Summary
The Vehicle Routing Problem with Soft Time Windows consists in computing a minimum cost set of routes for a fleet of vehicles of limited capacity that must visit a given set of customers with known demand, with the additional feature that each customer expresses a preference about the time at which the visit should occur. If a vehicle serves the customer out of its specified time window, an additional cost is incurred. Here we consider the case with penalties linearly depending on the time windows violation. We present an exact optimization algorithm for the pricing problem which arises when the vehicle routing problem with soft time windows is solved by column generation. The algorithm exploits bi-directional and bounded dynamic programming with decremental state space relaxation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balakrishnan N (1993) Simple heuristics for the vehicle routeing problem with soft time windows Journal of the Operational Research Society 44:279–287.
Boland N, Dethridge J, Dumitrescu I (2006) Accelerated label setting algorithms for the elementary resource constrained shortest path problem Operations Research Letters 34:58–68.
Bramel J, Simchi-Levi D (2001) Set-covering-based algorithms for the capacitated VRP. In: Toth P, Vigo D (eds) The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia.
Chiang WC, Russell RA (2004) A metaheuristic for the vehicle-routeing problem with soft time windows Journal of the Operational Research Society 55:1298–1310.
Cordeau JF, Desaulniers G, Desrosiers J, Solomon MM, Soumis F (2001) The VRP with time windows. In: Toth P, Vigo D (eds) The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications, Philadelphia.
Desaulniers G, Lessard F, Hadjar A (2006) Tabu search, generalized k-path inequalities, and partial elementarity for the vehicle routing problem with time windows. Les Cahiers du GERAD 45, GERAD, Canada.
Dror M (1994) Note on the complexity of the shortest path models for column generation in VRPTW Operations Research 42:977–978.
Feillet D, Dejax P, Gendreau M, Gueguen C (2004) An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems Networks 44:216–229.
Ibaraki T, Imahori S, Kubo M, Masuda T, Uno T, Yagiura M (2005) Effective local search algorithms for routing and scheduling problems with general time-window constraints Transportation Science 39:206–232.
Irnich S (2006) Resource extension functions: properties, inversion, and generalization to segments Technical report, RWTH Aachen University, Germany.
Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2006) A non-robust Branch-and-Cut-and-Price algorithm for the Vehicle Routing Problem with Time Windows. Technical report 06-03, DIKU University of Copenhagen, Denmark.
Kallehauge B, Larsen J, Madsen OBG, Solomon MM (2005) Vehicle routing problem with time windows. In: Desaulniers G, Desrosiers J, Solomon MM (eds) Column generation. Springer, New York.
Koskosidis YA, Powell WB, Solomon MM (1992) An optimization based heuristic for vehicle routeing and scheduling with soft time window constraints Transportation Science 26:69–85.
Sexton T, Choi Y (1986) Pickup and delivery of partial loads with soft time windows American Journal of Mathematical and Management Sciences 6:369–398.
Taillard E, Badeau P, Gendreau M, Guertin F, Potvin JY (1997) A tabu search heuristic for the vehicle routing problem with soft time windows Transportation Science 31:170–186.
Righini G, Salani M (2005) New dynamic programming algorithms for the resource-constrained elementary shortest path problem. Note del Polo - Ricerca 69, DTI, University of Milan, Italy. Accepted for publication on Networks.
Righini G, Salani M (2006) Symmetry helps: bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints Discrete Optimization 3:255–273.
Righini G, Salani M (2006) Dynamic programming for the orienteering problem with time windows. Note del Polo - Ricerca 91, DTI, University of Milan, Italy.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liberatore, F., Righini, G., Salani, M. (2009). A Pricing Algorithm for the Vehicle Routing Problem with Soft Time Windows. In: Nunen, J., Speranza, M., Bertazzi, L. (eds) Innovations in Distribution Logistics. Lecture Notes in Economics and Mathematical Systems, vol 619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92944-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-92944-4_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92943-7
Online ISBN: 978-3-540-92944-4
eBook Packages: Business and EconomicsBusiness and Management (R0)