Solving the Heterogeneous Capacitated Vehicle Routing Problem using K-Means Clustering and Valid Inequalities

The Capacitated Vehicle Routing Problem (CVRP) is one of the most popular routing problems. In the CVRP, a fleet of capacitated vehicles located at a central depot are used to deliver products to a set of geographically dispersed customers with known demand. In this work, a new two-step approach to solve the CVRP with a heterogeneous fleet is proposed. In the first step; a balanced K-means clustering algorithm is used to aggregate the customers into balanced clusters. In the second step, clusters are assigned to vehicles and a MIP model is solved with adding valid inequalities that are used to reduce the volume of the mathematical model. Then the problem is disaggregated to find the detailed tours for each vehicle. The proposed approach was used to solve benchmark problems from literature, and it proved its efficiency in terms of quality, vehicle utilization, and computational time. The contribution of this work is combining the clustering algorithm with cutting techniques in order to find near-optimal solutions within reasonable computational times.