Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints

• Published in: European journal of operational research Vol. 234; no. 1; pp. 49 - 60
• Main Authors: Luo, Zhixing, Qin, Hu, Lim, Andrew
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2014; Elsevier Sequoia S.A
• Subjects: Algorithms; Benchmarks; Branch-and-price; Branch-and-price-and-cut; Computation; Customers; Distance constraint; Effectiveness studies; Mathematical problems; Optimization; Optimization algorithms; Pricing; Shortest path algorithms; Strategy; Transportation problem (Operations research); Traveling repairmen problem; Vehicles; Traveling repairmen problem; Branch-and-price; Distance constraint; Branch-and-price-and-cut
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2013.09.014

•Introduced a new TRP variant that considers multiple vehicles and distance constraint.•Designed a tailored branch-and-price-and-cut algorithm for the problem.•Proposed a bounded bi-directional label-setting algorithm for the pricing subproblem.•Identified the best branch-and-price-and-cut implementation by extensive experiments.•Produced benchmark results for future researchers of the problem. In this paper, we extend the multiple traveling repairman problem by considering a limitation on the total distance that a vehicle can travel; the resulting problem is called the multiple traveling repairmen problem with distance constraints (MTRPD). In the MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers. Each vehicle that starts from and ends at the depot is not allowed to travel a distance longer than a predetermined limit and each customer must be visited exactly once. The objective is to minimize the total waiting time of all customers after the vehicles leave the depot. To optimally solve the MTRPD, we propose a new exact branch-and-price-and-cut algorithm, where the column generation pricing subproblem is a resource-constrained elementary shortest-path problem with cumulative costs. An ad hoc label-setting algorithm armed with bidirectional search strategy is developed to solve the pricing subproblem. Computational results show the effectiveness of the proposed method. The optimal solutions to 179 out of 180 test instances are reported in this paper. Our computational results serve as benchmarks for future researchers on the problem.