A periodic tabular policy for scheduling of a single stage production-inventory system

Abstract

In this paper, we consider scheduling of a multi-item single stage production-inventory system in the presence of uncertainty regarding demand patterns, production times and switchover times. For a given specification of base-stock levels of individual items and under (S - 1, S) requests for replenishment policy, a mathematical program to minimize long-run average system wide costs is formulated. We derive approximations for the first two moments of demand over lead time using residual service analysis of vacation queue models. Subsequently, we develop an approximate convex program for the original cost model and determine optimal production frequencies for individual types. Based on these relative frequencies, we determine a table size and devise an efficient heuristic to construct a tabular sequence in which individual items appear according to their respective absolute frequencies and items are positioned such that variance of their inter-visit times is minimized. A numerical study that demonstrates effectiveness of the proposed policy against cyclic policies is given.