Subject: Operational Research
Scientific area:
Mathematics
Contact hours:
80 Hours
Number of ECTS:
6 ECTS
Language:
Portuguese
General 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.
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.
Contents / Syllabus:
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.
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.
Bibliography / Information Sources:
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
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
Assessment 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.
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.