Week 4 - Linear Programming And Excel Output Flashcards Preview

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Flashcards in Week 4 - Linear Programming And Excel Output Deck (13)
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1
Q

What does the Excel Sensitivity Report include?

A

1) Objective coefficient (Allowable increase and decrease)
2) Shadow Price
3) R.H.S constraint (Allowable increase and decrease)

2
Q

What does the allowable increase and decrease mean in relation to the objective coefficient?

A
  • 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.

3
Q

What is the shadow price?

A

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.

4
Q

What does the allowable increase and decrease mean in relation to the shadow price?

A

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.

5
Q

What happens if there is an increase in profit but within the allowable range?

A

ONLY the profit is increased, the number of each unit produced remains the same.

6
Q

What happens if a constraint is given additional units but within the allowable range?

A

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.

7
Q

What is the 100% rule?

A

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.

8
Q

How are the percentages calculated for the ‘100% rule’?

A

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

9
Q

What are the two options when dealing with optimal solutions that aren’t whole numbers?

A
  1. Round down to the closest integer.

2. Force variables to be integers via software such as excel software.

10
Q

What is a ‘Binary Variable’?

A

A binary variable takes either 0 or 1. They can be used for yes or no decisions.

11
Q

What is the advantage of using ‘Binary Variables’?

A

They make linear programming models more adaptable to real-world applications.

12
Q

What does the ‘Reduced Cost’ vale mean in the Excel sensitivity output?

A

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.

13
Q

When does the ‘Reduced Cost’ apply?

A

The reduced cost applies when a variable isn’t included in the optimal solution.

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