Approximation procedures for the one-warehouse multi-retailer system
Management Science
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Multistage Lot Sizing Problems via Randomized Rounding
Operations Research
A global optimum search algorithm for the joint replenishment problem under power-of-two policy
Computers and Operations Research
Primal-dual algorithms for deterministic inventory problems
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
An efficient polynomial-time approximation scheme for the joint replenishment problem
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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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 byWildeman 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.