Knowledge and understanding: capability of understanding (a) the conceptual approach of Operations Research as a tool for formulating, solving and evaluating decision-makimg problems related to complex systems, (b) the methodologies for the formalization of quantitative models and algorithmic solutions, and (c) the theoretical aspects underlying the solution techniques, their mathematical justifications and their implications and applicative potentialities.
Applying knowledge and understanding: capability of actually applying the solution techniques and algorithms, by executing the necessary procedures to attain the solution of numerical problems and being able to critically analyze the solutions obtained.
Making judgments: capability of applying the acquired knowledge to autonomously formulate quantitative models and solve the associated optimization problems, by also manually executing the appropriate solution algorithms.
Communication skills: capability of introducing decision-making problems and their possible solutions, both in written and oral form, and to critically discuss the validity and the limits of formulations and solutions.
Learning skills: capability of gathering information from textbooks, scientific papers and other material for the formulation and autonomous solution of decision-making problems.
Knowledge of the linear algebra formalism (vectors, matrices, their operations and space representations) and of the graph theory (classification, properties, trees, paths, circuits) can favor the understanding. However, it is not an essential condition.
No strict prerequisite.
1. Introduction to Operations Research
Application areas (Activity management, resource planning and management. manufacturing, logistics & transportation, economy, finance, healthcare services, public administration)
2. Linear programming (LP)
Properties, characteristics and applicability of LP.
LP models formulation: decision variables, objective, constraints.
Geometric interpretation for problems in two dimensions.
Possible outcomes for a PL problem: feasibility, unique and multiple optimality.
Standard form, slack and surplus variables.
Generality of the standard form.
Base solution. Basic and non basic solutions.
Improvement of a non optimal basic solution.
3. DUALITY in PL.
Multipliers, dual variables, constraints and problem.
Weak and strong duality.
Relations between primal and dual solutions.
Postoptimality and sensitivity analysis.
Modifying rhs terms, objective function.
5. NONLINEAR PROGRAMMING
Examples and graphical representation of nonlinear programming problems
Unconstrained optimization (one variable)
Unconstrained optimization (multiple variables)
Karush-Kuhn-Tucker (KKT) conditions for constrained optimization
Lectures and Exercises.
The final exam consists of a written test that involves the resolution of exercises and possibly the answer to theoretical questions. This will verify both the knowledge of the topics covered during the course and students' ability of understanding and autonomy of judgment.
Any changes to the information presented here, which are necessary to ensure the application of the safety protocols related to the COVID19 emergency, will be communicated on the Department, Study Program and teaching website.
F. S. Hillier and G. J. Liebermann: Ricerca Operativa, 9th Ed. McGraw-Hill