460-4062/01 – Operational Research I (OV )
| Gurantor department | Department of Computer Science | Credits | 4 |
| Subject guarantor | doc. MSc. Donald David Davendra, Ph.D. | Subject version guarantor | doc. MSc. Donald David Davendra, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2013/2014 | Year of cancellation | 2014/2015 |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The aim of this course is to teach the basic deterministic and advanced stochastic methods for solving different complex combinatorial / discrete problems of an optimization nature. This course will also introduce different problems in transportation, assignment and scheduling, which are common and have a practical foundation.
Upon completion of the course, the students will be able to solve, (by making use of various methods) various tasks from the area of production control and planning, logistics, routing etc. The emphasis will be also on obtaining the practical experience with solving the tasks from this area.
Teaching methods
Lectures
Tutorials
Summary
Operations Research (OR) is a discipline of applying advanced analytical methods to help make better decisions. Also known as management science or decision science, it involves the application of information technology in designing systems to operate in the most effective way or deciding how to allocate scarce human resources, money, equipment, or facilities.
This course will address the three different aspects of OR, which are:
1. Simulation: the ability to try out approaches and test ideas for improvement
2. Optimisation: Narrowing choices to the very best when there are virtually innumerable feasible options and comparing them is difficult
3. Probability and Statistics: measure risk, mine data to find valuable connections and insights, test conclusions, and make reliable forecasts.
Lectures:
1. Linear programming formulation
2. Linear programming solution – graphical method
3. Linear programming solution – algebraic method
4. Simplex algorithm
5. Big-M Method
6. Two Phase Method
7. Simplex algorithm – Initialisation and Iteration
8. Simplex algorithm – Termination
9. Primal – Dual Relationship
10. Dual Simplex Algorithm
11. Introduction to Sensitivity Analysis
12. Transportation problem
13. Assignment problems
14. Hungarian Algorithm
Compulsory literature:
1. Taha Hamdy (2010) Operations Research: An Introduction (9th Edition). ISBN-13: 978-0132555937
2. Winston Wayne (2003) Operations Research: Applications and Algorithms. ISBN-13: 978-0534380588
3. Pinedo M. (2012) Scheduling: Theory, Algorithms, and Systems. Springer. ISBN-13: 978-1461419860
Recommended literature:
Way of continuous check of knowledge in the course of semester
Conditions for granting the credit:
The tasks that form the program of exercises must be worked out.
E-learning
Other requirements
Additional requirements are placed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures
● General Introduction to Operations Research. Overview of OR terminology and history.
● Linear Programming (LP) Model Formulation: LP Model formulation, Simplex Method
● Integer Programming (IP) Model Formulation.
● Evolutionary Algorithms: Introduction to the most common algorithms, which are used for solving optimization problems including Genetic Algorithms, Differential Evolution, Particle Swarm etc.
● Transportation and Assignment Problems; vehicle routing problems, bin packing problem, traveling salesman problem.
● Scheduling Problems; flow shop scheduling, flow shop with blocking, flow shop with no wait, flow shop with lot streaming problems.
● Software systems for operational research.
Seminars
The assignments will consist the coding of the following problems/routines:
● Linear programming
● Integer Programming
● Genetic Algorithms
● Differential Evolution
● Transportation Problem coding
● Scheduling Problem Coding
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction