Stochastic Modeling and Optimization

The module covers different state-of-the art methods for decision support in stochastic real- world environments. This contains methodology for multi-period problems and takes into account different states of the world. The module covers both, the mathematical theory behind the methods and presents their applications to industry problems such as inventory management or call center staffing. Specifically, the module covers the topics: • Uncertainty Modeling: Probability Theory, Stochastic Processes, • Fuzzy Set Theory, • Newsvendor Problems, Bayes Updating, Forecast Evolution • Stochastic Dynamic Programming and Approximate Dynamic Programming • Markov Chains and Markov Decision Processes: LP, Value Iteration, Policy Iteration • Stochastic Programming: Chance Constrained Programming, • Two-Stage Models with Recourse, Sample Average Approximation, Sampling Strategies • Simulation Optimization Applications: Queuing Theory, Queuing Networks, Factory Physics, Inventory Theory (single echelon, multi-echelon)

After participating in this module, students are able to understand and interpret a set of advanced stochastic methods. They are able to apply these concepts in practice and transfer the methods to real life. Students further comprehend the weaknesses and strengths of the methods. They are able to assess which method to apply in which context. Students further have the ability to make appropriate use of related software. Through (voluntary) homework and the discussion and presentation of different solutions in class, students further improve their skills of carrying out discussions within a research environment. They gain insights into academic work, as most material will be learned from scientific papers rather than from books. The course will prepare the students for their master thesis.

The grading is based on a written exam (90 minutes) consisting of 4 questions, the participants can choose 3 out of 4. Each question has several parts assessing the different competence levels. Students show that they understand a set of advanced stochastic methods. Each question requires the application of a stochastic method, or combinations of several methods. That shows students’ ability to compare, choose and, combine different stochastic methods. Students have to conduct 1) practical implementation exercises and 2) theoretical proofs. The exam is open-book, students are allowed to use their own laptops for solving the programming exercises.

The module requires a solid knowledge in probability theory and linear optimization. The knowledge of a programming language is helpful and the course “Modelling, Optimization, and Simulation” due to extensive use of Mixed-Integer Programming and Simulation methods.

In lectures, students learn to understand the mathematical theory and obtain insights in applications of the stochastic methods to a practice context. Students get exercise sheets with problems that go beyond the examples in the lecture and allow them to reproduce and extend their knowledge. For solving the exercises, they are provided with the necessary software, such as Matlab or Xpress. In exercise classes, students discuss their solutions of the homework, and find out about the differences in practicability of one method over the other. In addition, there are guest lectures of practitioners who apply advanced methodology in their daily work and motivate new fields of application of the models beyond the scope of the lectures.