Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Approximation Algorithms for Stochastic Inventory Control Models
Mathematics of Operations Research
A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales
Mathematics of Operations Research
A Comparison of the Optimal Costs of Two Canonical Inventory Systems
Operations Research
On the Structure of Lost-Sales Inventory Models
Operations Research
Mathematics of Operations Research
Mathematics of Operations Research
Online algorithms for the newsvendor problem with and without censored demands
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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We study a single-product single-location inventory system under periodic review, where excess demand is lost and the replenishment lead time is positive. The performance measure of interest is the long-run average holding cost and lost sales penalty cost. For a large class of demand distributions, we show that when the lost sales penalty becomes large compared to the holding cost, the relative difference between the cost of the optimal policy and the best order-up-to policy converges to zero. For any given cost parameters, we establish a bound on this relative difference. Numerical experiments show that the best order-up-to policy performs well, yielding an average cost that is within 1.5% of the optimal cost when the ratio between the lost sales penalty and the holding cost is 100. We also propose a heuristic order-up-to level using two newsvendor expressions; in our experiments, the cost of this order-up-to policy is 2.52% higher, on an average, than the best order-up-to policy.