A graph theoretic interpretation of the sufficiency conditions for the contiguous-binary-switching (CBS)-rule

A sufficient condition for the optimality of the CBS-rule due to W. Smith is given a graphic interpretation in terms of ‘convex’ graphs. A convex graph is uniquely constructed (except for a homomorphism), and has the property that the optimum is achieved from any starting point.     

Toward a study of bidding processes part IV - games with unknown costs

This paper represents a continuation of three previous papers [1-.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.     

Bounds on parallel-processing of queues with multiple-phase jobs

Currently, both the hardware and software designs of many large computing systems aim at improved system performance through exploitation of parallelism in multiprocessor systems. In studying these systems, mathematical modelling and analysis constitute an important step towards providing design tools that can be used in building such systems. With this view the present paper describes a queueing model of a multiprocessor system operating in a job-shop environment in which arriving jobs consist of a random number of segments (sub-jobs). Two service disciplines are considered: one assumes that the sub-jobs of a given job are capable of parallel operation on different processors while the other assumes that the same sub-jobs must be operated in a strictly serial sequ'snce. The results (in particular, the mean number in the system and waiting time in queue) obtained for these two disciplines are shown to be bounds for more general job structures.     

An attack-defense game with matrix strategies

This paper presents the results and the method of analysis for an attack-defense game involving allocation of resources. Each player is assumed to have several different types of resources to be divided in optimal fashion among a fixed set of targets. The payoff function of the game is convex. The “No Soft-Spot” principle of M. Dresher, and the concept of the generalized inverse of a matrix are used to determine optimal strategies for each player and the value of the game.     

Economic impact and the notion of compensated procurement

The paper consists essentially of two parts. In the first part a linear economic impact model is presented whose structure is based on subcontracting flows. The structural coefficients are defined in terms of flows per area. The model is derived from two identities that are analogous to the income and expenditure identities of national income accounting. The parameters are prime contracts and when one or several of the prime contracts are changed, the model determines the impacts of such changes on the various regions that have been selected. The impacts can be combined with regional multipliers to derive changes in regional income and regional employment. Fragmentary data for this kind of model have been collected on a one-time basis by DOD in 1965 and some results based on the data are presented. The second part of the paper is concerned with normative economics. A scheme is suggested, called compensated procurement, that outlines how the Department of Defense might employ the impact model in a macroeconomic setting. The basic idea is that a stabilization fund be established to finance an array of potential projects which are contracted for to balance sudden shifts in defense demand. Only short-run stabilization is advocated.