Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
On the Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs
SIAM Journal on Optimization
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Handbook of Learning and Approximate Dynamic Programming (IEEE Press Series on Computational Intelligence)
Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Stochastic Optimization is (Almost) as easy as Deterministic Optimization
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Adaptivity and approximation for stochastic packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling-based Approximation Algorithms for Multi-stage Stochastic
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Sampling bounds for stochastic optimization
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
A practical inventory control policy using operational statistics
Operations Research Letters
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 consider two fundamental stochastic optimization problems that arise in the context of supply-chain models, the single-period newsvendor problem and its multiperiod extension with independent demands. These problems are among the most well-studied stochastic optimization problems in the Operations Research literature. Most commonly, these problems are studied from the perspective that the input probability distributions are given in terms of specific probability distribution functions that are computationally tractable; under this assumption, both problems can be solved efficiently. Unfortunately, this information is unlikely to be available in practice, and hence we make the more realistic assumption that the probability distribution is given by a "black box" from which independent samples can be drawn. We give the first fully polynomial randomized approximation schemes for these two problems in this sampling-based model.Our work provides new insights into the power of two of the most often-used approaches to solving stochastic optimization problems, the sample average approximation (SAA) and stochastic dynamic programming. For the newsvendor problem, we show that by taking a polynomial number of samples and then solving the newsvendor problem with respect to the resulting approximation to the true distribution, we obtain provably near-optimal solution. This significantly extends the class of problems for which the SAA is known to yield a scheme. Finally, we show how to adapt the framework of stochastic dynamic programming to yield an approximation scheme for the multiperiod newsvendor problem with independent demands. We believe that this is an interesting first step towards the goal of providing a mechanism for deriving efficient approximate stochastic dynamic programming methods for a wide range of multistage stochastic optimization problems.