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Logic-based Benders decomposition for an inventory-location problem with service constraints

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  • Wheatley, David
  • Gzara, Fatma
  • Jewkes, Elizabeth

Abstract

We study an integrated inventory-location problem with service requirements faced by an aerospace company in designing its service parts logistics network. Customer demand is Poisson distributed and the service levels are time-based leading to highly non-linear, stochastic service constraints and a nonlinear, mixed-integer optimization problem. Unlike previous work in the literature, which propose approximations for the nonlinear constraints, we present an exact solution methodology using logic-based Benders decomposition. We decompose the problem to separate the location decisions in the master problem from the inventory decisions in the subproblem. We propose a new family of valid cuts and prove that the algorithm is guaranteed to converge to optimality. This is the first attempt to solve this type of problem exactly. Then, we present a new restrict-and-decompose scheme to further decompose the Benders master problem by part. We test on industry instances as well as random instances. Using the exact algorithm and restrict-and-decompose scheme we are able to solve industry instances with up to 60 parts within reasonable time, while the maximum number of parts attempted in the literature is 5.

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  • 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.
    • Handle: RePEc:eee:jomega:v:55:y:2015:i:c:p:10-23
    DOI: 10.1016/j.omega.2015.02.001
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    Cited by:

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    8. Roshanaei, Vahid & Naderi, Bahman, 2021. "Solving integrated operating room planning and scheduling: Logic-based Benders decomposition versus Branch-Price-and-Cut," European Journal of Operational Research, Elsevier, vol. 293(1), pages 65-78.
    9. Karim Pérez Martínez & Yossiri Adulyasak & Raf Jans, 2022. "Logic-Based Benders Decomposition for Integrated Process Configuration and Production Planning Problems," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2177-2191, July.
    10. Guo, Penghui & Zhu, Jianjun, 2023. "Capacity reservation for humanitarian relief: A logic-based Benders decomposition method with subgradient cut," European Journal of Operational Research, Elsevier, vol. 311(3), pages 942-970.
    11. 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.
    12. Zhang, Zhe & Song, Xiaoling & Huang, Huijung & Zhou, Xiaoyang & Yin, Yong, 2022. "Logic-based Benders decomposition method for the seru scheduling problem with sequence-dependent setup time and DeJong’s learning effect," European Journal of Operational Research, Elsevier, vol. 297(3), pages 866-877.
    13. Arslan, Okan & Karaşan, Oya Ekin, 2016. "A Benders decomposition approach for the charging station location problem with plug-in hybrid electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 670-695.
    14. Han, Jialin & Hu, Yaoguang & Mao, Mingsong & Wan, Shuping, 2020. "A multi-objective districting problem applied to agricultural machinery maintenance service network," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1120-1130.
    15. Hassan Zohali & Bahman Naderi & Vahid Roshanaei, 2022. "Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 315-332, January.
    16. Gohram Baloch & Fatma Gzara, 2020. "Strategic Network Design for Parcel Delivery with Drones Under Competition," Transportation Science, INFORMS, vol. 54(1), pages 204-228, January.
    17. Dezhi Zhang & Shuxin Yang & Shuangyan Li & Jiajun Fan & Bin Ji, 2020. "Integrated Optimization of the Location–Inventory Problem of Maintenance Component Distribution for High-Speed Railway Operations," Sustainability, MDPI, vol. 12(13), pages 1-25, July.
    18. Teodor Gabriel Crainic & Mike Hewitt & Francesca Maggioni & Walter Rei, 2021. "Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design," Transportation Science, INFORMS, vol. 55(2), pages 414-435, March.
    19. Kafiabad, Shayan Tavakoli & Kazemi Zanjani, Masoumeh & Nourelfath, Mustapha, 2020. "Integrated planning of operations and on-job training in maintenance logistics networks," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    20. Witthayapraphakorn, Aphisak & Charnsethikul, Peerayuth, 2019. "Benders decomposition with special purpose method for the sub problem in lot sizing problem under uncertain demand," Operations Research Perspectives, Elsevier, vol. 6(C).
    21. Roshanaei, Vahid & Luong, Curtiss & Aleman, Dionne M. & Urbach, David R., 2020. "Reformulation, linearization, and decomposition techniques for balanced distributed operating room scheduling," Omega, Elsevier, vol. 93(C).
    22. Olga Porro & Francesc Pardo-Bosch & Núria Agell & Mónica Sánchez, 2020. "Understanding Location Decisions of Energy Multinational Enterprises within the European Smart Cities’ Context: An Integrated AHP and Extended Fuzzy Linguistic TOPSIS Method," Energies, MDPI, vol. 13(10), pages 1-29, May.
    23. Abbasi, B. & Hosseinifard, Z. & Alamri, O. & Thomas, D. & Minas, J.P., 2018. "Finite time horizon fill rate analysis for multiple customer cases," Omega, Elsevier, vol. 76(C), pages 1-17.
    24. Barzanji, Ramin & Naderi, Bahman & Begen, Mehmet A., 2020. "Decomposition algorithms for the integrated process planning and scheduling problem," Omega, Elsevier, vol. 93(C).

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