Learning objectives
The new and reinforced sensibilities for environmental issues at the global level need deeper economic and quantitative skills to evaluate the effects of environmental policies on environmental resource availability. This course aims to provide a set of theoretical and operational skills to face, develop and solve decision problems within the environmental policy framework, through models based on mathematical programming tools and Cost-Benefit Analysis (CBA). Students can acquire knowledge about methods and operational tools for evaluating the economic relationships between economic activities and environmental resources. In particular, the study of mathematical optimization techniques and CBA will provide students with skills for facing environmental policy and projects evaluation issues.
Prerequisites
Course unit content
The course aims to provide theoretical and applied knowledge on mathematical programming models for the efficient management of environmental resources and on the methods for developing cost-benefit analysis. The course is divided into 4 parts. The first part presents the technique of mathematical programming in the economic theory framework. Some microeconomics reminds will help the interpretation of the economic problems by mathematical programming. The second part of the course provides the techniques for the construction of mathematical programming models. The Tableau technique and the duality will be the guides for the analytical model development. The third part of the course focuses on the tools to solve the problems of mathematical programming. In particular, the simplex algorithm will be applied through the use of spreadsheets and GAMS (General Algebraic Modeling System). All applications and exercises will focus on the management of environmental resources and the implementation of environmental policies. The fourth and last part of the course will be devoted to the economic assessment of the environmental projects trough the Cost-Benefit Analysis (CBA) technique. The methods and the analysis of the results will be discussed under the theory of economics and through the use of exercises
Full programme
1. The Linear Programming (LP)
1.1 Economic principles of linear programming
1.2 LP problem formulation
1.3 The duality
1.4 The information organization using the TABLEAU
1.5 LP problem solving: the simplex algorithm
1.6 LP and Langrange function
2. Quantitative tools for developing LP models
2.1 The GAMS (General Algebraic Modeling System) language for mathematical programming model formulation
2.2 Exercises using pc
3. The analysis of environmental issues using mathematical programming
3.1 Evaluating and managing environmental issues through economic MP models
3.2 MP approaches based on transportation problems
3.3 Multiobjective programming applied to sustainability problems
3.3 Exercises using pc
4. Cost-Benefit Analysis (CBA)
4.1 Theoretical foundation of CBA
4.2 Operational aspects of CBA (costs and benefits assessment, time horizon, discount factor, analysis of the results, NPV, IRR, PBT, BEP)
4.3 Exercises using pc
Bibliography
Recommended readings
- Quirino Paris (1992), An economic interpretation of linear programming, Iowa State Press, Ames;
- Paris, Q. (2016), An economic interpretation of linear programming, Springer.
- Documents distributed by the lecturer.
- Kaiser, H. M., Messer, K. D. (2011), Mathematical programming for agricultural, environmental and resource economics. Wiley;
- Richard Rosenthal (2008), GAMS: a user’s guide, Gams Development Corporation, Washington.
Teaching methods
Acquisition of knowledge: lectures (face-to-face and via Teams), seminars and training for using optimization packages (GAMS) and CBA
Acquisition of the ability to apply knowledge: exercises with PC
Formulate judgments with autonomy: During the course, students will be encouraged to develop a capacity for a critical analysis of the economic and environmental evaluation issues.
Learning skills: Along the learning process, students will deal with the application of the knowledge acquired through the exercises planned, so that they can undertake further applications with autonomy.
Technical language: students will learn the meaning of the terminology commonly used in the context of the operational research applied to environmental resources.
Assessment methods and criteria
The exam is organized in written form and divided into two parts. The first part (2 hours) consists of two open questions, including one designed to test the knowledge acquired on the theory of mathematical programming and CBA, and the second concerning the application of mathematical programming models and CBA in the context of environmental issues. The open form of the two questions aims to assess the ability of the student to trace the links between the economic theory and the analytical techniques of optimization behavior and economic assessment of environmental projects. The answers to the two questions are valued out of thirty. The second part of the exam (about 3 hours) consists of an exercise of mathematical programming or CBA to set up and solve with the techniques learned during the course and with the support of specific software for mathematical programming and CBA. The aim of the second part is to evaluate the ability to apply the constrained optimization techniques for the efficient allocation of scarce environmental resources and CBA for evaluating the economic impact of environmental projects. The maximum score assigned to the exercise is 30 points. The final assessment of the exam is calculated as the average of the two final scores.
The exam will take place face-to-face.
Other information
2030 agenda goals for sustainable development
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