## Learning objectives

The new and reinforced sensibilities for the environmental issues at global level need deeper economic and quantitative skills to evaluate the effects of environmental policies on environmental resource availability. The aim of this course is 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 on Life Cycle Assessment (LCA) methods.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 LCA methods will provide students with skills for facing environmental policy evaluation issues with respect to the economic agent behavior.

## Prerequisites

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## 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 life cycle assessment models. 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 be undertaken in relation to the management of environmental resources and the implementation of environmental policies. The fourth and last part of the course will be devoted to the environmental and economic assessment of products through a Lice Cycle Assessment (LCA) approach. Methods and techniques for carrying out a LCA will be discussed and applied to real world with the support of LCA software packages and environmental datatabases.

## 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 on 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 problems3.3 Multiobjective programming applied to sustainability problems3.3 Exercises on pc4. Life Cycle Assessment (LCA)4.1 Life Cycle Thinking: origin and scope (environmental labelling)4.2 LCA and ISO 14040 series4.3 LCA phases (with hints about Life Cycle Costing – LCC)4.4 Exercises on pc

## Bibliography

Recommended readings Italian readings

- Quirino Paris (1992), An economic interpretation of linear programming, Iowa State Press, Ames;

-Baldo, G. L., Marino, M., Rossi, S. (2008), Analisi del ciclo di vita, Edizioni Ambiente, Milano.

- Documents distributed by the lecturer.English reading- Paris, Q. (2016), An economic interpretation of linear programming, Springer.- 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; - Hauschild, Michael, Rosenbaum, Ralph K., Olsen, Stig (Eds.) (2018), Life Cycle Assessment - Theory and Practice, Springer.

## Teaching methods

Acquisition of knowledge: lectures, seminars and training for using optimization packages (GAMS) and LCA software (OpenLCA)

Acquisition of the ability to apply knowledge: exercises with PC

Formulate judgements with authonomy: During the course students will be encouraged to develop a capacity for critical analysis on economic and environmental evaluation issues.

Learning skills: Along the learning process, students will deal with the application of the knowledge acquired through 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 LCA, and the second concerning the application of mathematical programming models and LCA methods in the context of environmental issues . The open form of the two questions used to assess the ability of the student to trace the links between economic theory and analytical techniques of optimization behavior. The answers to the two questions are valued in thirtieths. The second part of the exam (3 hours) is an exercise of mathematical programming to set up and solve with the techniques learned during the course and with the support of specific software for mathematical programming. 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. 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.

## Other information

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