Variable neighborhood search incorporating a new bounding procedure for joint replenishment and delivery problem

In recent years, joint replenishment and delivery problem (JRD) has been examined extensively in the context of replenishment and inventory control. However, as an extension of joint replenishment problem, the JRD is more complex and difcult to optimize with an exact algorithm. In this study, lower and upper bounds of JRD are obtained approximately but quickly using a novel bounding procedure. Then, a variable neighborhood search (VNS) with the bounding method is developed to solve the JRD. Computational examples show that the bounding procedure can e?ectively and efciently determine satisfactory bounds, which are helpful for the proposed VNS. Results of randomly generated examples further indicate that the hybrid VNS performs better than the best known heuristic and metaheuristic for JRD in terms of accuracy.