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An efficient optimal solution method for the joint replenishment problem with minimum order quantities

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  • Porras Musalem, E.
  • Dekker, R.

Abstract

We study the joint replenishment problem (JRP) for M items under deterministic demand, with a minimum order quantity constraint for each item in the replenishment order. We first study an iterative procedure that proves to be not efficient in this case. Further, we derive bounds on the basic cycle time and propose an efficient global optimisation procedure to solve the JRP with constraints. Moreover, we also consider the case where a correction is made for empty replenishment occasions. The algorithms are tested in a real case.

Suggested Citation

  • Porras Musalem, E. & Dekker, R., 2003. "An efficient optimal solution method for the joint replenishment problem with minimum order quantities," Econometric Institute Research Papers EI 2003-52, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1084
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    References listed on IDEAS

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    1. Musalem, Eric Porras & Dekker, Rommert, 2005. "Controlling inventories in a supply chain: A case study," International Journal of Production Economics, Elsevier, vol. 93(1), pages 179-188, January.
    2. Eric Porras Musalem & Rommert Dekker, 2003. "Controlling Inventories in a Supply Chain," Tinbergen Institute Discussion Papers 03-012/4, Tinbergen Institute.
    3. Wildeman, R.E. & Frenk, J.B.G. & Dekker, R., 1997. "An efficient optimal solution method for the joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 99(2), pages 433-444, June.
    4. S. K. Goyal, 1974. "Determination of Optimum Packaging Frequency of Items Jointly Replenished," Management Science, INFORMS, vol. 21(4), pages 436-443, December.
    5. Porras Musalem, E. & Dekker, R., 2004. "On the efficiency of optimal algorithms for the joint replenishment problem: a comparative study," Econometric Institute Research Papers EI 2004-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. 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.
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    Cited by:

    1. Hellion, Bertrand & Mangione, Fabien & Penz, Bernard, 2012. "A polynomial time algorithm to solve the single-item capacitated lot sizing problem with minimum order quantities and concave costs," European Journal of Operational Research, Elsevier, vol. 222(1), pages 10-16.
    2. Zhu, Han & Liu, Xing & Chen, Youhua (Frank), 2015. "Effective inventory control policies with a minimum order quantity and batch ordering," International Journal of Production Economics, Elsevier, vol. 168(C), pages 21-30.
    3. 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.
    4. 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.
    5. Porras Musalem, E. & Dekker, R., 2004. "On the efficiency of optimal algorithms for the joint replenishment problem: a comparative study," Econometric Institute Research Papers EI 2004-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Okhrin, Irena & Richter, Knut, 2011. "The linear dynamic lot size problem with minimum order quantity," International Journal of Production Economics, Elsevier, vol. 133(2), pages 688-693, October.
    7. Tamar Cohen-Hillel & Liron Yedidsion, 2018. "The Periodic Joint Replenishment Problem Is Strongly š¯’©š¯’«-Hard," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1269-1289, November.
    8. Muriel, Ana & Chugh, Tammana & Prokle, Michael, 2022. "Efficient algorithms for the joint replenishment problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 300(1), pages 137-150.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Okhrin, Irena & Richter, Knut, 2011. "An O(T3) algorithm for the capacitated lot sizing problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 211(3), pages 507-514, June.
    15. 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.
    16. Vinod Kumar Mishra & Kripa Shanker, 2017. "Optimal ordering quantities for substitutable items under joint replenishment with cost of substitution," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(1), pages 77-104.
    17. 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.
    18. Saravanan Venkatachalam & Arunachalam Narayanan, 2016. "Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(14), pages 4087-4103, July.
    19. Amaya, Ciro Alberto & Carvajal, Jimmy & CastaƱo, 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.
    20. 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.
    21. 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.

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