- Introduction to the course and exam structure.
- Introduction: operations management, the scientific method, problems and methodologies.
- Mathematical programming: notation, optimization problems, convex programming.
- Linear Programming (LP): linear programming models, problems in two dimensions, general, canonical and standard forms, basis and basic solutions, convex polytopes, relations between vertices and basic solutions, degenerate basis.
- Simplex method: general strategy, tableau and pivoting, pivoting and solution value, pivoting rules, determination of initial solution.
- 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, other linear problems with integer variables, software for LP, ILP, MILP.
- Problems on graphs: introduction, terminology, shortest spanning tree, graphs representation, shortest paths, travelling 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.