TY - GEN
A1 - Hiller, Benjamin
A1 - Krumke, Sven O.
A1 - Saliba, Sleman
A1 - Tuchscherer, Andreas
T1 - Randomized Online Algorithms for Dynamic Multi-Period Routing Problems
N2 - The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.
T3 - ZIB-Report - 09-03
KW - Online-Optimierung
KW - Randomisierte Algorithmen
KW - Zweistufiges Problem
KW - Traveling-Salesman-Problem
KW - online optimization
KW - randomized algorithm
KW - two-stage problem
KW - traveling salesman problem
Y1 - 2009
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1113
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-11132
SN - 1438-0064
ER -