A mixed integer formulation and an efficient metaheuristic procedure for the k-Travelling Repairmen Problem

Abstract

In this paper, we study a k-Travelling Repairmen Problem where the objective is to minimize the sum of clients waiting time to receive service. This problem is relevant in applications that involve distribution of humanitarian aid in disaster areas, delivery and collection of perishable products and personnel transportation, where reaching demand points to perform service, fast and fair, is a priority. This paper presents a new mixed integer formulation and a simple and efficient metaheuristic algorithm. The proposed formulation consumes less computational time and allows solving to optimality more than three times larger data instances than the previous formulation published in literature, even outperforming a recently published Branch and Price and Cut algorithm for this problem. The proposed metaheuristic algorithm solved to optimality 386 out of 389 tested instances in a very short computational time. For larger instances, the algorithm was assessed using the best results reported in the literature for the Cumulative Capacitated Vehicle Routing Problem.

Keywords:

• k-Travelling Repairmen Problem
• total latency
• mixed integer formulation
• heuristics

Acknowledgements

This work is partially supported by the Research Chair in Industrial Engineering of Tecnológico de Monterrey (ITESM Research Fund CAT128) and by the Spanish Ministry of Economy and Competitiveness (project TIN2012-32608). These grants are gratefully acknowledged.