Location-Routing Problems with Distance Constraints

A important aspect of designing a distribution system is determining the locations of the facilities. For systems in which deliveries are made along multiple stop routes, the routing problem and location problem must be considered simultaneously. In this paper, a set-partitioning-based formulation of an uncapacitated location-routing model with distance constraints is presented. An alternate set of constraints is identified that significantly reduces the total number of constraints and dramatically improves the linear programming relaxation bound. A branch and price algorithm is developed to solve instances of the model. The algorithm provides optimal solutions in reasonable computation time for problems involving as many as 10 candidate facilities and 100 customers with various distance constraints.