Tobias Kuen – Optimization Online

Energy-efficient Timetables for Railway Traffic: Incorporating DC Power Models

Published: 2024/09/24, Updated: 2024/09/30

(Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Transportation benders decomposition, dc optimal power flow, integer non-linear programming, railway timetabling

Efficient operation of underground railway systems is critical not only for maintaining punctual service but also for minimizing energy consumption, a key factor in reducing operational costs and environmental impact. To evaluate the energy consumption of the timetables, this paper delves into the development of mathematical models to accurately represent energy dynamics within the underground … Read more

The if-then Polytope: Conditional Relations over Multiple Sets of Binary Variables

Published: 2024/04/17, Updated: 2024/04/20

Tobias Kuen

Robert Burlacu

Patrick Gemander

0-1 Programming, Polyhedra, Quadratic Programming Bipartite Graphs, boolean quadric polytope, branch-and-cut, convex hull, Fixed Recourse Stochastic Problem, integer programming, multiple-choice constraints, quadratic assignment problem, railway timetabling

Inspired by its occurrence as a substructure in a stochastic railway timetabling model, we study in this work a special case of the bipartite boolean quadric polytope. It models conditional relations across three sets of binary variables, where selections within two “if” sets imply a choice in a corresponding “then” set. We call this polytope … Read more