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ACCA F5
Performance Management (PM)
业绩管理
ACCA Lecturer: Kimberley Gong
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1
2
What are limiting factors?
One limiting factor/Multi-limiting factor
Content of chapter 8
3 Shadow prices
4 Lecture example
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Limiting factor analysis
What are limiting factors?
A limiting factor is any factor that is in scarce supply
and that stops the organisation from expanding its
activities further. Examples:
Demand
Materials
Labour
Machine hours
Money
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Limiting factor analysis
One limiting factor
Usual objective is to maximise profit
Fixed costs are unaffected in short term
Maximise contribution
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Limiting factor analysis
One limiting factor-key factor analysis
1. Identify the scarce resource.
2. Calculate the contribution per unit for each
product.
3. Calculate the contribution per unit of the scarce
resource for each product.
4. Rank the products in order of the result from 3.
5. Allocate the resources using this ranking.
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Lecture example 1
Cotton ltd produces three products P1, P2, P3. The
maximum machine hours per week and labor hours
are 1000hours and 900 hours. What is the optimal
production plan?
Selling prince 250 240 200
Variable cost 130 130 100
Fixed cost 80 80 80
Profit 40 30 20
Demand per
week
60 60 60
Machine hour
per unit
12 10 5
Labour hour
per unit
6 5 4
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Lecture example 1
Step1 : Total machine hrs needs
60 * ( 12 + 10 + 5 ) = 1620 > 1000 hrs
Total labour hours needs
60 * ( 6 + 5 + 4 ) = 900
MACHINE HOURS IS LIMITED RESOURCES
Step2 : contribution per unit =
P1 P2 P3
120 110 100
120/12=10 11 20
3 2 1
Contribution
Contribution/hrs
Rank
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Lecture example 1
1st : P3 = 60*5 = 300 hrs
2nd : P2 = 60*10 = 600 hrs
3rd : P1(B) = 1000 – 900 = 100 hrs
100/12 = 8 , 8*12 = 96 hrs
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Limiting factor analysis
Multi-limiting factor---linear programming analysis
A) Define the variables (x, y)
B) Define and formulate the objective
C) Formulate the constraints
D) Draw a graph identifying the feasible region
E) Draw ISO contribution line to Solve the optimal
production plan
F) Answer the question
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Lecture example 2
Soft company makes 2 products in 3 departments.
Details are shown below:
Formulate a linear program and find the optimal
production plan.
Product A
Hours per
unit
Product B
Hours per
unit
Available
hours
Department X 10 15 18000
Department Y 5 15 12000
Department Z 15 8 15000
Contribution
per unit
8 12
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Lecture example 2
Step 1 : Identify X = the optimal number of product A
Y = the optimal number of product B
Step 2 : Identify ISO contribution line is to max 8X + 12Y
Step 3 : constraints
10X + 15 Y <=18000
5X + 15Y <= 12000
15X + 8Y <= 15000
X , Y >= 0
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Lecture example 2
Step 4 : feasible area
15X + 8Y = 15000
5X + 15Y = 12000
10X + 15Y = 18000
8X + 12 Y
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Lecture example 2
Step 5 : X = 697 , Y = 567
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Limiting factor analysis
Slack/Surplus
Slack: Resource actually used<Resource available.
Surplus: Actual outcome>minimal requirement
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Limiting factor analysis
Shadow prices
A shadow price or (dual price) is:
The additional contribution generated from one
additional unit of limiting factor.
The opportunity cost of not having the use of one
extra unit.
The maximum extra amount that should be paid
for one additional unit of scarce resource.
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Lecture example 3
WX manufactures two products A and B. Both
products pass through two production
departments, mixing and shaping. The company’s
objective is to maximise contribution to fixed costs.
Product A is sold for $ while product B is
priced at $2/unit. There is unlimited demand for A
but demand for B is limited to 13, 000 units per
annum. The machine hours of each department are
restricted to 2400 per annum.
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Lecture example 3
Required: Calculate the shadow price of one hour of
machine time in Shaping department
Machine hours required Variable cost
per unit
Mixing Shaping
Product A $
Product B $
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Lecture example 3
Step 1 : X = A , Y = B
Step 2 : max +
Step 3 : constraints
+ <= 2400
+ <= 2400
Y <= 13000
X , Y >= 0
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Lecture example 3
Y = 13000
+ = 2400 + = 2400
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Lecture example 3
Step 5 : X = 24000 , Y = 12000
X1 = 23986 , Y1 = 12015
Additional contribution = 8400 – =
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Limiting factor analysis
Implications of shadow price
Management can use shadow prices to measure
the maximum premium that they would be
willing to pay for one more unit of the scarce
resource.
It is possible for management to negotiate a
lower shadow price than calculation.
After a certain point there will be little point in
buying more of the scarce resource as any non-
critical constraints will become critical.
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