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Optimal Replenishment Order Placement in a Finite Time Horizon

Author

Listed:
  • Manlio Gaudioso

    (Università della Calabria)

  • Giovanni Giallombardo

    (Università della Calabria)

  • Giovanna Miglionico

    (Università della Calabria)

Abstract

Import companies operating in the globalized market and in a multi-item context are frequently faced with the need of aggregating their orders to benefit from scale economies associated to the use of containers for freight shipping. We introduce the problem of optimal replenishment order placement, namely the problem of scheduling and aggregating a fixed number of replenishment orders, along a given planning horizon, with the aim of minimizing the total inventory and backorder costs. For this problem, a continuous optimization formulation is provided, which is characterized by a nonconvex piecewise affine objective function. We introduce an ad hoc algorithm, based on the coordinate search approach, for the approximate numerical solution of the continuous model, and present the numerical results obtained on a set of randomly generated instances. In order to evaluate the quality of solutions returned by the algorithm, a discrete formulation of the problem is also provided, which falls into the well-known class of uncapacitated location models of the p-median type, whose exact solution on the same instance set can be obtained by means of an integer programming commercial solver.

Suggested Citation

  • Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2015. "Optimal Replenishment Order Placement in a Finite Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1078-1089, March.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-013-0452-z
    DOI: 10.1007/s10957-013-0452-z
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. 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.
    3. 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.
    4. 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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    7. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
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