Operational Research

Code:

EC0023

Acronym:

IOPE

Keywords
Classification	Keyword
OFICIAL	Territory Planning and Environment

Instance: 2013/2014 - 1S

Active?	Yes
E-learning page:	https://moodle.fe.up.pt/
Responsible unit:	Spatial Planning and Environment Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEC	206	Syllabus since 2006/2007	3	-	5	60	135

Teaching language

Portuguese

Objectives

General aims:
This course aims to acquaint students with skills (methods) on problem solving (processes and decision making).
This course also aims to develop students’ skills to identify and to have a structured approach to solve problems, to construct models of problems of decision, to use quantitative methods to obtain solutions, as a support to reasoned decisions, as well as to know how to use information from models to introduce organization changes.

Learning outcomes and competences

Pedagogical aims:
Knowledge: To be acquainted with research techniques used as a support of decision making processes. To command theoretical and practical techniques of linear programming (namely the simplex method, duality, transportation problems, allocation problems), networks and fluxes (network optimization problems, PERT and CPM networks), game theory and decision theory

Understanding:
To understand decision making and mathematical reasoning processes and geometrical visualization of methods of resolution problems of linear programming, sensitivity and post-optimal analysis, problems of transportation, allocation problems, network optimization problems, game theory and decisions problem theory. Generalization of the concepts related to any dimension of problems of decision, taking into account their different levels of complexity (decision variables, aims and different types of restrictions).

Application: To apply the analytical tools of operational investigation to the approach, structure and rational resolution of decision problems.

Analysis:
To analyse real problems that need a decision with different levels of complexity, different types and sources of information and different approaches. To organize them in models (deterministic and stochastic), where the objectives, decision variables and the different types of restrictions (physical, economic-financial, regulation, etc) are easily identified, in which the adequate decisions are reasoned. Post-optimal analysis of models to adjust their applicability conditions to the evolution of their external and internal constraints (company and processes).

Summary:
To summarize in models important information to different problems that require a decision, by a clear identification and mathematical expression of decision variables, objective function and restrictions, according to the type and structure of problem decision in analysis.

Assessment:
To assess different options of decision of real problems that engineers will come across and choosing in a rational way the best option.

Handling:
To handle different methodologies of decision support, by clearly identifying which are the most appropriate methodologies in decision in different types of situation. To develop skills on decision making.

Working method

Presencial

Program

1. Linear Programming.
1.1 Reference example: formulation of a linear programming problem: graphical method.
1.2. The linear programming model.
1.3. Properties of linear programming.

2. Simplex Method.
2.1. Simplex Method essence.
2.2. Problem formulation using the Simplex Method
2.3. Simplex Method Algebra.
2.4. The Simplex Method in tabular form.
2.5. Geometric interpretation of the Simplex Method.
2.6. Adaptation to other model forms.

3. The Transportation problem and the Assignment problem
3.1. Transportation Problem.
3.2. Simplex Model for the transportation problem
3.3. Assignment Problem

4. PERT/ CPM Network Analysis.
4.1. Reference example.
4.2. Terminology network.
4.3. The minimum path problem.
4.4. The maximum flow problem.
4.5. The minimum cost problem.
4.6. Project Planning: PERT/CPM

5. Project Management

DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
The curricular syllabus permit to understand decision making and mathematical reasoning processes and geometrical visualization of methods of resolution problems of linear programming, sensitivity and post-optimal analysis, problems of transportation, allocation problems, network optimization problems, game theory and decisions problem theory. Generalization of the concepts related to any dimension of problems of decision, taking into account their different levels of complexity (decision variables, aims and different types of restrictions).

Mandatory literature

Frederick S. Hillier, Gerald J. Lieberman; Introduction to operations research. ISBN: 007-123828-X
Goodwin, P. e Wright, G.; Decision Analysis for Management Judgment, John Wiley & Sons, Ltd, 2007. ISBN: 978-0-470-86108-0

Complementary Bibliography

Hamdy A. Taha; Operations research. ISBN: 0-13-281172-3 (brochada)
coord. Carlos Henggeler Antunes, Luís Valadares Tavares; Casos de aplicação da investigação operacional. ISBN: 972-773-075-2

Teaching methods and learning activities

Theoretical classes will be based on the presentation of concepts and relevant results of the subjects that are being covered, as well as its importance on civil engineering, examples and case studies will also be presented. Call for the understanding of concepts, its application and interrelation and interpretation of diverse information. In theoretical-practical classes students will be lead to the interpretation of information from case studies and problem solving, and to apply concepts on a group work.

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The teaching methodologies permit to apply the analytical tools of operational investigation to the approach, structure and rational resolution of decision problems, to analyse real problems that need a decision with different levels of complexity, different types and sources of information and different approaches. To organize them in models (deterministic and stochastic), where the objectives, decision variables and the different types of restrictions (physical, economic-financial, regulation, etc.) are easily identified, in which the adequate decisions are reasoned. Post-optimal analysis of models to adjust their applicability conditions to the evolution of their external and internal constraints (company and processes).

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Trabalho escrito	30,00
Total:	100,00

Eligibility for exams

Achieving final classification requires compliance with attendance at the course unit, according to the MIEC assessment rules. It is considered that students meet the attendance requirements if, having been regularly enrolled, the number of absences of 25% for each of the classes’ types is not exceeded.

Calculation formula of final grade

  

Observations

Working time estimated out of classes: 2.5 hours