The Joint Replenishment Problem with a Powers-of-Two Restriction

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Abstract
In this paper we consider the joint replenishment problem in the light of recent work by the second and third authors concerning the selection of realistic and consistent reorder intervals in production/ distribution systems. After stating a general dynamic programming formulation of the joint replenishment problem, we present its usual statement which assumes constant reorder intervals. We then restrict the problem further by assuming the constant reorder intervals are powers-of-two multiples of some base planning interval. We present an algorithm based on concepts we developed that solves the joint replenishment problem with the powers-of-two restriction. Like other algorithms proposed for this problem, it is a simple sorting algorithm. Finally, we establish that the algorithm yields a solution whose average annual cost is within 6% of the general problem's long-run minimum average annual cost.