Leveraging CPLEX to Solve the Vehicle Routing Problem with Time Windows

In recent years, the problem of urban traffic has become increasingly urgent when the number of vehicles has increased rapidly while the transport infrastructure has not kept up with the increasing needs of passengers and drivers. Ridesharing or vehicle sharing are the optimal solutions to save travel time and cost and enhance convenience for passengers and vehicle drivers. The vehicle routing problem with time window (VRPTW), an expansion of Vehicle Routing Problem (VRP), has been examined in recent literature to find the most effective solutions to address the arrangement of customers with known requests while minimizing the cost on a given set of routes. This paper presents a model to address the vehicle routing problem with time windows (VRPTW) applying Mixed-Integer Programming (MIP) to optimize transportation costs and vehicles' numbers. The mathematical model of MIP was conducted in Java using the Branch and Cut algorithm and dynamic search algorithm in the IBM CPLEX library (cplex.jar). The model has been tested with two well-known cases of Solomon's benchmarking problem. The testing results demonstrate that both the cost and the number of vehicles are optimized reasonably with this model. Furthermore, sensitivity analysis for passenger nodes conducted on this model results indicates that the computation time and the number of vehicles increased when the number of customer nodes increased. This paper has widened several directions for future research to develop optimal solutions to vehicle sharing.