Approximation algorithms and hardness results for the joint replenishment Problepm with constant demands
Author(s)Schulz, Andreas S.; Telha Cornejo, Claudio A.
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In the Joint Replenishment Problem (JRP), the goal is to coordinate the replenishments of a collection of goods over time so that continuous demands are satisfied with minimum overall ordering and holding costs. We consider the case when demand rates are constant. Our main contribution is the first hardness result for any variant of JRP with constant demands. When replenishments per commodity are required to be periodic and the time horizon is infinite (which corresponds to the so-called general integer model with correction factor), we show that finding an optimal replenishment policy is at least as hard as integer factorization. This result provides the first theoretical evidence that the JRP with constant demands may have no polynomial-time algorithm and that relaxations and heuristics are called for. We then show that a simple modification of an algorithm by Wildeman et al. (1997) for the JRP gives a fully polynomial-time approximation scheme for the general integer model (without correction factor). We also extend their algorithm to the finite horizon case, achieving an approximation guarantee asymptotically equal to √9/8.
19th Annual European Symposium, Saarbrücken, Germany, September 5-9, 2011. Proceedings
DepartmentMassachusetts Institute of Technology. Operations Research Center; Sloan School of Management
Algorithms – ESA 2011
Schulz, Andreas S., and Claudio Telha. “Approximation Algorithms and Hardness Results for the Joint Replenishment Problem with Constant Demands.” Algorithms – ESA 2011. Ed. Camil Demetrescu & Magnús M. Halldórsson. LNCS Vol. 6942. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. 628–639.
Author's final manuscript