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Questions and Answers
What is the type of model used to maximize the daily increase in profit?
What is the type of model used to maximize the daily increase in profit?
What is the restriction on the decision variables in the linear programming model?
What is the restriction on the decision variables in the linear programming model?
What is the designation of the model used to decide which recreation facilities to construct?
What is the designation of the model used to decide which recreation facilities to construct?
What is the purpose of the linear programming model in the machine shop example?
What is the purpose of the linear programming model in the machine shop example?
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What is the implicit assumption in the linear programming models in previous chapters?
What is the implicit assumption in the linear programming models in previous chapters?
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Why do we need to solve integer programming problems?
Why do we need to solve integer programming problems?
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How many types of integer linear programming models are there?
How many types of integer linear programming models are there?
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What is a characteristic of a 0-1 integer model?
What is a characteristic of a 0-1 integer model?
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What is a characteristic of a mixed integer model?
What is a characteristic of a mixed integer model?
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Study Notes
Apple Cider Production
- The Friendlys are considering producing apple cider, which requires 1.5 hours of cooking, 0.5 hour of labor, and 60 apples per batch, and sells for $45 per batch.
Integer Programming
- Integer programming models assume that solutions can only be integer values, not fractional or real numbers.
- Non-integer solutions are not always practical, and rounding off to the nearest feasible integer value can affect profit or cost.
- Learning outcomes include differentiating and analyzing integer programming models, and applying Excel and QM for Windows as computer solutions.
Integer Programming Models
- There are three basic types of integer linear programming models: total integer model, 0–1 integer model, and mixed integer model.
- Total integer model: all decision variables are required to have integer solution values.
- 0–1 integer model: all decision variables have integer values of zero or one.
- Mixed integer model: some of the decision variables (but not all) are required to have integer solutions.
Examples of Integer Programming Models
- Total integer model example: a machine shop owner wants to maximize daily profit by purchasing new machines (presses and lathes) within a budget of $40,000 and 200 square feet of available floor space.
- Linear programming model for an integer programming problem is formulated in the same way as linear programming examples, but with decision variables restricted to integer values.
- Decision variables in this model are restricted to whole machines.
0–1 Integer Model Example
- A community council must decide which recreation facilities to construct (swimming pool, tennis center, athletic field, and gymnasium).
- Decision variables in this model have integer values of zero or one.
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