The multi-depot k-traveling repairman problem

In this paper, we study the multi-depot k-traveling repairman problem. This problem extends the traditional traveling repairman problem to the multi-depot case. Its objective, similar to the single depot variant, is the minimization of the sum of the arrival times to customers. We propose two distinct formulations to model the problem, obtained on layered graphs. In order to find feasible solutions for the largest instances, we propose a hybrid genetic algorithm where initial solutions are built using a splitting heuristic and a local search is embedded into the genetic algorithm. The efficiency of the mathematical formulations and of the solution approach are investigated through computational experiments. The proposed models are scalable enough to solve instances up to 240 customers

A hybrid reactive GRASP heuristic for the risk-averse k-traveling repairman problem with profits

This paper addresses the k-traveling repairman problem with profits and uncertain travel times, a vehicle routing problem aimed at visiting a subset of customers in order to collect a revenue, which is a decreasing function of the uncertain arrival times. The introduction of the arrival time in the objective function instead of the travel time, which is common in most vehicle routing problems, poses compelling computational challenges, emphasized by the incorporation of the stochasticity in travel times. For tackling the solution of the risk-averse k-traveling repairman problem with profits, in this paper is proposed a hybrid heuristic, where a reactive greedy randomized adaptive search procedure is used as a multi-start framework, equipped with an adaptive local search algorithm. The effectiveness of the solution approach is shown through an extensive experimental phase, performed on a set of instances, generated from three sets of benchmark instances containing up to 200 nodes