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# Advanced Topics in Operations Research (BM)

Course
2021-2022

## Prerequisites

This is different for each student, since you can choose which chapters you want to hand in. On the
website of the course you can find a summary of which courses are needed for which chapters. It will
mostly be other courses on operational research. In Leiden this would be the courses Combinatoriek
en Optimalisering, Discrete Besliskunde and Stochastische Besliskunde.

## Description

This course covers several subjects that differ quite a bit. Some subjects are completely new, so
broaden your knowledge, and some give a deeper understanding of existing knowledge. Furthermore
some subjects are more application oriented and concerned with finding optimal solutions, while
others are more theoretical in nature. A few examples of the subjects are:

• Graph theory, in which matrix representations, planar and dual graphs, coloring problems, weighted
and unweighted matchings in bipartite and non-bipartite graphs and trees are treated.

• Network optimization.

• Matroid theory, a general theory that is concerned with the concept of independence.

• Inventory management and general decision theory where decisions have to be made while dealing
with stochastic circumstances.

• Knapsack problem.

• Reliability theory, where you deal with systems with multiple components, and each component
has a probability to fail, while you want your system to keep functioning.

• Linear optimization and special methods to find solutions for such problems.

• Non-linear optimization.

## Mode of instruction

This is a self-study course. You should discuss with the teacher what chapters you want to do, and
then read the chapter and make all of the exercises whenever suits you. In particular, there are no
classes for this course. There is, however, 1 deadline per year and 1 moment for the final exams (respectively the end of February and June). You can ask questions either through email or in person.

## Assessment Method

The homework exercises you hand in, and the final exam is an oral exam.

## Literature

Lecture Notes, which you can find this on the website of the course. The lecture notes are regularly
updated. Note that these lecture notes are in Dutch.