Adaptive Ordering and Pricing for Perishable Products
Operations Research
Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems
Mathematics of Operations Research
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales
Mathematics of Operations Research
On the Structure of Lost-Sales Inventory Models
Operations Research
A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand
Mathematics of Operations Research
Fully Distribution-Free Profit Maximization: The Inventory Management Case
Mathematics of Operations Research
Improved Inventory Targets in the Presence of Limited Historical Demand Data
Manufacturing & Service Operations Management
Online lot-sizing problems with ordering, holding and shortage costs
Operations Research Letters
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We consider a periodic-review, single-location, single-product inventory system with lost sales and positive replenishment lead times. It is well known that the optimal policy does not possess a simple structure. Motivated by recent results showing that base-stock policies perform well in these systems, we study the problem of finding the best base-stock policy in such a system. In contrast to the classical inventory literature, we assume that the manager does not know the demand distribution a priori but must make the replenishment decision in each period based only on the past sales (censored demand) data. We develop a nonparametric adaptive algorithm that generates a sequence of order-up-to levels whose running average of the inventory holding and lost sales penalty cost converges to the cost of the optimal base-stock policy, and we establish the cubic-root convergence rate of the algorithm. Our analysis is based on recent advances in stochastic online convex optimization and on the uniform ergodicity of Markov chains associated with bases-stock policies.