## Productivity Measurement Solved Problems : Multi factor Productivity

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In our previous text, we covered the basic solved problems based on productivity measurement highlighting the importance of single-factor productivity and multi-factor productivity. As we progress in the text, we will discover how important it is to measure process productivity and how it is proportional to the efficiency of the company. Productivity can be measured in a  variety of ways, such as labor, capital, energy, material usage, and so on.

## Productivity Measurement Problems

Here are the basic examples showing the changes in multifactor productivity when we make changes in labor and other factors with the introduction of new systems. In layman’s language, productivity is the ratio of outputs to inputs.  In most cases, outputs are goods and services and inputs include resources such as material, labor, management, and capital. Therefore to improve efficiency, operations managers always focus on improving productivity. Today, we are sharing solved examples such as productivity Measurement solved problems based on multi-factor productivity.

Multi-Factor Productivity: Indicates the ratio of more than one resource (input)  to goods/services produced (output)

P.M = output /more than one input = output / (capital + management + labor + material + energy + other)

### Chapter 1, Problem 1.18

Kleen Karpet cleaned 65 rugs in October, consuming  the following resources:
Labor: 520 hours at \$13 per hour
Solvent: 100 gallons at \$5 per gallon
Machine rental: 20 days at \$50 per day

A) What is labor productivity?
B) What is multifactor productivity?

### Solution

A) In order to find labor productivity, we need to know Labor in Dollars

Total Labor cost = Total Number of labor hours * Rate per hour

= 520  labor hours * 13 per hour

= \$ 6, 760

Productivity per labor dollar = Total rugs / Total Labor Cost …………………………………………………………eq(1)

Total rugs = 65 rugs

Total Labor Cost  = \$ 6, 760

Put the values in eq(1)

Therefore Productivity per labor dollar= 65 / 6, 760  = 0.0096 rugs / labor dollar

B) Multifactor Productivity = output  / more than one input

In this case Input include labor , solvent , machine rental

Total Labor Productivity cost  = 520 hours * \$13 per hour = \$ 6, 760

Solvent cost = 100 gallons *  \$5 per gallon = \$ 500

Machine rental cost = 20 days * \$50 per day = \$ 1,000

Output = 65 rugs

Input = Adding up all the cost ( i.e Total Labor Productivity cost , Total solvent cost  ,Total Machine rental cost)

Multifactor Productivity = 65 rugs / ( 520 h * 13 \$ + 100 gallons * 5 \$ + 20
days * 50 \$ ) =  65 / 6760 + 500+ 1000 = 65/ 8260 =.00787 rugs / dollar

#### Book Referred, in this case, is Operations Management by Jay Heizer and Barry Render

There are some points that one should keep in mind while working on numerical based on productivity measurement. These are

By observing the equation, we can improve productivity in two ways:

• Reduce the Input and keeping the output constant
•  Reduce the Output and keeping the Input constant

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