/operations-research

Teaching repository for the undergraduate course in Operations Research at Technical University Munich.

Primary LanguageJava

Tutorial for Operations Research SS22 Konstantin Kuchenmeister

Teaching repository for the tutorial of the undergraduate course in Operations Research at Technical University Munich.

Logistics:

Every:

  • Tuesday 2pm-3:30pm GMT+2
  • Friday 3pm-4:30pm GMT+2

Location:

  • Zoom

Recordings:

Channel link:

https://www.youtube.com/channel/UCUMv1AN6eQvcCCL4Gg5av4A

Playlist link:

https://www.youtube.com/playlist?list=PLkmX_gkRxWIPS69e_lJQVtN8QaWNd2-50

Week 1: Modeling (of linear optimization systems)

Provided resources:

  • Notes
  • Created Gurobi code in Java to solve Exercise 1.1 (In order to run this file you need a working installation of Gurobi https://www.gurobi.com, and add the gurobi.jar file to the Java Classpath)

The code solves the following linear programming problem: (Exercise 1.1):

Minimize $ 200 x_{1}+160 x_{2}=z $ such that $$ \begin{aligned} 6 x_{1}+2 x_{2} & \geq 12 \ 2 x_{1}+2 x_{2} & \geq 8 \ 4 x_{1}+12 x_{2} & \geq 24 \ x_{1}, x_{2} & \leq 7 \ x_{1}, x_{2} & \geq 0 \end{aligned} $$

Week 2: Solving linear optimization systems

  • Graphically
  • Normal-, standard-, canonical -Form
  • Simplex Algorithm
  • Big M Method
  • Edge cases of linear optimization systems

Week 3: Revised Big M Method Simplex in Matrix Notation, Modelling preemptive and weighted goal programming problems

  • Revised Simplex in Matrix Form and Big-M-Method
  • Goal Programming

Week 4: Sensitivity Analysis

Week 5: Duality Theory, Complementary Slackness Theory, Derivation

Week 6: Modeling of Integer Programming Problems

Week 7: Solving Integer Programs with the Branch&Bound and the Gomory Cutting-Plane Method

Week 8: Advanced Solution Methods for Integer Programs: Column-Generation, Dynamic Programming and Heuristics

Week 9: Network Flow Problems, Matroids, Hungarian Method

Week 10: Traveling Salesperson Problem (TSP)

Disclaimer:

All resources here I have created myself and I can in no way guarantee the accuracy of the information. The faculty's lecture slides and practice materials are crucial with regard to the exam, not my notes.