Combinatorially Simple Pickup and Delivery Paths

Pickup and delivery problems discussed in the literature often allow for only particularly simple solutions in terms of the sequence of visited locations. We study the very simplest pickup and delivery paths which are concatenations of short patterns visiting one or two requests. This restricted variant, still N P -hard, is close to the traveling salesman problem with the additional choice of what patterns to visit. We compare the number of restricted and unrestricted paths, and evaluate their respective path lengths. We conclude with two polynomially solvable cases.

[1]  Jacques Desrosiers,et al.  Time Constrained Routing and Scheduling , 1992 .

[2]  Jacques Desrosiers,et al.  THE MULTIPLE VEHICLE DIAL-A-RIDE PROBLEM , 1988 .

[3]  Gilbert Laporte,et al.  Vehicle routing with full loads , 1985, Comput. Oper. Res..

[4]  Martin Grötschel,et al.  Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System , 1999 .

[5]  Kjetil Fagerholt,et al.  A combined ship scheduling and allocation problem , 2000, J. Oper. Res. Soc..

[6]  John J. H. Forrest,et al.  Column generation and the airline crew pairing problem. , 1998 .

[7]  Mwp Martin Savelsbergh,et al.  VEHICLE ROUTING WITH TIME WINDOWS: OPTIMIZATION AND APPROXIMATION. VEHICLE ROUTING: METHOD AND STUDIES. STUDIES IN MANAGEMENT SCIENCE AND SYSTEMS - VOLUME 16 , 1987 .

[8]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[9]  Srini Ramaswamy,et al.  Solving Large Airline Crew Scheduling Problems: Random Pairing Generation and Strong Branching , 2001, Comput. Optim. Appl..

[10]  Uwe T. Zimmermann,et al.  Engine Routing and Scheduling at Industrial In-Plant Railroads , 2003, Transp. Sci..

[11]  Donald E. Knuth,et al.  The art of computer programming: V.1.: Fundamental algorithms , 1997 .

[12]  Jacques Desrosiers,et al.  The Pickup and Delivery Problem with Time Windows , 1989 .

[13]  Mikael Rönnqvist,et al.  Extraction of logs in forestry using operations research and geographical information systems , 1999, Proceedings of the 32nd Annual Hawaii International Conference on Systems Sciences. 1999. HICSS-32. Abstracts and CD-ROM of Full Papers.

[14]  Uwe T. Zimmermann,et al.  Computer Aided Scheduling of Switching Engines , 2003 .

[15]  Jacques Desrosiers,et al.  A Request Clustering Algorithm for Door-to-Door Handicapped Transportation , 1991, Transp. Sci..

[16]  Jacques Desrosiers,et al.  VRP with Pickup and Delivery , 2000, The Vehicle Routing Problem.

[17]  Marco E. Lübbecke,et al.  Engine Scheduling by Column Generation , 2001 .

[18]  E. Balas,et al.  New classes of efficiently solvable generalized Traveling Salesman Problems , 1999, Ann. Oper. Res..