Abstract
In this paper, we study a variant of the well-known single-vehicle pickup and delivery problem where the demands can be unloaded/reloaded at any node. By proving new complexity results, we give the minimum information which is necessary to represent feasible solutions. Using this, we present integer linear programs for both the unitary and the general versions. We then show that the associated linear relaxations are polynomial-time solvable and present some computational results.
Similar content being viewed by others
References
Anily S, Gendreau M, Laporte G (2011) The preemptive swapping problem on a tree. Networks (forthcoming)
Atallah M, Kosaraju S (1988) Efficient solutions to some transportation problems with applications to minimizing robot arm travel. SIAM J Comput 17:849–869
Berbeglia G, Cordeau J, Gribkovskaia I, Laporte G (2007) Static pickup and delivery problems: a classification scheme and survey. Top 15(1):1–31
Cortés CE, Matamala M, Contardo C (2005) The pickup and delivery problem with transfers: formulation and solution approaches. In: VII French–Latin American congress on applied mathematics. Springer, Berlin
Frederickson G, Guan D (1992) Preemptive ensemble motion planning on a tree. SIAM J Comput 21:1130–1152
Grünert T, Sebastian H (2000) Planning models for long-haul operations of postal and express shipment companies. Eur J Oper Res 122(2):289–309
Ilog, Inc (2003) Solver cplex. http://www.ilog.fr/products/cplex/
Kerivin HLM, Lacroix M, Mahjoub AR, Quilliot A (2008) The splittable pickup and delivery problem with reloads. Eur J Ind Eng 2(2):112–133
Kerivin HLM, Lacroix M, Mahjoub AR (2010) On the complexity of the Eulerian closed walk with precedence path constraints problem. Electron Notes Discrete Math 36:899–906
Lacroix M (2009) Le problème de ramassage et livraison préemptif : complexité, modèles et polyèdres. PhD thesis, Université Blaise-Pascal, Clermont-II, France
Lougee-Heimer R (2003) The common optimization interface for operations research. IBM J Res Dev 47(1):57–66
Mitrović-Minić S, Laporte G (2006) The pickup and delivery problem with time windows and transshipment. Inf Syst Oper Res 44:217–227
Oertel P (2000) Routing with reloads. Doktorarbeit, Universität zu Köln
Parragh S, Doerner K, Hartl R (2008) A survey on pickup and delivery problems. J Betriebswirtsch 58(1):21–51
Queyranne M, Schulz A (1994) Polyhedral approaches to machine scheduling. Tech rep
Reinelt G (1991) TSPLIB—A traveling salesman problem library. ORSA. J Comput 3(4):376–384
Renaud J, Boctor FF, Laporte G (2002) Perturbation heuristics for the pickup and delivery traveling salesman problem. Comput Oper Res 29:1129–1141
Rinaldi G (1996) RUDY: a generator for random graphs. http://www-user.tu-chemnitz.de/helmberg/sdp_software.html
Savelsberg MWP, Sol M (1995) The general pickup and delivery problem. Transp Sci 29(1):17–29
Schrijver A (2002) Combinatorial optimization: Polyhedra and efficiency. Springer, Berlin
Siek J, Lee L, Lumsdaine A (2000) Boost graph library. http://www.boost.org/libs/graph/
Sirdey R, Kerivin HLM (2007) Polyhedral combinatorics of a resource-constrained ordering problem part I: on the partial linear ordering polytope. Tech rep PE/BSC/INF/017912 V01
Vygen J (1995) NP-completeness of some edge-disjoint paths problems. Discrete Appl Math 61(1):83–90
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kerivin, H.L.M., Lacroix, M. & Mahjoub, A.R. Models for the single-vehicle preemptive pickup and delivery problem. J Comb Optim 23, 196–223 (2012). https://doi.org/10.1007/s10878-010-9349-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-010-9349-z