The multi-vehicle cumulative covering tour problem
This paper introduces the multi-vehicle cumulative covering tour problem whose motivation arises from humanitarian logistics. The objective is to determine a set of tours that must be followed by a fleet of vehicles in order to minimize the sum of arrival times (latency) at each visited location. There are three types of locations: mandatory, optional, and unreachable. Each mandatory location must be visited, and optional locations are visited in order to cover the unreachable locations. To guarantee the vehicle autonomy, the duration of each tour should not exceed a given time limit. A mixed integer linear formulation and a greedy randomized adaptive search procedure are proposed for this problem. The performance of the algorithm is assessed over a large set of instances adapted from the literature. Computational results confirm the efficiency of the proposed algorithm.
KeywordsCumulative vehicle routing problem Multi-vehicle covering tour problem Minimum latency problem Humanitarian logistics
Partial funding for this project has been provided by CONACYT (National Council of Science and Technology from Mexico), the SMI program (Soutien á la Mobilité Internationale) of the National Polytechnical Institute of Toulouse (INP-Toulouse) and the French National Research Agency through the ATHENA project under the Grant ANR-13-BS02-0006, and by the Canadian Natural Sciences and Engineering Research Council under Grant 39682-10. Thanks are due to the referees who provided valuable comments and to Há et al. (2013) for sharing their instance set with us.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- Archer, A., & Blasiak, A. (2010). Improved approximation algorithms for the minimum latency problem via prize-collecting strolls. In Proceedings of the twenty-first annual ACM-SIAM symposium on discrete algorithms (SODA), Philadelphia, USA, pp. 429–447.Google Scholar
- Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., & Sudan, M. (1994). The minimum latency problem. In Proceedings of the twenty-sixth annual ACM symposium on theory of computing (STOC), Montreal, Canada, pp. 163–171.Google Scholar
- Hmayer, A., & Ezzine, I. (2013). CLARANS heuristic based approch for the \(k\)-traveling repairman problem. In International conference on advanced logistics and transport (ICALT), Sousse, Tunisie, pp. 535–538.Google Scholar
- Jozefowiez, N. (2011). A column generation approach for the multi-vehicle covering tour problem. In ROADEF 2011, March 2–4, Saint-Etienne, France.Google Scholar
- Murakami, K. (2014). A column generation approach for the multi-vehicle covering tour problem. In IEEE international conference on automation science and engineering (CASE), New Taipei, Taiwan, pp. 1063–1068).Google Scholar
- Oliveira, W. A., Mello, M. P., Moretti, A. C., & Reis, E. F. (2013). The multi-vehicle covering tour problem: Building routes for urban patrolling. arXiv:1309.5502.
- Sahni, S., & Gonzales, T. (1974). P-complete problems and approximate solutions. In IEEE conference record of 15th annual symposium on switching and automata theory, New York, USA, pp. 28–32.Google Scholar
- Sitters, R. (2014). Polynomial time approximation schemes for the traveling repairman and other minimum latency problems, Portland, USA, pp. 604–616. doi: 10.1137/1.9781611973402.46.