Tabla de Contenidos

**Course code number and name:**300ICIP003, Mathematical Modeling and Programming.**Credits and contact hours:**3 credit hours, 4 hours per week.**Course coordinator:**María Gulnara Baldoquín**Prerequisites:**Linear Algebra (300MAG006) and 51 approved credit hours.**Type of course:**Required.

- Operations Research, 9th Edition, H.A. Taha, 2010.

**Supplemental materials**

- Introduction to Operations Research, H. Lieberman, 2012.
- Operations Research: Applications and Algorithms, W.L. Winston, 2003.

This course is concerned with the fundamentals and applications of linear optimization. The formulation of linear programming models and their applications to solving Industrial Engineering problems is emphasized. The Simplex method and its variants are studied in the context of linear programming. Specialized software applications are used to solve linear programming models. At the end of the course students are expected to appreciate the importance of linear programming as a aid in the taking of decisions.

- To review the methodology of system analysis.
- To identify the components of a linear programming model and formulate the equations of typical linear programming models.
- To solve linear programming problems with the Simplex method.
- To establish the relationship between the primal and dual models of a linear programming problem.
- To formulate and solve dual linear programming problems.
- To formulate shortest-route models for the solution of multi-period and replacement problems.

Student Outcomes | |||||||||||
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A | B | C | D | E | F | G | H | I | J | K | |

Relevance | 3 | 2 | 3 | 3 | 2 |

1: low relevance; 2: medium relevance; 3: high relevance.

- Organizations and the process of decision taking; use of quantitative methods; origin, nature and methodology of operations research.
- Features of linear programming.
- Mathematical modeling.
- Formulation of linear programming models.
- Definition and solution of the dual problem; interpretation of results.
- Properties and relationships between the primal and dual models.
- Solution of linear programming models with AMPL/CPLEX/LINGO/AIMMS.
- Sensitivity analysis.
- Solution of integer programming problems; branching and bounding algorithm.
- Formulation of network problems and models.
- Problem of the shortest route.
- Minimal expansion tree.
- Maximal flow problem.