Integrated production and multiple trips vehicle routing with time windows and uncertain travel times

We study the integrated production and multiple trips vehicle routing problem with time windows and uncertain travel times involving two phases. The first phase considers scheduling a set of jobs on parallel machines with machine-dependent ready times, and the second phase focuses on the delivery of completed jobs by a fleet of identical vehicles, which may differ in their ready times. In addition, the travel times in distribution are uncertain. The objective is to minimize the total cost comprising the travel cost and penalty cost caused by tardiness. We present a robustness approach, known as “Elastic p-Robustness” to deal with travel time variations when historical risk data are limited or non-existent, and develop a memetic algorithm with an effective search strategy to solve the problem. We conduct numerical studies on randomly generated data based on real experience to assess the effectiveness and efficiency of the proposed method. The computational results show that the proposed solution approach yields relatively good solutions in comparison with current mainstream heuristic algorithms.