The knowledge that the course aims to provide students with: students will explore the theory, methods, and algorithms for solving linear continuous optimization problems (i.e., where the variables are continuous) and flows on networks. Outline of linear integer optimization problems (i.e., where the variables are integer) will also be given. Skills that the course aims to provide students with: students will develop skills to construct, given real-life problems, corresponding and adequate mathematical models, and solve them using appropriate algorithms and optimization solvers.

No prerequisites are required. The only prior knowledge is those already acquired in the first-year engineering courses.

1. Continuous linear optimization: problems and models, simplex method, duality (40% of the course). 2. Analysis of the computational complexity of decision problems (5% of the course). 3. Flows on networks: fundamental concepts of graph theory, finding a spanning tree of minimum cost, transportation problem, shortest path problem, minimum cost flow problem, maximum flow problem, and minimum cut problem (50% of the course). 4. Outline of integer linear optimization (e.g., problems of network design, service location, data analysis, routing): exact methods (Branch and Bound) and heuristics (greedy algorithms, Tabu Search, Simulated Annealing, Genetic Algorithms) (5% of the course).

The course integrates properly teaching hours and hours of practice, to the extent of about 60% and 40% of the course, respectively. The exercises are carried out in the classroom and follow the lecture topics. In the LADISPE laboratory, http://www.ladispe.polito.it/ up-to-date, optimization solvers able to solve real-life problems are available to students. Instructions for their use will be provided in the classroom. No specialized programming skills are required.

Books used for teaching: R. Tadei, F. Della Croce, Elementi di Ricerca Operativa, Progetto Leonardo, Editrice Esculapio, Bologna, 2010. M. Ghirardi, A. Grosso, G. Perboli, Esercizi di Ricerca Operativa, Progetto Leonardo, Editrice Esculapio, Bologna, 2009. Other teaching materials, along with examples of previous exams, is available on the course website. Recommended books for further information: H. P. Williams, Model building in Mathematical Programming, 4th ed., Wiley, 1999. H. P. Williams, Logic and Integer Programming, Springer, 2009.

Exam: Written test;

The exam is written and is aimed to check the knowledge of the topics listed in the program of the course and the ability to apply the optimization theories and methods seen in class to the solution of the proposed exercises. The exam has a duration of 2 hours and consists of a written test with 4 questions on the topics contained in the course program. The exam aims to verify the skills referred to in the paragraph "Expected Learning Outcomes": the exam, in fact, includes a first question, of particular importance, which consists in writing, for a given real problem, a corresponding mathematical model of linear optimization that represents it appropriately (see also part 1 of the Program). The remaining questions are related to the computational complexity of decision-making problems and the resolution of optimization problems on networks seen in class (see also Part 2 and Part 3 of the Program). During the written test it will not be possible to consult texts, lecture notes and forms. Furthermore, multimedia devices with access to the web (for example, smartphones, smartwatches and tablets) are not allowed in the classroom. The exam is passed if the written test gets a vote from 18/30 to 30/30 (including praise). A scale of 0 to 32 points will be used for evaluation. The honors will be awarded if the vote is 32/30. The outcome of the test will be communicated to the students through a notice on the teaching portal. Students can view the task and its assessment during a general meeting whose date will be fixed from time to time. The date of the meeting will be communicated to the students through a notice on the teaching portal in conjunction with the publication of the results of the written test.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

Exam: Computer-based written test using the PoliTo platform;

The exam takes place with the help of the Exam platform (accessible from the student page, in the "Esami in remoto" section, 30 minutes before the start of the appeal to which you are enrolled), the Virtual Classroom and the Elaborati section (tab accessible from the main web page of the course). Besides, the Respondus software is used to inhibit any software in addition to the browser on the student computer. The exam program and its structure remain unchanged compared to what is written in the Study Manifesto. Furthermore, due to possible complications introduced by the remote mode, the exam difficulty and length are reduced, so that it can be completed in one hour and a half instead of in two hours, as in previous years. The remaining hour, of the two and a half hours available for the exam, will be devoted to performing Phases I and III (see below). Equipment needed • A computer (hereafter PC) equipped with a webcam, microphone, speakers, and internet access [will mainly serve to view the exam text]. The "Respondus LockDown Browser" program must be installed on the PC. The PC must be connected to the power outlet for the duration of the test. • A mobile device, such as a mobile phone or tablet (henceforth CELL), equipped with a camera and internet access [will be used to interface with the teacher and for the final scan/upload of the homework]. An app for creating pdfs from camera images must be installed on the CELL (CamScanner is recommended). The CELL must be connected to the power outlet for the duration of the test. All on-screen notifications must be disabled (e.g., WhatsApp, Telegram, email messages, etc.). • Pen and enough white sheets. The use of any other electronic device, accessory or peripheral (e.g., earphones, headphones, smartwatches, cell phones, additional screens, etc.) is not allowed. The use and consultation of books, notes, or other materials are not allowed. However, the use of pencils, erasers, and rulers is permitted. It is also possible to have something to drink (e.g., a bottle of water). The exam must be carried out in a quiet and adequately lit place in your home, free of other people for the duration of the test. The CELL must be positioned in such a way that a good and full camera frames the student's torso/face and position (hands and sheets). Furthermore, the CELL must not be reachable by the student when sitting at the desk. We recommend finding the best location in advance. Conduct of the test The conduct of the test, lasting a total of two and a half hours, involves the following steps in sequence. PHASE I - Appeal and checks [maximum 40 min] The student connects to the Virtual Classroom through the CELL within the time indicated for the exam, keeping the webcam and microphone temporarily disabled, and awaits the teacher's instructions. The invitation to the Virtual Classroom will be sent 30 minutes before the exam begins. The student also connects to Exam via PC, where the exam topic will be present (but will not be accessible because it is password protected). The teacher starts the registration and carries out the appeal. The student who, for any reason, will not respond to the appeal within 15 minutes of its start will be considered "absent". The teacher then interacts with each student (who will activate the CELL webcam and microphone). The student will be asked to: • show a valid identification document • show the compliance of the workplace and the surrounding environment • position the CELL and stabilize the frame, which must be maintained for the whole duration of the exam. The CELL is muted, and the student sits at the station, waiting for the start of the test. PHASE II - Examination procedure [1 hour and a half] 1. The teacher orally communicates the password to all those present. 2. The student starts the exam (this involves Respondus blocking the browser) and carries out the test. 3. At the end of the time, notified by the teacher, all students immediately stop writing. The student who finishes first must still wait for the deadline. PHASE III - Loading the homework [maximum 20 min] 1. Upon instruction from the teacher, students stop the browser block (Respondus) on the PC and the audio/video streaming on Virtual Classroom from the CELL and access the Virtual Classroom via PC (with webcam and audio-activated). 2. Through the CELL, the student scans his/her assignment and uploads it to the portal in the appropriate "Elaborati" section (see the upload and format of the assignment). Students are advised to recheck by downloading it to the PC from the "Elaborati" section, that the uploaded file is readable, correct, and complete. If not, delete the old version and upload a new one. 3. The student, satisfied with its uploading, communicates it to the teacher. The teacher makes sure of the delivery and talks to the student that he/she is free to leave the Virtual Classroom, ending the exam. Students, who for any reason, have not been able to upload their assignment will be considered "withdrawn". Only the parts of the homework delivered will be evaluated. Uploads/cancellations of assignments after the end of the exam will not be evaluated. Other important clarifications Homework upload and format Each sheet of the assignment must include the student's family name, name, and registration number. The student must upload ONE SINGLE FILE, in pdf format and named "FamilynameName.pdf", obtained by aggregating the photographs of the different sheets through a particular app (e.g., CamScanner). The behavior to be maintained for the duration of the test • the audio/video streaming both in and out of the CELL must be active; • it is not possible to get up or move away from the position; • it is not possible to contact/communicate with other people outside the teacher; • no one must enter the student's room; • it is not possible to use the CELL except during the initial control or final loading phases of the homework, and only for those operations; • it is not possible to eat. Maximum silence is recommended so as not to disturb other students. Anyone wishing to ask a question during the test can do so by specifying their family name and name first. Withdrawals A student can withdraw from the exam at any time. In that case, however, the student must have the following behavior: • communicate their decision to the teacher, who will notify the withdrawal. This decision will be permanent; • must remain connected to the Virtual Classroom and comply with the above rules until the end of Phase II. At that point, the student must not upload any files and can abandon the Virtual Classroom. Infringements The exam is invalidated for anyone, for any reason, who does not comply with even one of the rules above or who is discovered (even later with the aid of the registrations) in behaviors that do not comply with them. If these violations occur during the test, students must withdraw at the request of the teacher, and they must behave as in "Withdrawals". Based on the gravity of the infringement, the teacher may decide whether to communicate this behavior to the appropriate University disciplinary commissions. Special Needs Students who request Special Needs will have 30% more time (therefore, half an hour more) available for the test. In any case, at the end of PHASE II, those students will also temporarily stop writing, so that the teacher can devote himself to the delivery by the other students, and they are not disturbed by these operations. Once the delivery is over, and silence returns, those students can resume their test. Emergencies For any emergency during the exam, students can call the following mobile numbers: Prof. Roberto Tadei 335 6604376 Prof. Daniele Manerba 339 5454453. Honor code At least 48 hours before the start of the exam and not earlier than 7 days from the day of the exam, students enrolled in the exam must upload a file in pdf format on the course portal under "Elaborati", called "SurnameName_codeofhonour.pdf" , containing the form "CODE-OF-HONOR-STATEMENT ON WRITTEN & ORAL EXAMS IN REMOTE MODE", duly completed and signed. Students who do not upload the file within the scheduled time cannot take the exam. Rating As usual, students will receive notification of the test result via the portal. At the same time, the date and time of the vision of the homework will be communicated, which will take place through Virtual Classroom. The registration of the exam will immediately follow the vision of the homework. Students, who wish to reject their mark, even after viewing the assignment, must communicate it by email to Prof. Tadei (roberto.tadei@polito.it) by the date of registration.

Exam: Written test; Computer-based written test using the PoliTo platform;

Online exam: See "Assessment and grading criteria for online exam". Onsite exam: As for the online exam, where the exam test is done in the classroom instead of online.