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We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We introduce a new decision rule, called Global Stochastic Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing decision rules, such as MSA. In particular, we show that GSA fully integrates nonanticipativity constraints so that it leads to better decisions in our stochastic context. We describe a new heuristic approach for efficiently approximating our GSA rule. We introduce a new waiting strategy. Experiments on dynamic and stochastic benchmarks, which include instances of different degrees of dynamism, show that not only our approach is competitive with state-of-the-art methods, but also enables to compute meaningful offline solutions to fully dynamic problems where absolutely no a priori customer request is provided.

The Static and Stochastic Vehicle Routing Problem with Random Requests (SS-VRP-R) describes realistic operational contexts in which a fleet of vehicles has to serve customer requests appearing dynamically. Based on a probabilistic knowledge about the appearance of requests, the SS-VRP-R seeks a priori sequences of vehicle relocations, optimizing the expected responsiveness to the requests. In this paper, an existing computational framework, based on recourse strategies, is adapted to meet the objectives of the SS-VRP-R. The resulting models are applied to a real case study of the management of police units in Brussels. In this context, the expected average response time is minimized. To cope with the reality of the urban context, a time-dependent variant is also studied (TD-SS-VRP-R) in which the travel time between two locations is a function that depends on the departure time at the first location. Experiments confirm the contribution and the adaptability of the recourse strategies to a real-life, complex operational context. Provided an adequate solution method, simulation-based results show the high quality of the a priori solutions designed, even when compared to those designed by field experts. Finally, the experiments provide evidence that there is no potential gain in considering time-dependency in such an operational context.

We compare both deterministic and robust stochastic approaches to the problem of scheduling a set of scientific tasks under processing time uncertainty. While dealing with strict time windows and minimum transition time constraints, we provide closed-form expressions to compute the exact probability that a solution has to remain feasible. Experiments, taking uncertainty on the stochastic knowledge itself into account, are conducted on real instances involving the constraints faced and objectives pursued during a recent twoweek Mars analog mission in the desert of Utah, USA. The results reveal that, even when using very bad approximations of probability distributions, solutions computed from the stochastic models we introduce, significantly outperform the ones obtained from a classical deterministic formulation, while preserving most of the solution’s quality.