A heuristic Approach for the k-Traveling Repairman Problem with Profits under Uncertainty

This paper addresses the k-traveling repairman problem with profits under uncertain travel times, a new vehicle routing problem aimed at visiting a subset of customers in order to collect a revenue, defined as decreasing function of the uncertain arrival times. We adopt a risk-averse approach, enabling the decision maker to manage and control risk, and develop a mean-risk model in which only the first and the second moment of the travel times distribution are required to be known. We propose an adaptive local search heuristic in which, in each iteration, a Greedy Randomized Adaptive Search Procedure is used to generate the initial solution. The effectiveness of the solution approach is shown by the computational experiments performed on a set of instances.