Upon completion of MSCI 331, students are able to:
- Formulate linear and integer programs to model real-life problems
- Solve linear programs using the graphical solution and simplex methods
- Formulate and interpret the dual of a linear program
- Implement sensitivity analyses to account for uncertainties
- Collect data to determine or estimate the values of problem parameters
- Use Microsoft Excel to solve linear and integer programs
What is optimization?
Example
A company manufactures two products A and B and the profit per unit sold is $3 and $5, respectively. Each product has to be assembled on a particular machine, each unit of product A takes 3 hours of assembly time and each unit of product B takes 2 hours of assembly time. The company estimates that the effective daily working hour of the machine used for assembly is 18 hours. At least 2 units of product A and 1 unit of product B must be produced daily.
Q: What is the optimum number of products A and B to produce daily to maximize total profit?
To solve this type of problem, we model it mathematically, as follows:
Let x1 and x2 be the number of product A and B to be produced, respectively. We call x1 and x2decision variables.
We then seek to maximize the objective function Z = 3x1 + 5x2
This maximization is subject to a number of constraints:
3x1 + 2x2 <= 18
x1>= 2
X2 >= 1
What is mathematical modelling?
What is operations research?
Optimization is just one of many methodologies used in the field of operations research.
Applications of operations research
Finance
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Supply chain
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Health care
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Sports
....and much more! |