This document contains practice problems related to productivity measurement. It provides the calculations to measure total factor productivity, multi-factor productivity, partial productivity, and labor productivity. It examines these measures for a clay pigeon corporation and car manufacturer. It also calculates labor productivity, multi-factor productivity, and the maximum labor rate that does not reduce productivity, given information on production units, labor hours, material costs, and selling prices.

1. 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. 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. 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*$9/hour) = 26.67
(unitless)
c. 24
000,10
=
X
units
units/hour 4177.416000,1024 ≈=⇒=⇒ XX hours
d. MFP = 10,000 units/$(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
X
X
At maximum, we can pay $12.81/hour.)