operations research

Application of scientific methods to management and administration of military, government, commercial, and industrial systems. It began during World War II in Britain when teams of scientists worked with the Royal Air Force to improve radar detection of enemy aircraft, leading to coordinated efforts to improve the entire system of early warning, defense, and supply. It is characterized by a systems orientation, or systems engineering, in which interdisciplinary research teams adapt scientific methods to large-scale problems that must be modeled, since laboratory testing is impossible. Examples include resource allocation and replacement, inventory control, and scheduling of large-scale construction projects.

operations research

See management science.

operations research

the analysis of problems in business and industry involving the construction of models and the application of linear programming, critical path analysis, and other quantitative techniques

operations research [‚äp·ə′rā·shənz ri‚sərch]

(mathematics)

The mathematical study of systems with input and output from the viewpoint of optimization subject to given constraints.

(science and technology)

The application of objective and quantitative criteria to decision making previously undertaken by empirical methods.

Operations research

The application of scientific methods and techniques to decision-making problems. A decision-making problem occurs where there are two or more alternative courses of action, each of which leads to a different and sometimes unknown end result. Operations research is also used to maximize the utility of limited resources. The objective is to select the best alternative, that is, the one leading to the best result.

To put these definitions into perspective, the following analogy might be used. In mathematics, when solving a set of simultaneous linear equations, one states that if there are seven unknowns, there must be seven equations. If they are independent and consistent and if it exists, a unique solution to the problem is found. In operations research there are figuratively “seven unknowns and four equations.” There may exist a solution space with many feasible solutions which satisfy the equations. Operations research is concerned with establishing the best solution. To do so, some measure of merit, some objective function, must be prescribed.

In the current lexicon there are several terms associated with the subject matter of this program: operations research, management science, systems analysis, operations analysis, and so forth. While there are subtle differences and distinctions, the terms can be considered nearly synonymous. See Systems engineering

Methodology

The success of operations research, where there has been success, has been the result of the following six simply stated rules: (1) formulate the problem; (2) construct a model of the system; (3) select a solution technique; (4) obtain a solution to the problem; (5) establish controls over the system; and (6) implement the solution.

The first statement of the problem is usually vague and inaccurate. It may be a cataloging of observable effects. It is necessary to identify the decision maker, the alternatives, goals, and constraints, and the parameters of the system. A statement of the problem properly contains four basic elements that, if correctly identified and articulated, greatly eases the model formulation. These elements can be combined in the following general form: “Given (the system description), the problem is to optimize (the objective function), by choice of the (decision variable), subject to a set of (constraints and restrictions).”

In modeling the system, one usually relies on mathematics, although graphical and analog models are also useful. It is important, however, that the model suggest the solution technique, and not the other way around.

With the first solution obtained, it is often evident that the model and the problem statement must be modified, and the sequence of problem-model-technique-solution-problem may have to be repeated several times. The controls are established by performing sensitivity analysis on the parameters. This also indicates the areas in which the data-collecting effort should be made.

Implementation is perhaps of least interest to the theorists, but in reality it is the most important step. If direct action is not taken to implement the solution, the whole effort may end as a dust-collecting report on a shelf.

Mathematical programming

Probably the one technique most associated with operations research is linear programming. The basic problem that can be modeled by linear programming is the use of limited resources to meet demands for the output of these resources. This type of problem is found mainly in production systems, but is not limited to this area. See Linear programming

Stochastic processes

A large class of operations research methods and applications deals with stochastic processes. These can be defined as processes in which one or more of the variables take on values according to some, perhaps unknown, probability distribution. These are referred to as random variables, and it takes only one to make the process stochastic.

In contrast to the mathematical programming methods and applications, there are not many optimization techniques. The techniques used tend to be more diagnostic than prognostic; that is, they can be used to describe the “health” of a system, but not necessarily how to “cure” it.

Scope of application

There are numerous areas where operations research has been applied. The following list is not intended to be all-inclusive, but is mainly to illustrate the scope of applications: optimal depreciation strategies; communication network design; computer network design; simulation of computer time-sharing systems; water resource project selection; demand forecasting; bidding models for offshore oil leases; production planning; classroom size mix to meet student demand; optimizing waste treatment plants; risk analysis in capital budgeting; electric utility fuel management; optimal staffing of medical facilities; feedlot optimization; minimizing waste in the steel industry; optimal design of natural-gas pipelines; economic inventory levels; optimal marketing-price strategies; project management with CPM/PERT/GERT; air-traffic-control simulations; optimal strategies in sports; optimal testing plans for reliability; optimal space trajectories. See GERT, Inventory control, PERT