Operation research

Control of nitrogen oxides ia aircraft exhaust is of increa sing concern because nitrogen oxides react with ozone ia the protective layer of atmosphere which exists ia the altitude region where supersonic aircraft operate. Research is under way to produce a new type of combustor which minimizes NO formation. It is an essential component of the advanced propulsion unit needed for a successflil supersonic transport fleet. 

The ease with which nuclei can be produced by contact nucleation is a clear indication that this mechanism is dominant in many industrial operations. Research on contact nucleation is continuing with the objective of building an understanding of the phenomenon that will allow its successful inclusion in models describing commercial systems. 

Control of Crushers Lower-grade raw materials, higher energy costs, larger-scale operations, and more complex, capital-intensive plants make automatic control of size-reduction equipment more important (Suominen, 21st International Symposium—Applications of Computers and Operations Research in the Mineral Industry, 1011-1018). Benefits are increased productivity, process stability and safety, improved recoveiy of mineral values, and reduced costs [Horst and Enochs, Engineering Mining J., 181(6), 69-171 (1980)]. 

In 1960 the author was charged with the review and improvement of the ethylene oxide technology of Union Carbide Corporation (UCC). A historic overv iew revealed some interesting facts. The basic French patent of Lefort (1931,1935) for ethylene oxide production was purchased by UCC in 1936. In 1937, a pilot-plant was operated and commercial production started in 1938. By 1960, UCC s production experience was several hundred reactor-years. This was expressed as the sum of the number of production reactors, each multiplied by the number of years it had been in operation. Research and development had continued since the purchase of the original patent and the total number of people involved in ethylene oxide related research at one time reached one hundred. 

FTAP The Eault Tree Analysis Erogram (Willie, 1978, Section 6.4, and di.stribution disk) is a cutset generation code developed at the University of California, Berkeley Operation Research I iter. FTAP is unique in offering the user a choice of three processing methods to >wn. 

Pande, P. K. et al., 1975, Computerized Fault Tree Analysis TREEL and MICSUP, Operations Research Center, U.C. Berkeley., ORC 75.3. 

Willie, R. R., 1978. Computer Aided Fault Tree Analysis," Operations Research Center, of Ca ifornia Berkeley. 

Process decision program chart - used in operations research... 

Pattemotte, P. H., Verhagen, L. H. J. M. (1979). Human Operator Research with a Simulated Distillation Process. Ergonomics 22,19-28. 

This chapter consists of a series of mostly self-contained sections discussing several generalized CA models reversible CA, coupled-map lattices, quantum CA, reaction-diffusion models, immunologically motivated CA models, random Boolean networks, sandpile models (in the context of self-organized criticality), and structurally dynamic CA (in which the temporal evolution of the value of individual sites of a lattice are dynamically linked to an evolving lattice structure), and simple CA models of combat (that are increasingly finding their way into the military operations research community). 

Thus, decision-making is an important aspect of operations research. Analysis of the existing alternatives available contributes information, and guides the authority responsible for an operation in effecting... 

Operations research is a scientific approach that draws on the other sciences, whether exact or applied (mathematics, physics, economics, etc.), and on known calculation procedures in order to 1... 

Operations research has occasionally been defined as the art of giving bad answers to questions that would otherwise receive worse answers. The significance of this definition is best realized by those who have looked seriously at the world about them. 

The pursuit of operations research consists of (a) the judgment phase (what are the problems ), (b) the research phase (how to solve these problems), and (c) the decision phase (how to act on the finding and eliminate the problems). These phases require the evaluation of objectives, analysis of an operation and the collection of evidence and resources to be committed to the study, the (mathematical) formulation of problems, the construction of theoretical models and selection of measures of effectiveness to test the models in practice, the making and testing of hypotheses as to how well a model represents the problem, prediction, refinement of the model, and the interpretation of results (usually as possible alternatives) with their respective values (payoff). The decision-maker generally combines the findings of the... 

To a considerable extent, operations research as a formal discipline is occupied with the construction of models. This is closely related to the analysis of alternatives for decision-making. It is generally assumed that it is preferable to have a model to represent an operation, even though it is oversimplified and perhaps imperfect, than to have none. A model may be purely logical or it may be a physical analogue. A mathematical formula is an example of the former, a wind tunnel an illustration of the latter. In both cases, the model provides a ooherent framework for coping with the complexities of a problem. 

An operations research problem may be remedial in that it seeks to... 

Thomas L. Saaty, Mathematical Methods of Operation Research, McGraw-Hill Book Co, New York, 1959. 

One observes that operations research tends to regard a problem within the operation as a whole in order to avoid overlooking significant factors that affect those parts of the operation relating to the problem. 

An interesting problem solved by operations research methods is that of the flow of traffic through the New York tunnels. The presence of toll booths causes congestion of traffic at the entrances and exits of tunnels. Economical operation of the toll booths necessitates that not all booths be open at all times. By studying the statistics of the traffic, a schedule was developed indicating the number of booths to be operated at different times of the day. In this manner congestion was alleviated, and the frequency of traffic jams was reduced considerably.8... 

Another illustration of operations research is the use of linear programming techniques (Section 5.14) to obtain optimal mixtures of gasoline ingredients that will produce a result suitable for different climatic conditions and subject to demand constraints on a long-range basis. 

An illustration of an operations research problem for which no model is yet available is the following, which occurs in queueing theory.4 Everyone has observed, and perhaps been displeased to notice, persons in a waiting line, before a theater box-office, for example, who arrive after the observer s arrival, but who go to persons in front to solicit their cooperation in obtaining service. Thus, an... 

Leslie 0. Edie, Traffic Delays at Toll Booths, Operations Research, 2, 107-38 (1954). 

The problems of operations research have stimulated new developments in several mathematical fields various aspects of game theory, stochastic processes, the calculus of variations, graph theory, and numerical analysis, to name a few. 

So far operations research has utilized the talents of individuals from a wide spectrum of fields ranging from chess players and physical and social scientists to mathematicians, pure and applied. Imagination and a good background in technical excellence are the basic elements in this choice of individuals. A significant consequence of all this is an opportunity for broad intellectual contacts and cross-fertilization of ideas in many diverse fields. 

There are, at present, eleven operations research societies in different countries. There is also an International Federation of Operations Research Societies (IFORS). In addition to the journals published by these societies, a journal called International Abstracts in Operations Research has made its appearance. 

Interest in developing and refining the mathematical methods of operations research has become intensified and sophisticated. Attention is generally given to a priori upper bounds on the number of solutions of a problem, the existence and uniqueness of solutions,... 

Whatever model is used to describe an operations research problem, be it a differential equation, a mathematical program, or a stochastic process, there is a natural tendency to seek a maximum or a minimum with a certain purpose in mind. Thus, one often finds optimization problems imbedded in the models of operations research. 

We shall start out with elementary general topological considerations of flow by studying network flow. We shall follow this by a variety of models from operations research that illustrate analytical methods and problems. No illustrations of statistical methods will be given here because statistics, a fundamental tool of science, is abundantly discussed in the literature of science. 

Fig. 5-2. we shall discuss at some length in this section. This problem is applicable to operations research, and, hence, we give a brief outline of maximum flow through networks. 

What is needed for operations research purposes is an extension of the theory of network flow to stochastic flow in edges that, in turn, have capacities, lengths, etc. that assume values stochastically. 

Leslie C. Edie, Car-following and Steady-state Theory for Noil-congested Traffic, Operations Research, 9, No. I, 66-76 (1961). 

Probability Theory.—To pursue our study of methods of operations research, a brief, although incomplete, and somewhat abstract, presentation of ideas from probability theory will be given. In part it shows that mathematical abstraction and rigor are also in the nature of operations research. Illustrations of this topic will be given in later sections. We then give a longer discussion of maximization and minimization methods and in turn illustrate the ideas in subsequent sections. Probability and statistics and optimization methods are two major sources of operations research tools. 

Queueing Theory.14—Queueing theory occupies a prominent position in operations research because of a wide range of applications with possible transfer of the ideas to other fields, e.g., inventory, and for the use of sophisticated stochastic models.15... 

Thomas L. Saaty, "Time-Dependent Solution of the Many-server Poisson Queue/2 Operations Research, 8, No. 6 (1960). 

Maximization, Minimization, and Minmax.—We shall discuss three wide classes of optimization problems that illustrate the ideas of the title of this section as used in operations research. They are ... 

H. W. Kuhn and A. W. Tucker, Non-linear Programming, in J. Neyman, ed., Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1951 Thomas L. Saaty, Mathematical Methods of Operations Research, McGraw-Hill Book Co., New York, 1959. 

Hilton Ash, Flood s Assignment Model for Small Kill Levels, Operations Research, 7, No. 2 (1959). 

Edward H Bowman, Production Scheduling by the Transportation Method of Lmear Programming, Operations Research, 4, 100-3 (1956). 

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