A simple and fast 2-approximation algorithm for the one-warehouse multi-retailers problem

Authors:
Gautier Stauffer;Guillaume Massonnet;Christophe Rapine;Jean-Philippe Gayon
Affiliations:
Bordeaux Institute of Mathematics, Talence, France;Laboratoire G-SCOP, Grenoble INP, Grenoble Cedex, France;Laboratoire G-SCOP, Grenoble INP, Grenoble Cedex, France;Laboratoire G-SCOP, Grenoble INP, Grenoble Cedex, France
Venue:
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Year:
2011

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Abstract

We consider a well-known NP-hard deterministic inventory control problem: the One-Warehouse Multi-Retailer (OWMR) problem. We present a simple combinatorial algorithm to recombine the optimal solutions of the natural single-echelon inventory subproblems into a feasible solution of the OWMR problem. This approach yields a 3-approximation. We then show how this algorithm can be improved to a 2-approximation by halving the demands at the warehouse and at the retailers in the subproblems. Both algorithms are purely combinatorial and can be implemented to run in linear time for traditional linear holding costs and quadratic time for more general holding cost structures. We finally show that our technique can be extended to the Joint Replenishment Problem (JRP) with backorders and to the OWMR problem with non-linear holding costs.