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An efficient optimal solution method for the joint replenishment problem

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  • Wildeman, R.E.
  • Frenk, J.B.G.
  • Dekker, R.

Abstract

During the last two decades, many heuristic procedures for the joint replenishment problem have appeared in the literature. The only available optimal solution procedure was based on an enumerative approach and was computationally prohibitive. In this paper we present an alternative optimal approach based on global optimisation theory. By applying Lipschitz optimisation one can find a solution with an arbitrarily small deviation from an optimal value. An efficient procedure is presented which uses a dynamic Lipschitz constant and generates a solution in little time. The running time of this procedure grows only linearly in the number of items.
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  • 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.
    • Handle: RePEc:eee:ejores:v:99:y:1997:i:2:p:433-444
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    1. Ben-Daya, M. & Hariga, M., 1995. "Comparative study of heuristics for the joint replenishment problem," Omega, Elsevier, vol. 23(3), pages 341-344, June.
    2. 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.
    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. 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.
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