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A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design

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  • Ali Diabat
  • Jean-Philippe Richard
  • Craig Codrington

Abstract

We study a multi-echelon joint inventory-location model that simultaneously determines the location of warehouses and inventory policies at the warehouses and retailers. The model is formulated as a nonlinear mixed-integer program, and is solved using a Lagrangian relaxation-based approach. The efficiency of the algorithm and benefits of integration are evaluated through a computational study. Copyright The Author(s) 2013

Suggested Citation

  • Ali Diabat & Jean-Philippe Richard & Craig Codrington, 2013. "A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design," Annals of Operations Research, Springer, vol. 203(1), pages 55-80, March.
    • Handle: RePEc:spr:annopr:v:203:y:2013:i:1:p:55-80:10.1007/s10479-011-0915-2
    DOI: 10.1007/s10479-011-0915-2
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    1. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    2. Chung-Piaw Teo & Jia Shu, 2004. "Warehouse-Retailer Network Design Problem," Operations Research, INFORMS, vol. 52(3), pages 396-408, June.
    3. Jayaraman, Vaidyanathan & Ross, Anthony, 2003. "A simulated annealing methodology to distribution network design and management," European Journal of Operational Research, Elsevier, vol. 144(3), pages 629-645, February.
    4. Leroy B. Schwarz, 1973. "A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem," Management Science, INFORMS, vol. 19(5), pages 555-566, January.
    5. Mark Daskin & Collette Coullard & Zuo-Jun Shen, 2002. "An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results," Annals of Operations Research, Springer, vol. 110(1), pages 83-106, February.
    6. Sourirajan, Karthik & Ozsen, Leyla & Uzsoy, Reha, 2009. "A genetic algorithm for a single product network design model with lead time and safety stock considerations," European Journal of Operational Research, Elsevier, vol. 197(2), pages 599-608, September.
    7. Pablo Miranda & Rodrigo Garrido, 2006. "A Simultaneous Inventory Control and Facility Location Model with Stochastic Capacity Constraints," Networks and Spatial Economics, Springer, vol. 6(1), pages 39-53, March.
    8. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    9. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    10. Jayaraman, Vaidyanathan & Pirkul, Hasan, 2001. "Planning and coordination of production and distribution facilities for multiple commodities," European Journal of Operational Research, Elsevier, vol. 133(2), pages 394-408, January.
    11. Wee, H. M. & Yang, P. C., 2004. "The optimal and heuristic solutions of a distribution network," European Journal of Operational Research, Elsevier, vol. 158(3), pages 626-632, November.
    12. Antony Svoronos & Paul Zipkin, 1991. "Evaluation of One-for-One Replenishment Policies for Multiechelon Inventory Systems," Management Science, INFORMS, vol. 37(1), pages 68-83, January.
    13. Eskigun, Erdem & Uzsoy, Reha & Preckel, Paul V. & Beaujon, George & Krishnan, Subramanian & Tew, Jeffrey D., 2005. "Outbound supply chain network design with mode selection, lead times and capacitated vehicle distribution centers," European Journal of Operational Research, Elsevier, vol. 165(1), pages 182-206, August.
    14. Gary D. Eppen, 1979. "Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem," Management Science, INFORMS, vol. 25(5), pages 498-501, May.
    15. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    16. Zuo-Jun Max Shen & Collette Coullard & Mark S. Daskin, 2003. "A Joint Location-Inventory Model," Transportation Science, INFORMS, vol. 37(1), pages 40-55, February.
    17. John A. Muckstadt & Robin O. Roundy, 1987. "Multi-Item, One-Warehouse, Multi-Retailer Distribution Systems," Management Science, INFORMS, vol. 33(12), pages 1613-1621, December.
    18. Robin Roundy, 1985. "98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems," Management Science, INFORMS, vol. 31(11), pages 1416-1430, November.
    19. Romeijn, H. Edwin & Shu, Jia & Teo, Chung-Piaw, 2007. "Designing two-echelon supply networks," European Journal of Operational Research, Elsevier, vol. 178(2), pages 449-462, April.
    20. Leyla Ozsen & Collette R. Coullard & Mark S. Daskin, 2008. "Capacitated warehouse location model with risk pooling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 295-312, June.
    21. Gunasekaran, A. & Patel, C. & McGaughey, Ronald E., 2004. "A framework for supply chain performance measurement," International Journal of Production Economics, Elsevier, vol. 87(3), pages 333-347, February.
    22. Chan, Felix T. S. & Chung, S. H. & Wadhwa, Subhash, 2005. "A hybrid genetic algorithm for production and distribution," Omega, Elsevier, vol. 33(4), pages 345-355, August.
    23. K S Hindi & K Pieńkosz, 1999. "Efficient solution of large scale, single-source, capacitated plant location problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(3), pages 268-274, March.
    24. Jia Shu & Chung-Piaw Teo & Zuo-Jun Max Shen, 2005. "Stochastic Transportation-Inventory Network Design Problem," Operations Research, INFORMS, vol. 53(1), pages 48-60, February.
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    19. Diabat, Ali, 2014. "Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain," European Journal of Operational Research, Elsevier, vol. 238(1), pages 114-121.
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    23. Diabat, Ali & Al-Salem, Mohammed, 2015. "An integrated supply chain problem with environmental considerations," International Journal of Production Economics, Elsevier, vol. 164(C), pages 330-338.

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