A new approach to (s, S) inventory systems

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Abstract
In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm.(s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES