OVERVIEW

The course presents mathematical models and methods, in particular of Operations Research, with which decision-making problems can be tackled in various fields, from production to logistics. The approaches studied 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.

AIMS AND CONTENT

LEARNING OUTCOMES

The course presents mathematical models and methods, in particular of Operations Research, with which decision-making problems can be tackled in various fields, from production to logistics. The approaches studied 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. The main objective is to provide students with the ability to face problems using the tools made available by Operations Research. The problems treated constitute a reference for large classes of real application problems of a complex nature. Specifically, they will deal with applications for manufacturing planning and scheduling and for logistics and transportation (network flow, location and vehicle routing). Most of the models studied will be mixed integer programming; models of network flow and multi-criteria models will be also considered. A large space will be dedicated to heuristic and metaheuristic methods that constitute the main tool with which to face complex decisional situations in reality.

AIMS AND LEARNING OUTCOMES

The main objective is to provide students with the ability to face problems using the tools made available by Operations Research. The problems treated constitute a reference for large classes of real application problems of a complex nature. Specifically, they will deal with applications for manufacturing planning and scheduling and for logistics and transportation (network flow, location and vehicle routing). Most of the models studied will be mixed integer programming; models of network flow and multi-criteria models will be also considered. A large space will be dedicated to heuristic and metaheuristic methods that constitute the main tool with which to face complex decisional situations in reality.

PREREQUISITES

Basic concepts of Operations Research and Computer Science

TEACHING METHODS

Frontal classes and some practices using a mixed integer programming solver

SYLLABUS/CONTENT

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 Problems, Algorithms for Max Flow and Min Cost Flow; 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.

RECOMMENDED READING/BIBLIOGRAPHY

Teaching material available on aulaweb.

TEACHERS AND EXAM BOARD

Exam Board

MASSIMO PAOLUCCI (President)

MAURO GAGGERO

MARCELLO SANGUINETI (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral testing and / or development of a project (for students who have attended classes with assiduity).

ASSESSMENT METHODS

At the end of the course the acquired skills will enable students to structure decision-making problems of medium complexity and to choose the right solution methodologies as well as to use simple software packages as decision support tools

Exam schedule