The Cumulative Capacitated Vehicle Routing Problem with Profits Under Uncertainty

Abstract

In this paper, we introduce the cumulative capacitated vehicle routing problem with profits and uncertain travel times. The aim is to visit a subset of customers maximizing the total collected revenue expressed as a decreasing function of the uncertain arrival times. The selective nature of the problem, the stochasticity of travel times, and the introduction of the capacity of vehicles make the problem quite challenging. We present a risk-averse approach leading to a non-linear mixed integer mathematical model. To solve the model, we develop a very fast and efficient metaheuristic designed to address the selective nature of the problem. The performance of the metaheuristic is shown by preliminary results obtained for two sets of benchmark instances.