Stochastic Allocation Rules

Abstract

This paper considers the allocation of a fixed amount of resource across competing activities, where the rate of use of the allocated amounts is stochastic. The allocated amounts are said to have run out when the first of the allocations is used up and another distribution must then be considered. This problem arises in the allocation of stocks of a commodity to branch warehouses and in the allocation of production time to items that are jointly produced. It also occurs in the allocation of spares to subsystems when the total number of spares is constrained by volume or cost and when failure of one subsystem causes a failure of the whole system. Two alternative formulations are presented: the Maximization of Expected Time to Runout and the Minimization of Expected Discounted Time to Runout. Bounds are developed on the problems by using deterministic and exponential models for the time to runout. The case of two competing processes is investigated numerically, and it appears that the solutions to the bounding problems provide effective heuristics at least for such small problems.

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