Course contents *

Basic theory for Markov chains and Markov processes. Some models for reliability and queues based on Markov theory, including queueing models with Erlang distributed service times. Jackson’s models for queueing networks. Deterministic inventory models, including the Wilson formula. Stochastic inventory models, including the “newsvendor problem”. Sherbrooke’s models for optimization of spareparts. Marginal allocation. Dynamic programming. Markov decision processes.

Intended learning outcomes *

The overall purpose of the course is that you should be well acquainted with some operations research models (i.e. mathematical decision support models) which are relevant for analysis and optimization of technical systems. Moreover, you should be able to apply these models on various problems. In particular, you should be able to formulate, analyze, and apply

• reliability models based on Markov chains and Markov processes,
• queueing models based on Markov processes, including models for queueing networks,
• inventory models, deterministic as well as stochastic,
• models for spare parts optimization,
• dynamic programming, for reqursive decision-making,
• optimal policy design for Markov decision processes.

Course Disposition

No information inserted

Specific prerequisites *

In general:

150 university credits (hp) including 28 hp in Mathematics and 6 hp in Mathematical Statistics.

6 hp in Optimization is recommended.

Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis.

Optimization is recommended.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

Hillier and Lieberman: Introduction to operations research, samt kompletterande kursmaterial från institutionen.

Hillier and Lieberman: Introduction to operations research, and some written course material from the department.

Grading scale *

A, B, C, D, E, FX, F

Examination *

• TEN1 - Examination, 7.5 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade *

A written examination (TEN1; 7,5 hp).

Homework assignments can give bonus points for the written exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Per Enqvist

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Offered by

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

SF2812 Applied linear optimization. SF2822 Applied nonlinear optimization. SF2852 Optimal control.

Contact

Per Enqvist (penqvist@kth.se)

Ethical approach *

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.