|SCIENTIFIC DISCIPLINARY SECTOR||MAT/09|
The course presents mathematical models and methods of Operations Research, studying how decision-making problems arising in various fields can be tackled, in particular, manufacturing production and logistics. The studied approaches are mainly aimed at situations in which the decisions have a discrete nature (combinatorial problems), presenting techniques to the state of the art of scientific literature.
Modeling and solving complex decision problems. Applications to manufacturing planning and scheduling and to logistics (network flow, location and vehicle routing). Integer programming, heuristic and metaheuristic models and methods for combinatorial optimization problems are studied. Fundamental concepts for solving multicriteria problems are introduced and multi-objective optimization methods are presented
The main objective is to provide students with the ability to face problems using the tools made available by Operations Research. The problems considered are of reference for large classes of real applications of complex nature. Specifically, the students will be able to develop models for manufacturing planning and scheduling and for logistics and transportation applications (network flow, location and vehicle routing). The students will be able to use mixed integer programming modele, in particular network flow models and multi-criteria models. The students will learn the main features of heuristic and metaheuristic methods that constitute the main tools for facing complex decisional situations in reality. Finally, the students will learn basic concepts to face multi-objective decision problems.
Basic concepts of Operations Research and Computer Science
Frontal classes and some practices using a mixed integer programming solver.
Working students and students with a certified DSA, disability or other special educational needs are advised to contact the lecturer at the beginning of the course to agree on teaching and examination methods that, while respecting the teaching objectives, take into account the individual's of individual learning.
Introduction to decision problems, to decision making methodologies and their limits.
Linear optimization models: Example of formulations, use of LP solver and interpretation of the results.
Network Flow models. Network Simplex.
Production planning models: Dynamic Lot Sizing Problem (single item, multi - item) and variants. Multi-stage planning models. Comparison of alternative planning models. Planning in the presence of life-time constraints.
Decision models on graphs and networks with application in the logistics sector.
Mixed integer programming models (planning, location, scheduling). MIP models for single and parallel machine scheduling: alternative formulations. Implementation of models in OPL language and solution of examples with the IBM-Cplex MIP solver.
Linear integer models: references to general concepts (solution methods, total unimodularity, convex hull). The branch and cut. Relaxation techniques. Lagrangian relaxation.
Metaeuristic methods for the solution of combinatorial problems. Neighborhood Search Methods. Trajectory Methods (Iterated Local Search, Tabu Search, Simulated Annealing, Variable Neighborhood Search, GRASP, Iterated Greedy Algorithm, Adaptive Large Neighborhood Search). Population - based Methods (Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization).
Models for the routing of vehicles in transport networks (Vehicle Routing Problems). Exact and heuristic routing models on nodes (Traveling Salesman Problem, Capacitated Vehicle Routing Problem). Introduction to the Arc Routing problem: Eulerian graphs. The Chinese Postman Problem on an undirected, oriented and mixed graph.
Deterministic decision models based on multiple criteria (Multicriteria Decision Making). Multi-objective decision methods: definition of Pareto optimality; classic approaches to multi-objective decisions; Non-dominated Sorting Genetic Algorithm. Multi-attribute decision methods.
Teaching material available on aulaweb.
Office hours: Students can ask appointments directly contacting the professor by email or phone
All class schedules are posted on the EasyAcademy portal.
Oral testing and / or development of a project (only for students who have attended classes with high assiduity).
The dates for the oral exam can be fixed by appointment.
Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities.
The students will be required to structure and solve decision-making problems of medium complexity. They will be required to explain the methods and models learnt during the lectures, both from the theorectic and practical point of view.