Subject: Operational Research

Scientific Area:



80 Hours

Number of ECTS:




Overall objectives:

O1 - To know the basic principles necessary for understanding and formulating of various optimization problems addressed in this course.
O2 - To be able to manipulate a generalist software (Excel solver) to calculate optimal solutions of linear programming problems, as well as having the ability to provide recommendations based on such solutions and sensitivity analysis and post-optimization.
O3 - To be able to identify problems that may be modeled using networks (graphs) and how to use appropriate methods for solving them.
O4 - To have the ability to model a project using networks, how to identify critical activities and time slacks, how to analyze time-cost trade-offs and how to manage resources allocation throughout its execution.


C1 - Introduction to operational research.
C2 - Linear programming: problem formulation; the Simplex method; duality in linear programming; economic interpretation; sensitivity analysis and post-optimization; examples of problem solving using optimization software (using Excel solver).
C3 - Network problems: the shortest path problem; the minimum-cost spanning tree problem; maximum flow problems; minimum-cost maximum flow problems; examples.
C4 - Project management: network representation: activities on arcs (AOA) and activities on nodes (AON); the PERT/CPM method; scheduling issues: critical activities and time slacks; the PERT/CPM chronogram; resource availability/constraints; financial issues: time-cost trade-offs.


H. A. Taha , 2010 , Operations Research: An Introduction , Pearson
M. S. Bazaraa, J. J. Jarvis, H. D. Sherali , 2010 , Linear Programming and Network Flows , Wiley
M. M. Hill, M. M. Santos , 2015 , Investigação Operacional , Edições Sílabo
W. L. Winston , 2004 , Operations Research: Applications and Algorithms , Tomson Brooks/Cole

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Lectures, problem solving and discussion sessions and presentation problems. Some problem solving with appropriate software (Excel solver). Enhancing student self-study attitude and research with problem solving outside the classroom. The evaluation consists of two mandatory tests. The final grade is obtained by arithmetic mean of both test results.