OPERATIONS RESEARCH II

Course Description

Elementary mathematical models will be developed for stochastic processes. Markov processes and decision analysis. Basic models, such as discrete and continuous time Markov Chains, decision trees, and elementary solution techniques related to these models are discussed.This course introduces uncertainty, risk, and probabilistic approaches to Operations Research. Review of probability theory with illustrations from inventory is applied; decision analysis; decision trees and Bayes rule; utility theory approach; Markov chain models, Chapman-Kolmogorov equations, steady-state probabilities and their computation and applications; M/M/c infinite and finite capacity queuing models and optimization, queuing networks; two-person, constant and non-constant sum games , their analysis and applications are discussed during the semester.

OPERATIONS RESEARCH II

Evaluation Tools (Active Term)

No evaluation items have been defined.

Course outcomes

1. 01 Construct ability to make decision by using probability techniques
2. 02 Create decisions under uncertainty by using utility theory and decision trees.
3. 03 Be able to apply the knowledge that they gain from Game Theory and and Markov Chain to the real-life situtations.
4. 04 Be able to draw Queuing theory and stochastic processes during the answering real life problems.
5. 05 Identify and develop operational research models from the verbal description of the real system.

Course Syllabus

Reference Books & Course Materials

1. 01 Wayne L. Winston, Operations Research: Applications and Algorithms, 4th ed., Canada Thomson, 2004. ISBN: 0-534-42362-0
2. 02 Taha, Hamdy A., Operations Research, 6th ed., Prentice Hall, 1997.
3. 03 Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research, 7th ed., McGraw Hill, 2001

Learning Outcomes

1. L01 Apply probability concepts and stochastic process principles to solve uncertainty-based Operations Research problems SOLO 3
2. L02 Formulate and solve decision-making problems under uncertainty using decision trees, expected value, utility theory, and Bayes’ rule. SOLO 3.5
3. L03 Analyze Markov chain models and compute transition probabilities, state classifications, steady-state probabilities, and mean first passage times. SOLO 3.5
4. L04 Construct and evaluate queueing models using arrival/service processes, birth-death processes, and basic M/M/c queueing structures. SOLO 4
5. L05 Solve and analyze two-person zero-sum or constant-sum game theory problems using pure strategies, mixed strategies, and linear programming methods. SOLO 3.5

Program Outcomes

1. P01 Knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline.
2. P02 Ability to apply knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline to the solution of complex engineering problems.
3. P03 Ability to define complex engineering problems by using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) related to the problem addressed.
4. P04 Ability to formulate complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
5. P05 Ability to analyse and solve complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
6. P06 Ability to design creative solutions to complex engineering problems.
7. P07 Ability to design complex systems, processes, devices, or products in a way that meets present and future needs while considering realistic constraints and conditions.
8. P08 Ability to select and use appropriate techniques and resources—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
9. P09 Ability to select and use modern engineering and computational tools—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
10. P10 Ability to conduct literature research and use appropriate research methods for the investigation of complex engineering problems.
11. P11 Ability to design experiments for the investigation of complex engineering problems.
12. P12 Ability to conduct experiments, collect data, analyse results, and interpret findings for the investigation of complex engineering problems.
13. P13 Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the framework of the United Nations Sustainable Development Goals (SDGs).
14. P14 Awareness of the legal implications of engineering solutions within the framework of the United Nations Sustainable Development Goals (SDGs).
15. P15 Knowledge of ethical responsibility and adherence to the principles of professional engineering conduct.
16. P16 Awareness of acting impartially without discrimination in any matter and of being inclusive of diversity.
17. P17 Ability to work effectively as an individual.
18. P18 Ability to work effectively as a team member or leader in intra-disciplinary teams (face-to-face, remote, or hybrid).
19. P19 Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote, or hybrid).
20. P20 Ability to communicate effectively in spoken form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
21. P21 Ability to communicate effectively in written form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
22. P22 Knowledge of professional practices such as project management and economic feasibility analysis.
23. P23 Awareness of entrepreneurship and innovation.
24. P24 Ability for independent and lifelong learning.
25. P25 Ability to adapt to new and emerging technologies.
26. P26 Lifelong learning ability that includes the capacity to think critically about technological changes.

Po-Lo Matrix