# Review On Productivity

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Quantitative Review I
Spring 2013
Vicky Gu

Key Concepts: 1. Productivity
2. Productivity Change
Ch.1, p.14
Productivity is the ratio of outputs (goods and services) divided by the inputs (resources, such as labor and capital)
Productivity (P) =

=

Productivity Change (Productivity index) is used to compare a process’ productivity at a given time (P2) to the same process’ productivity at an earlier time (P1)

P2  P1
Growth Rate 
P1

Example
– Last week a company produced 150 units using 200 hours of labor, and found to have 10 defective units
– This week, the same company produced 180 units with
3 defective units using 230 hours of labor

What is the change in productivity?

(150  10) units
P1 
0.70 units / hour
200 hours
(180  3) units
P2 
0.77 units / hour
230 hours
P2  P1 0.77  0.70
Growth Rate 

0.1
P1
0.70
A 10% increase in productivity

Productivity of last week
Productivity of this week

Productivity change

If inputs increase by 30% and outputs decrease by 15%, what is the percentage change in productivity?
P1= outputs/inputs = 1/1
P2 = (1- 0.15)/ (1+0.3) =0.654
Productivity change = (P2-P1)/ P1
= 0.654-1 = -0.3462
1

Key Concept: Multifactor Productivity
It measures productivity using ratio of outputs to several inputs such as labor, material, energy…… Ch 1. p.15
• Convert all inputs & outputs to \$ value
• Example:
– 200 units produced sell for \$12.00 each
– Materials cost \$6.50 per unit
– 40 hours of labor were required at \$10 an hour

Calculate the multifactor productivity

200 units \$12 / unit
\$2400

1.41
 200 units \$6.50 / unit    40 hours \$10 / hour  \$1700

Revenue Management Systems
(also called Yield Management)

Ch.2

•Airline booking
Overbooking –accepting more reservations than capacity available, assuming that a certain percentage of customers will not show up or will cancel prior to using the service

Example: A regional airline that operates a 50-seat jet prices the ticket for one popular business flight at \$250. If the airline overbooks the reservations, overbooked passengers receive a \$450 travel business flight voucher. The airline is considering overbooking by up to 2 seats, and the demand for the flight always exceeds the number of reservations it might accept. The probabilities of the number of passengers who show up is given for each booking scenario in the following table:
Number of passengers showing up Number of reservations 45

46

47

48

49

50
0.1

51

50

0.18 0.25 0.15 0.22

0.1

51

0.06 0.13 0.13

0.28 0.28 0.02

52

0.06 0.125 0.175 0.2

0.1

How many passengers should they book?

52

0.35 0.05 0.02 0.02

# of passengers actually showed up

# of seats booked

45

46

47

48

49

50
0.1

51

50

0.18 0.25 0.15 0.22

0.1

51

0.06 0.13 0.13

0.28 0.28 0.02

52

0.06 0.125 0.175 0.2

Reservations

0.1

52

0.35 0.05 0.02 0.02

Expected Profit

50

=250*(45*0.18+46*0.25+47*0.15+48*0.22+49*0.1+50*0.1)
=\$11777.5

51

=250*(45*0.06+46*0.13+47*0.13+48*0.1+49*0.28+50*0.28) -450*0.02
=\$11818.5

52

=250*(45*0.06+46*0.125+47*0.175+48*0.2+49*0.35+50*0.05)-450*(0.02+0.02)
=\$11463.2

They should book 51 passengers

•Hotel Management
-Hotel Management Effectiveness

Contribution to profit and overhead (\$)
= (PB - VC)*DB+(PC -VC)*DC
= (\$125 - \$25)*260 + (\$85- \$25)*400
= \$50000

Hotel Management

Effectiveness (%)

=

Actual hotel revenue
Maximum possible hotel revenue

(Actual prices for each room night)*(Actual number of room nights rented)
Maximum price for each room night)*(Maximum number of room nights available
125 * 260 +85* 400
150 *300+110* 700

=

=

54.5%

=

Key Concept: Forecasting
Forecasting is the art and science of predicting future events.
Quantitative forecasting involves taking historical data and project them
Into the future with mathematical models. Ch. 4. p.104

Important forecasting methods to project the demand
1)
2)
3)
4)
5)

Moving Average (Simple vs. Weighted)
Exponential