## Advanced mathematical modeling and optimization

• Teaching

### Details

 Faculty Faculty of Science and Medicine Domain Computer Science Code UE-SIN.08611 Languages English Type of lesson Lecture Level Master Semester SA-2022

### Schedules and rooms

 Summary schedule Tuesday 14:15 - 17:00, Hebdomadaire (Autumn semester) Struct. of the schedule 3h par semaine durant 14 semaines Contact's hours 42

### Teaching

 Responsibles Ries Bernard Teachers Pacheco Paneque Meritxell Description This course considers modeling and optimization aspects of mixed-integer linear programming (or integer programming for short). This important subdomain of mathematical programming and extension of linear programming considers the problem of optimizing a linear function of many variables, some or all of them restricted to be integers, subject to linear constraints.Integer programming is a thriving area of optimization. It has countless applications in production planning and scheduling, logistics, layout planning and revenue management, to name just a few. Thanks to effective and reliable software, it is widely applied in industry to improve decision-making.In this course, we cover the theory and practice of integer programming. In the first part, we address mathematical modeling aspects. We discuss how integer variables can be used to model various practically relevant, complex decision problems. We then introduce some standard optimization problems and develop, analyze and compare different integer programming formulations for them. We also introduce powerful modeling and solving tools and test them on the optimization problems given in the course. In the second part, we address optimization aspects, in which we discuss the basic methodology applied to solve integer programs. In particular, we consider implicit enumeration techniques (branch and bound), polyhedral theory, cutting planes and primal heuristics. We also look at some advanced techniques, such as Danzig-Wolfe decomposition and column generation. Training objectives With this course, the students gain the ability to formulate and solve practically relevant decision problems using integer programming, and they understand the basic methodology for solving integer programs and its implications with respect to modeling decisions. Condition of access This course is designed for information systems, computer science and management student who have a good understanding of modeling and solving linear programs (as taught in the course Decision Support I). Comments MSc-CS BENEFRI - (Code Ue: 53073 / Track: T5) The exact date and time of this course as well as the complete course list can be found at http://mcs.unibnf.ch/.Course and exam registration on ACADEMIA (not myunifr.ch). Please follow the instructions on https://mcs.unibnf.ch/organization/ Softskills No Off field No BeNeFri Yes Mobility Yes UniPop No

### Documents

 Bibliography Conforti, Michele, Gérard Cornuéjols, and Giacomo Zambelli. Integer programming, Graduate Texts in Mathematics. Springer (2014).
• Dates and rooms
Date Hour Type of lesson Place
20.09.2022 14:15 - 17:00 Cours PER 21, Room C130
27.09.2022 14:15 - 17:00 Cours PER 21, Room C130
04.10.2022 14:15 - 17:00 Cours PER 21, Room C130
11.10.2022 14:15 - 17:00 Cours PER 21, Room C130
18.10.2022 14:15 - 17:00 Cours PER 21, Room C130
25.10.2022 14:15 - 17:00 Cours PER 21, Room C130
08.11.2022 14:15 - 17:00 Cours PER 21, Room C130
22.11.2022 14:15 - 17:00 Cours PER 21, Room C130
29.11.2022 14:15 - 17:00 Cours PER 21, Room C130
06.12.2022 14:15 - 17:00 Cours PER 21, Room C130
13.12.2022 14:15 - 17:00 Cours PER 21, Room C130
20.12.2022 14:15 - 17:00 Cours PER 21, Room C130
• Assessments methods

### Written exam

 Assessments methods By rating
• Assignment
Valid for the following curricula:
Version: ens_compl_sciences
Paquet indépendant des branches > Specialized courses in Computer Science (Master level)

Additional programme requirements for PhD studies [PRE-DOC]
Version: 2020_1/v_01
Additional programme requirements for PhD studies (Faculty of Science and Medicine) > Specialized courses in Computer Science (Master level)

Computer Science [3e cycle]
Version: 2015_1/V_01
Continuing education > Specialized courses in Computer Science (Master level)

Computer Science [POST-DOC]
Version: 2015_1/V_01
Continuing education > Specialized courses in Computer Science (Master level)

MSc in Computer science (BeNeFri)
Version: 2023_1/V_01
MSc in Computer science (BeNeFri), lectures, seminars and Master thesis > T5 : Information Systems and Decision Support

Version: 2020/SA_V02
Courses - 60 ECTS > Option Group > Information Management > Cours > Module Wirtschaftsinformatik > DADS: Data Analytics & Decision Support

Ma - Business Informatics - 90 ECTS
Version: 2020/SA-v01
Classes - min. 45 ECTS > Modules IT Management - min. 22 ECTS > DADS: Data Analytics & Decision Support
Classes - min. 45 ECTS > Module IT and IT Management > DADS: Data Analytics & Decision Support

Ma - Management - 90 ECTS [MA]
Version: 2017/SA_v01
Courses: min. 63 ECTS > 3 modules with min 12 ECTS each > BINF: Business Informatics

MiMa - Business Informatics - 30 ECTS
Version: 2020/SA_V01
Cours > Module Wirtschaftsinformatik > DADS: Data Analytics & Decision Support

MiMa - Data Analytics - 30 ECTS
Version: 2020/SA-v01
À choix 9 crédits ECTS > DADS: Data Analytics & Decision Support