Operational Research II

Code:

EIG0026

Acronym:

IO II

Keywords
Classification	Keyword
OFICIAL	Quantitative Methods

Instance: 2009/2010 - 2S

Active?	Yes
Responsible unit:	Department of Industrial Engineering and Management
Course/CS Responsible:	Master in Engineering and Industrial Management

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEIG	81	Syllabus since 2006/2007	3	-	6	56	160

Teaching language

Portuguese

Objectives

BACKGROUND
In order to become leaders of organizations in today's highly competitive business environment, managers must be aware of fundamental tools and methods for quantitative modelling. The purpose of the Operational Research II course is to make students aware of the main concepts and key-aspects of advanced operational research techniques, as well as to develop the skills required to apply these techniques successfully.

SPECIFIC AIMS
This course unit aims to acquaint students with advanced knowledge in Operational Research techniques, including stochastic methods.

PREVIOUS KNOWLEDGE
EIG0015 - Statistics I
EIG0018 - Statistics II
EIG0022 - Operational Research I

PERCENTUAL OUTCOMES
Scientific component: 70%
Technological component: 30%

LEARNING OUTCOMES
This course unit aims to endow students with the following skills:
1. Know the key-concepts and features of the different Operational Research techniques and algorithms included in the course program.
2. Construct models to represent real-word problems
3. Solve those problems using the techniques presented in this course.

Program

MARKOV CHAINS: Characterisation of stochastic processes and Markov chains. Classification of states in a Markov Chain. Transition matrix of a Markov Chain. Analysis of ergodic chains and absolving chains. Generalisations.
QUEUING THEORY: Characterisation and classification of queuing processes. The M/M/1: (GD,+00 ) queuing system. Queuing systems with more than one server. Finite source models and models “blocked customers cleared” models. Priority queuing models. Generalisations.
SIMULATION: Objectives and limitations. Event and process-based approaches to discrete simulation. Discrete simulation software. Design, test and validation of a simulation model. Analysis of simulation output. Application of the simulation method to case-studies.
INTEGER PROGRAMMING: Formulating the problem. Solving IP problems: The Branch-and-Bound method, the Implicit Enumeration method, The Cutting Plane algorithm. Obtaining the optimal solution of IP models with Excel.
SEPARABLE PROGRAMMING: Separability of the objective function and constraints. Linearization of the original problem. The use of the Simplex algorithm to obtain the solution to the approximating approximating problem. Conditions of optimality.
NONLINEAR PROGRAMMING:
Analytical solutions to nonlinear optimisation problems. Unconstrained maximisation and minimisation problems with one variable and with several variables. Methods for solving NonLinear Problems (NLPs ) with constraints: Lagrange Multiplers and the Kuhn-Tucker Conditions.
Numerical solutions to nonlinear optimisation problems.

Mandatory literature

Hillier, Frederick S.; Introduction to operations research. ISBN: 007-123828-X
Kelton, W. David; Simulation with Arena. ISBN: 0-07-121934-X
Ana S. Camanho; Resolução dos problemas propostos da disciplina de Investigaçao Operacional II, 2008
Ana S. Camanho; Problemas propostos da disciplina de Investigação Operacional II, 2008
Hillier, Frederick S.; Introduction to operations research. ISBN: 007-123828-X
Kelton, W. David; Simulation with Arena. ISBN: 0-07-121934-X
Ana S. Camanho; Cópias dos acetatos das aulas, 2008
Ana S. Camanho; Resolução dos problemas propostos da disciplina de Investigaçao Operacional II, 2008

Complementary Bibliography

Winston, Wayne L.; Operations research. ISBN: 0-534-20971-8
Hillier, Frederick S.; Introduction to management science. ISBN: 0-07-119554-8
Winston, Wayne L.; Operations research. ISBN: 0-534-20971-8
Hillier, Frederick S.; Introduction to management science. ISBN: 0-07-119554-8

Teaching methods and learning activities

The course combines lectures covering the OR techniques, and tutorials to apply these techniques to problems and discuss simuation case studies.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	64,00
Simulation project	Trabalho escrito	20,00
Exam paper	Exame	3,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Regular subject study	Estudo autónomo	55
Exam paper preparation	Estudo autónomo	20
	Total:	75,00

Eligibility for exams

Not exceeding the number of absences allowed;
Make a group project using the Simulation technique.

Calculation formula of final grade

The final classification results of the weighted average of the classification in the two tests done during the semester (weight of 40% each) and the classification of the Simulation project (weight of 20%).

Examinations or Special Assignments

Simulation Project (Group work)