IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v267y2018i3p806-817.html
   My bibliography  Save this article

A Generalized Benders Decomposition based algorithm for an inventory location problem with stochastic inventory capacity constraints

Author

Listed:
  • Tapia-Ubeda, Francisco J.
  • Miranda, Pablo A.
  • Macchi, Marco

Abstract

This paper deals with an inventory location problem with order quantity and stochastic inventory capacity constraints, which aims to address strategic supply chain network design problems and is of a nonlinear, nonconvex mixed integer programming nature. The problem integrates strategic supply chain networks design decisions (i.e., warehouse location and customer assignment) with tactical inventory control decisions for each warehouse (i.e., order size and reorder point). A novel decomposition approach that deals with the nonconvex nature of the problem formulation is proposed and implemented, based on the Generalized Benders Decomposition. The proposed decomposition yields a Master Problem that addresses warehouses location and customer assignment decisions, and a set of underlying Subproblems (SPs) that deal with warehouse inventory control decisions. Based on this decomposition, nonlinearity of the original problem is captured by the SPs that are solved at optimality, while the Master Problem is a mixed integer linear programming problem. The master is solved using a commercial solver, the SPs are solved analytically by inspection, and cuts to be added into the Master Problem are obtained based on Lagrangian dual information. Optimal solutions were found for 160 instances in competitive times.

Suggested Citation

  • Tapia-Ubeda, Francisco J. & Miranda, Pablo A. & Macchi, Marco, 2018. "A Generalized Benders Decomposition based algorithm for an inventory location problem with stochastic inventory capacity constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 806-817.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:3:p:806-817
    DOI: 10.1016/j.ejor.2017.12.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717311359
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.12.017?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. Miranda, Pablo A. & Garrido, Rodrigo A., 2008. "Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(1), pages 47-65, January.
    2. Zhang, Ying & Qi, Mingyao & Miao, Lixin & Liu, Erchao, 2014. "Hybrid metaheuristic solutions to inventory location routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 305-323.
    3. Semra Ağralı & Joseph Geunes & Z. Taşkın, 2012. "A facility location model with safety stock costs: analysis of the cost of single-sourcing requirements," Journal of Global Optimization, Springer, vol. 54(3), pages 551-581, November.
    4. 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.
    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. James R. Bradley & Bruce C. Arntzen, 1999. "The Simultaneous Planning of Production, Capacity, and Inventory in Seasonal Demand Environments," Operations Research, INFORMS, vol. 47(6), pages 795-806, December.
    7. 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.
    8. Pourya Pourhejazy & Oh Kyoung Kwon, 2016. "The New Generation of Operations Research Methods in Supply Chain Optimization: A Review," Sustainability, MDPI, vol. 8(10), pages 1-23, October.
    9. 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.
    10. 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.
    11. Farahani, Reza Zanjirani & Rezapour, Shabnam & Drezner, Tammy & Fallah, Samira, 2014. "Competitive supply chain network design: An overview of classifications, models, solution techniques and applications," Omega, Elsevier, vol. 45(C), pages 92-118.
    12. Wheatley, David & Gzara, Fatma & Jewkes, Elizabeth, 2015. "Logic-based Benders decomposition for an inventory-location problem with service constraints," Omega, Elsevier, vol. 55(C), pages 10-23.
    13. Guerrero, W.J. & Prodhon, C. & Velasco, N. & Amaya, C.A., 2013. "Hybrid heuristic for the inventory location-routing problem with deterministic demand," International Journal of Production Economics, Elsevier, vol. 146(1), pages 359-370.
    14. 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.
    15. H. Emir-Farinas & R. Francis, 2005. "Demand Point Aggregation for Planar Covering Location Models," Annals of Operations Research, Springer, vol. 136(1), pages 175-192, April.
    16. Escalona, P. & Ordóñez, F. & Marianov, V., 2015. "Joint location-inventory problem with differentiated service levels using critical level policy," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 83(C), pages 141-157.
    17. Miranda, Pablo A. & Garrido, Rodrigo A., 2004. "Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 40(3), pages 183-207, May.
    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. 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.
    20. Amiri-Aref, Mehdi & Klibi, Walid & Babai, M. Zied, 2018. "The multi-sourcing location inventory problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 266(1), pages 72-87.
    21. 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.
    22. Francis, R. L. & Lowe, T. J. & Tamir, A. & Emir-Farinas, H., 2004. "A framework for demand point and solution space aggregation analysis for location models," European Journal of Operational Research, Elsevier, vol. 159(3), pages 574-585, December.
    23. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    24. H. Theil & C. Van De Panne, 1960. "Quadratic Programming as an Extension of Classical Quadratic Maximization," Management Science, INFORMS, vol. 7(1), pages 1-20, October.
    25. Gabriel R. Bitran & Elizabeth A. Haas & Arnoldo C. Hax, 1982. "Hierarchical Production Planning: A Two-Stage System," Operations Research, INFORMS, vol. 30(2), pages 232-251, April.
    26. Xiang Li & Asgeir Tomasgard & Paul I. Barton, 2011. "Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 425-454, December.
    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. 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.
    2. Bei, Xiaoqiang & Zhu, Xiaoyan & Coit, David W., 2019. "A risk-averse stochastic program for integrated system design and preventive maintenance planning," European Journal of Operational Research, Elsevier, vol. 276(2), pages 536-548.
    3. Hu, Yuting & Li, Shukai & Dessouky, Maged M. & Yang, Lixing & Gao, Ziyou, 2022. "Computationally efficient train timetable generation of metro networks with uncertain transfer walking time to reduce passenger waiting time: A generalized Benders decomposition-based method," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 210-231.
    4. Wang, Minke & Wu, Jiang & Kafa, Nadine & Klibi, Walid, 2020. "Carbon emission-compliance green location-inventory problem with demand and carbon price uncertainties," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).

    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. 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.
    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. 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.
    4. Zheng, Xiaojin & Yin, Meixia & Zhang, Yanxia, 2019. "Integrated optimization of location, inventory and routing in supply chain network design," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 1-20.
    5. Shuangyan Li & Xialian Li & Dezhi Zhang & Lingyun Zhou, 2017. "Joint Optimization of Distribution Network Design and Two-Echelon Inventory Control with Stochastic Demand and CO2 Emission Tax Charges," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-22, January.
    6. 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.
    7. Emilio Carrizosa & Alba V. Olivares-Nadal & Pepa Ramírez-Cobo, 2020. "Embedding the production policy in location-allocation decisions," 4OR, Springer, vol. 18(3), pages 357-380, September.
    8. Miranda, Pablo A. & Garrido, Rodrigo A., 2009. "Inventory service-level optimization within distribution network design problem," International Journal of Production Economics, Elsevier, vol. 122(1), pages 276-285, November.
    9. Amiri-Aref, Mehdi & Klibi, Walid & Babai, M. Zied, 2018. "The multi-sourcing location inventory problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 266(1), pages 72-87.
    10. 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.
    11. 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.
    12. 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.
    13. Congdong Li & Hao Guo & Ying Zhang & Shuai Deng & Yu Wang, 2018. "An Improved Differential Evolution Algorithm for a Multicommodity Location-Inventory Problem with False Failure Returns," Complexity, Hindawi, vol. 2018, pages 1-13, October.
    14. 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.
    15. 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.
    16. Joy Chang & Miao Yu & Siqian Shen & Ming Xu, 2017. "Location Design and Relocation of a Mixed Car-Sharing Fleet with a CO 2 Emission Constraint," Service Science, INFORMS, vol. 9(3), pages 205-218, September.
    17. Escalona, P. & Marianov, V. & Ordóñez, F. & Stegmaier, R., 2018. "On the effect of inventory policies on distribution network design with several demand classes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 229-240.
    18. 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.
    19. 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).
    20. Snoeck, André & Winkenbach, Matthias & Fransoo, Jan C., 2023. "On-demand last-mile distribution network design with omnichannel inventory," Other publications TiSEM 83b06c9f-2a65-4aaf-880b-2, Tilburg University, School of Economics and Management.

    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:eee:ejores:v:267:y:2018:i:3:p:806-817. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.