An approach to the allocation of common costs of multi-mission systems

Many Naval systems, as well as other military and civilian systems, generate multiple missions. An outstanding problem in cost analysis is how to allocate the costs of such missions so that their true costs can be determined and resource allocation optimized. This paper presents a simple approach to handling this problem for single systems. The approach is based on the theory of peak-load pricing as developed by Marcel Boiteux. The basic principle is that the long-run marginal cost of a mission must be equal to its “price.” The implication of this is that if missions can cover their own marginal costs, they should also be allocated some of the marginal common costs. The proportion of costs to be allocated is shown to a function of not only the mission-specific marginal costs and the common marginal costs, but also of the “mission price.” Thus, it is shown that measures of effectiveness must be developed for rational cost allocation. The measurement of effectiveness has long been an intractable problem, however. Therefore, several possible means of getting around this problem are presented in the development of the concept of relative mission prices.     

Multi-class inventory models with demand a function of inventory level

This paper considers the problem of maintaining an inventory of an item which can deteriorate and become useless. A periodic review procedure is used and new items ordered may experience a time lag in delivery. Items are considered to deteriorate through one or two states before becoming useless. Thus the deterioration process in each period plays the role of the usual demand process and is a function of the inventory level at the beginning of each period. For the case of no time lag in delivery, one stage deterioration, and either binomial or uniform deterioration, optimal ordering policies are obtained for the n-period dynamic model with the standard cost structure. (For the shortage probability criterion see the other paper by Iglehart and Jaquette, in this issue.) These policies are of the single critical number type. For more complicated models suboptimal policies of this same type are found.     

Optimal policies under the shortage probability criterion for an inventory model with unknown dependent demands

The principal innovation in this paper is the consideration of a new objective function for inventory models which we call the shortage probability criterion. Under this criterion we seek to minimize the total expected discounted cost of ordering subject to the probability that the stock level at the end of the period being less than some fixed quantity not exceed some prescribed number. For three different models we show that the minimum order policy is optimal. This result is then applied to a particular inventory model in which the demand distribution is not completely known. A Bayesian procedure is discussed for obtaining optimal policies.     

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.     

On maximization of the integral of a bell-shaped function over a symmetric set

Given a target T in Euclidean n-space Rⁿ and a point bomb whose point of impact in Rⁿ is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit v_a(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for v_a(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.     

Landmarks in defense literature

Achtung-Panzer! By Major General Heinz Guderian, Translated by Christopher Duffy with Introduction and Notes by Paul Harris. (Arms & Armour Press £16.99. ISBN 1-85409-138-7, 220 pages)     

Cycles and trends in the procurement system: Anticipating changes in acquisition legislation, regulation and policy

In conclusion, let me raise the question of whether the Law Panel can impact these cycles or reverse these trends. If they are regarded as historical imperatives, the answer is clearly No. But we have been urged to be bold and to try to devise a new, simplified statute that will take us back to a better day. We are going to do that, without regard to the question whether Congress will accept the solution.

There probably has never been a better time for the Panel's report than the present; the window of opportunity is open. But what the Panel recommends is going to be awfully hard to sell, even in a window-of-opportunity year. If the predictions come true about the defense budget's going down to the level of the period when Eisenhower remained a Major for 14 years, maybe Congress will be receptive to anything that adds a little bit of value to the defense dollar. With this in mind, the Law Panel is likely to be very bold in its attempt to streamline the procurement system and reduce oversight. Hope springs eternal . . . .