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.