The vehicle routing problem with service level constraints

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.

A concise guide to existing and emerging vehicle routing problem variants

“…To guarantee a certain service level, most 3PL providers establish contracts that stipulate a minimum ratio of on-time deliveries. This gives rise to the VRP with service-level constraints (Bulhões et al 2018a). In this problem, the deliveries are partitioned into groups, and a minimum percentage of the deliveries (or delivery load) must be fulfilled for each group.…”

A generic exact solver for vehicle routing and related problems

“…The same model as for the CTOP, except that i) the only resource is the vehicle capacity, ii) the objective is the difference between the total profit and the transportation cost. The parameterization of the solver is the following: τ soft = 5 sec., τ hard = 10 sec., ψ buck = 200, φ bidir = 1, σ stab = 1, ω labels = 5 • 10 5 , ω routes = 2.5 • 10 6 , η max = 30, θ mem = 1, δ gap = 1.5%, Only open instances from [5] are considered, which could not be solved by Bulhoes et al [20]. The same initial upper bounds were used as for the branch-and-price algorithm in [20].…”

“…The parameterization of the solver is the following: τ soft = 5 sec., τ hard = 10 sec., ψ buck = 200, φ bidir = 1, σ stab = 1, ω labels = 5 • 10 5 , ω routes = 2.5 • 10 6 , η max = 30, θ mem = 1, δ gap = 1.5%, Only open instances from [5] are considered, which could not be solved by Bulhoes et al [20]. The same initial upper bounds were used as for the branch-and-price algorithm in [20]. Note that only one of them was improved: for instance "p13-4-200" the optimum value is 304.15, whereas the best known solution is 303.18.…”

Vehicle Routing for Dynamic Road Network Based on Travel Time Reliability

“…They didn't consider multiple destinations. Teobaldo Bulhões et al [9] proposed a branch price algorithm and hybrid genetic algorithm for the vehicle routing problem with service level restrictions, and established an adaptive balance penalty mechanism between service level and cost. Liu Yanqiu et al [10] established an integer linear programming model with the objective of minimizing the sum of vehicle call cost, vehicle transportation cost and third-party logistics transportation cost, constructed a new variable dimension matrix coding structure, and proposed a new intelligent optimization algorithm.…”