Design of a Distribution Network Using Primal-Dual Decomposition

A method to solve the design of a distribution network for bottled drinks company is introduced. The distribution network proposed includes three stages: manufacturing centers, consolidation centers using cross-docking, and distribution centers. The problem is formulated using a mixed-integer programming model in the deterministic and single period contexts. Because the problem considers several elements in each stage, a direct solution is very complicated. For medium-to-large instances the problem falls into large scale. Based on that, a primal-dual decomposition known as cross decomposition is proposed in this paper. This approach allows exploring simultaneously the primal and dual subproblems of the original problem. A comparison of the direct solution with a mixed-integer lineal programming solver versus the cross decomposition is shown for several randomly generated instances. Results show the good performance of the method proposed.

[1]  Mohd Rizam Abu Bakar,et al.  Development of a new approach for deterministic supply chain network design , 2009, Eur. J. Oper. Res..

[2]  K. Jörnsten,et al.  Cross decomposition applied to the stochastic transportation problem , 1984 .

[3]  Francisco Saldanha-da-Gama,et al.  Facility location and supply chain management - A review , 2009, Eur. J. Oper. Res..

[4]  Tony J. Van Roy,et al.  Cross decomposition for mixed integer programming , 1983, Math. Program..

[5]  Sunil Chopra,et al.  Designing the distribution network in a supply chain , 2003 .

[6]  Shu-Hsien Liao,et al.  A multi-objective evolutionary optimization approach for an integrated location-inventory distribution network problem under vendor-managed inventory systems , 2011, Ann. Oper. Res..

[7]  Yuehwern Yih,et al.  Production-distribution network design of a global supply chain alliance from the key player's perspective , 2007 .

[8]  Vaidyanathan Jayaraman.  An Efficient Heuristic Procedure for Practical-Sized Capacitated Warehouse Design and Management* , 1998 .

[9]  Pierre Hansen,et al.  A Plant and Warehouse Location Problem , 1977 .

[11]  Hanif D. Sherali,et al.  Dual formulations and subgradient optimization strategies for linear programming relaxations of mixed-integer programs , 1988, Discret. Appl. Math..

[12]  Alain Martel,et al.  A variable neighborhood search heuristic for the design of multicommodity production–distribution networks with alternative facility configurations , 2011, OR Spectr..

[13]  Lixin Tang,et al.  A hybrid algorithm of tabu search and benders decomposition for multi-product production distribution network design , 2009, 2009 IEEE International Conference on Automation and Logistics.

[14]  Nathalie Bostel,et al.  A linear relaxation-based heuristic approach for logistics network design , 2010, Comput. Ind. Eng..

[15]  Jabalameli M.Saeed,et al.  CAPACITATED FACILITY LOCATION PROBLEM WITH VARIABLE COVERAGE RADIUS IN DISTRIBUTION SYSTEM , 2010 .

[16]  John Johansen,et al.  Manufacturing network evolution: a manufacturing plant perspective , 2011 .

[17]  Henrik Sternberg,et al.  Design of global production and distribution networks: A literature review and research agenda , 2015 .

[18]  A. M. Geoffrion,et al.  Multicommodity Distribution System Design by Benders Decomposition , 1974 .

[19]  C. Y. Lee.  Application of a Cross Decomposition Algorithm to a Location and Allocation Problem in Distributed Systems , 1995, Comput. Commun..

[20]  Jacques F. Benders,et al.  Partitioning procedures for solving mixed-variables programming problems , 2005, Comput. Manag. Sci..

[21]  Ali Amiri,et al.  Production , Manufacturing and Logistics Designing a distribution network in a supply chain system : Formulation and efficient solution procedure , 2005 .

[22]  Oliverio Cruz-Mejia,et al.  Reverse logistics of recovery and recycling of non-returnable beverage containers in the brewery industry , 2014 .

[23]  Trevor S. Hale,et al.  A framework for an integrated distribution system optimisation model , 2008 .

[24]  I. Litvinchev,et al.  Multiperiod optimal planning of thermal generation using cross decomposition , 2011 .

[25]  Jose A. Ventura,et al.  Multi-criteria mathematical model for designing the distribution network of a consumer goods company , 2010, Comput. Ind. Eng..

[26]  Hasan Pirkul,et al.  Production, Transportation, and Distribution Planning in a Multi-Commodity Tri-Echelon System , 1996, Transp. Sci..

[27]  Halit Üster,et al.  A Benders decomposition approach for a distribution network design problem with consolidation and capacity considerations , 2011, Oper. Res. Lett..

[28]  Halit Üster,et al.  Tabu Search and Benders Decomposition Approaches for a Capacitated Closed-Loop Supply Chain Network Design Problem , 2009, Transp. Sci..

[29]  Hongwei Ding,et al.  Stochastic multi-objective production-distribution network design using simulation-based optimization , 2009 .

[31]  Hasan Pirkul,et al.  A multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution , 1998, Comput. Oper. Res..

[32]  Ignacio E. Grossmann,et al.  A Novel Cross-decomposition Multi-cut Scheme for Two-Stage Stochastic Programming , 2014 .

[33]  Hasan Pirkul,et al.  Planning and coordination of production and distribution facilities for multiple commodities , 2001, Eur. J. Oper. Res..