The coordinated replenishment dynamic lot-sizing problem with quantity discounts

In the classical coordinated replenishment dynamic lot-sizing problem, the primary motivation for coordination is in the presence of the major and minor setup costs. In this paper, a separate element of coordination made possible by the offer of quantity discounts is considered. A mathematical programming formulation for the extended problem under the all-units discount price structure and the incremental discount price structure is provided. Then, using variable redefinitions, tighter formulations are presented in order to obtain tight lower bounds for reasonable size problems. More significantly, as the problem is NP-hard, we present an effective polynomial time heuristic procedure, for the incremental discount version of the problem, that is capable of solving reasonably large size problems. Computational results for the heuristic procedure are reported in the paper.