Malaguti, Enrico

Almae Matris Studiorum Campus

Algorithms for decisions making MA.A. 2016/2017 - Enrico MalagutiCorso di Laurea in Ingegneria Gestionale, Scuola di Ingegneria, Universita` di BolognaCourse Syllabus• Notation, Linear Programming, standard and canonical form (equivalence), Integer Linear Pro-gramming (ILP);• Duality: Lagrangean relaxation, Dual problem, weak duality, strong duality, the diet problemand pill maker problem: primal and dual interpretation;• Complexity theory: complexity of an algorithm, complexity of a problem: P, NP, NP-complete.Ideal formulations for problems in P and NP;• LP relaxation, Branch-and-Bound algorithm for ILP;• Uncapacitated Facility Location problem, formulation;• Set Covering, Packing and Partitioning problems, formulations;• Capacitated Facility Location problem, Bin Packing: descriptive formulation, set covering for-mulation, Cutting Stock problem, Gilmore-Gomory formulation (exponential size);• Fixed Charge, big M constraints;• Stable Set problem: edge constraints, clique constraints formulations; Stable Set and Set Pack-ing.• Vertex Coloring problem: descriptive formulation, set covering formulation;• Traveling Salesman problem: formulation, subtour elimination constraints;• Models with exponentially-many constraints: separation; example: asymmetric Traveling Sales-man problem;• Models with exponentially-many variables: column generation; examples: Bin Packing prob-lem, Vertex Coloring, Cutting Stock problem;• Vehicle Routing Problem. Two and three index formulations, separation. Set Partitioning for-mulation, column generation;• Cutting and Packing problems; 2D-Knapsack problem: geometric formulation. Guillotine cut-ting; exponential-size formulation (Gilmore-Gomory), column generation.• AMPL: basic functions, use. Column generation in AMPL (Bin Packing example).1

Programma AA 16/17

http://campus.unibo.it/262968/1/syllabus_16-17.pdf

Programma AA 16/17

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Almae Matris Studiorum Campus