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An Efficient Algorithm for Computing an Optimal r, Q Policy in Continuous Review Stochastic Inventory Systems

Authors:

Awi Federgruen,

Yu-Sheng ZhengAuthors Info & Claims

Operations Research, Volume 40, Issue 4

Pages 808 - 813

Published: 01 August 1992 Publication History

Abstract

The reorder point/reorder quantity policies, also referred to as r, Q policies, are widely used in industry and extensively studied in the literature. However, for a period of almost 30 years there has been no efficient algorithm for computing optimal control parameters for such policies. In this paper, we present a surprisingly simple and efficient algorithm for the determination of an optimal r*, Q* policy. The computational complexity of the algorithm is linear in Q*. For the most prevalent case of linear holding, backlogging and stockout penalty costs in addition to fixed order costs, the algorithm requires at most 6r* + 13Q* elementary operations additions, comparisons and multiplications, and hence, no more than 13 times the amount of work required to do a single evaluation of the long-run average cost function in the point r*, Q*.

References

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FEDERGRUEN, A., AND Y. S. ZHENG. 1988. A Simple and Efficient Algorithm for Computing Optimal (r, Q) Policies in Continuous-Review Stochastic Inventory Systems. Working Paper (Unabridged Version). Decision Sciences Department, The Wharton School, University of Pennsylvania, Philadelphia.

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GALLIHER, H. P. MORSE AND M. SIMMOND. 1959. Dynamics of Two Classes of Continuous-Review Inventory Systems. Opns. Res. 7, 362-384.

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Cited By

Lee C(2020)A continuous review inventory model with complex correlations among componentsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20001439:5(6935-6947)Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.3233/JIFS-200014
Ang MSigman KSong JZhang H(2017)Closed-Form Approximations for Optimal (r, q) and (S, T) Policies in a Parallel Processing EnvironmentOperations Research10.1287/opre.2017.162365:5(1414-1428)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1287/opre.2017.1623
Hu MYang Y(2014)Modified Echelon r, Q Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory SystemsOperations Research10.5555/2773183.277319162:4(812-828)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.5555/2773183.2773191
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An Efficient Algorithm for Computing an Optimal r, Q Policy in Continuous Review Stochastic Inventory Systems

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Published In

cover image Operations Research

Operations Research Volume 40, Issue 4

August 1992

194 pages

ISSN:0030-364X

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 August 1992

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inventory/production: stochastic policies

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Cited By

Lee C(2020)A continuous review inventory model with complex correlations among componentsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-20001439:5(6935-6947)Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.3233/JIFS-200014
Ang MSigman KSong JZhang H(2017)Closed-Form Approximations for Optimal (r, q) and (S, T) Policies in a Parallel Processing EnvironmentOperations Research10.1287/opre.2017.162365:5(1414-1428)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1287/opre.2017.1623
Hu MYang Y(2014)Modified Echelon r, Q Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory SystemsOperations Research10.5555/2773183.277319162:4(812-828)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.5555/2773183.2773191
Hu MYang Y(2014)Modified Echelon r, Q Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory SystemsOperations Research10.5555/2765026.276503462:4(812-828)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.5555/2765026.2765034
(2014)Modified Echelon (r, Q) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory SystemsOperations Research10.5555/2726276.272628462:4(812-828)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.5555/2726276.2726284
Ünlü YRossetti M(2011)Evaluating variance reduction techniques within a sample average approximation method for a constrained inventory policy optimization problemProceedings of the Winter Simulation Conference10.5555/2431518.2431710(1629-1640)Online publication date: 11-Dec-2011
https://dl.acm.org/doi/10.5555/2431518.2431710
Song JZhang HHou YWang M(2010)The Effect of Lead Time and Demand Uncertainties in (r, q) Inventory SystemsOperations Research10.1287/opre.1090.071158:1(68-80)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.1287/opre.1090.0711
Bruzzone ACimino ADiaz RLongo FMcGraw RImsand EChinni M(2010)Inventory control with products returnsProceedings of the 2010 Spring Simulation Multiconference10.1145/1878537.1878606(1-7)Online publication date: 11-Apr-2010
https://dl.acm.org/doi/10.1145/1878537.1878606
Axsäter S(2003)A New Decision Rule for Lateral Transshipments in Inventory SystemsManagement Science10.1287/mnsc.49.9.1168.1656849:9(1168-1179)Online publication date: 1-Sep-2003
https://dl.acm.org/doi/10.1287/mnsc.49.9.1168.16568
Zhang RHopp WSupatgiat C(2001)Spreadsheet Implementable Inventory Control for a Distribution CenterJournal of Heuristics10.1023/A:10096139210017:2(185-203)Online publication date: 1-Mar-2001
https://dl.acm.org/doi/10.1023/A%3A1009613921001
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