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A duality‐based relaxation and decomposition approach for inventory distribution systems
Author(s) -
Kunnumkal Sumit,
Topaloglu Huseyin
Publication year - 2008
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20306
Subject(s) - lagrange multiplier , mathematical optimization , computer science , set (abstract data type) , relaxation (psychology) , duality (order theory) , lagrangian relaxation , distribution (mathematics) , decomposition , function (biology) , inventory control , value (mathematics) , inventory theory , operations research , mathematics , discrete mathematics , psychology , ecology , evolutionary biology , machine learning , biology , programming language , social psychology , mathematical analysis
We propose a new method for making the inventory replenishment decisions in distribution systems. In particular, we consider distribution systems consisting of multiple retailers that face random demand and a warehouse that supplies the retailers. The method that we propose is based on formulating the distribution problem as a dynamic program, and relaxing the constraints that ensure the nonnegativity of the shipments to the retailers, by associating Lagrange multipliers with them. We show that our method provides lower bounds on the value functions, and a good set of values for the Lagrange multipliers can be obtained by maximizing a concave function in a relatively straightforward manner. Computational experiments indicate that our method can provide significant improvements over the traditional approaches for making the inventory replenishment decisions, in terms of both the tightness of the lower bounds on the value functions and the performance of the policies. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008