Systems Modelling


The Operational Research approach to problems involves several steps. The first step includes a modelling phase – modelling a system and/or a process. This phase requires imagination, conceptualization ability and uses knowledge from different areas, like Statistics, Probabilities and Computing.
This course intends to increase the skill of coordinating knowledge in different  areas and help students to learn how to model processes and systems. Classes will take place in computational laboratories and, whenever possible, Excel spreadsheet will be used to solve case studies. Students will have the opportunity to create procedures using the Visual Basic module in Excel spreadsheets.
If necessary, the case study subjects will be introduced. Afterwards, the students will have a limited time to write a small report describing the different techniques used in the case study resolutions and main results. Finally, different approaches will be presented. The case study will also be analysed in the global framework of Operational Research.

General characterization





Responsible teacher

Ruy Araújo da Costa


Weekly - 4

Total - 64

Teaching language



Students should have a basic knowlwdge in O.R.. It is important that a student has some proficiency in working with worksheets.


How to Model It - Problem Solving in the Computer Age (1990), Starfield,A; Smith,K. e Bleloch,A. - Mc Graw Hill Int.
Strategies for Creative Problem Solving (1994), Fogler,H.S.;LeBlanc,S.E - Prentice Hall.
Nonparametric Statistics for the Behavioral Sciences (1988), Siegel,S. Castellan Jr.,N. - Mc Graw Hill Int..

4.  Excel 2007 - Data Analysis and Business Modelling (2007), Winston,W - Microsoft Press

Teaching method

Taking into account the pandemic situation and the high number of studentes, in 2021/22 classes will be online, recriating the computational laboratories setup using Zoom and the e-learning platform Moodle.  

In each lesson students receive a small case study and, sometimes, a file with data.

When necessary, the general subject of the case study is presented in the beginning of the lesson.

Students are divided in small teams, each team has 60 to 90 minutes to write a small report describing the techniques used in the resolution of the case study, and results obtained. Each team sends its report to the Professor through Moodle.

Afterwards, each teampresents its approach, and in the end all the strategies and results are object of discussion. Afterwards, the teacher will present one (or several) possible resolutions, and the case study is analysed in the global framework of Operational Research.

Finally, students are encouraged to carry out some extensions of the studied problem.  

In Midterm, students will carry out a Team Assignment that will consolidate knowledge acquired through the case studies.

Each student will also be assessed in one Test or Exam.

Evaluation method

I – General Aspects

1 – Any detected fraud implies failing in the course and a report to the Dean''s Office.
2 – For evaluation at FCT, students should buy one “examination folio” and hand it to the professor before the exam.
3 – Every student must obtain Course Frequency before being admitted to exam.

II – Evaluation

Evaluation has 3 components: Case Studies, Group Assignment and Written Test/Exam.
1 – Case Studies: The best n individual grades are selected and averaged (CPF is the case study grade).  n is the highest integer inferior or equal to 3/4 of the total case studies. Any student must submit at least half of the case studies in the semester. 
2 – Group Assignment: The assignment and data will be available in the beginning of November. Each group has 4 weeks to submit a report. The report will be object of a written discussion. The assignment grade (CTrab) is the average of report and discussion grades.
3 – Frequency: To obtain frequency, a student should be present in, at least, 2/3 of lessons, have submitted at least half of all case studies and the average between CPF and CTrab should be greater than to 9,5.
4 – Final Grade: Each student - with Frequency - will be evaluated in a written Test/Exam (180 minutes). In the Season 1 there will be one online Test. In Season 2 there will be one online Exam, for students who had failed in Season 1, or are trying to raise their previous grades. Let CE be the Test/Exam grade.   A Student Fails if CE < 9,5.
If CEX >=
9,5 then the student passes the course and his final grade (CF) is the rounding of 0,25 CPF + 0, 45 CTrab + 0,30 CE.

5 – Raising Grades: A student that has passed the course, can apply for Raising the grade of his(her) CE.

To raise his Examination grade, a student must be evaluated in a new examination. Let CEMelh be the grade of the new Examination. 
The Final Rasing Grade (CFMelh) will be:
CFMelh = 0,25 CPF + 0,45 CTrab + 0,30 CEMelh
The final grade will be Max(CF; CFMelh).

Please see the formal Assessment Method file in this site Documentação de Apoio > Outros

Subject matter

1 – Introduction to Processes and Systems Modelling
2 – Case Studies:
            2.1 – Introduction to Heuristics: the knapsack problem.
            2.2 – Optimization with constraints – Lagrange multipliers.
            2.3 – Characterization of the dependence relation between consecutive values in a time series.
            2.4 – Introduction to the Extreme Values Statistics - Gumbel distribution.
            2.5 – Poisson Processes Modelling.
            2.6 – Queuing Theory: additivity of Poisson processes.
            2.7 – Inventory Management – discounts policies and budget constraints.
            2.8 – Forecasting – Models with trend and seasonality.
            2.9 – Markov Chains – Equipment Maintenance Policies.
            2.10 – Simulation.
            2.11 – Reliability.
            2.12 – Project Management.