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Productivity
Outputs
Productivity =
Inputs
• Single-factor measures
– Output / (Single Input)
• All-factors measure
– Output / (Total Inputs)
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Measures of Productivity
Single-factor Output
measures
Labor
All-factors
measure
Output
Machine
Output
Capital
Output
Energy
Output
All inputs
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Single Factor
Single-factor Output
measures
Labor
Output
Machine
Output
Capital
Output
Energy
If we produce only one product, the numerator can be either
the total units of the product or the total $ value of the
product. If we produce several products, the numerator is
the total $ value of all products.
The denominator can be the units of input or the total $
value of input.
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Example: Single Factor Productivity
10,000 Units Produced
Sold for $10/unit
500 labor hours
Labor rate: $9/hr
What is the
labor productivity?
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Example: Labor Productivity
• 10,000 units / 500hrs = 20 units/hr
• (10,000 units * $10/unit) / 500hrs = $200/hr
• 10,000 units / (500hrs * $9/hr) = 2.2 unit/$
• (10,000 units * $10/unit) / (500hrs * $9/hr) = 22.22
•The last one is unit-less
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Some Single Factor Measurements
• Labor Productivity
– Quantity (or value) of output / labor hrs
– Quantity (or value) of output / shift
• Machine Productivity
– Quantity (or value) of output / machine hrs
• Energy Productivity
– Quantity (or value of output) / kwh
• Capital Productivity
– Quantity (or value) of output / value of input
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All Factors
All-factors
measure
Goods or Services produced
All inputs used to produce them
If we produce only one product, the numerator can be either
the total units of product or total $ value of the product.
If we produce several products, the numerator is the total
$ value of all products.
Usually, the numerator is the total $ value of all outputs.
The denominator is total $ value of all inputs.
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Example
10,000 Units Produced
Sold for $10/unit
500 labor hours
Labor rate: $9/hr
Cost of raw material: $30,000
Overhead: $15,500
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Example : All-Factor Productivity
AFP =
AFP =
Output
Labor + Materials + Overhead
(10,000 units) * ($10)
(500)*($9) + ($30,000) + ($15,500)
AFP = 2.0
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What are the factors that affect productivity?
Training
Technology
Methods
Management
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Assignment 1.1…………….. Due at the beginning of the next class
1.
A company that makes shopping carts for supermarkets recently purchased
new equipment, which reduced the labor content needed to produce the
carts. Information concerning the old system (before adding the new
equipment) and the new system (after adding the new machines) includes:
Output/hr
Workers
Wage $/hr
Machine $/hr
a)
b)
c)
Old System
80
5
10
40
New System
84
4
10
50
Compute labor productivity for both the Old System and the New System.
Compute AFP productivity for both the Old System and the New System.
Suppose production with old equipment was 30 units of cart A at a price of
$100 per cart, and 50 units of cart B at a price of $120. Also suppose that
production with new equipment is 50 units of cart A, at a price of $100 per
cart, and 30 units of cart B at a price of $120. Compare all-factor productivity
for the old and the new systems.
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Assignment 1.2…………….. Due at the beginning of the next class
2.
A company has introduced a process improvement that reduces the
processing time for each unit and increases output by 25% with less
material but one additional worker.
Under the old process, five workers could produce 60 units per hour.
Labor costs are $12/hour, and material input was $16/unit.
For the new process, material input is now $10/unit and overhead is
charged at 1.6 times direct labor cost. Finished units sell for $31 each.
a)
b)
Compute single factor productivity of labor in the old system.
(Compute it in four possible ways.)
Compute all factor productivity for both old and new systems.
Factor
Old System
New System
Output
# of workers
Worker cost
Material
Overhead
Price
60
5
$12/hr
$16/unit
1.6(labor cost)
31
60(1.25) = 75
6
$12/hr
$10/unit
1.6(labor cost)
31
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Assignment 1.3……… For your own practice
3.
A milk factory seeks advice from an external consulting company concerning its
business and production processes. The final consulting report describes
several steps to increase productivity including implementation of cutting-edge
processing techniques through more powerful filtering systems.
Existing System
Proposed System
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Milk Output/hour
1,000 gallons
1,400 gallons
Wage Rate/hour
$12
$12
Filtration Cost/hour
$120
$170
Workers
a)
b)
c)
Calculate the labor productivity for the existing as well as the proposed system.
Find the All-Factor Productivity for both systems.
Assume that current processing includes 700 gallons of Grade-A milk sold at
$2.40/gallon and 300 gallons of Grade-B milk at $1.90/gallon. Furthermore,
assume that under the proposed system, processing will include 600 gallons of
Grade-A milk at $2.40/gallon and 400 gallons of Grade-B milk at $1.90/gallon.
Compare all-factor productivity for both the existing and the new system.
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