Solving vehicle routing problem with time windows using metaheuristic approaches

Drugs are strategic products with essential functions in human health. An optimum design of the pharmaceutical supply chain is critical to avoid economic damage and adverse effects on human health. The vehicle-routing problem, focused on finding the lowest-cost routes with available vehicles and constraints, such as time constraints and road length, is an important aspect of this. In this paper, the vehicle routing problem (VRP) for a pharmaceutical company in Turkey is discussed.

A mixed-integer programming (MIP) model based on the vehicle routing problem with time windows (VRPTW) is presented, aiming to minimize the total route cost with certain constraints. As the model provides an optimum solution for small problem sizes with the GUROBI® solver, for large problem sizes, metaheuristic methods that simulate annealing and adaptive large neighborhood search algorithms are proposed. A real dataset was used to analyze the effectiveness of the metaheuristic algorithms. The proposed simulated annealing (SA) and adaptive large neighborhood search (ALNS) were evaluated and compared against GUROBI® and each other through a set of real problem instances.

The model is solved optimally for a small-sized dataset with exact algorithms; for solving a larger dataset, however, metaheuristic algorithms require significantly lesser time. For the problem addressed in this study, while the metaheuristic algorithms obtained the optimum solution in less than one minute, the solution in the GUROBI® solver was limited to one hour and three hours, and no solution could be obtained in this time interval.

The VRPTW problem presented in this paper is a real-life problem. The vehicle fleet owned by the factory cannot be transported between certain suppliers, which complicates the solution of the problem.