1

OPERATIONS MANAGEMENT (MGCR-472-061)

Productivity Practice Problems 1. The South Dakota Clay Pigeon Corporation showed the following results for last

year:

(A) What was the total factor productivity? (B) What was the multi-factor productivity measure for total output to labor and materials? (C) What was the multi-factor productivity measure for finished output to labor and materials? (D) What was the partial productivity measure for total output to energy? (E) What was the partial productivity ratio for finished units to energy?

2. Two types of cars (Deluxe and Limited) were produced by a car manufacturer in

2001. Quantities sold, price per unit and labor hours follow. What is the labor

productivity for each car? Explain the problem(s) associated with labor

productivity.

Quantity $ per unit

Deluxe Car 4,000 units sold $8,000 per car

Limited Car 6,000 units sold $9,500 per car

Labor Deluxe 20,000 hours $12 per hour

Labor Limited 30,000 hours $14 per hour

3. 10,000 units produced, sold for $10/unit, 500 labor hours, labor rate: $9/hr, cost of

raw material: $5,000, cost of purchased material: $25,000.

2

a. What is the labor productivity in units per hour and in unitless figure?

b. What will be the labor productivity if 12,000 units are produced using 500

labor hours (in units per hour and unitless figure)?

c. How much labor hour should we use in order to reach the productivity

level of part (b), if the product is 10,000 units.

d. What will be the multi-factor productivity (MFP), in unitless figure and in

terms of units/dollar, taking into account the labor and material costs?

e. Suppose we hire very efficient workers who can finish the job in 350

hours. What is now the MFP with labor rate of $9/hour?

f. However we have to pay higher wages for the more efficient workers.

How much extra can we pay without reducing productivity from the level

of part (d) in units/dollar?

Solution to Productivity Exercise Problems 1.

(A) What was the total factor productivity?

1,050,000/650,000 = 1.62

(B) What was the multi-factor productivity measure for total output to labor and

materials?

1,050,000/450,000 = 2.33

(C) What was the multi-factor productivity measure for finished output to labor

and materials?

1,000,000/450,000 = 2.22

(D) What was the partial productivity measure for total output to energy?

1,050,000/25,000 = 42

(E) What was the partial productivity ratio for finished units to energy?

1,000,000/25,000 = 40

3

2. Deluxe = (4,000 units*$8,000/car)/(20,000 labor hour*$12/hour) = 133.33 (unitless);

limited = (6,000 units *$9,500/car)/(30,000 labor hour*$14/hour) = 135.71 (unitless)

Deluxe = (4,000 units/car)/(20,000 labor hour) = 0.2 unit/hour;

limited = 6,000 units/30,000 labor hour = 0.2 unit/hour

Labor productivity in terms of units/hour does not take into account the quality of the

product (i.e., does not take into account the selling prices) and does not take into

account the skill level of the workers (i.e. does not take into account the labor rate).

Labor productivity in unitless terms might be difficult for department managers to

comprehend who has a better idea about what units/hour mean. Unitlesss is mostly

used by high-level managers while units/hour is used by departmental managers.

3. a. Labor productivity = 10,000 units/500 labor hour = 20 units/hour;

Labor productivity = (10,000 units*$10/unit)/(500 labor hour*$9/hour) = 22.22

(unitless)

b. Labor productivity = 12,000 units/500 labor hour = 24 units/hour;

Labor productivity = (12,000 units*$10/unit)/(500 labor hour*$9/hour) = 26.67

(unitless)

c. 24000,10=

Xunits units/hour 4177.416000,1024 ≈=⇒=⇒ XX hours

d. MFP = 10,000 units/$(500*9 + 5,000 + 25,000) = 0.29 units/dollar;

MFP = (10,000*$10/unit)/$(500*9 + 5,000 + 25,000) = 2.9

e. MFP = 10,000 units/$(350*9 + 5,000 + 25,000) = 0.3 units/dollar;

f. MFP = (10,000 unit)/$(350*X + 5,000 + 25,000) = 0.29

81.125.1018700000,10

)000,255000350(29.0000,1029.0)000,25000,5350(

000,10

=⇒=−⇒

++=⇒=++

XX

XX

At maximum, we can pay $12.81/hour.)