An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution

We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The...

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Bibliographic Details
Published in:Management science 2001-08, Vol.47 (8), p.1101-1112
Main Authors: Godfrey, Gregory A, Powell, Warren B
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Business studies
Censored Demands
Censorship
Concavity
Data smoothing
Demand
Distribution
Dynamic programming
Dynamic Programming Approximations
Estimation
Estimation methods
Inventories
Management science
Newsvendor Problem
Operations research
Order quantity
Revenue
Stochastic models
Stochastic Programming
Studies
Unit costs
Value
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Summary:We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The only information we use is the amount of inventory left over. Rather than attempting to estimate the demand distribution, we directly estimate the value function using a technique called the Concave, Adaptive Value Estimation (CAVE) algorithm. CAVE constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain. Since it is a sampling-based method, CAVE does not require knowledge of the underlying sample distribution. The result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi-gradient methods and more flexible than analytical techniques that require distribution information. In addition, we demonstrate near-optimal behavior of the CAVE approximation in experiments involving two different types of stochastic programs—the newsvendor stochastic inventory problem and two-stage distribution problems.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.47.8.1101.10231