A novel locust swarm algorithm for the joint replenishment problem considering multiple discounts simultaneously

In B2C E-Commerce operations, multiple quantity discount offers are commonly practiced in the multi-item replenishment environment. In this paper, a novel joint replenishment model (JRP) is presented considering two quantity discounts, all-unit quantity discount, incremental quantity discount, simultaneously. A novel swarms search technique, locust swarms algorithm (LS) is introduced and redesigned to solve the novel formulated JRP model. Numerical experiments and parameter sensitivity analyses reveal that LS is an effective and efficient algorithm for solving the proposed model in terms of solution quality and searching stableness comparing to some other meta-heuristic algorithms, such as GA, DE and PSO. Moreover, management insights such as the mutual effects of multiple quantity discounts to the total cost, and the role of multiple quantity discounts to different stakeholders in replenishment are outlined.