Complements of Operations Research

Code:

EM502

Acronym:

CIO

Instance: 2003/2004 - 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	20	Plano de Estudos EM Oficial a partir de 2000	5	3	6	-
		Plano para Bachareis EM a partir 2000	2	3	6	-

Teaching language

Portuguese

Objectives

To continue the study of operational research techniques, following the study initiated in the discipline “Operational Research” (3rd year, 2nd Semester).
The study of each technique addresses issues related to problem formulation, the fundamentals of the algorithms used to obtain the solution, and computational issues. It is discussed the applicability of the Operational Research techniques to real-world situations.

Program

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.
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, ) 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.

Main Bibliography

Course material covering the OR techniques studied, review problems and their solutions.
Winston, W.L. "Operations Research: Applications and Algorithms" Duxbury Press.
Brito A.C., e J.M. Feliz, "Simulação por Computador: Fundamentos e implementação de código em C e C++", Publindústria.

Complementary Bibliography

Hillier, F.S. and G.J. Lieberman, "Introduction to Operations Research", MacGraw-Hill International Editions, Business Quantitative Series, Singapura.
Hillier, F.S., M.S. Hillier, and G.J. Lieberman, "Introduction to Management Science: A Modelling and Case Studies Approach with Spreadsheets", McGraw-Hill International Editions, Singapura.
Law A.M, and W.D. Kelton, "Simulation Modelling and Analysis", McGraw-Hill International Editions, Singapura.
Pidd, M., "Computer Simulation in Management Science", John Wiley & Sons, Chichester, UK.

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 Simulation software

Evaluation Type

Distributed evaluation without final exam

Eligibility for exams

Not excedding the number of absences allowed.

Calculation formula of final grade

The final mark results of the weighted average of the classification obtained in the four tests made during the semester and the classification of the Simulation project.
The weight given to each test and to the simulation project is 20%.