Part A. Basic elements of using MATLAB
- Introduction to MATLAB and its command window
- Basic operations, arrays and matrices. Internal functions
- Programming tools using MATLAB
- Writing scripts and functions

Part B. Linear Programming (LP): methods and applications

B.1) Formulations of LP
- Optimization problems expressed in terms of LP
- Matrix representation of LP. Constraints, feasibility, solutions
- Representation of LP problems in 2 and 3 dimensions and graphical solutions
- Forms of LP (canonical, mix or max, standard forms and transformations)
- Convex and polyhedral feasible sets and characterization of solutions
- Optimal solutions and Kuhn-Tucker conditions
- The idea of the simplex method in the standard form
- Use of MATLAB for solving general LP problems
B.2) Duality in LP
- Optimal solutions and primal-dual variables
- Fundamental theorems of duality
- Examples of primal/dual pairs
- Interpretations of dual variables and examples using MATLAB
B.3) Sensitivity and parametric analysis
- Sensitivity with respect to the objective function
- Sensitivity with respect to the constraints
- Parametric analysis with respect to the objective function
B.3) Applications and extensions of LP
- Data Envelopment Analysis (DEA), input-oriented and output-oriented models
- Multiple objective LP (dominance, efficiency) and examples
- LP with uncertain costs
- General LP with interval-valued cost function (interval analysis)

Part C. Integer linear programming ILP and elements of Graph Theory
C.1) ILP, solutions and basic algorithmic issues
- Linear assignment, transportation and transshipment problems
- Examples of mixed LP-ILP problems
- Basic cutting plane method (Gomory cuts)
- Knapsack problem and capital budgeting problem
- Tree-search and Branch and Bound methods
C.2) Graphs and Optimization problems on graphs
- Basic definitions and representations of directed/undirected graphs.
- Reachability and connectivity; connected components
- Paths, cycles, spanning trees
- Graphs with costs on arcs, minimum spanning tree (Kruskal algorithm)
- Shortest path problem and algorithms
- Combinatorial optimization on graphs (TSP, VRP, Chinese postman)
- Network flows and max-flow problem
- Network flow with gains and applications

Part D. Project Management – Multiple Criteria Decision Making
D.1)- Project Management
- Representation of a project with activity on nodes and on arcs
- Time, durations, scheduling
- Critical path analysis (CPM, CPA) and time scheduling optimization
- Probabilistic and other approaches to uncertainty of durations (PERT)
D.2) – Mathematical models for decision making
- Conflicting objectives in decision making; dominance and efficient solutions
- Approaches to aggregation and ranking techniques
- Multiple criteria decision making (MCDM) and TOPSIS-VIKOR

Part E. Seminars
At least two seminars have to be attended:
E.1) Classification and Clustering
- Basic methods for data clustering
- Fuzzy Clustering and applications
E.2) Data uncertainty and Soft Computing
- Interval Analysis and applications
- Soft computing
E.3) Use of MATLAB for selected applications
- LP using linprog
- Routines for LP with interval costs
- A package for DEA

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it