Abstract
This work deals with the Vehicle Routing Problem with Simultaneous Pickup and Delivery. We propose undirected and directed two-commodity flow formulations, which are based on the one developed by Baldacci, Hadjiconstantinou and Mingozzi for the Capacitated Vehicle Routing Problem. These new formulations are theoretically compared with the one-commodity flow formulation proposed by Dell’Amico, Righini and Salani. The three formulations were tested within a branch-and-cut scheme and their practical performance was measured in well-known benchmark problems. The undirected two-commodity flow formulation obtained consistently better results. Several optimal solutions to open problems with up to 100 customers and new improved lower bounds for instances with up to 200 customers were found.
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
Min, H.: The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transportation Research 23(5), 377–386 (1989)
Dell’Amico, M., Righini, G., Salani, M.: A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection. Transportation Science 40(2), 235–247 (2006)
Angelelli, E., Mansini, R.: A branch-and-price algorithm for a simultaneous pick-up and delivery problem. In: Quantitative Approaches to Distribution Logistics and Supply Chain Management, pp. 249–267. Springer, Heidelberg (2002)
Dethloff, J.: Vehicle routing and reverse logistics: the vehicle routing problem with simultaneous delivery and pick-up. OR Spektrum 23, 79–96 (2001)
Montané, F.A.T., Galvão, R.D.: A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Computers & Operations Research 33(3), 595–619 (2006)
Baldacci, R., Hadjiconstantinou, E., Mingozzi, A.: An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Operations Research 52(5), 723–738 (2004)
Lysgaard, J.: A package of separation routines for the capacited vehicle routing problem. Technical report (2003), http://www.asdb.dk/~lys
Toth, P., Vigo, D.: Models, relaxations and exact approaches for the capacitated vehicle routing problem. Discrete Applied Mathematics 123, 487–512 (2002)
Gavish, B., Graves, S.: The traveling salesman problem and related problems. Working Paper (1979)
Gouveia, L.: A result on projection for the vehicle routing problem. European Journal of Operational Research 85, 610–624 (1995)
Lysgaard, J., Letchford, A.N., Eglese, R.W.: A new branch-and-cut algorithm for the capacitated vehicle routing problem. Mathematical Programming 100, 423–445 (2004)
Salhi, S., Nagy, G.: A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling. Journal of the Operational Research Society 50, 1034–1042 (1999)
Subramanian, A., Drummond, L.M.A., Bentes, C., Ochi, L.S., Farias, R.: A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery. Computers & Operations Research (to appear, 2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Subramanian, A., Uchoa, E., Ochi, L.S. (2010). New Lower Bounds for the Vehicle Routing Problem with Simultaneous Pickup and Delivery. In: Festa, P. (eds) Experimental Algorithms. SEA 2010. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13193-6_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-13193-6_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13192-9
Online ISBN: 978-3-642-13193-6
eBook Packages: Computer ScienceComputer Science (R0)