Charlemagne's Challenge: The Periodic Latency Problem
Operations Research
On minimizing the maximum flow time in the online dial-a-ride problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Profit-based latency problems on the line
Operations Research Letters
Vehicle routing problems on a line-shaped network with release time constraints
Operations Research Letters
The uncapacitated swapping problem on a line and on a circle
Discrete Applied Mathematics
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In dial-a-ride problems, items have to be transported from a source to a destination. The characteristics of the servers involved as well as the specific requirements of the rides may vary. Problems are defined on some metric space, and the goal is to find a feasible solution that minimizes a certain objective function. The structure of these problems allows for a notation similar to the standard notation for scheduling and queueing problems. We introduce such a notation and show how a class of 7,930 dial-a-ride problem types arises from this approach. In examining their computational complexity, we define a partial ordering on the problem class and incorporate it in the computer program DARCLASS. As input DARCLASS uses lists of problems whose complexity is known. The output is a classification of all problems into one of three complexity classes: solvable in polynomial time, NP-hard, or open. For a selection of the problems that form the input for DARCLASS, we exhibit a proof of polynomial-time solvability or NP-hardness.