## Course Description

**Course: TECHNIQUES OF MATHEMATICAL PROGRAMMING **

**Code: QNT303 **

**1 ^{st} Semester**

**Tutor: Dimitrios Giokas**

**Aims and Objectives**

The objective of this course is to introduce students to linear programming (LP) model. LP is the most known branch of Mathematical Programming, with applications to several problems, such as product mix, resource allocation, blending, portfolio selection, financial decisions, production planning, diet, workforce scheduling, transportation, and other. Linear programming deals with the optimization of a linear function subject to a number of constraints. Emphasis in this course is given on formulation and application of linear programming problems, and understanding the methods used to solve them. We conclude the course with application of LP to specially-structured linear programming problems. Appropriate computer programs will be used to solve the problems.

**Contents:**

- Linear Programming: Formulation of linear programming models, the graphical solution of two variable linear programming problems, the simplex method, applications of linear programming.
- Duality theory
- Sensitivity analysis
- Special cases of LP problems: The transportation problem (formulation and applications, solutions of transportation problems), integer programming, etc.
- Case studies
- Goal programming
- Introduction to non-linear programming

**Course Books**:

K.Drakatos-G.Donatos- B.Hombas “Methods and Problems of Programming”, Papazissis Editions 1981, in Greek.

G. Economou & A.Georgiou “Operations Research for Decision Making, G.Benos Editions, 2001, in Greek.

D.Giokas, “Notes for Mathematical programming techniques”, lecture notes, in Greek.

**Other books**:

Hillier, Frederick S., Lieberman, Gerald J., Introduction to Operations Research, Seventh Edition, McGraw-Hill, 2001.

Taha H.A. Operations Research: An Introduction, Eighth Edition, edition, Prentice Hall, 2006.