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.
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Acknowledgements
We are grateful to two anonymous referees for a number of valuable comments on the first version of this paper.
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Communicated by Francis Tin-Loi.
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Gaudioso, M., Giallombardo, G. & Miglionico, G. Optimal Replenishment Order Placement in a Finite Time Horizon. J Optim Theory Appl 164, 1078–1089 (2015). https://doi.org/10.1007/s10957-013-0452-z
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DOI: https://doi.org/10.1007/s10957-013-0452-z