Fixed-Dimensional Stochastic Dynamic Programs: An Approximation Scheme and an Inventory Application

43 Pages Posted: 23 Dec 2012

See all articles by Wei Chen

Wei Chen

University of Texas at Dallas - Department of Information Systems & Operations Management

Milind Dawande

University of Texas at Dallas - Department of Information Systems & Operations Management

Ganesh Janakiraman

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: December 22, 2012

Abstract

We study fixed-dimensional stochastic dynamic programs in a discrete setting over a finite horizon. Under the primary assumption that the cost-to-go functions are discrete L♮-convex, we propose a pseudo-polynomial time approximation scheme that solves this problem to within an arbitrary pre-specified additive error of ε>0. The proposed approximation algorithm is a generalization of the explicit-enumeration algorithm and offers us full control in the tradeoff between accuracy and running time. The main technique we develop for obtaining our scheme is approximation of a fixed-dimensional L♮-convex function on a bounded rectangular set, using only a selected number of points in its domain. Furthermore, we prove that the approximation function preserves L♮-convexity. Finally, to apply the approximate functions in a dynamic program, we bound the error propagation of the approximation. The usefulness of our approximation scheme is illustrated by applying it to a well-known problem in inventory theory, namely the single-product problem with lost sales and lead times (Morton 1969, Zipkin 2008).

Keywords: Discrete convexity, multi-dimensional stochastic dynamic programs, approximation algorithms

Suggested Citation

Chen, Wei and Dawande, Milind and Janakiraman, Ganesh, Fixed-Dimensional Stochastic Dynamic Programs: An Approximation Scheme and an Inventory Application (December 22, 2012). Available at SSRN: https://ssrn.com/abstract=2193021 or http://dx.doi.org/10.2139/ssrn.2193021

Wei Chen

University of Texas at Dallas - Department of Information Systems & Operations Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Milind Dawande (Contact Author)

University of Texas at Dallas - Department of Information Systems & Operations Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Ganesh Janakiraman

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
57
Abstract Views
569
Rank
659,215
PlumX Metrics