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An efficient algorithm for a generalized joint replenishment problem

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  • Frenk, J.B.G.
  • Kleijn, M.J.
  • Dekker, R.

Abstract

In most multi-item inventory systems, the ordering costs consist of a major cost and a minor cost for each item included. Applying for every individual item a cyclic inventory policy, where the cycle length is a multiple of some basic cycle time, reduces the major ordering costs. An efficient algorithm to determine the optimal policy of this type is discussed in this paper. It is shown that this algorithm can be used for deterministic multi-item inventory problems, with general cost rate functions and possibly service level constraints, of which the well-known joint replenishment problem is a special case. Some useful results in determining the optimal control parameters are derived, and worked out for piecewise linear cost rate functions. Numerical results for this case show that the algorithm significantly outperforms other solution methods, both in the quality of the solution as in the running time.

Suggested Citation

  • Frenk, J.B.G. & Kleijn, M.J. & Dekker, R., 1997. "An efficient algorithm for a generalized joint replenishment problem," Econometric Institute Research Papers EI 9701-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:1423
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    References listed on IDEAS

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    1. Frenk, J. B. G. & Kleijn, M. J. & Dekker, R., 1999. "An efficient algorithm for a generalized joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 118(2), pages 413-428, October.
    2. 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.
    3. S. K. Goyal, 1973. "Determination of Economic Packaging Frequency for Items Jointly Replenished," Management Science, INFORMS, vol. 20(2), pages 232-235, October.
    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. Arthur F. Veinott, Jr., 1966. "The Status of Mathematical Inventory Theory," Management Science, INFORMS, vol. 12(11), pages 745-777, July.
    6. A. Federgruen & H. Groenevelt & H. C. Tijms, 1984. "Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands," Management Science, INFORMS, vol. 30(3), pages 344-357, March.
    7. Goyal, Suresh K. & Satir, Ahmet T., 1989. "Joint replenishment inventory control: Deterministic and stochastic models," European Journal of Operational Research, Elsevier, vol. 38(1), pages 2-13, January.
    8. Edward A. Silver, 1976. "A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand," Management Science, INFORMS, vol. 22(12), pages 1351-1361, August.
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    Cited by:

    1. Frenk, J. B. G. & Kleijn, M. J. & Dekker, R., 1999. "An efficient algorithm for a generalized joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 118(2), pages 413-428, October.
    2. Bayindir, Z.P. & Birbil, S.I. & Frenk, J.B.G., 2007. "A deterministic inventory/production model with general inventory cost rate function and piecewise linear concave production costs," European Journal of Operational Research, Elsevier, vol. 179(1), pages 114-123, May.
    3. Bayindir, Z.P. & Birbil, S.I. & Frenk, J.B.G., 2006. "The joint replenishment problem with variable production costs," European Journal of Operational Research, Elsevier, vol. 175(1), pages 622-640, November.
    4. Birbil, S.I. & Frenk, J.B.G. & Bayindir, Z.P., 2004. "A Deterministic Inventory/Production Model with General Inventory Cost Rate Function and Concave Production Costs," Econometric Institute Research Papers ERS-2004-064-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Rempala, Ryszarda, 2003. "Joint replenishment multiproduct inventory problem with continuous production and discrete demands," International Journal of Production Economics, Elsevier, vol. 81(1), pages 495-511, January.
    6. Birbil, S.I. & Frenk, J.B.G. & Bayindir, Z.P., 2004. "A Deterministic Inventory/Production Model with General Inventory Cost Rate Function and Concave Production Costs," ERIM Report Series Research in Management ERS-2004-064-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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