A Branch and Cut method for the Capacitated Location-Routing Problem

Jose-Manuel Belenguer (1) , Enrique Benavent (1) , Christian Prins (2) , Caroline Prodhon (2) , Roberto Wolfler Calvo (2)

1 UV - Universitat de València
2 LOSI - Laboratoire d'Optimisation des Systèmes Industriels

Most of the time in a distribution system, depot location and vehicle routing are interdependent and recent researches have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents two formulations of the location-routing problem with capacities on routes and depots and proposes an exact method based on a branch and cut approach using these formulations. The method is evaluated on two sets of randomly generated instances, and compared to heuristics and another lower bound.

Keywords: Routing; Costs; Vehicles; Iterative algorithms; Logistics; Stochastic processes; Testing; Lagrangian functions; Fitting; Simulated annealing; Location-Routing; Branch and Cut; Lower Bound

Domains: Operations Research [cs.RO]

Jose-Manuel Belenguer, Enrique Benavent, Christian Prins, Caroline Prodhon, Roberto Wolfler Calvo. A Branch and Cut method for the Capacitated Location-Routing Problem. 2006 International Conference on Service Systems and Service Management, Oct 2006, Troyes, France. pp.1541-1546, ⟨10.1109/ICSSSM.2006.320765⟩. ⟨hal-02474696⟩