Knowledge that Transforms

A survey of the current relationship between the many different problem areas investigated by means of Game Theory and the study of Industrial Organization is presented. Several examples are provided to illustrate the nature and relevance of work on (1) two-person constant-sum games; (2) the extensive form of a game; (3) theories of solution for n-person games; (4) theories of solutions for games against nature; and (5) theories of solution for dynamic games. The nature and state of the current applications of game theory to organizational problems and to parts of the behavorial sciences are summarized.

The chief feature of the method is that it fans out from the origin working out the shortest path to one new node from the origin and never having to backtrack. No more than n(n − 1)/2 comparisons are needed to find the shortest route from a given origin to all other nodes and possibly less between two fixed nodes. Except for details and bias of various authors towards a particular brand of proof, this problem has been solved the same way by many authors. This paper refines these proposals to give what is believed to be the shortest procedure for finding the shortest route when it is little effort to arrange distances in increasing order by nodes or to skip consideration of arcs into nodes whose shortest route to the origin has been determined earlier in the computation. In practice the number of comparisons is much less than indicated bounds because all arcs leading to nodes previously evaluated are deleted from further consideration. A further efficiency can be achieved in the event of ties by including least distances from origin to many nodes simultaneously during the fanning out process. However, these are shown as separate steps to illustrate the underlying principle.

The article describes a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities. First the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form. The constraints which are then violated are added in a similar way to the constraints already imposed. It is shown that under certain general conditions this procedure leads to the required optimum in a finite number of steps. The procedure is illustrated by an example while also a directory of computations is given.

This paper presents a heuristic procedure for balancing production assembly lines and a computer program for carrying out that procedure. This research was undertaken to investigate the application of complex information processing techniques (as used in producing the Chess Machine and Logic Theorist) to a typical industrial problem. The assembly line balancing problem is stated as: Given an assembly process made up of elemental tasks, each with a time required per unit of product and an ordering with other tasks, what is the least number of work stations needed to attain a desired production rate? The heuristic procedure for assembly line balancing consists of three phases: repeated simplification of the initial problem by grouping adjacent elemental tasks into compound tasks; solution of the simpler problems thus created by assigning tasks to work stations at the least complex level possible, breaking up the compound tasks into their elements only when necessary for a solution; smoothing the resulting balance by transferring tasks among work stations until the distribution of assigned time is as even as possible. The heuristics used in each phase are considered in some detail. Appropriate means for mechanizing such a procedure are discussed, and operating results of the program on actual problems are presented.

This paper is concerned with the lack of significant progress in the application of electronic computers for expanding the scope of systems of information flow. The weapon systems management concept, and more particularly its civilian counterpart the product mission concept, is presented as a possible frame of reference for top management and systems analysts to use in long-range planning. The functions necessary for successful product mission accomplishment are outlined and the role of systems analysts in the performance of these functions is emphasized. The feasibility of long-range planning for systems of information flow without reference to existing applications or hardware is also discussed.

The author of the work “Mathematical Methods of Organizing and Planning Production”, Professor L. V. Kantorovich, is an eminent authority in the field of mathematics. This work is interesting from a purely mathematical point of view since it presents an original method, going beyond the limits of classical mathematical analysis, for solving extremal problems. On the other hand, this work also provides an application of mathematical methods to questions of organizing production which merits the serious attention of workers in different branches of industry. This is the English translation of the famous 1939 article by L. V. Kantorovich, originally published in Russian.

This is a report of the results of some digital computer simulation studies of a simplified model of a job shop production process. Such factors as the average effectiveness of schedules under the impact of random variations in processing times and the effect of changing operating policies are considered. The average manufacturing times and predictability of completion times were used as measures of effectiveness.