IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v20y2020i4d10.1007_s12351-018-0423-0.html
   My bibliography  Save this article

Modeling and solving a bi-objective joint replenishment-location problem under incremental discount: MOHSA and NSGA-II

Author

Listed:
  • Seyed Hamid Reza Pasandideh

    (Kharazmi University)

  • Seyed Taghi Akhavan Niaki

    (Sharif University of Technology)

  • Reza Abdollahi

    (Islamic Azad University, Qazvin Branch)

Abstract

In this paper, the joint replenishment-location problem of some distribution centers (DCs) with a centralized decision maker who is responsible for ordering and dispatching shipments of a single product is modeled. The warehouse spaces of the DCs are limited and the product is sold under an incremental discount policy. The model seeks to minimize the total cost of the supply chain under the joint replenishment policy along with minimizing the cost of locating the DCs in potential sites as the first objective. The second objective is to minimize the warehouse space of all DCs using the revisable approach. As the proposed model is a bi-objective integer non-linear optimization problem (NP-Hard) and cannot be solved by an exact method in a reasonable computational time, a multi-objective harmony search algorithm is developed to solve it. Since there is no benchmark available in the literature, the non-dominated sorting genetic algorithm II is utilized as well to validate the results obtained. As the performance of a meta-heuristic algorithm is largely influenced by the choice of its parameters, the response surface methodology is employed to tune the parameters. Several numerical illustrations are provided at the end to not only demonstrate the application of the proposed methodology, but also to analyze and compare the performances of the two solution algorithms in terms of several multi-objective measures.

Suggested Citation

  • Seyed Hamid Reza Pasandideh & Seyed Taghi Akhavan Niaki & Reza Abdollahi, 2020. "Modeling and solving a bi-objective joint replenishment-location problem under incremental discount: MOHSA and NSGA-II," Operational Research, Springer, vol. 20(4), pages 2365-2396, December.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:4:d:10.1007_s12351-018-0423-0
    DOI: 10.1007/s12351-018-0423-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-018-0423-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-018-0423-0?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. Alikar, Najmeh & Mousavi, Seyed Mohsen & Raja Ghazilla, Raja Ariffin & Tavana, Madjid & Olugu, Ezutah Udoncy, 2017. "Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 1-10.
    2. Claudia Archetti & Luca Bertazzi & Gilbert Laporte & Maria Grazia Speranza, 2007. "A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem," Transportation Science, INFORMS, vol. 41(3), pages 382-391, August.
    3. Porras, Eric & Dekker, Rommert, 2006. "An efficient optimal solution method for the joint replenishment problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1595-1615, November.
    4. Lin Wang & Hui Qu & Shan Liu & Can Chen, 2014. "Optimizing the Joint Replenishment and Channel Coordination Problem under Supply Chain Environment Using a Simple and Effective Differential Evolution Algorithm," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-12, June.
    5. Chan, Chi Kin & Cheung, Bernard K. -S. & Langevin, André, 2003. "Solving the multi-buyer joint replenishment problem with a modified genetic algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 37(3), pages 291-299, March.
    6. Sana Bouajaja & Najoua Dridi, 2017. "A survey on human resource allocation problem and its applications," Operational Research, Springer, vol. 17(2), pages 339-369, July.
    7. Hoque, M.A., 2006. "An optimal solution technique for the joint replenishment problem with storage and transport capacities and budget constraints," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1033-1042, December.
    8. Francisco Silva & Lucia Gao, 2013. "A Joint Replenishment Inventory-Location Model," Networks and Spatial Economics, Springer, vol. 13(1), pages 107-122, March.
    9. Cha, B.C. & Moon, I.K. & Park, J.H., 2008. "The joint replenishment and delivery scheduling of the one-warehouse, n-retailer system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(5), pages 720-730, September.
    10. Olsen, Anne L., 2008. "Inventory replenishment with interdependent ordering costs: An evolutionary algorithm solution," International Journal of Production Economics, Elsevier, vol. 113(1), pages 359-369, May.
    11. R Y K Fung & X Ma, 2001. "A new method for joint replenishment problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 358-362, March.
    12. Fatemeh RanjbarTezenji & Mohammad Mohammadi & Seyed Hamid Reza Pasandideh, 2017. "Bi-objective location-allocation-inventory-network design in a two-echelon supply chain using de novo programming, NSGA-II and NRGA," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 28(3), pages 308-337.
    Full references (including those not matched with items on IDEAS)

    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. Wang, Lin & He, Jing & Wu, Desheng & Zeng, Yu-Rong, 2012. "A novel differential evolution algorithm for joint replenishment problem under interdependence and its application," International Journal of Production Economics, Elsevier, vol. 135(1), pages 190-198.
    2. Baller, Annelieke C. & Dabia, Said & Dullaert, Wout E.H. & Vigo, Daniele, 2019. "The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1013-1033.
    3. Yao, Ming-Jong & Lin, Jen-Yen & Lin, Yu-Liang & Fang, Shu-Cherng, 2020. "An integrated algorithm for solving multi-customer joint replenishment problem with districting consideration," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    4. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    5. Shiyu Liu & Ou Liu & Xiaoming Jiang, 2023. "An Efficient Algorithm for the Joint Replenishment Problem with Quantity Discounts, Minimum Order Quantity and Transport Capacity Constraints," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    6. Amaya, Ciro Alberto & Carvajal, Jimmy & Castaño, Fabian, 2013. "A heuristic framework based on linear programming to solve the constrained joint replenishment problem (C-JRP)," International Journal of Production Economics, Elsevier, vol. 144(1), pages 243-247.
    7. Porras, Eric & Dekker, Rommert, 2008. "A solution method for the joint replenishment problem with correction factor," International Journal of Production Economics, Elsevier, vol. 113(2), pages 834-851, June.
    8. Xuefei Shi & Haiyan Wang, 2022. "Design of the cost allocation rule for joint replenishment to an overseas warehouse with a piecewise linear holding cost rate," Operational Research, Springer, vol. 22(5), pages 4905-4929, November.
    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. Ji Seong Noh & Jong Soo Kim & Biswajit Sarkar, 2019. "Stochastic joint replenishment problem with quantity discounts and minimum order constraints," Operational Research, Springer, vol. 19(1), pages 151-178, March.
    11. Chan, Chi Kin & Yuk-on Li, Leon & To Ng, Chi & Kin-sion Cheung, Bernard & Langevin, Andre, 2006. "Scheduling of multi-buyer joint replenishments," International Journal of Production Economics, Elsevier, vol. 102(1), pages 132-142, July.
    12. Tamar Cohen-Hillel & Liron Yedidsion, 2018. "The Periodic Joint Replenishment Problem Is Strongly 𝒩𝒫-Hard," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1269-1289, November.
    13. Porras Musalem, E. & Dekker, R., 2005. "Generalized Solutions for the joint replenishment problem with correction factor," Econometric Institute Research Papers EI 2005-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    14. Hoque, M.A., 2008. "Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain," European Journal of Operational Research, Elsevier, vol. 188(3), pages 811-825, August.
    15. Hoque, M.A., 2006. "An optimal solution technique for the joint replenishment problem with storage and transport capacities and budget constraints," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1033-1042, December.
    16. 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.
    17. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    18. Zaretalab, Arash & Sharifi, Mani & Guilani, Pedram Pourkarim & Taghipour, Sharareh & Niaki, Seyed Taghi Akhavan, 2022. "A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    19. A. Mor & M. G. Speranza, 2020. "Vehicle routing problems over time: a survey," 4OR, Springer, vol. 18(2), pages 129-149, June.
    20. Alireza Pooya & Morteza Pakdaman, 2021. "A new continuous time optimal control model for manpower planning with promotion from inside the system," Operational Research, Springer, vol. 21(1), pages 349-364, March.

    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:operea:v:20:y:2020:i:4:d:10.1007_s12351-018-0423-0. 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.