The close–open mixed vehicle routing problem

We consider the Close–Open Mixed Vehicle Routing Problem (COMVRP) in this paper. The COMVRP differs from the classical vehicle routing problems because simultaneously considering open and close routes in the solution of the problem. The objective of the problem is to minimize the fixed and variable costs for operating the open and close routes. No attention was devoted to this problem. A mix integer programming (MIP) model and an effective metheuristic, i.e., memetic algorithm, are established for the COMVRP. Computational experiments are conducted. The results of experiments show that the proposed metheuristic algorithm is able to produce satisfied solutions within an acceptable running time, and outperforms the robust MIP solver CPLEX.