The Future of Operational Research

Abstract

THOSE of you who are familiar with the works of the Chinese logician Hao Wang will recall his saying: One who is situated at the bottom of a well can hardly offer a satisfactory view of the sky. He went on to say, To compensate for my restricted range of vision I intend to indulge occasionally in irresponsible speculations. I shall make no futile attempt to be impartial.... In this, I intend to follow his precept, if not his example. The future of operational research can be understood in several ways. For one thing, we can think of the techniques we use, and their possible further development. As one who has come to operational research from the mathematical side, I may have a tendency to exaggerate the importance of these techniques in the practice of operational research; but nonetheless I think that it is an urgent matter for us in this country to provide for the further development of existing techniques, and the creation of new ones. If we count the methods of statistics among operational research techniques, then this country's contribution has been, and still is, I think, a good one it was a pleasure to hear, last summer, Professor John Tukey state as his opinion that in no major scientific field, at an international conference, would the absence of a British delegation be more noticed than in statistics; and of all national delegations at such a conference, the British would be most missed. And one could feel that he was not just exercising the American genius for making one feel welcome! But we in this country cannot be so proud of our record in other directions. Where have the ideas of linear programming, dynamic programming, critical path scheduling, and so many others originated? Not, I fear, in this country; and I think we should ask ourselves why. I can illustrate many aspects of my theme tonight by reference to the special allocation problem which has been known as the marriage problem, but which would perhaps better be called the stable engagement problem. We have n men and n women; each man can rank all the women in order of preference as wife, and each woman can rank all the men in order of preference as husband. We are then required to pair off the women and men to form engagements which are required to be stable, given freedom of each partner to end the engagement on finding someone whom they prefer and who prefers them to their present partner. I think it was Professor David Gale in the U.S.A. who first raised the problem and showed that a solution is always possible, and indeed that there is usually more than one solution. He gave a method, which could be carried through on a computer (i.e. an algorithm), for finding a solution