Journal of Combinatorial Optimization

, Volume 35, Issue 2, pp 512–529 | Cite as

From theory to practice: maximizing revenues for on-line dial-a-ride

  • Ananya Christman
  • William Forcier
  • Aayam Poudel


We consider the on-line dial-a-ride problem, where a server fulfills requests that arrive over time. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that the server earns for fulfilling the request. The goal is to serve requests within a time limit while maximizing the total revenue. We first prove that no deterministic online algorithm can be competitive unless the input graph is complete and edge weights are unit. We therefore focus on these graphs and present a 2-competitive algorithm for this problem. We also consider two variations of this problem: (1) the input graph is complete bipartite and (2) there is a single node that is the source for every request, and present a 1-competitive algorithm for the former and an optimal algorithm for the latter. We also provide experimental results for the complete and complete bipartite graphs. Our simulations support our theoretical findings and demonstrate that our algorithms perform well under settings that reflect realistic dial-a-ride systems.


Online algorithms Dial-a-ride Competitive analysis Graphs 


  1. Ascheuer N, Krumke S, Rambau J (2000) Online dial-a-ride problems: minimizing the completion time. In: Proceedings of the 17th international symposium on theoretical aspects of computer science. Lecture notes in computer science, vol 1770, pp 639–650Google Scholar
  2. Ausiello G, Feuerstein E, Leonardi S, Stougie L, Talamo M (2001) Algorithms for the on-line traveling salesman. Algorithmica 29(4):560–581MathSciNetCrossRefMATHGoogle Scholar
  3. Ausiello G, Bonifaci V, Laura L (2008) The on-line prize-collecting traveling salesman problem. Inf Process Lett 107(6):199–204CrossRefMATHGoogle Scholar
  4. Azi N, Gendreau M, Potvin J (2012) A dynamic vehicle routing problem with multiple delivery routes. Ann Oper Res 199(1):103–112MathSciNetCrossRefMATHGoogle Scholar
  5. Blum A, Chalasani P, Coppersmith D, Pulleyblank B, Raghavan P, Sudan M (1994) The minimum latency problem. In Proceedings of the 26th annual ACM symposium on theory of computing, pp 163–171Google Scholar
  6. Christman A, Forcier W (2014) Maximizing revenues for on-line dial-a-ride. In: Combinatorial optimization and applications, pp. 522–534Google Scholar
  7. de Paepe W, Lenstra J, Sgall J, Sitters A, Stougie L (2004) Computer-aided complexity classification of dial-a-ride problems. INFORMS J Comput 16(2):120–132MathSciNetCrossRefMATHGoogle Scholar
  8. Frederickson GN, Hecht MS, Kim CE (1978) Approximation algorithms for some routing problems. J Comput 7:178–193MathSciNetGoogle Scholar
  9. Gendreau M, Hertz A, Laporte G (1994) A tabu search heuristic for the vehicle routing problem. Manag Sci 40(10):1276–1290CrossRefMATHGoogle Scholar
  10. Guan DJ (1998) Routing a vehicle of capacity greater than one. Discrete Appl Math 81(1):41–57MathSciNetCrossRefMATHGoogle Scholar
  11. Jaillet P, Lu X (2011) Online traveling salesman problems with flexibility. Networks 58:137–146MathSciNetMATHGoogle Scholar
  12. Jaillet P, Wagner M (2008) Generalized online routing: new competitive ratios, resource augmentation and asymptotic analyses. Oper Res 56(3):745–757MathSciNetCrossRefMATHGoogle Scholar
  13. Jaillet P, Wagner M (2008) Online vehicle routing problems: a survey. In: The vehicle routing problem: latest advances and new challenges, pp 221-237Google Scholar
  14. Kergosien Y, Lente C, Piton D, Billauta J-C (2011) A tabu search heuristic for the dynamic transportation of patients between care units. Eur J Oper Res 214(2):442–452CrossRefMATHGoogle Scholar
  15. Krumke S (2004) On minimizing the maximum flow time in the online dial-a-ride problem. Networks 44:41–46MathSciNetCrossRefGoogle Scholar
  16. Liao C, Huang Y (2014) The covering Canadian traveller problem. Theor Comput Sci 530:80–88MathSciNetCrossRefMATHGoogle Scholar
  17. Lorini S, Potvin J-Y, Zufferey N (2011) Online vehicle routing and scheduling with dynamic travel times. Comput Oper Res 38(7):1086–1090CrossRefMATHGoogle Scholar
  18. Metropolitan Council. Transit link: dial-a-ride small bus service.
  19. Schilde M, Doerner K, Harti R (2011) Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports. Comput Oper Res 38(12):1719–1730CrossRefMATHGoogle Scholar
  20. Stagecoach Corporation. Dial-a-ride.
  21. Stougie L, Feuerstein E (2001) On-line single-server dial-a-ride problems. Theor Comput Sci 268(1):91–105MathSciNetCrossRefMATHGoogle Scholar
  22. Wen X, Xu Y, Zhang H (2012) Online traveling salesman problem with deadline and advanced information. Comput Ind Eng 63(4):1048–1053CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Middlebury CollegeMiddleburyUSA
  2. 2.Abbott LaboratoriesLake ForestUSA

Personalised recommendations