Operations Research Research Paper

The key elements of an operations research approach are the following:

(a) Formulate a problem to be studied.

(b) Construct a mathematical model that represents the system under study.

(c) Derive a solution from this model.

(d ) Test the model and the solution derived from it.

 (e) Establish rules for modifying the solution under specified system changes.

( f ) Implement the solution.

1.1 Evolution Of Operations Research

As the term implies, ‘operations research’ is concerned with research about operations. One of the earliest examples of OR are the Lanchester equations published during World War I. Frederick Lanchester was an aeronautical engineer who sought to translate complex military strategies into mathematical formulas. His book, Aircraft in Warfare, published in 1916, included the ‘N square’ law relating victory, numerical superiority, and weapon superiority for situations in which all units of two opposing forces engage simultaneously. Lanchester concluded that, under these assumed conditions, numerical superiority was relatively more important than weapon system accuracy, and that available combatant forces were most effective if deployed in a single force that split the enemy into two or more component units.

During World War II, the British government employed operations analysts to determine whether quantitative assessment of sensitive military data could produce recommendations that would enhance the effectiveness of British military operations. Numerous successes followed. For example, data analyzed from the Eighth Bomber Command in England in 1942 led to several operational modifications: Simultaneous release of bombs by all bombardiers instead of individualized release by each bombardier; decrease in the number of aircraft per formation from 18–36 to 12–14; and salvoing of bombs instead of presetting them to release in a string produced startling results. In 1942, less than 15 percent of bombs dropped landed within 1,000 feet of their aim point. This figure rose to more than 60 percent in 1944 after the operational modifications were adopted.

This example illustrates a number of the characteristics of OR: Systematic analysis of operational data led to the recommendation of ‘counter-intuitive’ recommendations that ran contrary to the experiences of the operational experts, and that, once implemented, yielded greatly improved overall system effectiveness.

The British establishment of ‘operational research’ units in the early 1940s were replicated by the USA during and immediately after World War II. The US Navy formed an Operations Evaluation Group, and this organization was later incorporated into the Center for Naval Analyses which performs OR and related studies for the Navy. The US Air Force, with the help of Donald Douglas of Douglas Aviation, established The RAND Corporation which has played a leading role in the creation and application of OR techniques since the 1940s. And the Weapons System Evaluation Group, reporting to the Joint Chiefs of

Staff, later became a key part of the Institute for Defense Analysis. (The US Army’s Operations Research Office operated independently for a number of years, but later became a ‘project’ within The RAND Corporation.)

In the late 1940s and early 1950s, it was realized on both sides of the Atlantic that these quantitative techniques could be applied fruitfully to industrial as well as to military operations. Initially, some of these techniques were employed by management consultants and industrial engineers to improve industrial efficiency through quality control, time-and-motion studies, and marketing analyses. But the 1950s saw the proliferation of sophisticated mathematical methods that greatly enhanced the analytical power, academic prestige, and organizational applicability of OR. These techniques included mathematical programming (‘linear,’ ‘nonlinear,’ and ‘dynamic’) that derived optimal allocation solutions under constraints; queuing or waiting line theory; advances in game theory, and other aspects of competitive decision-making; and the early stages of computer simulation methods.

Robert McNamara, who was a graduate of the Harvard Business School and had become familiar with these approaches as a senior executive at the Ford Motor Company, was named Secretary of Defense by President Kennedy in 1961, just after having been appointed as president of Ford. McNamara formed a ‘systems analysis office’ at the Pentagon, headed by Alain Enthoven, a prominent economist who had applied OR techniques at The RAND Corporation. This was the first time that OR was legitimized as an important method of analysis in US defense policy. Moreover, McNamara urged his colleagues in domestic agencies to consider the application of these techniques.

In the 1960s, the Johnson administration established the Great Society, a set of federally-funded initiatives to enhance the well-being of individuals on the bottom rungs of American society. Such domestic programs as health policy and management began to receive extensive political and then analytical attention. Simultaneously, significant numbers of military analysts active in OR development and its applications became disaffected with the escalation of American military involvement in Vietnam and sought to apply their analytical skills in nonmilitary areas. Collectively, these developments produced a third wave of OR application: domestic, government-funded programs involving social, environmental, transportation, and criminal justice policy, to name some of the more prominent areas of work.

By the 1970s, operations research groups could be found not only in the major branches of the military services and in large numbers of corporations. They were also prevalent in federal and state agencies concerned with health and human services, environmental regulation, transportation, and numerous other areas of specialization. And they were the focal point for work among many of the nongovernmental organizations that arose during this period to support and/or critique government programs.

Another noteworthy feature of the application of OR techniques is that, historically, they were conducted largely by teams of analysts rather than by individual analysts. OR became associated widely with multidisciplinary, team problem-solving.

1.2 Academic Bases Of Operations Research

The burgeoning literature on the collection of OR techniques was both a product of, and a stimulus to, academically-based graduate programs in the field. Originally, OR was represented in units within departments of industrial engineering, or groups within graduate schools of business. In some cases, separate OR departments were established on faculties of colleges of engineering, or as part of applied mathematics and statistics departments. These disciplines— mathematics and statistics, engineering, and business—became the principal bases for university advancement of the field. They were joined by economics as the applicability of game theory—formal consideration of competitive situations emphasizing the decision-making processes of the adversaries—became widely used. And, in the 1980s, as rational choice theory, a derivative of game theory, took hold in political science departments, these units also became the home for elements of operations research teaching and research.

A wide variety of US educational institutions became prominent in the teaching and research of OR. The Massachusetts Institute of Technology, the Wharton School of the University of Pennsylvania, Carnegie Mellon University, Johns Hopkins University, Case Western Reserve University, the University of California at Berkeley, and Stanford University, among others, became known internationally for the quality of their OR programs. These academic activities were matched by important programs at major universities in Europe, Israel, Japan, and elsewhere– including Lancaster in the United Kingdom, Louvain in Belgium, and Tel Aviv and Tokyo Universities.

Not unexpectedly, a corollary of these academic programs was the establishment of academic societies whose purposes were to publish the latest research in the field, to promote professional networks that would enhance interaction among specialists, and to serve as a recruiting ground for placement in academic institutions, corporations, government agencies, and nonprofit organizations.

Most noteworthy, the Operations Research Society of America (ORSA) focused on mathematical advances in the field and its many applications in the military area. A separate society, the Military Operations Research Society (MORS), was devoted exclusively to this sector. By contrast, as larger numbers began to utilize OR for industrial applications, The Institute of Management Sciences (TIMS) was organized to meet the needs of those interested in corporate environments. Eventually, in the 1990s, ORSA and TIMS merged into the Institute for Operations Research and the Management Sciences (INFORMS), reflecting the growing interaction among OR in the military, corporate, governmental, and nonprofit sectors.

2. Major Classes Of Operations Research Applications

Over the decades, clusters of problems have proven to be especially amenable to treatment by operations research. They fall into the following six categories of model: inventory, allocation, waiting time, replacement, competitive, and computer simulation.

2.1 Inventory Models

Inventory models deal with the time at which orders for certain goods are to be placed, and the quantity of the order. The research problem concerns ways of optimizing these decisions, taking into account the cost of obtaining the goods, the cost of holding a unit in inventory, and the cost of shortages. More advanced inventory models deal with situations in which there are restrictions on production facilities, storage facilities, time and/or money. For several decades, more OR effort was focused on inventory models than any other area of application.

2.2 Allocation Models

This class of problems concerns a number of activities to be performed, several alternative methods for carrying them out, and a constraint that the resources or facilities available do not permit each activity to be performed in the most effective way. The analytical challenge of these problems is to combine activities and resources to optimize overall effectiveness. Of particular relevance to this work is the applicability of ‘linear programming’—a class of optimization problems that address the interaction of many variables subject to a set of constraints. Subsequent advances in ‘nonlinear’ and ‘dynamic’ programming permitted the tackling of more complex assignment problems where a number of the constraints themselves vary with time.

2.3 Waiting Time Models

A third class of problems that have long been addressed by operations researchers have dealt with waiting times—when either units requiring service or facilities available for providing service wait, or stand idle. These phenomena have been the subject of a whole class of mathematical formulations known collectively as ‘queuing theory.’ In these problems, the OR analyst is faced with determining the optimal number of service facilities, the optimal arrival rate or times of arrival, or both.

2.4 Replacement Models

There are a class of problems concerned with the prediction of costs for a group of items that have a probability distribution of lifespan. Decision-makers must choose between operating aging equipment or incurring the cost of replacing old equipment with new. At what age does the saving from use of new equipment compensate for its initial cost? For many years, OR analysts have developed methods for predicting costs based on the probability distribution of lifespans. These are classified as replacement models.

2.5 Competitive Models

Unlike the models cited above, which deal with issues internal to the organization, competitive models are concerned with situations in which the effectiveness of decisions by one party are dependent on decisions by another party. At the core of these models is the theory of games which assesses the strategies that players should adopt to ‘win,’ however that is measured. A game is competitive if there is an end-state that each player desires but not all can obtain. The players are in conflict relative to the goal. Each player has a set of possible choices which eventually bring the game to the end state.

2.6 Computer Simulation Models

With the development of advanced computer technology, OR analysts began to use these machines to build mathematical models that could simulate real-world problem situations. Then, by varying the assumptions of the model, the analysts could determine the sensitivity of the model to different parameters and conditions. The power of this technique has permitted highly complex systems to be evaluated carefully in relatively short periods of time.

3. The Intellectual Challenges

Operations research techniques have advanced enormously over the almost six decades of their development since the 1940s. The mathematical rigor of the techniques is especially impressive. Its application in both the military sectors and the commercial sectors has been extensive. Areas of government/social action and of public policy more generally have been less amenable to contributions from the operations researcher. This is because OR analysts are committed to the studying of a complex problem through the lens of a mathematical model that can be tested in quantitative terms. But a number of broader social and political issues reflect deep political struggles, and adjustments in human behavior that are exceedingly difficult to quantify. Many military operations and corporate activities have agreed widely upon quantitative measures of effectiveness.

Here, the intellectual power of OR techniques can be enormously helpful. In public policy issues, where a clash of values is often at the heart of the matter (e.g., should the US Department of Energy be twice its size, or eliminated?), quantitative models appear to be of limited value in furthering the identification of optimal choices.

A second challenge is to make OR applicable in the age of the information technology revolution. This revolution has permitted vast amounts of information to be available to people all over the globe with access to the World Wide Web. Will this revolution strengthen or marginalize the role of OR as a tool of executive decision-making? Practitioners of these techniques must tailor their models as well as their areas of application to take advantage of this revolution, or they will be left behind by new analytical approaches that are found to be more ‘user friendly’ for these incredibly powerful technological devices.

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