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.     

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.     

A two-phase procedure for allotting geostationary orbital locations to communications satellites

We consider the problem of allotting locations in the geostationary orbit to communication satellites, subject to angle of elevation and electromagnetic interference constraints. An optimization framework is used as a means of finding feasible allotment plans. Specifically, we present a two-phase solution procedure for the satellite location problem (SLP). The objective in SLP is to allot geostationary orbital locations to satellites so as to minimize the sum of the absolute differences between the locations prescribed for the satellites and corresponding specified desired locations. We describe two heuristics, an ordering procedure and a k-permutation algorithm, that are used in tandem to find solutions to SLP. Solutions to a worldwide example problem with 183 satellites serving 208 service areas are summarized.     

A family of games on 1,∞)2 with payoff a function of y/x

A two-parameter class of games on 1,∞)² is studied. The games may be regarded as analogs of Silverman games, having continuous payoff function in place of a step function of y/x. This change is motivated by a desire to move toward a model for competitive situations where the penalty for overspending increases with the amount of overspending. There are some similarities to games with bell-shaped kernel. For most of the region considered in the plane of the two parameters there are solutions of finite type, which are obtained explicitly. There are, however, pockets in this plane where no optimal strategies have been found and possibly where none of finite type exist.     

Congestion tolls: Equilibrium and optimality

An example of a network with flow costs depending on congestion is presented for which no system of tolls and subsidies exists which can ensure that all equilibria in the game of route selection are Pareto optimal.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are 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.