Linear Programming
1. |
Subject title |
Linear Programming Линеарно програмирање |
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2. |
Code |
m23_s_060 |
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3. |
Study program |
Cloud Computing, Data science in computer science and engineering, IT management, Bioinformatics, Security, Cryptography and Coding, Еducation with ICT, Eco-informatics, Inteligent Systems, Internet Technologies and cyber security, Computer Science, Statistics and Data Analytics, Software for embedded systems, Software Engineering, Cloud Computing, Bioinformatics, Security, Cryptography and Coding, Statistics and Data Analytics, IT management, Software Engineering, |
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4. |
Organizer of the study program (unit, institute, department, division) |
Faculty of Information Sciences and Computer Engineering |
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5. |
Study cycle (first, second, third) |
Втор циклус |
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6. |
Academic year / semester 5 / Летен |
7. Number of ECTS credits 6.0 |
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8. |
Instructor |
ворн. проф. д-р Методија Јанчески |
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9. |
Prerequisites for enrollment |
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10. |
Subject goals and competencies: The purpose of the course is to get acquainted with the mathematical theory of linear programming, with the calculating aspects and the most popular practical applications of linear programming. Upon completion of the course candidates: will have deepened knowledge of many different algorithms of linear programming and will be able to solve a wide range of tasks in the field of economic and technical research, from the practice of planning and organization of production and management of systems related to Finding the smallest (or largest) value of a function of a large number of variables.
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11. |
Subject content: 1. Elements of convex polyhedra theory (convex sets, pair of mutual-dual systems of linear equations and inequalities, convex cones, convex plague cones, convex sets, convex polyhedra) 2. Linear Programming Task (LP) (equivalent form of LP task, permitted area, extreme programs, standard LP-task type, base programs, geometric interpretation of LP-defect in RN and RM) 3. Simplex method (basic theorems of Simplex method, simplex algorithm, finding an initial base program, degeneration and cichle, lexicographic form of Simplex method, modified simplex algorithm) 4. Duality in linear programming (definition of a pair of dual-dual LP-attacks, basic theorem in duality, function of Lagrange for the pair of intermittent-dual LP-deficit, dual simplex algorithm, finding an initial dual-permeable solution, economic interpretation. Dual tasks, matrix games and duality) 5. Special LP-Tasks and Methods (classic transportation task, rule of northwest angle, classic transportation solution, transportation variants, LP task with block structure, existing tasks, parametric tasks) 6. Discrete programming (examples of integer tasks, cutting methods, discreet algorithm, cyclic algorithm, approximate methods, additive algorithm, Belmann algorithm) |
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12. |
Learning methods: Предавања поддржани со презентации преку слајдови, интерактивни предавања, вежби, тимска работа, студии на случај, самостојна изработка и одбрана на проектна задача и семинарска работа. Покрај методот на усно излагање, ќе се применуваат активните методи на учење како: метод на проблемска настава, метод на проектна настава, метод на истражување, метод на самостојна работа и други. |
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13. |
Total available time fund |
6.0 ECTS x 30 hours = 180 hours |
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14. |
Time distribution |
50 + 30 + 20 + 40 + 40 = 180 hours
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15. |
Forms of teaching activities |
15.1. |
Lectures - theoretical teaching |
50 hours |
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15.2. |
Exercises (laboratory, classroom), seminars, team work |
30 hours |
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16. |
Other forms of activities |
16.1. |
Project tasks |
40 hours
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16.2. |
Independent tasks |
20 hours |
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16.3. |
Homework |
40 hours |
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17. |
Grading method |
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17.1. |
Tests |
20 points |
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17.2. |
Seminar work / project (presentation: written and oral) |
40 points |
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17.3. |
Activities and learning |
10 points |
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17.4. |
Final exam |
50 points |
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18. |
Grading criteria (points / grade) |
up to 50 points |
5 (five) (F) |
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from 51 to 60 points |
6 (six) (E) |
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from 61 to 70 points |
7 (seven) (D) |
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from 71 to 80 points |
8 (eight) (C) |
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from 81 to 90 points |
9 (nine) (B) |
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from 91 to 100 points |
10 (ten) (A) |
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19. |
Condition for signature and taking final exam |
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20. |
Language of instruction |
македонски |
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21. |
Quality assurance method |
механизам на интерна евалуација и анкети
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22. |
Literature |
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22.1. |
Mandatory literature |
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22.2. |
Additional literature |
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