URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2DD55&collegejaar=2025&taal=enOmschrijving
Optimization part:- Introduction: Formulation of practical problems as LP problems; Standard LP problem
- Solving LP problems: Simplex method; Optimality test
- Dual LP problem: Weak and strong duality; Complementary slackness relations
- Integer LP problems: Formuleration of practical problems as integer LP problems; Solving integer LP problems; Branch-and-bound-method
- Transportation problems: Definition; Simplex method for Transportation problems
Part Stochastic Operations Research:
- Markov chains: Definition, transient behavior, limiting behavior, cost models
- Markov processes: Definition, limiting behavior, Poisson processes, birth and death processes
- Renewal theory: Definition of renewal process, renewal-reward theorem with applications
- Queueing models
Exponential models (M/M/1, M/M/s, M/M/s/K)
Limiting distribution, performance measures like throughput, average number of customers and average waiting time
Non-exponential models (M/G/1, G/M/1, G/G/1)
Mean value analysis for M/G/1 model
Limiting distribution for G/M/1 model
Approximations for G/G/1 model
Doelstellingen
Part Optimization:Introduction to the mathematical modeling of optimization problems, in particular linear optimization problems. The main focus is on solution methods, and hence not on the modeling itself . Goal is that at the end of the course students are able to see which kind of problems can in principle be solved, which is a very important aspect in the formulation of practical problems. It does not make sense to formulate a model for a practical problem which can not be solved eventually. During the course the student hence will become familiar with solution methods for in particular linear optimization problems. Besides that, also attention will be paid to problems for which the solutions have to be necessarily integer valued.
Part Stochastic Operations Research:
The student is able to formulate a discrete-time Markov chain, a continuous-time Markov chain and a queueing model for relatively simple practical situations. For discrete-time Markov chains, the student cancalculate transient and limiting distributions, short-term and long-term costs and first passage times. For continuous-time Markov chains, the student can calculate the limiting distribution, long-term costs and first passage times. The student can apply the renewal-reward theorem in order to calculate the long-term cost rate in renewal processes. The student can calculate and interpret several performance measures in a number of queueing models.