In the real world, some heterogeneous items are prohibited from being transported together or penalty cost occurs when transporting them together. This paper firstly proposes the joint replenishment and delivery (JRD) model where a warehouse procures multi heterogeneous items from suppliers and deliveries them to retailers. The problem is to determine the grouping decision and when and how many to order and delivery to the warehouse and retailers such that the total costs are minimized. However, due to the JRD’s difficult mathematical properties, simple and effective solutions for this problem have eluded researchers. To find an optimal solution, an adaptive hybrid differential evolution (AHDE) algorithm is designed. Results of contrastive numerical examples show that AHDE outperforms genetic algorithm. The effectiveness of AHDE is further verified by randomly generated problems. The findings show that AHDE is more stable and robust in handling this complex problem. 
Modeling and optimization for the joint replenishment and delivery problem with heterogeneous items