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Academic Year 2023/2024 - Teacher: GABRIELLA COLAJANNI

Expected Learning Outcomes

The objectives of the course are as follows:

  • to formulate equilibrium traffic problems in the dynamic case using networks, including also capacity constraints, additional restrictions and delay terms;
  • to evaluate the importance of the single components of a network;
  • to build a multi-tiered network for production and distribution problems, for electrical models and in the case of merger of companies;
  • to apply theoretical models to business cases.

Knowledge and understanding:

At the end of the course, the student, in addition to having acquired the basic knowledge and skills in the field of optimization and mathematical modeling, will demonstrate:

  • being able to transform real situations of maximization of profits, minimization of costs and risks, ... into mathematical models;
  • possess knowledge and ability to understand texts.

Applying knowledge and understanding:

The theoretical and practical knowledge acquired during the course will allow the student to:

  • critically analyze various business situations;
  • propose optimal solutions to complex problems;
  • identify the essence of a problem and apply general principles to specific cases.

Making judgements:

The student, by virtue of the acquired training, also of an analytical-quantitative type, will be able to critically analyze and interpret the data provided.

Communication skills: 

At the end of the course the student will be able to:

  • pass on their experience and knowledge to others;
  • confronting others, especially in the development of projects in which you work in a team.

Learning skills:

  • The student will acquire the ability to learn, even independently, additional knowledge on applied mathematics problems. These skills will allow him to face and solve concrete optimization problems.

Course Structure

The course will be taught through lectures and exercises in the classroom and at the computer labs.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Learning assessment may also be carried out on line, should the conditions require it.

Required Prerequisites

The basic concepts of Linear Algebra (vectors and matrices), Mathematical Analysis I and II (differentiability, convexity of sets and functions, topology, ...), Operations Research (concept of network and variational inequality) and Optimization (minimum problems, subdifferentials,...) are required.

This knowledge is to be understood as important.

Attendance of Lessons

Attendance is strongly recommended, as exercises will take place in the classroom.

Detailed Course Content


• Horizontal mergers: the models before and after the merger; associated optimization problems; synergy. Models with environmental interests.

• Variational inequalities for auction problems: the model, equilibrium conditions and equivalent variational formulations.

Supply chain networks:

• Supply chain networks with three levels of decision-makers: economic model in the presence of manufacturers, retailers and consumers with e-commerce; optimality conditions and equivalent variational inequality for the representatives of all levels and for the entire chain. Dynamic case: model with production and demand excesses.

• Networks with critical needs with external sources: optimization problem and variational formulation.

• Electricity supply chain networks: the model with electric power producers, energy providers, transmission service providers and demand markets; optimality conditions and equivalent variational formulation for the representatives of all levels and for the entire network. Presentation of the model with non-renewable fuel suppliers and optimality conditions.

• Closed loop supply chains: direct chain and reverse chain. Behavior of raw material suppliers, producers, retailers, demand markets, the recovery centers. Variational formulation.

Matlab applications.

Textbook Information

  1. P. Daniele, “Dynamic Networks and Evolutionary Variational Inequalities", Edward Elgar Publishing, 2006.
  2. A. Nagurney, J. Dong, "Supernetworks", Edward Elgar Publishing, 2002.
  3. Papers on STUDIUM

Course Planning

 SubjectsText References
1Reti di traffico nel caso statico in presenza di vincoli di capacità1
2Reti di traffico nel caso dinamico1
3Il modello del traffico con vincoli aggiuntivi1
4La fusione tra due aziende con e senza interessi ambientali3
5Il modello matematico della vendita all'asta3
6Supernetwork con tre livelli di decisionisti2
7Reti di catene di offerte nel caso di bisogni critici con sorgenti esterne3
8Reti di catene di fornitura di energia elettrica con e senza i fornitori di combustibile non rinnovabile3
9Reti di catene di offerte a ciclo chiuso con riciclo di materiali3

Learning Assessment

Learning Assessment Procedures

The final exam consists of an oral test during which the candidate demonstrates that she/he has assimilated the topics covered in the course.

Verification of learning can also be carried out electronically, should conditions require it.

Information for students with disabilities and / or SLD

To guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and / or compensatory measures, based on the didactic objectives and specific needs. It is also possible to contact the referent teacher CInAP (Center for Active and Participated Integration - Services for Disabilities and / or SLD) of our Department, prof. Filippo Stanco.

Examples of frequently asked questions and / or exercises

Present the merger model between two companies with and without environmental interests.

Present the mathematical model of auction sales.

Present layered networks with three levels of decision makers.

Examine the behavior of producers.

Present supply chain networks in case of critical needs with external sources.

Present electricity supply chain networks with and without non-renewable fuel suppliers.

Present closed-loop supply chain networks with material recycling and examine the behavior of recovery centers.