Abstract
The Dial-a-Ride problem may contain various constraints for pickup-delivery requests, such as time windows and ride time constraints. For a tour, given as a sequence of pickup and delivery stops, there exist polynomial time algorithms to find a schedule respecting these constraints, provided that there exists one. However, if no feasible schedule exists, the natural question is to find a schedule minimising constraint violations. We model a generic fixed-sequence scheduling problem, allowing lateness and ride time violations with linear penalty functions and prove its APX-hardness. We also present an approach leading to a polynomial time algorithm if only the time window constraints can be violated (by late visits). Then, we show that the problem can be solved in polynomial time if all the ride time constraints are bounded by a constant. Lastly, we give a polynomial time algorithm for the instances where all the pickups precede all the deliveries in the sequence of stops.
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References
Atallah, M.J., Chen, D.Z., Lee, D.T.: An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications. Algorithmica 14(5), 429–441 (1995). https://doi.org/10.1007/BF01192049
Cordeau, J.F., Laporte, G.: The dial-a-ride problem (DARP): variants, modeling issues and algorithms. Q. J. Belg. Fr. Ital. Oper. Res. Soc. 1(2), 89–101 (2003)
Crescenzi, P.: A short guide to approximation preserving reductions. In: Proceedings of the 12th Annual IEEE Conference on Computational Complexity. CCC ’97, pp. 262–273. IEEE Computer Society, Washington (1997)
Desrosiers, J., Dumas, Y., Solomon, M.M., Soumis, F.: Time constrained routing and scheduling. Handb. Oper. Res. Manag. Sci. 8, 35–139 (1995)
Dumas, Y., Soumis, F., Desrosiers, J.: Optimizing the schedule for a fixed vehicle path with convex inconvenience costs. Transp. Sci. 24(2), 145–152 (1990)
Firat, M., Woeginger, G.J.: Analysis of the dial-a-ride problem of Hunsaker and Savelsbergh. Oper. Res. Lett. 39(1), 32–35 (2011)
Gatto, M., Jacob, R., Peeters, L., Schöbel, A.: The computational complexity of delay management. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 227–238. Springer, Heidelberg (2005). https://doi.org/10.1007/11604686_20
Gschwind, T.: Route feasibility testing and forward time slack for the synchronized pickup and delivery problem. Technical report, Citeseer (2015)
Hunsaker, B., Savelsbergh, M.: Efficient feasibility testing for dial-a-ride problems. Oper. Res. Lett. 30(3), 169–173 (2002)
Lampis, M., Kaouri, G., Mitsou, V.: On the algorithmic effectiveness of digraph decompositions and complexity measures. Discrete Optim. 8(1), 129–138 (2011). https://doi.org/10.1016/j.disopt.2010.03.010
Tang, J., Kong, Y., Lau, H., Ip, A.W.: A note on efficient feasibility testing for dial-a-ride problems. Oper. Res. Lett. 38(5), 405–407 (2010)
Tarjan, R.E.: Edge-disjoint spanning trees and depth-first search. Acta Informatica 6(2), 171–185 (1976)
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Chlebíková, J., Dallard, C., Paulsen, N. (2019). Complexity of Scheduling for DARP with Soft Ride Times. In: Heggernes, P. (eds) Algorithms and Complexity. CIAC 2019. Lecture Notes in Computer Science(), vol 11485. Springer, Cham. https://doi.org/10.1007/978-3-030-17402-6_13
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DOI: https://doi.org/10.1007/978-3-030-17402-6_13
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