Week 4 - Linear Programming And Excel Output Flashcards
What does the Excel Sensitivity Report include?
1) Objective coefficient (Allowable increase and decrease)
2) Shadow Price
3) R.H.S constraint (Allowable increase and decrease)
What does the allowable increase and decrease mean in relation to the objective coefficient?
- It shows the range in which the optimal solution will remain the same.
For example:
Between an increase of up to 25 and a decrease of down to 20, the optimal production solution will remain the same.
What is the shadow price?
The shadow price reflects the profit increase or decrease resulting from a change of 1 unit in one of the constraints.
For example:
An increase of 1 hour in the assembly constraint and a shadow price of 2.5 reflects the fact that a 1 hour increase or decrease in assembly results in a £2.5 change in profit.
What does the allowable increase and decrease mean in relation to the shadow price?
It shows the range in which the shadow price remains accurate.
For example:
If the upper limit is 40, that means that the shadow price remains accurate up until that point. After that the Linear Programme (Excel Solver) will have to be run again.
What happens if there is an increase in profit but within the allowable range?
ONLY the profit is increased, the number of each unit produced remains the same.
What happens if a constraint is given additional units but within the allowable range?
The profit changes, this can be calculated directly by ‘Shadow price x increase in constraint allowance’.
The optimal solution (of products) may also change, to calculate this we need to use both simultaneous equations for the constraints.
What is the 100% rule?
The 100% rule is concerned with the changes in multiple variables and the resulting effect on the optimal solution.
If the sum of all changes in variables is less than 100%, then the optimal solution will remain the same.
If the sum of all changes in variables is more than 100%, than the optimal solution MAY have changed and the solver needs to be run again.
How are the percentages calculated for the ‘100% rule’?
The percentage changes are calculated against the allowable increase or decrease, not against the previous value of the variable.
For example:
A decrease in profit for 20 to 18 with an allowable decrease of 5.4 is calculated as: (2/5.4)x100
What are the two options when dealing with optimal solutions that aren’t whole numbers?
- Round down to the closest integer.
2. Force variables to be integers via software such as excel software.
What is a ‘Binary Variable’?
A binary variable takes either 0 or 1. They can be used for yes or no decisions.
What is the advantage of using ‘Binary Variables’?
They make linear programming models more adaptable to real-world applications.
What does the ‘Reduced Cost’ vale mean in the Excel sensitivity output?
The reduced cost is a measure of how much the cost of the variable must be reduced before the variable is included in the optimal output.
When does the ‘Reduced Cost’ apply?
The reduced cost applies when a variable isn’t included in the optimal solution.
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