The vehicle routing problem with service level constraints

• Published in: European journal of operational research Vol. 265; no. 2; pp. 544 - 558
• Main Authors: Bulhões, Teobaldo, Hà, Minh Hoàng, Martinelli, Rafael, Vidal, Thibaut
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2018
• Subjects: Collaborative logistics; Genetic algorithms; Integer programming; Routing; Service level constraints; Integer programming; Routing; Collaborative logistics; Service level constraints; Genetic algorithms
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2017.08.027

•We introduce a routing problem with customer selection and service level constraints.•We present a compact mathematical formulation and a branch-and-price algorithm.•We design an efficient hybrid genetic search with problem-tailored operators.•The proposed methods generate high-quality solutions for a large variety of instances.•The best results known for two important subproblems are improved. 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.