An exact approach for the consistent vehicle routing problem (ConVRP)

This paper proposes a mathematical model for the Consistent Vehicle Routing Problem (ConVRP). The ConVRP is an extension of the VRP, considering customer satisfaction through consistent service. The consistency may be based on time or on the vehicle that offers the service. This paper proposes a novel mathematical model that allows solving the ConVRP for several companies for which visits to the customers need to be from the same service provider (namely, the same vehicle and driver). The efficiency of the model is tested on structured instances by changing customer distribution (uniform or clustered), depot location, and arrival time to the customer and re‐ moving certain constraints to see if they affect the performance of the objective function. The mathematical model is flexible and could be adapted to any characteristic of instances. The model was devel‐ oped in the AMPL programming language and solved with the solvers CPLEX and Gurobi. The results are promising based on the efficiency of the proposed method at solving the problem. This paper proposes a mathematical mixed‐integer linear programming model to solve the ConVRP. The proposed model can determine the total travel time of a vehicle fleet for a certain number of specific days, which routes should be taken by each vehicle per day, and the vehicles' arrival time for each customer. The mathematical model was tested on structured instances by analyzing changes to aspects such as customer distribution (uniform or clustered), depot loca‐ tion, arrival time at the customer, and removing certain constraints that affect the performance of the objective function. The model was developed in the AMPL programming language and solved with the solvers CPLEX and Gurobi. Although a mathematical model for the ConVRP at‐ tracts growing attention due to the few studies related to the problem. The mathematical struc‐ ture of the model is novel, and to the best of the author's knowledge, this is the first time a model for the ConVRP solves real and structured instances for companies that provide a consistent service over time, such as courier companies, elderly care service companies, and cleaning sec‐ tors, under realistic constraints.