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Fully Polynomial Time Approximation Schemes for Stochastic Dynamic Programs

Nir Halman (halman***at***mit.edu)
Diego Klabjan (d-klabjan***at***northwestern.edu)
Chung-Lun Li (chung-lun.li***at***polyu.edu.hk)
Jim Orlin (jorlin***at***mit.edu)
David Simchi-Levi (dslevi***at***mit.edu)

Abstract: We present a framework for obtaining Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone single-period cost functions. This framework is developed through the establishment of two sets of computational rules, namely the Calculus of K-approximation Functions and the Calculus of K-approximation Sets. Using our framework, we provide the first FPTASs for several NP-hard problems in various fields of research such as knapsack models, logistics, operations management, economics, and mathematical finance. Extensions of our framework via the use of the newly established computational rules are also discussed.

Keywords: Fully polynomial time approximation schemes; stochastic dynamic programming; K-approximation Sets and Functions

Category 1: Other Topics (Dynamic Programming )

Category 2: Combinatorial Optimization (Approximation Algorithms )

Citation: SIAM J. Discrete Math. 28, pp. 1725-1796, 2014.

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Entry Submitted: 06/10/2013
Entry Accepted: 06/10/2013
Entry Last Modified: 06/08/2015

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