Lower and upper bounds for the two-echelon capacitated location-routing problem

In this paper, we introduce two algorithms to address the two-echelon capacitated location-routing problem (2E-CLRP). We introduce a branch-and-cut algorithm based on the solution of a new two-index vehicle-flow formulation, which is strengthened with several families of valid inequalities. We also propose an adaptive large-neighbourhood search (ALNS) meta-heuristic with the objective of finding good-quality solutions quickly. The computational results on a large set of instances from the literature show that the ALNS outperforms existing heuristics. Furthermore, the branch-and-cut method provides tight lower bounds and is able to solve small- and medium-size instances to optimality within reasonable computing times.

[1]  David Pisinger,et al.  An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows , 2006, Transp. Sci..

[2]  J. Cordeau,et al.  A BRANCH-AND-CUT ALGORITHM FOR THE CAPACITATED LOCATION-ROUTING PROBLEM , 2010 .

[3]  Bernard Gendron,et al.  A Branch-And-Cut-And-Price Algorithm for the Capacitated Location Routing Problem , 2009 .

[4]  Günther R. Raidl,et al.  Variable Neighborhood Search Coupled with ILP-Based Very Large Neighborhood Searches for the (Periodic) Location-Routing Problem , 2010, Hybrid Metaheuristics.

[5]  Teodor Gabriel Crainic,et al.  Multi-start Heuristics for the Two-Echelon Vehicle Routing Problem , 2011, EvoCOP.

[6]  Christian Prins,et al.  A Memetic Algorithm with Population Management (MA|PM) for the Periodic Location-Routing Problem , 2008, Hybrid Metaheuristics.

[7]  Claudio Sterle,et al.  A Metaheuristic for a Two Echelon Location-Routing Problem , 2010, SEA.

[8]  Christian Prins,et al.  A multi-start iterated local search with tabu list and path relinking for the two-echelon location-routing problem , 2012, Eng. Appl. Artif. Intell..

[9]  Jean-François Cordeau,et al.  A computational comparison of flow formulations for the capacitated location-routing problem , 2013, Discret. Optim..

[10]  Claudio Sterle,et al.  Location-Routing Models for Designing a Two-Echelon Freight Distribution System , 2011 .

[11]  Principles and Practice of Constraint Programming — CP98 , 1999, Lecture Notes in Computer Science.

[12]  Christian Prins,et al.  A Memetic Algorithm with Population Management (MA|PM) for the Capacitated Location-Routing Problem , 2006, EvoCOP.

[13]  Angel B. Ruiz,et al.  Solving the Capacitated Location-Routing Problem by a Cooperative Lagrangean Relaxation-Granular Tabu Search Heuristic , 2007, Transp. Sci..

[14]  Guido Perboli,et al.  New Families of Valid Inequalities for the Two-Echelon Vehicle Routing Problem , 2010, Electron. Notes Discret. Math..

[15]  David Pisinger,et al.  A general heuristic for vehicle routing problems , 2007, Comput. Oper. Res..

[16]  G. Dueck,et al.  Record Breaking Optimization Results Using the Ruin and Recreate Principle , 2000 .

[17]  Christian Prins,et al.  Solving the two-echelon location routing problem by a GRASP reinforced by a learning process and path relinking , 2012, Eur. J. Oper. Res..

[18]  José-Manuel Belenguer,et al.  A Branch and Cut method for the Capacitated Location-Routing Problem , 2006, 2006 International Conference on Service Systems and Service Management.

[19]  Daniele Vigo,et al.  The Two-Echelon Capacitated Vehicle Routing Problem: Models and Math-Based Heuristics , 2011, Transp. Sci..

[20]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[21]  Jean-François Cordeau,et al.  A GRASP + ILP-based metaheuristic for the capacitated location-routing problem , 2014, J. Heuristics.

[22]  Roberto Baldacci,et al.  An Exact Method for the Capacitated Location-Routing Problem , 2011, Oper. Res..

[23]  Teodor Gabriel Crainic,et al.  An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics , 2012, Comput. Oper. Res..

[24]  Paul Shaw,et al.  Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems , 1998, CP.

[25]  Christian Prins,et al.  Solving the capacitated location-routing problem by a GRASP complemented by a learning process and a path relinking , 2006, 4OR.