Threshold results for the inventory cycle offsetting problem

Abstract

In a multi-item inventory system, given the order cycle lengths and volumes of the items, the determination of the replenishment times, so as to minimise the resource requirement, is known as the inventory cycle offsetting problem. In this paper we show that with probability one, there exists an interval , for which the resource requirement is near the minimum it could be, where C1 > 1 is a constant, K is the number of items and Q is the maximum cycle length. We further prove that there is also a certain constant C2 > C1 > 1 so that with high probability, the resource requirement for the time interval is near the worst that it could be. We also present some numerical experiments that suggest how C1 depends on certain problem parameters, which implies that for many practical cases, a random algorithm will find near-optimal solutions.