A hybrid heuristic algorithm for cyclic inventory-routing problem with perishable products in VMI supply chain

The VMI supply chain can bring benefit to concerned parties. The paper studies cyclic inventory-routing problem (IRP) under VMI policy. Cyclic IRP as a variant of the IRP belong to long-term decision. It means once the replenishment policy and vehicle routing are determined, they will stay the same in the following periods. This paper considers the loss cost caused by perishability of perishable products and assumes the demand is dependent on price and stock. Based on the above consideration, three different cyclic IRP models for perishable products with stock and price dependent demand in VMI supply chain are put forward. They are IRP model ending with shortage, IRP model starting with shortage, and IRP model with no shortage. These models are composed of a single manufacturer and multiple retailers. The objective is to minimize the average total cost. The total cost includes not only fixed and transportation cost of vehicles, inventory (order and holding) and shortage cost of retailers, but also startup and holding cost of manufacturer. The proposed models are nonlinear mixed integer programming models and NP-hard problem. In order to solve these models, a hybrid heuristic algorithm that is developed by combining cuckoo algorithm with improved Clarke-Wright savings algorithm is developed. In computational experiments, the proposed algorithm is compared with the optimization solver. The results demonstrate the proposed algorithm outperforms the optimization solver. In addition, the results show the average total cost may be reduced by using the strategy of stockout in some cases. Sensitivity analysis is also implemented to study the influence of parameters on optimal solution. The results of computational experiments validate the applicability of the proposed models and the effectiveness of hybrid heuristic algorithm. The study also provides policymakers with management implications. Finally, the conclusions and future research directions are given.