THE UNIFORM DISTRIBUTION OF INVENTORY POSITION FOR CONTINUOUS REVIEW (S, Q) POLICIES,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1968
- Accession Number
- AD0675984
Entities
People
- Richard Macey Simon
Organizations
- RAND Corporation