Title: Threshold results for the inventory cycle offsetting problem

Authors: Ernest Croot; Kai Huang

Addresses: Department of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA ' DeGroote School of Business, McMaster University, Hamilton, Ontario L8S4M4, Canada

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 [0, CK1 Q],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 [0, CK2,Q] 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.

Keywords: inventory cycle offsetting; replenishment times; number theory; concentration of measure; resource requirements; multi-item inventory systems.

DOI: 10.1504/IJMOR.2013.052463

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.2, pp.255 - 281

Available online: 05 Mar 2013 *

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