Mathematical model suggestion for a vehicle routing problem with the fleet of air and roadway vehicles

Recently, Vehicle Routing Problems (VRP) have played an important part in transportation. Transportation companies save from cost and resources such as human, vehicle and fuel using mathematical models related with VRP. Multi-Depot Vehicle Routing Problem with Heterogeneous Fleet and Time Window (MDHFTWVRP), which is one of the VRP types, is considered in the study. Besides the road vehicles, especially air vehicles have been used as heterogeneous fleet. Costs and criteria for air vehicles have been examined in detail. In the study, two mathematical models for MDHFTWVRP and their solutions are presented. In the solution of mathematical models, real demand, real air and road costs were used. GAMS software was used in the solutions of the mathematical models. Mathematical models were solved according to two scenarios. In the first scenario, the time wasn't considered in the delivery of the demands. In the other scenario, the time was considered in the delivery of the demands. When the time period wasn't considered, only the road vehicles were used for delivery of the demands. In the second scenario both air and road vehicles were used and the cost was higher than the first scenario. In the second mathematical model, two different depot opening cost were determined for the selection of the depot nodes. It is shown that different depot nodes could be selected according to the depot opening cost. As a result, the mathematical models and their solutions developed in the study present a suitable scientific approach in terms of multi-depot, time, air and road transportation in freight transportation for the transportation companies.