K. Brian Haley

Linear Programming Problems

One of the fundamentals of Operational Research is the development of a model of a system. Normally in an industrial, government or military situation many related activities contribute to the successful operation of the organisation. The form of the interrelationship is often very complex and a model is an idealised representation of the interactions in the real state. Frequently it has been possible to express the connection between the different activities in a mathematical form. The construction of the representation is the ‘model building’ of Operational Research. This book is concerned with a particular type of mathematical representation which has proved to be a very valuable model of many industrial problems.

The challenge of publications

This review of 60 years of publishing by the Operational Research Society concentrates on the Journal, the problems faced by the editors and the evolution of its contents. This paper describes the growth in size of the Society external influences and the financial contribution to the Society generated by the Journal. Some funds were used to expand the range and scope of the publications, which currently consist of six different titles and are available in hard copy of electronic format. The future challenge of maintaining the financial income to support the continuing change in the subject is highlighted.

The Appropriateness of O R

The early Operational Research literature is devoted to explaining the applications nature of the subject and appeared in a variety of publications. March 1950 saw the appearance of Volume 1, No.1 of the Operational Research Quarterly1 — a magazine of 15 pages of which 9 were devoted to abstracts of other papers. One of these papers appeared in the UK journal Research Volume 2 in October 1949 and was by G Preuschen2 of (Institut fur Landwirtschaftleich Arbeitswissenschaft und Landtecknik, Imtshausen). The paper reviews the work at Institutes in Pommritz, Bonim and Breslau from 1918 and is fascinating in that it clearly represents some pioneering work covering the interaction of a number of factors aimed at production improvement. These include human and mechanical variables as well as the variability of the environment. The use of experimentation and analytical models were considered.

Exploration Working Group Report

The exploration working group received a number of presentations which are summarized later in this report and in some cases appear in a fuller form in other parts of the proceedings. It concentrated on a brainstorming session which was aimed at identifying the potential for the use of search methods in exploration problems. Some details of potential and actual uses are included in papers by Wagner, Field, Fergusson, Lenoble, and Friedrich. A parallel was also seen to the medical work described by Kolesar. A parallel was also seen to the medical work described by Kolesar. This brief report attempts merely to indicate the ideas which seemed to be most important in exploration.

Surveillance Working Group Report

Surveillance was found to be a difficult concept to structure in the Working Group on Surveillance/Fishing. The work reported here may not reflect the opinions of all the participants. It is nevertheless hoped that the ideas discussed here may prove useful in the analysis of some surveillance-type systems.

Search and Rescue Working Group Report

Search and Rescue (SAR) is a very demanding activity; its challenges must be met by the practitioners with increased efficiency. Recent developments in search technology are being implemented in computer assisted search systems.

Practical Applications of the Transportation Model

The problem described in Chapter 3 is merely concerned with finding the minimum transport cost allocation. In this chapter costs of production and distribution will be considered. It will be assumed that overtime may be worked at a higher unit production cost. Various practical difficulties of real models will be discussed including (i) production capacity exceeding the demand, (ii) the demand exceeding the supply and (iii) new variables needing to be defined.

The Simplex Method

The most general technique of linear programming is called the Simplex method. This method can be applied to all linear programming problems but it is not used if a simpler method is available. The transportation technique described in Chapter 3 is an example of a simpler method. The general problem is to find the values of several variables which are limited by a number of restrictions and which will maximise (or minimise) a linear expression of the variables. A typical problem would be to maximise the profit obtained from making a number of products. The products may use the same raw materials in different proportions. The supply of these materials may be limited and require processing on a group of machines. The machines, which operate on a single product at a time, are only available for a certain time each week. Certain demands may have to be met.

The Transportation Problem

Some linear programming problems have simple forms which enable easier or more efficient methods of solution to be used. Most of these methods rely on the basic simplex method already described. They follow the same sort of procedure in that a solution is found which satisfies the equations and this solution is altered to reduce the total cost.