The aim of studying and bibliography

The main aim of study: Preparing students to use linear programming algorithms and techniques to solve optimization problems

The general information about the module: The module is implemented in the fourth semester (15 hours of lectures, 30 hours of laboratory classes and 15 hours of project classes)

Bibliography required to complete the module

Bibliography used during lectures

1	J. G. Ecker, M. Kupferschmid	Introduction to Operations Research	John Wiley & Sons, New York.	1988
2	W. Sikora (red.)	Badania operacyjne	PWE, Warszawa.	2008

Bibliography used during classes/laboratories/others

1	T. Szapiro	Decyzje menedżerskie z Excelem	PWE, Warszawa.	2000
2	K. Masłowski	Excel 2016 PL. Ćwiczenia praktyczne	Helion, Gliwice.	2016

Bibliography to self-study

1	K. Kukuła (red.)	Badania operacyjne w przykładach i zadaniach	PWN, Warszawa.	2016
2	D. Rogalska	Programowanie liniowe: algorytmy i zadania	Wydawnictwo Uniwersytetu Łódzkiego, Łódź.	1998

Basic requirements in category knowledge/skills/social competences

Formal requirements: The fourth semester of a degree in engineering and data analysis. The student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge: Basic concepts of linear algebra and analytic geometry: matrices, determinants, systems of linear equations, vectors, vector and affine spaces

Basic requirements in category skills: Student knows operations on matrices and vectors, can solve systems of linear equations, has a basic practical knowledge of using the MS Excel spreadsheet

Basic requirements in category social competences: Willingness to continue to acquire mathematical knowledge. Ability to work in a group

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01	understands the basic concepts of linear programming, knows how to solve a simple problem of linear programming using the graphical method and duality	lectures, laboratory and project classes	written exam, project evaluation	K_W03++ K_U03++ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
02	knows the symplex method, can set the initial basic feasible solution and find the optimal solution (unique or multiple)	lectures, laboratory and project classes	written exam, project evaluation	K_W03++ K_U03++ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
03	identifies the transportation problem, knows how to determine the initial solution; solves the unbalanced transportation problem, recognizes the assignment problem and knows how to apply the Hungarian algorithm	lectures, laboratory and project classes	written exam, project evaluation	K_W03++ K_U03++ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
04	uses the MS Excel Solver package for modeling, solving and post-optimization analysis of linear programming problems	laboratory and project classes	project evaluation	K_W03++ K_U03+++ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
4	TK01	Formulation of a linear programming problem, canonical form of a linear program, geometric method, examples of applications in production optimization and network analysis	W1-W5, L1-L10	MEK01 MEK04
4	TK02	The symplex method: canonical form of a linear program, geometry of the symplex algorithm, sensitivity analysis	W6-W10, L11-L20	MEK02 MEK04
4	TK03	The transportation problem (balanced and unbalanced), the assignment problem, the Hungarian algorithm	W11-W15 , L21-L30	MEK03 MEK04
4	TK04	The MS Excel Solver package and its application to solving optimization problems and post-optimization analysis of linear programming problems	L1-L30, P1-P10	MEK01 MEK02 MEK03 MEK04
4	TK05	Project presentation	P11-P15	MEK04

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 4)		contact hours: 15.00 hours/sem.	Studying the recommended bibliography: 7.00 hours/sem.
Laboratory (sem. 4)	The preparation for a Laboratory: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Making the report: 10.00 hours/sem.
Project/Seminar (sem. 4)	The preparation for projects/seminars: 5.00 hours/sem.	contact hours: 15.00 hours/sem..	Doing the project/report/ Keeping records: 10.00 hours/sem. The preparation for the presentation: 2.00 hours/sem.
Advice (sem. 4)		The participation in Advice: 1.00 hours/sem.
Exam (sem. 4)	The preparation for an Exam: 8.00 hours/sem.	The written exam: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	The final grade of the lectures is a written exam mark
Laboratory	At least 3,0 mark for each project - the final grade is their arithmetic mean
Project/Seminar	Mark 3,0 for 70% of possible points. Mark 4,0 for 80% of possible points. Mark 5,0 for 90% of possible points
The final grade	The final grade is the arithmetic mean of grades of: the project, the laboratory classes and lectures

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: no