Supplement
I Learning Curve Analysis
PROBLEMS
Developing Learning Curves
1. Mass Balance Company
a. Time for the second unit
r=
Time for the first unit
48
=
60
= 0.8
b. b = log r log 2
= log ( 0.80 ) log 2
= −0.321928
k n = k1n b
−0.321928
k 40 = 60 ( 40 )
= 18.30 hr
c. Estimated total time for 40 units, from Table I.1, conversion factor = 0.42984.
40 units (0.42984 × 60 hr/unit) = 1031.616 hr.
d. Estimated total time for 30 units, from Table I.1, conversion factor = 0.46733.
30 units (0.46733 × 60 hr/unit) = 841.194 hr.
The last 10 units (#31 – #40) require (1031.616 – 841.194) = 190.422 hours.
I-1
Copyright © 2016 Pearson Education, Inc.
, I-2 l SUPPLEMENT I l Learning Curve Analysis
2. Cambridge Instruments
b = log r log 2
= log 0.93 log 2 = −0.1047
b
k n = k1 n
−0.1047
k5 = 85 ( 5 )
= 71.82 hr
−0.1047
k10 = 85 (10 )
= 66.79 hr
−0.1047
k15 = 85 (15 )
= 64.02 hr
−0.1047
k30 = 85 ( 30 )
= 59.53 hr
Using Learning Curves
3. A large grocery corporation
The first unit required 30 hours. k1 = 30 . We can use Table I.1 and straight-line
interpolation to get the cumulative average time factor for a 90 percent learning
curve. The following solution was developed with the use of a computer routine.
Units Cumulative Cumulative Total Total
Week Scheduled Production Total Hr Hr/Wk Employees/Wk
1 20 20 438 438 11
2 65 85 1,518 1,080 27
3 100 185 2,947 1,429 36
4 140 325 4,758 1,811 46
5 120 445 6,217 1,459 37
The production schedule is not feasible because the number of employees needed in
week 4 exceeds the maximum of 40 by 6 workers.
To obtain a feasible schedule, we can produce some of the requirements in week 4
earlier, say in week 2 or 3. Such a change may result in excess inventory cost if the
customer does not accept early shipment. Furthermore, the production schedule of
other products may be affected by this alternative.
One possible production schedule is:
Units Cumulative Cumulative Total Total
Week Scheduled Production Total Hr Hr/Wk Employees/Wk
1 20 20 438 438 11
2 85 105 1,817 1,381 35
3 100 205 3,216 1,399 35
4 120 325 4,758 1,542 39
5 120 445 6,261 1,503 38
By shifting 20 units from week 4 to week 2, we obtain a feasible schedule.
Copyright © 2016 Pearson Education, Inc.
I Learning Curve Analysis
PROBLEMS
Developing Learning Curves
1. Mass Balance Company
a. Time for the second unit
r=
Time for the first unit
48
=
60
= 0.8
b. b = log r log 2
= log ( 0.80 ) log 2
= −0.321928
k n = k1n b
−0.321928
k 40 = 60 ( 40 )
= 18.30 hr
c. Estimated total time for 40 units, from Table I.1, conversion factor = 0.42984.
40 units (0.42984 × 60 hr/unit) = 1031.616 hr.
d. Estimated total time for 30 units, from Table I.1, conversion factor = 0.46733.
30 units (0.46733 × 60 hr/unit) = 841.194 hr.
The last 10 units (#31 – #40) require (1031.616 – 841.194) = 190.422 hours.
I-1
Copyright © 2016 Pearson Education, Inc.
, I-2 l SUPPLEMENT I l Learning Curve Analysis
2. Cambridge Instruments
b = log r log 2
= log 0.93 log 2 = −0.1047
b
k n = k1 n
−0.1047
k5 = 85 ( 5 )
= 71.82 hr
−0.1047
k10 = 85 (10 )
= 66.79 hr
−0.1047
k15 = 85 (15 )
= 64.02 hr
−0.1047
k30 = 85 ( 30 )
= 59.53 hr
Using Learning Curves
3. A large grocery corporation
The first unit required 30 hours. k1 = 30 . We can use Table I.1 and straight-line
interpolation to get the cumulative average time factor for a 90 percent learning
curve. The following solution was developed with the use of a computer routine.
Units Cumulative Cumulative Total Total
Week Scheduled Production Total Hr Hr/Wk Employees/Wk
1 20 20 438 438 11
2 65 85 1,518 1,080 27
3 100 185 2,947 1,429 36
4 140 325 4,758 1,811 46
5 120 445 6,217 1,459 37
The production schedule is not feasible because the number of employees needed in
week 4 exceeds the maximum of 40 by 6 workers.
To obtain a feasible schedule, we can produce some of the requirements in week 4
earlier, say in week 2 or 3. Such a change may result in excess inventory cost if the
customer does not accept early shipment. Furthermore, the production schedule of
other products may be affected by this alternative.
One possible production schedule is:
Units Cumulative Cumulative Total Total
Week Scheduled Production Total Hr Hr/Wk Employees/Wk
1 20 20 438 438 11
2 85 105 1,817 1,381 35
3 100 205 3,216 1,399 35
4 120 325 4,758 1,542 39
5 120 445 6,261 1,503 38
By shifting 20 units from week 4 to week 2, we obtain a feasible schedule.
Copyright © 2016 Pearson Education, Inc.
