Description
Objectives
At the end of the course, students must have the ability to do a Process Analysis and select the design variables that satisfy the degrees of freedom. Students should be able to write a mathematical programming model for linear systems in an interface language with existing solvers (Ex: GAMS). The model must include the constraints and the objective function. It is intended that an analysis of the results and an eventual analysis of sensitivity to parameters of the model be carried out.
Syllabus
- Nature History and significance of Planning in the context of Operational Research. Mathematical models. 2) Linear Programming (LP) Optimization of a linear function subject to linear constraints. Model formulation. Graphical problem solving with 2 decision variables. Economic significance of marginal values, sensitivity analysis. Resolution by the simplex algorithm (from Dantzig). Duality. 3) Examples of LP problems. Transport from sources to given destinations. Mixture of fuels. 4) Project planning problem. Representation of a project through a graph. Minimum path problems. Critical path method (CPM) and PERT. 5) Linear programming with integer variables (mixed integer linear programming). Resolution by the “branch-and-bound” algorithm. 6) Particular cases of MILP with its own algorithms. Ex: the affectation problem and the Hungarian algorithm; optimization for energy production in power plants with multiple generators.
Prerequisites
This course has no prerequisits.
Cross Competence Component
Emphasis will be given to teamwork, bibliographic research for the execution of TPCs and the ability to quickly present oral homework in the classroom. These skills will contribute with 10% to the global evaluation.
Laboratorial Component
The use of wet laboratories is not foreseen, only LTI-Lab. of Computer Technologies will be used
Programming And Computing Component
Programming skills are evident, as models are developed in language suitable for reading solvers. In principle, the GAMS- General Algebraic Modeling System language will be used. More than 50% of the UC will use a programming component.
Ethical Principles
All members of a group are responsible for the group´s work. In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.