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.     

Use of dimensionless ratios to determine minimum-cost inventory quantities

The iteration usually necessary for simultaneous determination of minimum-cost order quantity and reorder point in (Q, r) inventory systems may be eliminated by a graphical technique employing dimensionless ratios. This technique is illustrated for three different types of stock-out penalty.     

Book reviews

Export or Die: Britain's Defence Trade with Iran and Iraq. by Davina Miller, London: Cassell, 1996, ISBN 0-304-33852-4 (hbk), £40.00, 04-33853-2 (pbk), £11.99.

The Storm Passed By: Ireland and the Battle of the Atlantic, 1940-1941. by Trevor Allen, Dublin: Irish Academic Press, 1996, ISBN 0-7165-2616-6, (hbk) £17.50.

Arms Control Toward the 21st Century. by Jeffrey A. Larsen and Greqory J. Rattray (eds). Boulder: Lynne Rienner, 1996.

Asia-Pacific Security, Less Uncertainty, New Opportunities. Edited by Gary Klintworth. Melbourne: Addison Wesley Longman, 1996, ISBN 0-582-80321-7, £24.99.

Masters of War, Military Dissent and Politics in the Vietnam Era. by Robert Buzzanco, Cambridge: Cambridge University Press, 1996, ISBN 0-521-48046-9 (hbk), £29.95

Controlling the Arms Trade: the West Versus the Rest. By Paul Cornish, London: Bowerdean Publishing Co., 1996, ISBN 0-906097-44-4 (pbk), £9.99.

Secret Agencies: US Intelligence in a Hostile World. by Loch K. Johnson, London: Yale University Press, 1997, ISBN 0-300-06611-2 (hbk), £22.50.     

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.     

Flowshop/no-idle or no-wait scheduling to minimize the sum of completion times

This paper deals with flowshop/sum of completion times scheduling problems, working under a “no-idle” or a “no-wait” constraint, the former prescribes for the machines to work continuously without idle intervals and the latter for the jobs to be processed continuously without waiting times between consecutive machines. Under either of the constraints the problem is unary NP-Complete for two machines. We prove some properties of the optimal schedule for n/2/F, no-idle/σC_i. For n/m/P, no-idle/σC_i, and n/m/P, no-wait/σC_i, with an increasing or decreasing series of dominating machines, we prove theorems that are the basis for polynomial bounded algorithms. All theorems are demonstrated numerically.     

Selecting among weibull,lognormal and gamma distributions using complete and censored smaples

In a recent paper, Kent and Quesenberry [19] considered using certain optimal invariant statistics to select the best fitting member of a collection of probability distributions using complete samples of life data. In the present work extensions of this approach in two directions are given. First, selection for complete samples based on scale and shape invariant statistics is considered. Next, the selection problem for type I censored samples is considered, and both scale invariant and maximum likelihood selection procedures are studied. The two-parameter (scale and shape) Weibull, lognormal, and gamma distributions are considered and applications to real data are given. Results from a (small) comparative simulation study are presented.     

Minimizing costs of sequential and parallel personnel testing programs

We consider groups of tests for personnel selection purposes in which each test has a known a priori probability of being failed, such failure resulting in outright rejection and termination of testing. Each test has a fixed cost and given duration. We consider the minimization of the total expected cost due to both the fixed costs and the delay costs when the tests may be conducted sequentially or in parallel. In the latter situation, a heuristic algorithm is proposed and illustrated.     

A note on duality in homogeneous fractional programming

For a linear fractional programming problem, Sharma and Swarup have constructed a dual problem, also a linear fractional program, in which the objective functions of both primal and dual problems are the same. Craven and Mond have extended this result to a nonlinear fractional programming problem with linear constraints, and a dual problem for which the objective function is the same as that of the primal. This theorem is now further extended from linear to differentiable convex constraints.     

Some results of the queueing system E/M/c

This paper analyses the E/M/c queueing system and shows how to calculate the expected number in the system, both at a random epoch and immediately preceding an arrival. These expectations are expressed in terms of certain initial probabilities which are determined by linear equations. The advantages and disadvantages of this method are also discussed.