## Introduction to Operational Research

Code no:

**9.1.15.7.2.9****, (9120)**Semester:**7th**, Teaching hours: 4## core syllabus

An introduction to all the main techniques of Operational Research.

**PREREQUISITE**

Mathematics, Statistics and Probability Theory to the level of an introductory course is required. In particular, students should have covered elementary distribution theory and the Poisson Process, and have knowledge of linear algebra sufficient to handle matrix inversion. Students must be prepared to use computer packages when required.

## OBJECTIVES

The course aims at acquiring the knowledge for:

Skills and competences:

- mathematical Modeling, Solution of Linear Programming (LP) problems using the Simplex method, the Big M method, the two Phases method, the graphical method or even using the solvers embedded in various computer packages.
- Solution of Integer Linear Programming (ILP) Problems, Decision making problems, Inventory control problems and Queuing theory problems.
- Study of Duality, stability, accuracy, approximation, convergence etc.
- Sensitivity analysis of the methods where particular emphasis will be given.
- Project Management methods, to construct Gantt Charts, as well as S-Curves, and to use CPM, MPM, PERT methods and Prince II, PMbok protocols.
- Game theory, pure and mixed strategies to solve Two-Person zero (or constant) sum Games.
- Networks, the maximal Flow Problem, the minimum-cost Capacitated Flow Problem, the Shortest-Route Problem and the minimal Spanning Tree Problem.
- Dynamic Programming

Skills and competences:

- On completion of this course, Students should be armed with numerical and computational techniques for solving a wide variety of fundamental mathematical problems that arise in diverse scientific areas.
- In particular, upon successful completion of the course, the student will
- recognizes a physical problem and can model it.
- be able to choose between different methods to achieve the best result.
- be familiar with complex concepts such as the stability of a solution and the sensitivity analysis of a method.
- can use his / her knowledge of Statistics, Probabilities and Algebra on chapters such as Queuing Theory and Simplex method.
- be able to explain the difference between profit and opportunity loss.
- with the help of criticism of thought, can decide which of the assumptions of a model are realistic and which are not.
- can use technology to apply the modern algorithms of the various methods of Operational Research.

## SUBJECT CONTENT IN OUTLINE

- Operational Research approach to modeling.
- Formulation of OR problems and case studies.
- Analysis of Linear Programming models.
- Graphical modeling and solution.
- Simplex Method.
- Solution by using computer packages. Slack variables.
- Duality theory. Interpretation of Duality. Sensitivity Analysis. Transportation Problem.
- Project evaluation and management with or without limited resources.
- Integer programming.
- Decision making under uncertainty. Decision criteria. Decision trees.
- Inventory control and management. Economic order quantity and reorder point with or without uncertain demand.
- Queuing Theory. Dynamics of a queuing system with interarrival time and service time coming from any probability distribution, for a single or multiple servers.
- Project Management
- Game Theory
- Network Models
- Dynamic Progamming