A Branch and Price
Approach for an Airport
Vehicle Routing Problem
Michaël Schyns
QuantOM Research Center
Agenda
• Problem statement
• Goals
• Branch-and-Cut-and-Price for VRPTW
• Impact of the parameters
Problem Statement
• Project initiated by a main European
freight airport
• Set of planes (TW)
• Set of trucks (C
i
)
• Demand evolves…
Project goals (work in
progress)
• Model and solve the problem
– (Scheduling or) VRPTW
– Exact method (and/or heuristic: ant colonies)
• "Survey" of the exact methods for the VRPTW
– 30 last years of research: lots of "things"
– Selection of the methods, tricks and parameters:
impact
!
• Improvements?
Exact methods for the
VRPTW
Main papers
1.Baldacci R., Mingozzi A. and R. Roberti, 2012, Recent exact algorithms for solving the vehicle routing problem under capacity and time windows constraints, European Journal of Operational Research, 218, 1-6.
2.Cordeau JF., Desaulniers G., Desrosiers J., Solomon M. and F. Soumis, 2002, Vehicle Routing Problems with Time Windows, In: Toth P. and D. Vigo (Editors), "The Vehicle Routing Problem", Siam monographs on Discrete Mathematics and Applications, 157-195.
3.Desaulniers G., Lessard F. and A. Hadjar, 2008, Tabu Search, Partial Elementary, and Generalized k-Path Inequalitites for the Vehicle Routing Problem with Time
Windows, "Transportation Science", 42(3),387-404.
4.Desrochers M., Desrosiers J. and M. Solomon, 1992, A new optimization algorithm for the vehicle routing problem with time windows, "Operations Research", 40, March-April, 342-354
5.Desrosiers J. and M.E. Lübbecke, 2005, A primer in column generation, In: Desrosiers, Desaulniers, Solomon (Editors), "Column Generation", Springer, (GERAD, 25th anniversary)
6.Feillet D., 2010, A tutorial on column generation and branch-and-price for vehicle routing problems, "4OR-Q J Oper Res", 8, 407-424
7.Feillet D., Dejax P., Gendreau M. and C. Gueguen, 2004,An Exact Algorithm for the Elementary Shortest Path Problem with Resource Constraints: Application to
some Vehicle Routing Problems, Networks, 44, 216-229
8.Feillet D., Gendreau M. and LM Rousseau, ?after 2007?, New Refinements for the Solution of Vehicle Routing Problems with Branch and Price, Gerad, http://... 9.Gambardella L., Taillard E. and G. Agazzi, 1999, MACS-VRPTW: a multiple ant colony system for Vehicle Routing Problems with time windows, In: Corne D., Dorigo M. and F. Glover (Editors), "New Ideas in Optimization", McGraw-Hill.
10.Gutiérrez-Jarpa G., Desaulniers G., Laporte G. and V. Marianov, 2010, A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows", "European Journal of Operational Research", 206, 341-349.
11.Irnich, S. and G. Desaulniers, 2005, Shortest path with resource constraints, In: Desrosiers, Desaulniers, Solomon (Editors), "Column Generation", Springer, (GERAD, 25th anniversary)
12.Jepsen M., Petersen B., Spoorendonk S., D. Pisinger, 2008, Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows, Operations Research, 56(2), pp497-511.
13.Kallehauge B., Larsen J., Madsen O. and M. Solomon, 2005, Vehicle routing problem with time windows, In: Desrosiers, Desaulniers, Solomon (Editors), "Column Generation", Springer, (GERAD, 25th anniversary)
14.Laporte G., 1992, The Vehicle Routing Problem: An Overview of exact and approximate algorithms, "European Journal of Operational Research, 59, 345-358. 15.Lozano, L., Medaglia, A. L., 2012, An Exact Algorithm for the Elementary Shortest Path Problem with Resource Constraints, Tech. Rep. COPA-2012-2, Universidad de los Andes.
16.Righini G. and M. Salani, 2006, Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource
constraints, "Discrete Optimization", 3, 255-273.
17.Righini G. and M. Salani, 2008, New Dynamic Programming Algorithms for the Resource Constrained Elementary Shortest Path Problem, "Networks", 51(3), 155-170.
