LEARNING OUTCOMES

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. Models for combinatorial optimization problems, in particular mixed integer programming (MIP) models, heuristic and metaheuristic methods. MIP models as well as heuristics and metaheuristics approach are applied to scheduling and vehicle routing problems (VRP). Multi-criteria decision problems, in particular fundamental concepts and approaches for multi-objective optimization problems.

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 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 models of network flow 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.

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 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.

RECOMMENDED READING/BIBLIOGRAPHY

Teaching material available on aulaweb.