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Integrated Inventory Control and Facility Location Decisions in a Multi-Echelon Supply Chain Network with Hubs

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  • Mehrdad Shahabi
  • Shirin Akbarinasaji
  • Avinash Unnikrishnan
  • Rachel James

Abstract

This paper develops mathematical models to coordinate facility location and inventory control for a four-echelon supply chain network consisting of multiple suppliers, warehouses, hubs and retailers. The hubs help in reducing transportation costs by consolidating products from multiple warehouses and directing the larger shipments to the retailer. The integrated models studied in this paper simultaneously determines three types of decisions: (i) facility location—the number and location of warehouses and hubs, (ii) allocation—assignment of suppliers to located warehouses and retailers to located warehouses via the location hubs, and (iii) inventory control decisions at each located warehouse. The goal is to minimize the facility location, transportation and the inventory costs. A mixed integer nonlinear programming formulation is first presented. The nonlinear integer programming formulation is then transformed into a conic mixed integer program and a novel and compact conic mixed integer programming formulation. Computational runs are conducted using commercial solvers to compare the performance of the different formulations. The compact conic mixed integer programming formulation was found to significantly outperform the other formulations by achieving significant computational savings. The results demonstrate that large scale instances of certain multi-echelon supply chain network design problems can be solved using commercial solvers through intelligent reformulation of the model. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Mehrdad Shahabi & Shirin Akbarinasaji & Avinash Unnikrishnan & Rachel James, 2013. "Integrated Inventory Control and Facility Location Decisions in a Multi-Echelon Supply Chain Network with Hubs," Networks and Spatial Economics, Springer, vol. 13(4), pages 497-514, December.
    • Handle: RePEc:kap:netspa:v:13:y:2013:i:4:p:497-514
    DOI: 10.1007/s11067-013-9196-4
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    Cited by:

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    2. Tatsuaki Kuroda, 2015. "A Model of Stratified Production Process and Spatial Risk," Networks and Spatial Economics, Springer, vol. 15(2), pages 271-292, June.
    3. Laura Scrimali, 2022. "On the Stability of Coalitions in Supply Chain Networks via Generalized Complementarity Conditions," Networks and Spatial Economics, Springer, vol. 22(2), pages 379-394, June.
    4. Darmawan, Agus & Wong, Hartanto & Thorstenson, Anders, 2021. "Supply chain network design with coordinated inventory control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    5. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2015. "A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 238-255.
    6. Shahabi, Mehrdad & Unnikrishnan, Avinash, 2014. "Robust hub network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 356-373.
    7. Schuster Puga, Matías & Minner, Stefan & Tancrez, Jean-Sébastien, 2019. "Two-stage supply chain design with safety stock placement decisions," International Journal of Production Economics, Elsevier, vol. 209(C), pages 183-193.
    8. Seyed Mohsen Mousavi & Ardeshir Bahreininejad & S. Nurmaya Musa & Farazila Yusof, 2017. "A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 191-206, January.
    9. Chih-Kang Lin & Shangyao Yan & Fei-Yen Hsiao, 2021. "Optimal Inventory Level Control and Replenishment Plan for Retailers," Networks and Spatial Economics, Springer, vol. 21(1), pages 57-83, March.
    10. Soumen Kumar Das & Magfura Pervin & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2023. "Multi-objective solid transportation-location problem with variable carbon emission in inventory management: a hybrid approach," Annals of Operations Research, Springer, vol. 324(1), pages 283-309, May.
    11. Jahani, Hamed & Abbasi, Babak & Sheu, Jiuh-Biing & Klibi, Walid, 2024. "Supply chain network design with financial considerations: A comprehensive review," European Journal of Operational Research, Elsevier, vol. 312(3), pages 799-839.
    12. Puntipa Punyim & Ampol Karoonsoontawong & Avinash Unnikrishnan & Chi Xie, 2018. "Tabu Search Heuristic for Joint Location-Inventory Problem with Stochastic Inventory Capacity and Practicality Constraints," Networks and Spatial Economics, Springer, vol. 18(1), pages 51-84, March.
    13. Sushil Poudel & Mohammad Marufuzzaman & Md Abdul Quddus & Sudipta Chowdhury & Linkan Bian & Brian Smith, 2018. "Designing a Reliable and Congested Multi-Modal Facility Location Problem for Biofuel Supply Chain Network," Energies, MDPI, vol. 11(7), pages 1-24, June.
    14. Simone Caschili & Francesca Medda & Alan Wilson, 2015. "An Interdependent Multi-Layer Model: Resilience of International Networks," Networks and Spatial Economics, Springer, vol. 15(2), pages 313-335, June.
    15. Wu, Xin & Nie, Lei & Xu, Meng & Zhao, Lili, 2019. "Distribution planning problem for a high-speed rail catering service considering time-varying demands and pedestrian congestion: A lot-sizing-based model and decomposition algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 61-89.
    16. Erfan Babaee Tirkolaee & Alireza Goli & Abbas Mardani, 2023. "A novel two-echelon hierarchical location-allocation-routing optimization for green energy-efficient logistics systems," Annals of Operations Research, Springer, vol. 324(1), pages 795-823, May.
    17. Anderson Rogério Faia Pinto & Antonio Fernando Crepaldi & Marcelo Seido Nagano, 2018. "A Genetic Algorithm applied to pick sequencing for billing," Journal of Intelligent Manufacturing, Springer, vol. 29(2), pages 405-422, February.
    18. Behnam Vahdani & Elham Ahmadzadeh, 2021. "Incorporating Price-Dependent Demands into a Multi-Echelon Closed-Loop Network Considering the Lost Sales and Backorders: a Case Study of Wireless Network," Networks and Spatial Economics, Springer, vol. 21(3), pages 639-680, September.
    19. Onur Kaya & Dogus Ozkok, 2020. "A Blood Bank Network Design Problem with Integrated Facility Location, Inventory and Routing Decisions," Networks and Spatial Economics, Springer, vol. 20(3), pages 757-783, September.
    20. Paul Berglund & Changhyun Kwon, 2014. "Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms," Networks and Spatial Economics, Springer, vol. 14(1), pages 117-132, March.
    21. Shahabi, Mehrdad & Tafreshian, Amirmahdi & Unnikrishnan, Avinash & Boyles, Stephen D., 2018. "Joint production–inventory–location problem with multi-variate normal demand," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 60-78.
    22. Schuster Puga, Matías & Tancrez, Jean-Sébastien, 2017. "A heuristic algorithm for solving large location–inventory problems with demand uncertainty," European Journal of Operational Research, Elsevier, vol. 259(2), pages 413-423.
    23. Gabriella Colajanni & Patrizia Daniele, 2022. "A Mathematical Network Model and a Solution Algorithm for IaaS Cloud Computing," Networks and Spatial Economics, Springer, vol. 22(2), pages 267-287, June.
    24. Shahabi, Mehrdad & Unnikrishnan, Avinash & Jafari-Shirazi, Ehsan & Boyles, Stephen D., 2014. "A three level location-inventory problem with correlated demand," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 1-18.

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