B019393 - FLOW NETWORKS OPTIMIZATION

Italian; slides and lecture notes in english

1) Discrete ptimization models and algorithms
2) Models and optimization algorithms for production planning and logistics
3) Introduction to nonlinear optimization models and methods
4) Introduction to machine learning models

Handouts of the course, relevant scientific papers and other supporting material will be made available

Suggested texts for further reading and optional consultation:
G. L. Nemhauser, L.A. Wolsey, "Integer and Combinatorial Optimization", Wiley Interscience, 2014

Y- Pochet, L.A. Wolsey, Production Planning by Mixed Integer Programming, Springer, 2006

D. Simchi-Levi, X. Chen. J. Bramel, The Logic of Logistics, Springer, 2005

M. Gendreau, J.-Y. Potvin (eds), Handbook of Metaheuristics, Springer, 2019

T. Hastie, R. Tibshirani, J. Friedman, Data Mining, Inference and Prediction, Springer, 2017

The course presents advanced optimization methods and models oriented towards applications relevant for management engineering and in particular for optimized production planning, organization, prescriptive analytics models.
The contents of the course are transversal and relevant for many roles included in the degree project. In particular, a production manager (RM1) will learn data science techniques for the development of predictive models, Service Managers (RM3) will learn advanced methods for optimal resource management, Operations and Supply Chain Managers will learn advanced methods for production planning

The knowledge provided will be the following:

Starting from a solid basic mathematical background the course will develop knowledge in the fields of and optimization theory and methods, both discrete and continuous (cc1) and in the field of machine learning for automatic classification (cc1). In these areas applied
aspects will be studied in the context of management engineering (cc7); moreover, through laboratory sessions (ca1), the applications of what presented in the course will be critically analyzed (cc7, cc8). Students will be able to combine theory and practice for engineering and organizational problems, in complex contexts and will be able to use some data mining and machine learning tools (ca5).
In general, the operational research approach presented in the course will be oriented towards the development of the ability to use theory, algorithms and practical experience to solve multidisciplinary problems (ca7)

Knowledge of linear algebra, mathematical analysis and geometry at the level of a three-year degree in Engineering is required. Knowledge of the basics of operational research, in particular linear programming, is also required. Knowledge and ability to use simple programming languages are required.

Mainly frontal teaching; there will be also seminar activities, group activities; some of the material will be made available through e-learning systems

The exam consists of a test (oral or, alternatively, written) to check the acquired knowledge. Students must know how to present the models, illustrate the algorithms and demonstrate understanding of their structure, of their applications and limits.

The exam also includes a project on data science topics in which students, possibly in groups, will be required to analyze a dataset and extract knowledge, for example, in order to construct a predictive model.
The exam will be organized to evaluate the students' acquired ability to use theory and algorithms for the solution of relevant management engineering problems (ca7), once the most suitable tools and methods have been correctly identified. for a specific situation (ca1). The project will allow the verification of students' ability to model and solve stochastic problems using machine learning techniques (ca5).

The relative weight of the two parts of the exam is: 75% (theory) and 25% (project).

Part I: combinatorial optimization

Combinatorial optimization models and problems
Heuristics: greedy algorithms, local search heuristics, tabu search methods
Heuristics based on Mixed Integer Linear Programming models. Lagrangian methods, column generation

Part II: Applications

Inventory, lot sizing, scheduling, location and routing models and algorithms

Part III: Introduction to non-linear optimization:

Nonlinear optimization problems and models (regression, parameter calibration)
Introduction to optimality conditions (KKT)
Introduction to nonlinear optimization algorithms: gradient descent, Newton, Quasi Newton, Frank-Wolfe

Part IV: Introduction to data science

Classification and regression problems

Expected risk minimization, support vectors machines (SVM)
Feature extraction

Other optimization-based classification models: kNN, decision trees, random forest, neural networks

Training of classification / regression models

During the course some software tools and languages ​​such as python will be introduced