Abstract
The pickup and delivery problem (PDP) asks to find a set of routes with the minimum travel cost to serve a given set of requests. PDP is called the multi-trip PDP with consecutive pickups and deliveries (PDPCMT) if it has an additional requirement such that any vehicle which has begun a delivery action is not allowed to take pickup actions until all of the loads on the vehicle are delivered. In this paper, we are interested in how the least travel cost can be increased by the additional requirement, and examine the maximum ratio of the optimal value of PDPCMT to that of PDP over all instances with p requests. We show that the maximum ratio is bounded from above by O(logp) and from below by Ω(logp/loglogp).
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
Archetti, C., Savelsbergh, M.W.P., Speranza, M.G.: Worst-case analysis for split delivery vehicle routing problems. Transportation Science 40, 226–234 (2006)
Arkin, E., Hassin, R., Klein, L.: Restricted delivery problems on a network. Networks 29, 205–216 (1997)
Charikar, M., Khuller, S., Raghavachari, B.: Algorithms for capacitated vehicle routing. In: STOC, pp. 349–358 (1998)
Dror, M., Trudeau, P.: Split delivery routing. Naval Research Logistics 37, 383–402 (1990)
Li, H., Lim, A.: A metaheuristic for the pickup and delivery problem with time windows. International Journal on Artificial Intelligence Tools 12, 173–186 (2003)
Mitrović-Minić, S., Laporte, G.: The pickup and delivery problem with time windows and transshipment. INFOR 44, 217–227 (2006)
Nakao, Y., Nagamochi, H.: Worst case analysis for pickup and delivery problems with transfer. IEICE Transaction 91-A(9), 2328–2334 (2008)
Nanry, W.P., Barnes, J.W.: Solving the pickup and delivery problem with time windows using reactive tabu search. Transportation Research Part B 34, 107–121 (2000)
Pankratz, G.: A grouping genetic algorithm for the pickup and delivery problem with time windows. OR Spectrum 27, 21–41 (2005)
Toth, P., Vigo, D.: The granular tabu search and its application to the vehicle-routing problem. INFORMS Journal on Computing 15, 333–346 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nakao, Y., Nagamochi, H. (2009). Worst Case Analysis for Pickup and Delivery Problems with Consecutive Pickups and Deliveries. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_57
Download citation
DOI: https://doi.org/10.1007/978-3-642-10631-6_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
Online ISBN: 978-3-642-10631-6
eBook Packages: Computer ScienceComputer Science (R0)