Base Knowledge
Preferably with knowledge of Linear Algebra
Teaching Methodologies
The course adopts a pedagogy based on active learning focused on solving real-world problems. The integration of theory, practice, and project work ensures effective skill consolidation.
The theoretical component is addressed through dialogic exposition, with concept presentation followed by discussions of real cases. This approach ensures understanding of mathematical fundamentals without overwhelming students with excessive formalism, maintaining a focus on applicability.
The practical component is the central axis of learning, following a “learning by doing” methodology. Students work with computational tools, using free software such as GLPK, OpenSolver, and DEA-Solver to ensure continuity of learning outside the classroom. Sessions include demonstrations by the instructor, followed by supervised practice where students replicate examples and solve progressively more complex exercises.
The development of an applied project throughout the semester enables integrated consolidation of competencies. Students select a real problem, apply the learned methodologies, and communicate results in a format suitable for decision-makers. This project is supported through individual tutorials and feedback sessions.
Formative assessment is promoted through weekly non-graded exercises, allowing progress monitoring and identification of comprehension difficulties, adjusting pedagogical intervention accordingly.
The combination of theoretical exposition, intensive computational practice, problem-solving, and project development ensures students consolidate technical knowledge, critical thinking, and decision-oriented communication skills.
Learning Results
On completion students should be able to:
O1. Grasp fundamentals of linear and integer programming and interpret solutions for decisions.
O2. Apply DEA for relative efficiency assessment and benchmarking.
O3. Formulate and solve simple optimization problems in planning, production and performance evaluation.
O4. Implement models using accessible computational tools and interpret outputs.
O5. Communicate quantitative results clearly to decision-makers.
Teaching mixes concise theory, guided practice and a short applied mini-project. practice, and project
Program
1. Fundamentals of Linear Programming and Interpretation
1.1. Fundamental concepts: variables, objective function, constraints.
1.2. Formulation of LP and ILP models and applications.
1.3. Duality, shadow prices, sensitivity analysis.
1.4. Applications: transportation, assignment, and planning.
2. Computational Tools
2.1. Introduction to solvers (GLPK, OpenSolver/Pyomo).
2.2. Data preparation, modeling, and result visualization.
2.3. Reproducibility (files, scripts, documentation).
3. Data Envelopment Analysis
3.1. Fundamentals: relative efficiency, efficient frontier, advantages and limitations.
3.2. Classical models: CCR (CRS), BCC (VRS) and interpretation of scores.
3.3. Practical implementation and benchmarking.
3.4. Practice: case implementation (using DEA-Solver / DEAP), input/output selection, outlier identification, interpretation and benchmarking (simplified case).
4. Multicriteria Decision-Making and Communication
4.1. Pareto concepts and weighted-sum method.
4.2. Communication of results and model limitations.
5. Guided practical project and presentation
Curricular Unit Teachers
Maria do Castelo Baptista GouveiaGrading Methods
Written exam (mandatory): 50% of the final grade. Minimum score of 7.5/20 to consider the project component.
Applied project (optional, group of 2–3): 50% of the final grade (considered only if exam score ≥ 7.5/20).
Grading Schemes:
Without Applied Project: Final Grade = 100% Exam.
With Applied Project: Final Grade = 0.5·Exam + 0.5·Project (applicable only if the minimum exam score is met).
Written Exam:
Includes theoretical questions, modeling exercises, interpretation of software outputs, and problem-solving.
Applied Project:
Includes a report (max. 15 pages) + technical appendices (data, models, and outputs) + oral presentation (15 min + 5 min Q&A).
Applied Project Assessment Criteria:
Technical and methodological rigor: 35%
Quality of analysis and interpretation: 30%
Practical relevance of the application: 20%
Clarity and effectiveness in communication: 15%
The combination of exam and project ensures students demonstrate conceptual mastery, practical ability, and communication skills.
Internship(s)
NAO
Bibliography
Mandatory Bibliography
Hillier, F. S., & Lieberman, G. J. (2014). Introduction to operations research (10th ed.). McGraw-Hill Education.
Coelli, T. J., Rao, D. S. P., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis (2nd ed.). Springer.
Zhu, J. (2014). Quantitative models for performance evaluation and benchmarking: Data envelopment analysis with spreadsheets (3rd ed.). Springer.
Steuer, R. E. (1986). Multiple criteria optimization: Theory, computation, and application. John Wiley & Sons.
Hart, W. E., Laird, C. D., Watson, J. P., Woodruff, D. L., Hackebeil, G. A., Nicholson, B. L., & Siirola, J. D. (2017). Pyomo – Optimization modeling in Python (2nd ed., Vol. 67). Springer.
Complementary Bibliography
Charnes, A., Cooper, W. W., Lewin, A. Y., & Seiford, L. M. (Eds.). (1994). Data envelopment analysis: Theory, methodology, and application. Kluwer Academic Publishers.
Cooper, W.W., Seiford, L.M., & Zhu, J. (2011). Handbook on Data Envelopment Analysis (2nd ed.). Springer.
Charnes, A., Cooper, W.W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. EJOR.
Cooper, W. W., Seiford, L. M., & Tone, K. (2006). Introduction to data envelopment analysis and its uses. Springer.
Ehrgott, M. (2005). Multicriteria optimization. Springer.
Rardin, R. L. (1998). Optimization in operations research. Prentice Hall.