# PRODUCTIONS/OPERATIONS MANAGEMENT

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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    Output    Output    Output
measures      Labor     Machine   Capital   Energy

All-factors     Output
measure         All inputs

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Single Factor

Single-factor Output     Output     Output    Output
measures      Labor      Machine    Capital   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 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
What is the
labor productivity?
Labor rate: \$9/hr

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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   7
All Factors

All-factors        Goods or Services produced
measure           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

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

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Example : All-Factor Productivity

Output
AFP =    Labor + Materials + Overhead

(10,000 units) * (\$10)
AFP =
(500)*(\$9) + (\$30,000) + (\$15,500)

AFP = 2.0

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What are the factors that affect productivity?

Training                    Methods

Technology                 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:

Old System                New System
Output/hr                  80                        84
Workers                     5                         4
Wage \$/hr                  10                        10
Machine \$/hr               40                         50

a)   Compute labor productivity for both the Old System and the New System.
b)   Compute AFP productivity for both the Old System and the New System.
c)   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
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)   Compute single factor productivity of labor in the old system.
(Compute it in four possible ways.)
b)   Compute all factor productivity for both old and new systems.
Factor           Old System                New System
Output           60                        60(1.25) = 75
# of workers     5                         6
Worker cost      \$12/hr                    \$12/hr
Material         \$16/unit                  \$10/unit
Price            31                        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
Workers                       12                   9
Milk Output/hour         1,000 gallons       1,400 gallons
Wage Rate/hour                \$12                 \$12
Filtration Cost/hour         \$120                 \$170

a)   Calculate the labor productivity for the existing as well as the proposed system.
b)   Find the All-Factor Productivity for both systems.
c)   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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