Stochastic vehicle routing problem with heterogeneous vehicles and multiple prioritized time windows: Mathematical modeling and solution approach

This study addresses the vehicle routing problem with multiple hard prioritized time windows (VRPMPTW) with heterogeneous fleet of vehicles based on restrictions of a real-life distribution system. Three multi-objective models are proposed to address the VRPMPTW from different perspectives. The first one formulates the VRPMPTW, where travel times and transportation costs are deterministic. In the second model, a linear bi-objective model with stochastic fixed and variable transportation costs is developed to minimize total transportation costs and maximize satisfaction of customers, simultaneously. Third, a novel multi-objective stochastic VRPMPTW model, where travel times and costs are normal random variables. Due to the NP-hard essence of the problem, a binary artificial bee colony (ABC) algorithm is developed to solve the problem. The ABC algorithm is tuned via the Taguchi method. To validate the proposed algorithm, the results obtained by the ABC algorithm are compared with the optimal solutions of several small-size test problems. For the case study tackled in this paper, the ABC algorithm is utilized to solve the problem. The results of the binary ABC algorithm are approved by management experts.