Prof. Dr. Shoaib ud Din
Mathematics Department
Punjab University, Lahore, Pakistan
Operations Research has had an increasingly great impact on the management of organizations in the recent years. In fact, with the exception of advent of electronic computer, the extent of this impact seems to be unrivalled by that of any other recent development. However, all the development in this field has gone almost unnoticed in most developing countries including Pakistan. This article is an effort to introduce Mathematics community in the country to the subject and its achievements.
In order to appreciate the importance of OR in the world today it is important that we know something of its history and evolution. Although roots of Operations Research can be traced back many decades, it is generally agreed that this discipline began during World War II. During the War team of British scientists with diverse background were called upon to study the strategic and tactical problems associated with air and land defense of the country. The establishment of this scientific team marked the first formal Operations Research activity. Their efforts were allegedly instrumental in winning the Air Battle of Britain, The Island Campaign in the Pacific, the Battle of the North Atlantic, and so on. The name Operations Research-Operational Research in the United Kingdom – was apparently coined because the problems assigned to this team were in the nature of military operations.
After the War many of the scientists who had been active in the military OR teams turned their attention to the possibilities of applying a similar approach to civilian problems. The first civilian organization to adopt OR methodology were large corporations. It was apparent that the problems caused by the increasing complexity and specialization in these organizations were basically the same as had been faced by the military but in different context. In the early years when all Operations Research activity was in the nature of basic research, only large corporations could afford it. Later, as research began to recognize common categories of problems (inventory, allocation, replacement, scheduling, etc.) and the technique for dealing with such problems became standardized, smaller companies were able to benefit from the pool of accumulated knowledge without investing heavily in research.
Applications of Operation Research in public sector did not begin until the mid 1960’s. Nowadays, however, banks, hospitals, judicial systems, and government agencies in the developed countries are effectively, using Operations Research in their planning and policy making activities.
An important factor that played a key role in the rapid growth of operations research was the concurrent development of electronic computers. A large amount of computation usually required to deal effectively with the problems typically tackled by standard would be impractical without modern computer. By generating practical uses for increasingly larger and faster machines, OR has both benefited from and contributed to the growth of computer capability that has occurred over the past four decades.
Linear programming is a prominent area of Operations Research. Many people rank the development of linear programming among the most important scientific advances of the mid twentieth century. The more common type of application of linear programming involves the general problem of planning the allocation of limited resources among competing activities in the best possible (optimal) way. Linear programming uses a mathematical model to describe the problem. The adjective linear means that all the mathematical functions (objective and constraints) in the model are linear. The word programming does not refer here to computer programming; rather, it is essentially a synonym for planning.
Simplex method is generally used for solving linear programming problems. This method was developed by Geoge Dantzig inn 1947. It is an iterative solution procedure with begins by picking up a corner-point of the feasible solution space of the problem as a starting solution. This corner-point is then used to find another corner-point of the feasible solution space which yields a better value for the objective function. At this step the simplex method considerably improves its efficiency by implicitly eliminating from consideration all those corner-points whose objective function values are worse than the present one. The process of using the current corner-point solution for finding another feasible corner-point solution with a better objective function value continues until it is no more possible to improve the solution.
More recently there has been a dramatic new development that promises to give further impetus to the impact of linear programming. In 1984, Narendra Karmarkar at AT&T Bell laboratories announced a new algorithm for solving huge linear programming problems. In contrast to the simplex methods approach of focusing on corner-point feasible solution of the space, Karmarkar’s algorithm is an interior-point algorithm that cuts through the interior of the feasible region to reach an optimal solution. It is claimed that this new algorithm can solve huge linear programming problems up to 50 times as fast as the simplex method.
Throughout the War practitioners were far too busy with current problems to devote themselves either to a conscious an analysis of methodology or to the writing of books that would pave the way for their successors. After the War some of these scientists returned to universities and concentrated their efforts on providing a sound foundation for many of the techniques that had been hastily developed earlier, while others devoted renewed efforts to developing new techniques. The Operation Research Society of America was founded in 1952 to serve the professional needs of scientists working in the OR area. A parallel movement resulted, in 1953, in the formation of The Institute of Management Science, helped to draw together the many diverse results into some semblance of a coherent body of knowledge. Text begin to appear then with increasing vigour and OR achieved recognition as a subject worthy of academic study in universities. Since then, not only have a large number of colleges and universities provided courses leading to advanced degrees in OR but the subject has been recognized as becoming more and more important to students of economics, management, public administration, behavioural science, social work, mathematics and statistics and the many branches of engineering.
At present the opportunities of OR practice in the industrial sector are very limited. Experts are of the opinion that the political and economic situation of the country is not conducive to OR activity. Our industrialists are generally not much interested in saving a few million rupees here and there by minimizing wastage or by improving efficiency of their industrial processes. The real competition in Pakistan is for getting soft loans, getting subsidies and getting wavers of tax and other duties. In spite of that there are a few individuals who are practicing OR techniques in isolation, although they don’t get much encouragement or appreciation for their work. Some of the industries which have successfully employed OR techniques fare Lever Brothers, Dawood Hercules, and Packages Limited. There is no Operations Research Society in Pakistan and in the absence of such a society it is arduous to keep track of what ever OR activity is going on in the country.
Islamia University, Bahawalpur, was probably the first university in Punjab to introduce Course of OR in M.Sc. Mathematics in 1980. Presently Operation Research is being offered in almost all the universities as a elective subject in the departments of Mathematics and Statistics. The subject is also being taught by the various departments of Management, Commerce, Computer Science and Engineering. OR was a very popular subject among students in 80’s because students were hoping that this new subject will provide new job opportunities to the. But their expectations have nut fulfilled and their interest in the subject is dwindling.
Occasionally various training programs of short duration are offered to executives who are employed in different public and private organizations. But these courses don’t normally do anything more than providing a few days holiday in a five star hotel to these officials.
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