Variable neighborhood search based algorithms to solve a rich k-travelling repairmen problem

In this paper, we consider a Rich k-travelling repairmen problem (R-k-TRP), motivated by an application for the maintenance and repair of electronic transaction equipment. It consists of designing routes of polyvalent repairmen to perform customers requests. The objective is to minimize a linear combination of total weighted travelled distance, breaks and overtime, minus gain associated with performed requests, under a set of constraints such as multiple time windows, parts inventory, breaks, and special parts. A benchmark of small and medium instances are considered from literature and new larger instances are generated. A Variable Neighborhood Search (VNS) and a General Variable Neighborhood Search algorithms (GVNS), both coupled with a technique called Adaptive memory (AM), are proposed to address this problem. The computational results show the effectiveness and efficiency of the GVNS with AM for solving the R-k-TRP, in comparison with other provided VNS algorithms and the current state of the art Branch and Price method.