Optimal Control Policy for Stochastic Inventory Systems with Markovian Discount Opportunities

Yu-Shen Zheng
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Yu-Shen Zheng: University of Pennsylvania, Philadelphia, Pennsylvania

Operations Research, 1994, vol. 42, issue 4, 721-738

Abstract: In this paper, we study a single-item continuous-review inventory system with Poisson demand. In addition to the standard cost structure of a fixed setup cost and a quasiconvex expected inventory holding and shortage cost, special opportunities for placing orders at a discounted setup cost occur according to a Poisson process that is independent of the demand process. This model has been studied as a subproblem of multi-item/location inventory systems where there are economies-of-scale in joint replenishment. For the single-item model, the literature proposes the ( s , c , S ) policy, under which an order is placed to increase the inventory position to S either when the inventory position drops to s , or when the inventory position is at or below c and a discount opportunity occurs. We prove that the ( s , c , S ) policy is optimal for the model, develop an efficient algorithm for computing optimal control parameters s *, c *, S*, and carry out a parametric analysis showing the effects of changes in problem parameters on the optimal control parameters and the minimum cost.

Keywords: inventory/production: lot sizing policies; stochastic models (search for similar items in EconPapers)
Date: 1994
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