Course Goals

The course aims to provide an introduction into the main methodological approaches in operations research (OR) and the role of OR in analytics. Students shall gain a solid foundation of modeling approaches and solution algorithms for optimization problems in business. Different modelling approaches and solution algorithms are discussed. The course shall enable students to model optimization problems in a structured way and to select an appropriate solution methodology based on the decision context.

• Learning Outcome 2 (LO2): Explain the key ideas of the simplex method, duality theory, branch-and-bound, construction and improvement heuristics, dynamic programming, decision analysis, two-stage stochastic programming and robust optimization.
• Learning Outcome 3 (LO3): Solve toy problems by hand with the appropriate algorithmic approaches.
• Learning Outcome 4 (LO4): Develop mathematical programs (LPs and MIPs) for a given simple verbally described problem setting.
• Learning Outcome 5 (LO5): Solve LPs and MIPs on small data sets with excel solver (or another optimization tool) and interpret the obtained results.

Course Topics

Part I: Decisions under certainty

1. Linear programming (the basics of the simplex method, the basics of duality theory)
2. (Mixed) integer programming (the basics of branch-and-bound as well as modeling (simple) optimization problems in a business context as mixed integer linear programs, such as facility location problems)
3. Dynamic programming (multi-stage problems with finitely many states, knapsack problem, shortest path)
4. Heuristics (traveling salesman problem, construction and improvement heuristics, local search, tabu search)

Part II: Decisions under uncertainty

1. Decision analysis (pay-off tables, decision trees, value of stochastic solution, experimentation)
2. Linear Programming under uncertainty (two-stage stochastic programs, the very basics of robust optimization)
3. Overview of queuing theory
4. Very basics of simulation