Abstract
We address the Collection and Delivery Problem (CDP) with multiple vehicles, such that each collects a set of items at different locations and delivers them to a dropoff point. The goal is to minimize either delivery time or the total distance traveled.We introduce an extension to the CDP: what if a vehicle can transfer items to another vehicle before making the final delivery? By dividing the labor among multiple vehicles, the delivery time and cost may be reduced. However, introducing transfers increases the number of feasible schedules exponentially. In this paper, we investigate this Collection and Delivery Problem with Transfers (CDP-T), discuss its theoretical underpinnings, and introduce a two-approximate polynomial time algorithm to minimize total distance travelled. Furthermore, we show that allowing transfers to take place at any location for the CDP-T results in at most a factor of two improvement. We demonstrate our approximation algorithms on large simulated problem instances. Finally, we deploy our algorithms on robots that transfer and deliver items autonomously in an office building.
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
Alton, K., Mitchell, I.: Efficient dynamic programming for optimal multi-location robot rendezvous. In: IEEE Conference on Decision and Control, pp. 2794–2799. IEEE (2008)
Bansal, N., Blum, A., Chawla, S., Meyerson, A.: Approximation algorithms for deadline-tsp and vehicle routing with time-windows. In: Proceedings of the ACM Symposium on Theory of computing, pp. 166–174. ACM (2004)
Berbeglia, G., Cordeau, J., Gribkovskaia, I., Laporte, G.: Static pickup and delivery problems: a classification scheme and survey. Top 15(1), 1–31 (2007)
Bhattacharya, B., Hu, Y.: Approximation algorithms for the multi-vehicle scheduling problem. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010, Part II. LNCS, vol. 6507, pp. 192–205. Springer, Heidelberg (2010)
Biswas, J., Coltin, B., Veloso, M.: Corrective gradient refinement for mobile robot localization. In: Proc. of IEEE Conf. on Intelligent Robots and Systems (IROS), pp. 73–78. IEEE (2011)
Charikar, M., Raghavachari, B.: The finite capacity dial-a-ride problem. In: Proc. of 39th Annual Symposium on Foundations of Computer Science 1998, pp. 458–467. IEEE (1998)
Coltin, B., Veloso, M., Ventura, R.: Dynamic user task scheduling for mobile robots. In: Proc. of the Work. on Automated Action Planning for Autonomous Mobile Robots. AAAI (2011)
Cortés, C., Matamala, M., Contardo, C.: The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method. European Journal of Operational Research 200(3), 711–724 (2010)
Gerkey, B., Matarić, M.: A formal analysis and taxonomy of task allocation in multi-robot systems. The International Journal of Robotics Research 23(9), 939–954 (2004)
Gørtz, I.L., Nagarajan, V., Ravi, R.: Minimum makespan multi-vehicle dial-a-ride. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 540–552. Springer, Heidelberg (2009)
Gupta, A., Hajiaghayi, M., Nagarajan, V., Ravi, R.: Dial a ride from k-forest. ACM Transactions on Algorithms (TALG)Â 6(2), 41 (2010)
Ivanov, A., Tuzhilin, A.: The steiner ratio gilbert–pollak conjecture is still open. Algorithmica, 1–3 (2011)
Kirkpatrick, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 220(4598), 671 (1983)
Mitrovic-Minic, S., Laporte, G.: The pickup and delivery problem with time windows and transshipment. Information Systems and Operational Research 44(3), 217–228 (2006)
Nakao, Y., Nagamochi, H.: Worst case analysis for a pickup and delivery problem with single transfer. Numerical Optimization Methods, Theory and Applications 1584, 142–148 (2008)
Parragh, S., Doerner, K., Hartl, R.: A survey on pickup and delivery problems. Journal für Betriebswirtschaft 58(2), 81–117 (2008)
Takahashi, H., Matsuyama, A.: An approximate solution for the steiner problem in graphs. Math. Japonica 24(6), 573–577 (1980)
Thangiah, S., Fergany, A., Awan, S.: Real-time split-delivery pickup and delivery time window problems with transfers. Central European Journal of Op. Research 15(4), 329–349 (2007)
Toth, P., Vigo, D.: The vehicle routing problem, vol. 9. Soc. for Industrial Mathematics (2002)
Waisanen, H., Shah, D., Dahleh, M.: Fundamental performance limits for multi-stage vehicle routing problems. Operations Research (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Coltin, B., Veloso, M. (2014). Optimizing for Transfers in a Multi-vehicle Collection and Delivery Problem. In: Ani Hsieh, M., Chirikjian, G. (eds) Distributed Autonomous Robotic Systems. Springer Tracts in Advanced Robotics, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55146-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-55146-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-55145-1
Online ISBN: 978-3-642-55146-8
eBook Packages: EngineeringEngineering (R0)