Combining simheuristics with Petri nets for solving the stochastic vehicle routing problem with correlated demands

This paper analyzes a stochastic version of the vehicle routing problem in which customers' demands are not only stochastic but also correlated. In order to solve this stochastic and correlated optimization problem, a simheuristic approach is combined with an adaptive demand predictor. This predictor is based on the use of machine learning methods and Petri nets. The information on real demands, provided by the vehicles as they visit the nodes of the logistic network, allows for a real-time forecast of the demand, as well as for an updated estimate of the correlation between them. A constrained prediction is provided by our hybrid algorithm, which is able to forecast an increase of 50% in the mean value of the demands of all nodes. With a very limited amount of information and reduced computational requirements, our algorithm provides a forecast with a high degree of reliability and a balanced capacity to reject false positives as well as false negatives. To illustrate its effectiveness, the methodology is applied to a wide range of benchmarks. The results show the benefits of applying this methodology in a context of correlated variation of the demands.