Heuristic approaches for a two-echelon constrained joint replenishment and delivery problem

This paper addresses the optimization of the total cost for an inventory and distribution system which consists of a Distribution Center (DC), multiple retailers, and multiple items. The problem known as constrained 1-warehouse, N-Retailers, with multiple item inventory systems (C-OWNRMI), additionally considers budgetary and storage capacity constraints. The former limits the amount of inventory that can be held at any moment at the DC. Similarly, capacity constraints at retailers’ facilities restrict the number of items which may be delivered and stored at each retailer location. Although several authors have proposed various approaches for solving the problem in a multi-item scenario, they often consider only one item to be sold and delivered by each retailer. This study, in contrast, considers multiple items to be sold and delivered by all retailers. Further, herein, orders are placed in a coordinated manner. The main objective of this research was to identify cost-efficient solutions for the inventory system under study. With this goal, we proposed a hybrid mat-heuristic that combines the search strategy and mixed-integer programming. Furthermore, a memetic algorithm (MA) is introduced, which includes a local search operator that exploits certain mathematical properties derived from the problem. The results suggest that both approaches are appropriate for resolution of this problem. However, the hybrid method often leads to better quality solutions than those obtained with the memetic algorithm.