Research for Computational Methods

In World War II, the phrase 'operations research' has come to describe the scientific, quantitative study of operations of war. This report is a first attempt to describe some of the methods which have proved most valuable in the study of warfare, and to indicate possible fruitful lines for further development, military and nonmilitary. The first chapter outlines the scope and methods of the subject. The second chapter discusses the relevant portions of the theory of probability, which is the field of mathematics most useful for this work. The rest of the chapters discuss techniques which have been particularly useful, with illustrations picked from work done in the recent war.

A computer model was developed to aid in studying naval war scenarios in which anti-shipping operations are the main consideration. Performance of the forces involved is specified by probabilities of carrying out assigned missions, such as penetrating escort screens and attacking convoyed shipping. The model calculates expected values of the losses suffered by these forces. The model programming and inputs are designed to cover a wide range of problems.

In general, the single product inventory model in which demands in successive periods are not independent is difficult to treat. This paper defines a large class of such problems, when there is a positive lead time for delivery, which can be treated by the classical formulation with a single state variable. All results which hold for inventory models with a constant delivery lag can be shown to hold also for this model. An application is made to a system in which demands are generated by part failure and in which a portion of these failures are repaired after a given (constant or probabilistic) time.

A differential game is one in which, as the action progresses, both the environment and the decisions available to the players are subject to a consistent, logical law, so that the problem is amenable to mathematical analysis. Usually, the action is continuous, and solutions can actually be obtained for a wide range of problems of extended conflict between two antagonists. The applications include various models of battles, pursuit and evasion games, dogfights and other contests of maneuvering, such as football, and some aiming and evasion problems. By allowing one player to be passive, certain programs can be optimized. A chapter is devoted to collision avoidance, in which the players cooperate rather than conflict. In what are termed games of degree the players respectively seek to maximize and minimize some numerically valued payoff. In games of kind the criterion is sharp, such as whether or not capture will occur in a pursuit situation. The two types have separate but related theories. The text concludes with chapters on the case of incomplete information and the practical aspects of applications to warfare. This is not a revised version. It was assigned a .10 version because under an original numbering system which was abandoned, there were two CNA RC's numbered 1.