Operations-research

Ein Schnelleinstieg in die lineare Optimierung: was ein LP ausmacht, ein durchgerechnetes Produktionsbeispiel, die geometrische Intuition hinter dem Optimum und ein Blick auf Simplex und Solver.

From LP to IP: why integrality matters, the combinatorial explosion, LP relaxations, and why rounding fails.

Branch and bound: the workhorse algorithm for integer programming, explained with a complete example showing all three pruning types.

Cutting planes: tightening LP relaxations by slicing off fractional solutions, with Gomory cuts and cover inequalities.

Branch-and-cut and how modern IP solvers work: combining branch and bound with cutting planes, presolve, heuristics, and parallelism.

An introduction to linear programming: definitions, standard form, geometric intuition, and practical examples.

The simplex method explained: slack variables, tableaux, pivoting, degeneracy, and a complete worked example.

Duality in linear programming: the dual problem, strong duality, complementary slackness, shadow prices, and sensitivity analysis.

Construction and improvement heuristics for the TSP: nearest neighbor, greedy, 2-opt, 3-opt, and Or-opt.

Metaheuristics for the TSP: simulated annealing, genetic algorithms, and ant colony optimization.

A brief introduction to the Traveling Salesperson Problem (TSP)