Purchasing Policy of New Containers Considering the Random Returns of Previously Issued Containers

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Abstract
A number of organizations sell products in containers that can be reused. The time from issue to return of an individual container is usually not known with certainty and there is a chance that the container is never returned (because of loss or irrepairable damage). Consequently, even under a level demand pattern new containers must be acquired from time to time. In this paper a purchasing policy of these new containers is determined for a finite time horizon so as to minimize the total purchasing and expected carrying costs under a prescribed service level. The associated stochastic model is reduced to a deterministic, dynamic lot-sizing problem with possible occurrence of negative net demand (demand minus return). A transformation into the usual nonnegative demand case allows us to apply well-known deterministic lot-sizing procedures to obtain the solution.