# Operations Research & Optimization

## Course Description:

Basic principles of systems analysis. Linear programming, linear programming under multiple constraints, special topics on linear programming. Integer programming, topics on transportation, transit, placement, networks. Introduction to dynamic and non-linear programming, metahueristsic methods. Algorithms on optimization with MATLAB.

• Semester 5
• Teaching hours 3

### Prerequisite Knowledge

Knowledge of Algebra, Numerical Analysis, use of computers and MATLAB.

### Course Units

# Title Description Hours
1 Introduction to Operational Research Introduction to Operational Research (OR). Concepts on optimization models, mathematical models, and decision-making problems. Engineering optimization problems. 1Χ3=3
2 Problem of Linear Programming The problem of Linear Programming (LP). Graphic solution. Concepts on unique solution, infinite solutions, no solution and others. 1Χ3=3
3 SIMPLEX method SIMPLEX method. Solution of maximization LP problem. 1Χ3=3
4 Problem of duality Problem of duality. Solution of minimization LP problem. Big M method. 1Χ3=3
5 Transportation problem Transportation problem (TP). Northwest square method. Lowest cost method. 1Χ3=3
6 Assignment problem. Integer Programming Assignment problem. Integer programming (IP). Branch and Bound method. 1Χ3=3
7 Introduction to Nonlinear Programming Introduction to Nonlinear Programming (NP). Introduction to Multicriteria Programming (MP). 1Χ3=3
8 MATLAB optimization Toolbox Laboratory class: Presentation of MATLAB optimization toolbox. Solution of problems using the toolbox and MATLAB scripts. 1Χ3=3
9 Laboratory classes Formulation and solution of LP and IP problems using computers. 4Χ3=12
10 Laboratory class: Revision Laboratory class: Revision: formulation and solution of older exams. 1Χ3=3

### Learning Objectives

Upon successful completion of the course, students will be able to: 1. know the basic principles of operational research and systems’ optimization, specifically for Civil Engineering problems, 2. realize the value of computers to the solution of difficult problems in the area of applied mathematics, a branch of which is the operational research, 3. understand the behavior of special case algorithms, 4. structure the formulation of LP and IP problems, and 5. compute either analytically by hand, or numerically by the optimization toolbox of MATLAB, the solution of LP and IP problems, both on the decision making level and on the design of civil engineering problems.

### Teaching Methods

 Teaching methods Class lectures and workshops. Theory - Applications and Exercises, teaching using blackboard without slides, from a tutor for each group. Yes. This is a laboratory course. Six weeks of the course take place in a computer lab where each student formulates and solves engineering optimization problems in a MATLAB environment. Yes (computational package of the MATLAB optimization toolbox) Yes

### Student Assessment

• Final written exam: 70%
• Problems - Applications: 30%

### Textbooks - Bibliography

1. Karlaftis, M., Lagaros, N. (2010) Operational Research & Optimization for engineers, Simmetria Publications, Athens.
2. Teaching notes.

© 2017 School of Civil Engineering, ΕΜΠ