1. Limiting factor analysis
F5-Chapter 4
Limiting factor analysis
Lecturer: Ji Weili
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2. Limiting factor analysis Make or buy decisions and scare resources
Chapter Preview
Limiting factor analysis
Limiting factors
Linear programming
Slack and surplus
Make or buy decisions and scare resources
Shadow price
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3. Overview A revision of linear programming technique.1
Some new concepts: slack,
surplus, shadow price or dual price 2
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4. Limited resources
A business needs to identify the optimal production plan for utilising its resources to maximise profit
2 techniques
Single limiting factor
Linear programming (>1 limiting factor)
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5. Single limiting factor analysis1
Identify limiting factor(except sales
demand) 2
Calculate contribution per unit 3
Calculate contribution per limiting factor 4
Rank products 5
Prepare a production plan
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6. Example: two potentially limiting factors
step3
Plan 4
step2
Rank
step1
Identify which of the limiting
factors is a binding constraint.
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7. Make or buy decisions and scarce resources
Combining internal and external production
Decision rule---- minimise costs
Example: P107
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8. Linear programming steps1
Define variables P110
let x = number of the Super produced
let y = number of the Deluxe produced
let p = contribution per month
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9. Linear programming steps2
Establish constraints
subject to:
Machine hour 5x + 1.5y  400
Government restrictions x + y  150
Non-negativity x,y > 0
Formulate objective function
Max p =100x + 200y 3
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10. Linear programming steps4
Plot constraints on graph
Find co-ordinates
Machine hour 5x + 1.5y= 400
when x=0, y=267
y=0, x=80
Government restrictions x + y=150
When x=0, y=150
y=0, x= 150
Non-negativity x,y > 0
Set the inequalities to equations
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11. Linear programming steps
100 x y
200
300 50
150 5
Identify feasible region A
The feasible area is OABC. B
This is the area in which the solution will lie – likely to be on one of the points or on a line as want to maximise contribution.
Can use letters or shade in the area C 11
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12. Linear programming steps
100 x y
200
300 50
150
5x+1.5y=400
Point out that the non-negativity is denoted by use of the positive quadrant of the graph
x+y =150 12
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13. Linear programming steps6
Plot objective function and identify optimal point
p =100x + 200y
Pick any value for p
Say p= 10000
When x=0, y=50
When y=0, x=100
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14. Linear programming steps
100 x y
200
300 50
150 A B C
Optimal point = A
p =100x + 200y
Plot the objective function and tell them to push it as far as possible to the edge of the feasible region to give the optimal point I.e. the maximum g and s and therefore the maximum contribution – use a ruler to keep it parallel
Alternative approach is to work out the contribution at each feasible point to see which one gives maximum – so need to do simultaneous equations at each point
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15. Linear programming steps7
Determine optimal solution
The optimal point is A, where the profit line is
passing through the intersection of x+y=150
with the y axis at (0,150).
Optimal production plan:
0 Super models
150 Deluxe models
Contribution:
p=200*150=30000
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16. Linear programming Please note the format of your answers.
Two methods to find the best solution—graphing or using simultaneous equations.
Attention: You must draw the graph whatever.
Let me see! 16

17. Slack and surplus
When maximum availability of a resource is not used, slack occurs.
When more than a minimum requirement is used, surplus occurs.
Slack is associated with ≤ constraints and surplus with ≥ constraints.
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18. Limiting factors and shadow prices
The shadow price or dual price is the extra contribution or profit that may be created by having one additional unit of the limiting factor at the original cost.
Key points:
1)The shadow price represents the maximum premium above the basic rate that an organization should be willing to pay for one extra unit of a resource.
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19. Limiting factors and shadow prices
2)If a constraint is not binding at the optimal solution, the shadow price is zero.
3)Shadow prices are only valid for a small range.
4)Shadow prices provide a measure of the sensitivity of the effect of a unit change in a constraint.
Example: calculating shadow prices P
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20. End of Chapter 4
Thank You !
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