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A complete computational approach for finding optimal (s, S) inventory policies is developed. The method is an efficient and unified approach for all values of the model parameters, including a non-negative set-up cost, a discount factor 0 ≦ α ≦ 1, and a lead time. The method is derived from renewal theory and stationary analysis, generalized to permit the unit interval range of values for α. Careful attention is given to the problem associated with specifying a starting condition (when α < 1); a resolution is found that guarantees an (s, S) policy optimal for all starting conditions is produced by the computations. New upper and lower bounds on the optimal values of both s and S are established. The special case of linear holding and penalty costs is treated in detail. In the final section, a model in which there is a minimum guaranteed demand in each period is studied, and a simplified method of solution is developed.
Veinott et al. (Mon,) studied this question.
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