@article{SisLab2574,
           title = {The vehicle routing problem with service level constraints},
          author = {Teobaldo Bulh{\~o}es and Minh Hoang Ha and Rafael Martinelli and Thibaut Vidal},
       publisher = {Elsevier},
            year = {2017},
         journal = {European Journal of Operational Research},
             url = {https://eprints.uet.vnu.edu.vn/eprints/id/eprint/2574/},
        abstract = {We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems.}
}