highly simplified illustrative example and the numbers here as well as the suggested data collection methods are also vastly simplified. In practice, these types of numbers can often be very difficult to obtain exactly, and the final values are typically based on extensive analyses of the system and represent compromises that are agreeable to everyone on the project team.
As an example, a marketing manager might cite historical production data or data from similar environments and tend to estimate resource availability in very optimistic terms. On the other hand, a production planner might cite scrap rates or machine downtimes and come up with a much more conservative estimate of the same.
The final estimate would probably represent a compromise between the two that is acceptable to most team members. There is no single "correct" way to build a model and as often noted, model-building is more an art than a science.
The key point to be kept in mind is that most often there is a natural trade-off between the accuracy of a model and its tractability. At the one extreme, it may be possible to build a very comprehensive, detailed and exact model of the system at hand; this has the obviously desirable feature of being a highly realistic representation of the original system.
While the very process of constructing such a detailed model can often aid immeasurably in better understanding the system, the model may well be useless from an analytical perspective since its construction may be extremely time-consuming and its complexity precludes any meaningful analysis. At the other extreme, one could build a less comprehensive model with a lot of simplifying assumptions so that it can be analyzed easily.
However, the danger here is that the model may be so lacking in accuracy that extrapolating results from the analysis back to the original system could cause serious errors. Clearly, one must draw a line somewhere in the middle where the model is a sufficiently accurate representation of the original system, yet remains tractable.
Knowing where to draw such a line is precisely what determines a good modeler, and this is something that can only come with experience. In the formal definition of a model that was given above, the key word is "selective.
Physical Models : These are actual, scaled down versions of the original. Examples include a globe, a scale-model car or a model of a flow line made with elements from a toy construction set. In general, such models are not very common in operations research, mainly because getting accurate representations of complex systems through physical models is often impossible. Analogic Models : These are models that are a step down from the first category in that they are physical models as well, but use a physical analog to describe the system, as opposed to an exact scaled-down version.
Perhaps the most famous example of an analogic model was the ANTIAC model the acronym stood for anti-a utomatic- c omputation which demonstrated that one could conduct a valid operations research analysis without even resorting to the use of a computer. In this problem the objective was to find the best way to distribute supplies at a military depot to various demand points. Such a problem can be solved efficiently by using techniques from network flow analysis.
However the actual procedure that was used took a different approach. An anthill on a raised platform was chosen as an analog for the depot and little mounds of sugar on their own platforms were chosen to represent each demand point.
The network of roads connecting the various nodes was constructed using bits of string with the length of each being proportional to the actual distance and the width to the capacity along that link. An army of ants was then released at the anthill and the paths that they chose to get to the mounds of sugar were then observed. After the model attained a steady state, it was found that the ants by virtue of their own tendencies had found the most efficient paths to their destinations!
One could even conduct some postoptimality analysis. For instance, various transportation capacities along each link could be analyzed by proportionately varying the width of the link, and a scenario where certain roads were unusable could be analyzed by simply removing the corresponding links to see what the ants would then do. This illustrates an analogic model. More importantly, it also illustrates that while O.
Computer Simulation Models : With the growth in computational power these models have become extremely popular over the last ten to fifteen years. A simulation model is one where the system is abstracted into a computer program. Typically, such software has syntax as well as built-in constructs that allow for easy model development. Very often they also have provisions for graphics and animation that can help one visualize the system being simulated. Simulation models are analyzed by running the software over some length of time that represents a suitable period when the original system is operating under steady state.
The inputs to such models are the decision variables that are under the control of the decision-maker. These are treated as parameters and the simulation is run for various combinations of values for these parameters. At the end of a run statistics are gathered on various measures of performance and these are then analyzed using standard techniques.
The decision-maker then selects the combination of values for the decision variables that yields the most desirable performance. Simulation models are extremely powerful and have one highly desirable feature: they can be used to model very complex systems without the need to make too many simplifying assumptions and without the need to sacrifice detail.
They must make decisions about financing, where to build a plant, how much of a product to manufacture, how many people to hire, and so on. Often, the factors that make up business issues are complicated, and they may be difficult to comprehend. Operations research is a way to deal with these thorny problems. Operations research is a quantitative approach that solves problems, using a number of mathematical techniques.
It is helpful to use operations research when you're trying to make decisions but the conditions are uncertain, and when differing objectives are in conflict with each other. These mathematical techniques used in operations research help managers do their jobs more effectively:.
Managers use techniques of operations research to maintain better control over their subordinates. This is possible because operations research provides a basis in which to establish standards of performance and ways to measure productivity. Reporting deviations from standards enables managers to identify problem areas and to take corrective action.
The mathematical models of operations research allow people to analyze a greater number of alternatives and constraints than would usually be possible, if they were to use only an intuitive approach.
Using operations research, it is easier to analyze multiple alternatives, which results in greater confidence in the optimal choice. Operations research analysis blends together the objectives of different departments.
For example, operations research coordinates the aims of the marketing department with the schedules of the production department. The mathematical formulas used in operations research can increase productivity, as they offer a greater number of optimal choices of inventory mix, plant machine utilization, factory size, manpower planning and implementing new technologies.
Operations research has evolved into a standard framework that's used for identifying and solving problems. The steps are as follows:. A good example of how to use operations research analysis is to consider the plight of farmer Jones. He must decide how many acres of corn and wheat to plant this year.
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