## Operational Research I

Introduction to the scientific field of Operations Research (OR): Definitions, a glance at the history of OR science, Basic Disciplines. Methodological approaches, taxonomy of OR problems. Mathematical modeling, and introduction to Linear Programming: Introduction to mathematical modeling, Theory of Linear programming, solving linear problems-The simplex method, big M method, duality theory and sensitivity analysis, irregular types of linear programming models, the transportation problem, the assignment model, integer linear programming models, typical integer problems. Networked Analysis: Project planning, development of a project network, the critical path method (CPM), the project evaluation and review technique (PERT), cost optimization, minimal spanning tree problem, shortest route problem, traveling salesman problem. Risk analysis: Probability-based decision making, Monte Carlo simulation, sensitivity analysis, multicriteria decision making methods, analytic hierarchy process (AHP), analytic network process.

### Objectives

The lesson's objective is to assist the engineer in solving practical problems with the right mathematic modelling method.

### Prerequisites

There are no prerequisites for monitoring the Course .

### Syllabus

Introduction to Operations Research: Definition, history, basic characteristics, methodology, categories of problems. Mathematical Programming Problems. Linear Programming (LP): Definition and typical forms of mathematical model GL. Theory solving AI, SIMPLEX method to solve problems of AI, big M method, SIMPLEX, binary problem and sensitivity analysis. Special problem types GL, the transportation problem, the problem of matching. Introduction to Integer Programming (AP). Typical forms problems AP. Mesh analysis: Scheduling projects - Develop project network. Method CPM. Method PERT. Cost optimization. Problem shortest path spanning tree maximum flow problem problem and traveling salesman problem. Risk analysis: decisions using probability, simulation Monte Carlo, sensitivity analysis. Multi-criteria decision-making methods: Analytical Hierarchy Process - AHP. Analytical Network Process - ANP.

COURSE DETAILS
 Level: Type: Undergraduate (A-) Instructors: Stavros, Konstantinos Ponis, Kirittopoulos Department: School of Mechanical Engineering Institution: National Technical University of Athens Subject: Other Engineering and Technologies Rights: CC - Attribution-NonCommercial-NoDerivatives