Complements of Operations Research

Code:

EM502

Acronym:

CIO

Instance: 2006/2007 - 2S

Active?	Yes
Responsible unit:	Industrial Management and Engineering Section
Institution Responsible:	Faculty of Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEM	8	Plano de estudos de transição para 2006/07	5	6	6	-
MIEM	7	Plano de estudos de transição para 2006/07	5	-	6	-

Teaching language

Portuguese

Objectives

Specific objectives:

Kowledge of operational research techniques. Applicability of the Operational Research techniques to real-world problems.

At the end of the semester the students are supposed to be able to:

1. Know different Operational Research techniques
2. Construct models to represent real-word problems
3. Solve those problems using the thecniques presentes 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.
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.
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.
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 unconstrained NLPs with one variable and with several variables.

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.

Software

Microsoft Excel

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial
	Teste	25,00
	Trabalho escrito	25,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
	Estudo autónomo	56
	Total:	56,00

Eligibility for exams

Not excedding the number of absences allowed;
Do 2 tests;
Make a group project using Simulation technique.

Calculation formula of final grade

The final classification results of the weighted average of the classification obtained in the two tests made during the semester (weight of 40% each one in the final classification) and the classification of the Simulation project. The weight given to the simulation project is 20%.

Examinations or Special Assignments

Simulation Project (Group work)

Special assessment (TE, DA, ...)

Students must attend to both tests of the distributed evaluation, and make the Simulation project.

Classification improvement

Students can repeat one (and only one) of the tests.