IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v203y2013i1p55-8010.1007-s10479-011-0915-2.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0915-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-011-0915-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    4. 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.
    5. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    6. 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.
    7. 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.
    8. Chung-Piaw Teo & Jia Shu, 2004. "Warehouse-Retailer Network Design Problem," Operations Research, INFORMS, vol. 52(3), pages 396-408, June.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hadi Jahangir & Mohammad Mohammadi & Seyed Hamid Reza Pasandideh & Neda Zendehdel Nobari, 2019. "Comparing performance of genetic and discrete invasive weed optimization algorithms for solving the inventory routing problem with an incremental delivery," Journal of Intelligent Manufacturing, Springer, vol. 30(6), pages 2327-2353, August.
    2. Aaron Guerrero Campanur & Elias Olivares-Benitez & Pablo A. Miranda & Rodolfo Eleazar Perez-Loaiza & Jose Humberto Ablanedo-Rosas, 2018. "Design of a Logistics Nonlinear System for a Complex, Multiechelon, Supply Chain Network with Uncertain Demands," Complexity, Hindawi, vol. 2018, pages 1-16, November.
    3. Ao Lv & Baofeng Sun, 2022. "Multi-Objective Robust Optimization for the Sustainable Location-Inventory-Routing Problem of Auto Parts Supply Logistics," Mathematics, MDPI, vol. 10(16), pages 1-22, August.
    4. Amir Hossein Sadeghi & Ziyuan Sun & Amirreza Sahebi-Fakhrabad & Hamid Arzani & Robert Handfield, 2023. "A Mixed-Integer Linear Formulation for a Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design," Logistics, MDPI, vol. 7(1), pages 1-24, March.
    5. Alzaman, Chaher & Zhang, Zhi-Hai & Diabat, Ali, 2018. "Supply chain network design with direct and indirect production costs: Hybrid gradient and local search based heuristics," International Journal of Production Economics, Elsevier, vol. 203(C), pages 203-215.
    6. Ali Diabat & Tarek Abdallah & Tung Le, 2016. "A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods," Annals of Operations Research, Springer, vol. 242(2), pages 373-398, July.
    7. Thomas Bittar & Pierre Carpentier & Jean-Philippe Chancelier & Jérôme Lonchampt, 2022. "A decomposition method by interaction prediction for the optimization of maintenance scheduling," Annals of Operations Research, Springer, vol. 316(1), pages 229-267, September.
    8. 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.
    9. 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.
    10. Zhang, Zhi-Hai & Unnikrishnan, Avinash, 2016. "A coordinated location-inventory problem in closed-loop supply chain," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 127-148.
    11. 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.
    12. Hao Guo & Ying Zhang & Chunnan Zhang & Yu Liu & Yuan Zhou, 2020. "Location-inventory decisions for closed-loop supply chain management in the presence of the secondary market," Annals of Operations Research, Springer, vol. 291(1), pages 361-386, August.
    13. 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.
    14. 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).
    15. Hamdan, Bayan & Diabat, Ali, 2020. "Robust design of blood supply chains under risk of disruptions using Lagrangian relaxation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    16. 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.
    17. 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.
    18. Diabat, Ali & Jabbarzadeh, Armin & Khosrojerdi, Amir, 2019. "A perishable product supply chain network design problem with reliability and disruption considerations," International Journal of Production Economics, Elsevier, vol. 212(C), pages 125-138.
    19. 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.
    20. Jihane El Ouadi & Hanae Errousso & Nicolas Malhene & Siham Benhadou, 2022. "On understanding the impacts of shared public transportation on urban traffic and road safety using an agent-based simulation with heterogeneous fleets: a case study of Casablanca city," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(6), pages 3893-3932, December.
    21. Zhalechian, M. & Tavakkoli-Moghaddam, R. & Zahiri, B. & Mohammadi, M., 2016. "Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 182-214.
    22. 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.
    23. Peyman Taki & Farnaz Barzinpour & Ebrahim Teimoury, 2016. "Risk-pooling strategy, lead time, delivery reliability and inventory control decisions in a stochastic multi-objective supply chain network design," Annals of Operations Research, Springer, vol. 244(2), pages 619-646, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Shu, Jia & Li, Zhengyi & Shen, Houcai & Wu, Ting & Zhong, Weijun, 2012. "A logistics network design model with vendor managed inventory," International Journal of Production Economics, Elsevier, vol. 135(2), pages 754-761.
    3. Melo, M.T. & Nickel, S. & Saldanha-da-Gama, F., 2009. "Facility location and supply chain management - A review," European Journal of Operational Research, Elsevier, vol. 196(2), pages 401-412, July.
    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. Tancrez, Jean-Sébastien & Lange, Jean-Charles & Semal, Pierre, 2012. "A location-inventory model for large three-level supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 485-502.
    6. 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.
    7. 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.
    8. 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.
    9. Zhang, Zhi-Hai & Unnikrishnan, Avinash, 2016. "A coordinated location-inventory problem in closed-loop supply chain," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 127-148.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Wenjun Ni & Jia Shu & Miao Song & Dachuan Xu & Kaike Zhang, 2021. "A Branch-and-Price Algorithm for Facility Location with General Facility Cost Functions," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 86-104, January.
    15. Yu Li & Jia Shu & Xi Wang & Naihua Xiu & Dachuan Xu & Jiawei Zhang, 2013. "Approximation Algorithms for Integrated Distribution Network Design Problems," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 572-584, August.
    16. Ross, Anthony & Khajehnezhad, Milad & Otieno, Wilkistar & Aydas, Osman, 2017. "Integrated location-inventory modelling under forward and reverse product flows in the used merchandise retail sector: A multi-echelon formulation," European Journal of Operational Research, Elsevier, vol. 259(2), pages 664-676.
    17. 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.
    18. Fathi, Mahdi & Khakifirooz, Marzieh & Diabat, Ali & Chen, Huangen, 2021. "An integrated queuing-stochastic optimization hybrid Genetic Algorithm for a location-inventory supply chain network," International Journal of Production Economics, Elsevier, vol. 237(C).
    19. Zhong, Yuanguang & Shu, Jia & Xie, Wei & Zhou, Yong-Wu, 2018. "Optimal trade credit and replenishment policies for supply chain network design," Omega, Elsevier, vol. 81(C), pages 26-37.
    20. Lehilton L. C. Pedrosa & Maxim Sviridenko, 2018. "Integrated Supply Chain Management via Randomized Rounding," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 124-136, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:203:y:2013:i:1:p:55-80:10.1007/s10479-011-0915-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.