The distribution of the product of two noncentral beta variates

In this paper the exact distribution of the product of two noncentral beta variates is derived using Mellin integral transform. The density function of the product is represented as a mixture of Beta distributions and the distribution function as a mixture of Incomplete Beta Functions.     

Discounted production scheduling and employment smoothing

We consider the problem of minimizing the sum of production, employment smoothing, and inventory costs over a finite number of time periods where demands are known. The fundamental difference between our model and that treated in [1] is that here we permit the smoothing cost to be nonstationary, thereby admitting a model with discounting. We show that the values of the instrumental variables are nondecreasing in time when demands are nondecreasing. We also derive some asymptotic properties of optimal policies.     

Application of the fundamental theorem of games to an example concerning antiballistic missile defense

This paper considers a two sided resource allocation game in which both players initially have fixed resources which may be distributed over various targets. Their effectiveness depends on the manner of distribution and also on the strategy of the opponent, a natural payoff function for such a situation being used. The complete solution to the game is derived and a numerical example given.     

A linear programming approach to geometric programs

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.     

On the manipulation of transfer prices in a static environment

In a static environment, J. Hirschleifer's marginal cost solution to the transfer pricing problem is commonly accepted as analytically correct. However, actual pricing practice within Western corporations and socialist-planned economies generally deviates from marginal cost pricing. Some form of average cost pricing is more commonly chosen. Recently in this journal, H. Enzer has claimed to show that some form of average cost pricing is indeed the analytically correct solution to the transfer pricing problem when choice of technique and manipulation are allowed. Enzer claims that optimal decisions made by each of two divisions according to their individual self-interests are made compatible with overall firm optimization when the transfer price assigned to the internally-transferred commodity is any form of average cost. We show that the marginal cost solution is correct for Enzer's problem in the absence of manipulation by either division. Indeed, this was all that Hirschleifer claimed. In the process, we uncover a fundamental mathematical error in Enzer's argument. When manipulation of the transfer price by divisions is allowed, we demonstrate the faults with Enzer's average cost solution and conclude Hirschleifer's original statements on manipulation to be correct even in Enzer's environment. A final section briefly indicates the importance to the transfer pricing problem of a growing body of economic literature on incentive structures.     

An algorithm for 0-1 multiple-knapsack problems

The 0-1 multiple-knapsack problem is an extension of the well-known 0-1 knapsack problem. It is a problem of assigning m objects, each having a value and a weight, to n knapsacks in such a way that the total weight in each knapsack is less than its capacity limit and the total value in the knapsacks is maximized. A branch-and-bound algorithm for solving the problem is developed and tested. Branching rules that avoid the search of redundant partial solutions are used in the algorithm. Various bounding techniques, including Lagrangean and surrogate relaxations, are investigated and compared.     

Minimizing the average deviation of job completion times about a common due date

This paper considers a single-machine scheduling problem in which penalities occur when a job is completed early or late. The objective is to minimize the total penalty subject to restrictive assumptions on the due dates and penalty functions for jobs. A procedure is presented for finding an optimal schedule.     

Book reviews

Small Wars Manual. United States Marine Corps 1940, with introduction by Ronald Schaffer, Sunflower University Press, Manhattan, Kansas, (1990), ISBN: 0-89745-112-0.

Military Mindlessness: an Informal Compendium. Edited by Raymond Horricks. Transaction Publishers, New Brunswick and London, (1993), ISBN: 1-56000-105-4. Price $26.95

Sipri Yearbook 1993: World Armaments and Disarmament, Oxford University Press, Oxford, (1993) ISBN 0-19-829166-3 - Price £50.00

Nigeria: The Politics of Adjustment and Democracy. By Julius O. Ihonvbere. Transaction Publishers, London & New Brunswick (1994), ISBN 1-56000-093-7, Price £34.95     

Single-machine scheduling with early and tardy completion costs

We address a single-machine scheduling problem in which penalties are assigned for early and tardy completion of jobs. These penalties are common in industrial settings where early job completion can cause the cash commitment to resources in a time frame earlier than needed, giving rise to early completion penalties. Tardiness penalties arise from a variety of sources, such as loss of customer goodwill, opportunity costs of lost sales, and direct cash penalties. Accounting for earliness cost makes the performance measure nonregular, and this nonregularity has apparently discouraged researchers from seeking solutions to this problem. We found that it is not much more difficult to design an enumerative search for this problem than it would be if the performance measure were regular. We present and demonstrate an efficient timetabling procedure which can be embedded in an enumerative algorithm allowing the search to be conducted over the domain of job permutations.© 1993 John Wiley & Sons, Inc.