- Unit Coordinator: Juan-José Ramos Gonzalez
- ECTS Credits: 9
- Semester: 1
- Year: 2
- Campus: Autonomous University of Barcelona
- Language: English
- Aims:
To deepen in the modelling methods and quantitative techniques aimed to support the decision making process in logistics and supply chain management.
To practice the workflow from the recognition and analysis of a real case problem, to the identification of the feasible activities, and to the selection of good solutions.
Practical problems studied include demand forecasting, production planning, warehouse and inventory management, and transport networks.
- Content:
- Introduction to decision making.
- Linear and integer programming, constraint programming, artificial intelligence methods in optimisation.
- Production planning.
- Scheduling problems (job sequencing, resource allocation).
- Heuristics in transport planning.
- Reading list:
Main textbooks:
- Hartmurt Stadlert and Cristoph Kilger (Eds.) Supply Chain Management and Advanced Planning. Third Edition. Springer, 2005.
- Ioannis T. Christou. Quantitative Methods in Supply Chain Management. Models and Algorithms. Springer, 2012.
- H. Paul Williams. Model Building in Mathematical Programming. Wiley. 2013 (5th edition)
Further readings:
- Joseph Geunes, Panos M. Pardalos and H. Edwin Romeijn (Eds.) Supply Chain Management: Models, Applications, and Research Directions. Kluwer Academic Publishers, 2002.
- F. Robert Jacobs, William L. Berry, D. Clay Waybark and Thomas E. Vollmann. Manufacturing Planning and Control for Supply Chain Management. McGraw-Hill, 2011 (6th edition).
- F. Robert Jacobs and Richard B. Chase. Operations and Supply Chain management. McGraw-Hill Irwing, 2011 (13 th edition).
- Unit Coordinator: Paweł Błaszczyk
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Silesia in Katowice
- Language: English
- Programme: RealMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: Claude Bernard University Lyon 1
- Language: English
- Code: DT0704
- Unit Coordinator: Marco Di Francesco, Antonio Esposito
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of L'Aquila
- Language: English
- Aims:
This course contributes to one of the learning objectives of the degree programmes in Mathematical Modelling and Mathematical Engineering, namely the formation of the student on advanced mathematical modelling in an interdisciplinary context, in particular in the biology/medicine area, more specifically in the field of mathematical modelling applied to the diffusion of epidemics, which is the main goal of the curriculum "Modelling and simulation of infectious diseases" of the degree program in Mathematical Modelling. Moreover, the course contributes to forming the student in the context of mathematical modelling applied to population dynamics, in agreement with the objectives of the curriculum "Mathematicla Models in Social Sciences" of the degree programme in Mathematical Modelling.
At the end of the course, the student
1) will be equipped with a sound knowledge on population dynamics modelling, particularly compartmental models which can also be applied in epidemiology.
2) will be able to formulate "ad-hoc" deterministic models, such as ordinary differential equations, partial differential equations, interacting particle systems, that describe the dynamics of an epidemics in specific situations.
3) will possess analytical techniques allowing to resolve the models studied and to determine the qualitative behaviour of the solutions to those models.
4) complement the models with auxiliary terms in order to plan specific "containment strategies" for epidemiological models.
- Content:
1) Introduction to population dynamics modelling via ODEs.
2) Introduction to epidemic modelling. The Kermack-McKendrick models and its variants.
3) Modelling of vector-borne diseases. Models with delay.
4) Computing the basic reproduction number.
5) Complex epidemics modelling, multi-group modelling.
Control strategies in ODE models.6) Age structured population models and applications in epidemiology. Class-Age structured models in epidemiology.
7) Spatial heterogeneity in population dynamics. Models with diffusion.
8) Reaction-diffusion systems. Travelling waves.
Lagrangian movements. Particle models. Nonlocal models. Discrete vs Continuum modeling using integro-differential equations.10) SIR (and variants) models with local and nonlocal diffusion.
11) Graph modeling for population dynamics
- Pre-requisites:
Dynamical systems, analytical methods for to resolutoin of ordinary differential equations.
Basics of linear partial differential equations. - Reading list:
James D. Murray; Mathematical biology I: An introduction; Springer.
James D. Murray; Mathematical biology II: Spatial Models and biomedical applications; Springer.
Fred Brauer, Pauline van den Driessche, Jianhong Wu; Mathematical Epidemiology; Lecture notes in mathematics; Springer.
Maia Martcheva - An Introduction to Mathematical Epidemiology; Texts in Applied Mathematics 61, Springer.
Lecture notes by the lecturer.
