A novel multi-item joint replenishment problem considering multiple type discounts.

In business replenishment, discount offers of multi-item may either provide different discount schedules with a single discount type, or provide schedules with multiple discount types. The paper investigates the joint effects of multiple discount schemes on the decisions of multi-item joint replenishment. In this paper, a joint replenishment problem (JRP) model, considering three discount (all-unit discount, incremental discount, total volume discount) offers simultaneously, is constructed to determine the basic cycle time and joint replenishment frequencies of multi-item. To solve the proposed problem, a heuristic algorithm is proposed to find the optimal solutions and the corresponding total cost of the JRP model. Numerical experiment is performed to test the algorithm and the computational results of JRPs under different discount combinations show different significance in the replenishment cost reduction.