CFU: 6
Prerequisites
None.
Preliminary Courses
None.
Learning Goals
The objective of the course is to widen the modeling and algorithmic knowledge needed to analyze complex systems and optimize their functioning in order to solve real industrial problems (e.g., production planning, resource allocation and activity scheduling). The theoretical study will be supplemented by the introduction of optimization software. At the end of the course the student will gain the knowledge and instruments required to formulate and solve decision problems by exact mathematical programming and/or heuristic optimization methods, with applications in automated industrial context.
Expected Learning Outcomes
Knowledge and understanding
The course has the aim to provide the students with continuous, integer and mixed-integer methodologies required to model and solve engineering problems in the industrial context, with specific reference to production planning, resource allocation and task/activity scheduling problems. The student has to show to be able to use the methodologies needed to formulate a decision problem by a mathematical programming model with continuous and integer variables and has to be able to independently identity and develop the best exact and solution method with respect to the features and the complexity of the problem under investigation.
Applying knowledge and understanding
The course has the aim to provide the students with continuous, integer and mixed-integer methodologies required to model and solve engineering problems in the industrial context, with specific reference to production planning, resource allocation and task/activity scheduling problems. The student has to show to be able to use the methodologies needed to formulate a decision problem by a mathematical programming model with continuous and integer variables and has to be able to independently identity and develop the best exact and solution method with respect to the features and the complexity of the problem under investigation.
Course Content - Syllabus
-Introduction to optimization. Decision Process, Problem Solving, Mathematical Programming.
- Continuous optimization problems. Mono and multi-dimensional non-linear optimization (constrained and unconstrained).
- Linear programming (LP). Formulation of LP problems; simplex algorithm; algebraic structure of the LP; LP duality; post-optimality analysis; introduction to multi-criteria decision problems, multi-attribute and multi-objective methods.
- Integer linear programming (ILP). Formulation of integer and binary linear problems (ILP); ILP solving methods (branch-and-bound, cutting plane, column and row generation methods); ILP known problems (cutting stock, knapsack, assignment); industrial problem modelling (e.g. optimal allocation, operation sequencing).
- Graph theory and Network Optimization. Introduction to graphs; data structures and algorithms for the visit of a graph; formulation of network optimization problems and solving algorithms; path, flow and design problems; network industrial problem modeling (e.g. smart grid, flow control and equilibrium).
- Network based techniques for project scheduling and control. PERT and CPM.
The course has also a laboratory characterization. It foresees the development of sample projects and the solution of optimization problems using software instruments, among the others OPL-Cplex and Xpress-IVE.
Readings/Bibliography
- M. Caramia, S. Giordani, F. Guerriero, R. Musmanno, D. Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014.
- C. Guéret, C. Prins, M. Sevaux, Applications of optimization with Xpress-MP, Dash Optimization Ltd., 2010.
- F. S. Hillier, G. J. Lieberman, Ricerca operativa - Fondamenti, 9/ed., McGraw-Hill, 2010.
- A. Sforza, Modelli e Metodi della Ricerca Operativa, 3a ed., ESI, Napoli, 2018.
- Teaching matherials provided during the course.
Teaching Method
The teaching activities will be organized as follows: lectures for about 60% of the total hours; seminars for about 10%; , practical exercise in the classroom and introduction to the usage of optimization software for about 30%.
Examination/Evaluation criteria
Exam type
Written and oral.
The written exam aims at assessing the capability of the students to use independently the concepts and the methodologies shown during the course. It consists of several exercise focused on the usage of mathematical programming and optimization techniques to solve real-like problems. Typically, 3 hours are given for the written exam. The oral exam follows the written exam and it has a twofold aim: on one side, assessing the student capability of arguing the solutions implemented in the written exam; on the other side, the assessment of the methodological knowledge gained during the course.
Evaluation pattern
The written exam performance is binding to have access to the oral exam. Both the written and the oral exams contribute 50% each to the final mark. Therefore passing the written exam is only a necessary condition to pass the overall exam.