Worst Case Analysis for Pickup and Delivery Problems with Consecutive Pickups and Deliveries

Authors:
Yoshitaka Nakao;Hiroshi Nagamochi
Affiliations:
Department of Applied Mathematics and Physics Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Department of Applied Mathematics and Physics Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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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 驴(logp/loglogp).