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An integrated supply chain problem: a nested lagrangian relaxation approach

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  • Ali Diabat
  • Jean-Philippe Richard

Abstract

The integration of tactical-level with strategic-level decisions in the supply chain represents an opportunity for substantial cost savings and provides a means for companies to gain a competitive advantage. Much of the previous research on supply chain network design has handled facility location decisions and inventory management decisions independently. In this paper, we develop a new joint facility location inventory model that is based on an approximate one-warehouse multi-retailer inventory model for each warehouse, and on the uncapacitated facility location problem. The proposed integer programming model simultaneously makes decisions pertaining to location and inventory policies on two echelons of the supply chain, the warehouse and the retailers. We develop two Lagrangian-relaxation-based algorithms to solve this model, and compare their performance to that of a conventional branch-and-bound algorithm on randomly generated problems. Copyright Springer Science+Business Media New York 2015

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  • Ali Diabat & Jean-Philippe Richard, 2015. "An integrated supply chain problem: a nested lagrangian relaxation approach," Annals of Operations Research, Springer, vol. 229(1), pages 303-323, June.
    • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:303-323:10.1007/s10479-015-1818-4
    DOI: 10.1007/s10479-015-1818-4
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    1. Chu, Chi-Leung & Leon, V. Jorge, 2008. "Power-of-two single-warehouse multi-buyer inventory coordination with private information," International Journal of Production Economics, Elsevier, vol. 111(2), pages 562-574, February.
    2. Jia Shu & Qiang Ma & Sijie Li, 2010. "Integrated location and two-echelon inventory network design under uncertainty," Annals of Operations Research, Springer, vol. 181(1), pages 233-247, December.
    3. 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.
    4. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.
    5. 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.
    6. 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.
    7. Max Shen, Zuo-Jun & Qi, Lian, 2007. "Incorporating inventory and routing costs in strategic location models," European Journal of Operational Research, Elsevier, vol. 179(2), pages 372-389, June.
    8. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    9. 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.
    10. Donald Erlenkotter, 1990. "Ford Whitman Harris and the Economic Order Quantity Model," Operations Research, INFORMS, vol. 38(6), pages 937-946, December.
    11. Leyla Ozsen & Mark S. Daskin & Collette R. Coullard, 2009. "Facility Location Modeling and Inventory Management with Multisourcing," Transportation Science, INFORMS, vol. 43(4), pages 455-472, November.
    12. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    13. 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.
    14. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    15. Chung-Piaw Teo & Jia Shu, 2004. "Warehouse-Retailer Network Design Problem," Operations Research, INFORMS, vol. 52(3), pages 396-408, June.
    16. Snyder, Lawrence V. & Daskin, Mark S. & Teo, Chung-Piaw, 2007. "The stochastic location model with risk pooling," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1221-1238, June.
    17. Ahmadi Javid, Amir & Azad, Nader, 2010. "Incorporating location, routing and inventory decisions in supply chain network design," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(5), pages 582-597, September.
    18. Krarup, Jakob & Pruzan, Peter Mark, 1983. "The simple plant location problem: Survey and synthesis," European Journal of Operational Research, Elsevier, vol. 12(1), pages 36-57, January.
    19. 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.
    20. Navneet Vidyarthi & Emre Çelebi & Samir Elhedhli & Elizabeth Jewkes, 2007. "Integrated Production-Inventory-Distribution System Design with Risk Pooling: Model Formulation and Heuristic Solution," Transportation Science, INFORMS, vol. 41(3), pages 392-408, August.
    21. 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.
    22. 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.
    23. Ho‐Yin Mak & Zuo‐Jun Max Shen, 2009. "A two‐echelon inventory‐location problem with service considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 730-744, December.
    24. 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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    Cited by:

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    5. Abolfazl Gharaei & Alireza Amjadian & Ali Shavandi & Amir Amjadian, 2023. "An augmented Lagrangian approach with general constraints to solve nonlinear models of the large-scale reliable inventory systems," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-37, March.
    6. Xianpei Hong & Wang Chunyuan & Lei Xu & Ali Diabat, 2016. "Multiple-vendor, multiple-retailer based vendor-managed inventory," Annals of Operations Research, Springer, vol. 238(1), pages 277-297, March.
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    8. Debnath, Biswajit & El-Hassani, Rihab & Chattopadhyay, Amit K. & Kumar, T. Krishna & Ghosh, Sadhan K. & Baidya, Rahul, 2022. "Time evolution of a Supply Chain Network: Kinetic modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    9. 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.
    10. Modibbo, Umar Muhammad & Arshad, Mohd. & Abdalghani, Omer & Ali, Irfan, 2021. "Optimization and estimation in system reliability allocation problem," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    11. Wang, Qifei & Hong, Xianpei & Gong, Yeming (Yale) & Chen, Wanying (Amanda), 2020. "Collusion or Not: The optimal choice of competing retailers in a closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 225(C).
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    16. Nouira, Imen & Hammami, Ramzi & Frein, Yannick & Temponi, Cecilia, 2016. "Design of forward supply chains: Impact of a carbon emissions-sensitive demand," International Journal of Production Economics, Elsevier, vol. 173(C), pages 80-98.
    17. Mohammad Saeid Atabaki & Mohammad Mohammadi & Bahman Naderi, 2017. "Hybrid Genetic Algorithm and Invasive Weed Optimization via Priority Based Encoding for Location-Allocation Decisions in a Three-Stage Supply Chain," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(02), pages 1-44, April.
    18. Xianpei Hong & Wang Chunyuan & Lei Xu & Ali Diabat, 2016. "Multiple-vendor, multiple-retailer based vendor-managed inventory," Annals of Operations Research, Springer, vol. 238(1), pages 277-297, March.
    19. Roozbeh Nia, Ali & Awasthi, Anjali & Bhuiyan, Nadia, 2023. "Integrate exergy costs and carbon reduction policy in order to optimize the sustainability development of coal supply chains in uncertain conditions," International Journal of Production Economics, Elsevier, vol. 257(C).

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