Robust vehicle routing problem with hard time windows under demand and travel time uncertainty

• Published in: Computers & operations research Vol. 94; pp. 139 - 153
• Main Authors: Hu, C., Lu, J., Liu, X., Zhang, G.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.06.2018; Pergamon Press Inc
• Subjects: Adaptive algorithms; Adaptive variable neighborhood search; Algorithms; Computer science; Customer satisfaction; Customer services; Decision analysis; Demand; Design modifications; Heuristic; Logistics; Mathematical models; Numerical analysis; Operations research; Optimization algorithms; Robust optimization; Robustness (mathematics); Route optimization; Route planning; Solvers; Time windows; Travel time; Uncertainty; Vehicle routing; Vehicles; Windows (intervals); Time windows; Uncertainty; Robust optimization; Vehicle routing; Adaptive variable neighborhood search
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2018.02.006

•A robust version of the VRPTW with demand and travel time uncertainty is studied.•A two-stage algorithm based on a modified AVNS heuristic is developed.•The robust solutions can greatly improve the route robustness by adding little cost.•Managerial insights are derived for decision-makers in the logistics industry. Due to an increase in customer-oriented service strategies designed to meet more complex and exacting customer requirements, meeting a scheduled time window has become an important part of designing vehicle routes for logistics activities. However, practically, the uncertainty in travel times and customer demand often means vehicles miss these time windows, increasing service costs and decreasing customer satisfaction. In an effort to find a solution that meets the needs of real-world logistics, we examine the vehicle routing problem with hard time windows under demand and travel time uncertainty. To address the problem, we build a robust optimization model based on novel route-dependent uncertainty sets. However, due to the complex nature of the problem, the robust model is only able to tackle small-sized instances using standard solvers. Therefore, to tackle large instances, we design a two-stage algorithm based on a modified adaptive variable neighborhood search heuristic. The first stage of the algorithm minimizes the total number of vehicle routes, while the second stage minimizes the total travel distance. Extensive computational experiments are conducted with modified versions of Solomon’s benchmark instances. The numerical results show that the proposed two-stage algorithm is able to find optimal solutions for small-sized instances and good-quality robust solutions for large-sized instances with little increase to the total travel distance and/or the number of vehicles used. A detailed analysis of the results also reveals several managerial insights for decision-makers in the logistics industry.