Use of deterministic models and computers to study and optimize systems. Includes an introduction to modeling, calculus-based models, financial models, spreadsheet models, and linear programming models.
Prerequisite:
MTH 251
Required Topics (approximate week allocation):
Introduction to models and how models are used (1.5)
introduction to mathematical models, advantages, disadvantages
classification of mathematical models
mathematical model terminology
examples of mathematical needs
model formulation
Model examples (3)
calculus based optimization models
financial models
spreadsheet models
non linear models
solving simple unconstrained problems by search
Introduction to linear programming, problem formulation (2)
Systems of equations and matrix algebra (.5)
Simplex algorithm (2)
Sensitivity analysis and duality (2)
Heuristic search methods (1)
Optional optimization applications (2)
Transportation problem
Assignment problem
Network models
Data envelopment analysis
Other applications
Exams/Review (1)
Course Outcomes
To be able to use calculus to formulate and solve non linear optimization problems.
The student can formulate and solve multiple variable, unconstrained optimization problems.
To be able to use linear programming to formulate and solve linear optimization problems.
The student can formulate standard linear programming problems such as diet, scheduling, budgeting, and blending problems.
The student can solve two variable linear programming problems graphically and explain the concepts feasible solution, infeasible solution, optimal solution, active constraint, inactive constraint, multiple optimal solutions, unbounded solutions, and no feasible solutions.
The student can solve multiple variable linear programming problems using the simplex method and explain the concepts basic solution, basic feasible solution, adjacent basic feasible solution, basic variable, non basic variable, corner point, slack variable, surplus variable, artificial variable, reduced cost, shadow price, and degenerate basic solution.
The student can solve linear programming problems using a software tool.
The student can represent a linear programming problem and its solution in matrix form.
The student can perform sensitivity analysis to interpret the impact of changes in the objective coefficients, the constraint coefficients, and the constraint limits.
The student can formulate and solve one or more special types of linear programming problems such as goal programming problems, transportation problems, network problems, data envelopment problems, integer programming problems, or others.
To enhance the student's ability to use quantitative models in decision making.
The student can create optimization models for a wide variety of application areas.
The student can explain the role of models in problem solving.
The student can explain the role of data in modeling and is able to perform simple data analysis tasks.
The student is able to formulate a decision problem in terms of controllable variables, constraints, and objectives.
The student is able to construct simple financial models to compare investment alternatives considering time value of money and taxes.
Department of Computer Science and Software Engineering
