
Accession Number : AD0675984
Title : THE UNIFORM DISTRIBUTION OF INVENTORY POSITION FOR CONTINUOUS REVIEW (S, Q) POLICIES,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Simon,Richard Macey
Report Date : SEP 1968
Pagination or Media Count : 9
Abstract : The report considers inventory control of a single item at a single facility. We assume that demands are discrete, and that a stationary (s, Q) replenishment policy is used. We further assume that demands which cannot be satisfied from stock on hand are backlogged, and that the procurement lead times for orders placed are random variables with arbitrary distributions. We wish to focus attention on the stochastic process, x(t), t = or > 0 where X(t) denotes the inventory position of the facility at time t. Hadley and Whitin have shown for the continuous review case that if the demands upon the facility form a Poisson process, then the stationary probabilities for (1) are given by pi sub j = 1/Q, j = 1,...,Q where Pi sub j represents the stationary probability that the inventory position at a randomly chosen point in time is s + j. In this paper we approach the continuous review model directly, and demonstrate the validity of the formula for pi sub j for very general demand processes. (Author)
Descriptors : (*INVENTORY CONTROL, MANAGEMENT PLANNING AND CONTROL), REPLACEMENT THEORY, STOCHASTIC PROCESSES, STATISTICAL PROCESSES, QUEUEING THEORY, MATHEMATICAL MODELS, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE