Theory of linear and integer programming
Theory of linear and integer programming
A mathematical for periodic scheduling problems
SIAM Journal on Discrete Mathematics
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Optimizing over the first Chvátal closure
Mathematical Programming: Series A and B
The mixing set with divisible capacities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
The mixing set with divisible capacities: A simple approach
Operations Research Letters
Engineering the modulo network simplex heuristic for the periodic timetabling problem
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Improving the modulo simplex algorithm for large-scale periodic timetabling
Computers and Operations Research
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The Periodic Event Scheduling Problem (PESP) is the method of choice for real-world periodic timetabling in public transport. Its MIP formulation has been studied intensely for the case of uniform modules, i.e., when all events have the same period. In practice, multiple periods are equally important. Yet, the powerful methods developed for uniform modules generally fail for the multi-module case. We analyze a certain type of Diophantine equation systems closely related to the multi-module PESP. Thereby, we identify a structure, so-called sharp trees, that allows to solve the system in O(n2) time if the modules form a linear lattice. Based on this we develop the machinery to solve multi-module PESPs on real-world scale. In our computational results the new MIP-formulations considerably improve the solvability of multi-module PESPs.