A Constant Approximation Algorithm for the One-Warehouse Multiretailer Problem

Authors:
Retsef Levi;Robin Roundy;David Shmoys;Maxim Sviridenko
Affiliations:
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853;School of Operations Research and Information Engineering and Department of Computer Science, Cornell University, Ithaca, New York 14853;IBM T. J. Watson Research Center, Yorktown Heights, New York 10598
Venue:
Management Science
Year:
2008

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Abstract

Deterministic inventory theory provides streamlined optimization models that attempt to capture trade-offs in managing the flow of goods through a supply chain. We will consider two well-studied deterministic inventory models, called the one-warehouse multiretailer (OWMR) problem and its special case the joint replenishment problem (JRP), and give approximation algorithms with worst-case performance guarantees. That is, for each instance of the problem, our algorithm produces a solution with cost that is guaranteed to be at most 1.8 times the optimal cost; this is called a 1.8-approximation algorithm. Our results are based on an LP-rounding approach; we provide the first constant approximation algorithm for the OWMR problem and improve the previous results for the JRP.