A Two-Level Variable Neighborhood Descent for a Split Delivery Clustered Vehicle Routing Problem with Soft Cluster Conflicts and Customer-Related Costs

This paper introduces Split Delivery Clustered Vehicle Routing Problem with Soft cluster conflicts and Customer-related costs (SDCVRPSC) arising in automotive parts of milk-run logistics with supplier cluster distribution in China. In SDCVRPSC, customers are divided into different clusters that can be visited by multiple vehicles, but each vehicle can only visit each cluster once. Penalty costs are incurred when traveling between clusters. The transportation cost of a route is calculated as the maximum direct shipment cost between customers on the route plus the total drop costs. The SDCVRPSC aims to minimize the sum of transportation costs and penalty costs by determining the assignment of customers to vehicles and the visiting order of clusters. We propose an integer linear programming model and a two-level variable neighborhood descent algorithm (TLVND) that includes two-stage construction, intensification at cluster and customer levels, and a perturbation mechanism. Experimental results on designed SDCVRPSC benchmark instances demonstrate that TLVND outperforms the Gurobi solver and two adapted algorithms at the business operation level. Moreover, a real case study indicates that TLVND can bring significant economic savings compared to expert experience decisions. TLVND has been integrated into the decision support system of the case company for daily operations.