Title: A scenario analysis of a location problem with uncertain demand

Authors: Guy A. Tanonkou, Lyes Benyoucef, Xiaolan Xie

Addresses: INRIA-COSTEAM Project, ISGMP, Bat. A, Ile du Saulcy, 57000, Metz, France. ' INRIA-COSTEAM Project, ISGMP, Bat. A, Ile du Saulcy, 57000, Metz, France. ' Ecole National Superieure des Mines de Saint Etienne, Engineering and Health Division, 158, cours Fauriel 42023, St Etienne Cedex 2, France

Abstract: This paper considers the design of a distribution network composed of a single supplier serving a set of retailers through a set of Distribution Centres (DCs) to locate. The number and location of DCs are decision variables and they are chosen from the set of retailer locations. Each retailer faces a random demand and the supplier lead-time is constant. Furthermore, some parameters are random and described by scenarios, each with a specified probability of occurrence. The problem is formulated as a two-stage non-linear discrete stochastic optimisation problem. At the first stage, we decide on the DCs location and at the second stage, we assign retailers to located DCs with respect to a given scenario. The goal is to minimise the expected total cost resulted from the DCs location, transportation, working inventory and safety stocks costs. A Lagrangian relaxation based approach is proposed to generate efficient solutions. Computational results are presented and analysed showing the effectiveness of the proposed approach.

Keywords: location allocation problem; optimisation; Lagrangian relaxation; scenario analysis; distribution networks; distribution centres; distribution centre location; logistics; transportation costs; working inventory costs; safety stocks costs.

DOI: 10.1504/IJCAT.2008.021384

International Journal of Computer Applications in Technology, 2008 Vol.32 No.4, pp.290 - 297

Published online: 21 Nov 2008 *

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