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A solution method for the joint replenishment problem with correction factor

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  • Porras, Eric
  • Dekker, Rommert

Abstract

In this paper, we give a rather complete analysis of the joint replenishment problem (JRP) under constant demands and continuous time. We first investigate several methods for bounding the optimal cycle time. Next we show that under certain restrictions on the input data the standard JRP can be solved in polynomial time, implying that exact algorithms are practically feasible. Then we present a solution method for the JRP when a correction is made for empty replenishments. We show that the solutions obtained differ from the standard JRP when no correction is made in the cost function. The theoretical findings are corroborated by applying the proposed methods to a large set of experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:113:y:2008:i:2:p:834-851
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    1. Porras Musalem, E. & Dekker, R., 2005. "New Bounds for the Joint Replenishment Problem: Tighter, but not always better," Econometric Institute Research Papers EI 2005-18, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Moon, I.K. & Cha, B.C., 2006. "The joint replenishment problem with resource restriction," European Journal of Operational Research, Elsevier, vol. 173(1), pages 190-198, 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. 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.
    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. S Viswanathan, 2002. "On optimal algorithms for the joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1286-1290, November.
    7. Robin Roundy, 1989. "Rounding Off to Powers of Two in Continuous Relaxations of Capacitated Lot Sizing Problems," Management Science, INFORMS, vol. 35(12), pages 1433-1442, December.
    8. 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.
    9. S. K. Goyal, 1974. "Determination of Optimum Packaging Frequency of Items Jointly Replenished," Management Science, INFORMS, vol. 21(4), pages 436-443, December.
    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.
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    Cited by:

    1. Zhang, Ren-Qian, 2012. "An extension of partial backordering EOQ with correlated demand caused by cross-selling considering multiple minor items," European Journal of Operational Research, Elsevier, vol. 220(3), pages 876-881.
    2. Stefanny Ramirez & Laurence H. Brandenburg & Dario Bauso, 2023. "Coordinated Replenishment Game and Learning Under Time Dependency and Uncertainty of the Parameters," Dynamic Games and Applications, Springer, vol. 13(1), pages 326-352, March.
    3. 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.
    4. Young Hyeon Yang & Jong Soo Kim, 2020. "An adaptive joint replenishment policy for items with non-stationary demands," Operational Research, Springer, vol. 20(3), pages 1665-1684, September.
    5. Tsai, Chieh-Yuan & Tsai, Chi-Yang & Huang, Po-Wen, 2009. "An association clustering algorithm for can-order policies in the joint replenishment problem," International Journal of Production Economics, Elsevier, vol. 117(1), pages 30-41, January.
    6. Eksler, Leonid & Aviram, Roei & Elalouf, Amir & Kamble, Aakash, 2018. "An EOQ model for multiple products with varying degrees of substitutability," Economics Discussion Papers 2018-77, Kiel Institute for the World Economy (IfW Kiel).
    7. Dawande, Milind & Gavirneni, Srinagesh & Naranpanawe, Sanjeewa & Sethi, Suresh P., 2009. "Discrete forecast horizons for two-product variants of the dynamic lot-size problem," International Journal of Production Economics, Elsevier, vol. 120(2), pages 430-436, August.

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