Portale di Ateneo - En.Unibs.it

- Introduction to the course.
- Introduction: operations research, the scientific method, problems and methodologies.
- Mathematical programming: notation, optimization problems, convex sets and functions, convex programming.
- Linear programming (LP): linear programming models, problems in two dimensions, general, canonical and standard forms, bases and basic solutions, convex polytopes, relations between vertices and basic solutions, degenerate bases.
- Simplex method: general strategy, move from SBA to SBA, tableau and pivoting, pivoting and solution value, pivoting rules, determination of initial solution, polynomial and exponential algorithms.
- Duality: dual of a problem in standard form, dual of a problem in general form, duality properties, complementary slackness, sensitivity analysis, shadow prices.
- Integer linear programming (ILP): linear models with integer variables, integer linear programming, cutting-plane algorithms, branch-and-bound algorithms, exploration strategies, other linear problems with integer variables, 0-1 knapsack problem, branch-and-cut algorithms, software for LP, ILP, MILP.
- Problems on graphs: introduction, terminology, shortest spanning tree, graphs representation, shortest paths, traveling salesman problem, vehicle routing problems.
- Project management: project representations, CPM and PERT techniques, Gantt diagrams and software, time/cost trade-off.
- Queueing theory: problem description, characteristics of queueing systems, evaluation parameters, probability distributions, M/M/1 model, M/M/K model, Jackson networks.
- Discrete simulation: Monte Carlo simulation.
- Use of software: MPL and Project.