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In this paper, the authors consider the vehicle routing problem (VRP) with stochastic demand and/or dynamic requests. The classical VRP consists of determining a set of routes starting and ending at a depot that provide service to a set of customers. Stochastic demands are only revealed when the vehicle arrives at the customer location; dynamic requests mean that new orders from previously unknown customers can be received and scheduled over time. The variable neighborhood search algorithm (VNS) proposed in this study can be extended by sampling for stochastic scenarios and adapted for the dynamic setting. We use standard sets of benchmark instances to evaluate our algorithms. When applying sampling based VNS, on average we were able to improve results obtained by a classical VNS by 4.39 %. Individual instances could be improved by up to 8.12 %. In addition, the proposed VNS framework matches 32 out of 40 best known solutions and provides one new best solution. In the dynamic case, VNS improves on existing results and provides new best solutions for 7 out of 21 instances. Finally, this study offers results for stochastic and dynamic scenarios. Our experiments show that the sampling based dynamic VNS provides better results when the demand deviation is small, and reduces the excess route duration by 45-90 %.

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A vehicle routing problem with synchronization constraints arises in urban freight transportation, in which context customers require deliveries from one or more logistics service providers. These deliveries should be efficient to reduce idle times at the delivery locations. Idle time is defined as nonservice time between the first and the last delivery received by the customer. We propose a strategy which relies on self-imposed time windows, and we compare our approach with an exact determination of a feasible schedule and fixed time windows. The results show that idle times can be reduced by 54.12%-79.77%, with an average cost rise of 9.87%. In addition, self-imposed time windows provide solutions with 15.74%-21.43% lower costs than feasibility checks for short runtimes and 13.71%-21.15% lower than fixed time windows. KEYWORDSadaptive large neighborhood search, cooperation, metaheuristic, self-imposed time windows, synchronized transportation, vehicle routing problem This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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