Problem Set 6
9.13, 9.17, 10.29, E.3, E.5, and E.6
9.13 Sue Helms Appliances wants to establish an assembly line to manufacture its new product, the Micro Popcorn Popper. The goal is to produce five poppers per hour. The tasks,task times, and immediate predecessors for producing one Micro Popcorn Popper are as follows:
Task “Time
(min)” “Immediate
Predecessors”
A 10 –
B 12 A
C 8 A,B
D 6 B,C
E 6 C
F 6 D,E
a) What is the theoretical minimum for the smallest number of workstations that Helms can achieve in this assembly line? b) Graph the assembly line and assign workers to workstations. Can you assign them with the theoretical minimum?
c) What is the efficiency of your assignment?
9.17 The Mach 10 is a one-person sailboat manufactured by Creative Leisure. The final assembly plant is in Cupertino, California. The assembly area is available for production of the Mach 10 for 200 minutes per day. (The rest of the time it is busy making other products.) The daily demand is 60 boats. Given the information in the table on the next page,
Task Time (min) Predecessors
A 3 –
B 6 –
C 7 A
D 5 A,B
E 2 B
F 4 C
G 5 F
H 7 D,E
I 1 H
J 6 E
K 4 G,I,J
50
a) Draw the precedence diagram.
b) If the daily (24-hour) production rate is 96 units, what is the highest allowable cycle time?
c) If the cycle time after allowances is given as 10 minutes, what is the daily (24-hour) production rate?
d) With a 10-minute cycle time, what is the theoretical minimum number of stations with which the line can be balanced?
e) With a 10-minute cycle time and six workstations, what is the efficiency?
f) What is the total idle time per cycle with a 10-minute cycle time and six workstations?
g) What is the best work station assignment you can make without exceeding a 10-minute cycle time and what is its efficiency?
10.29 The Dubuque Cement Company packs 80-pound bags of concrete mix. Time-study data for the filling activity are shown in the following table. Because of the high physical demands of the job, the company’s policy is a 23% allowance for workers.
Element Observations (Seconds) “Performance
Rating (%)”
1 2 3 4 5
Grasp and place bag 8 9 8 11 7 110
Fill bag 36 41 39 35 122a 85
Seal bag 15 17 13 20 18 105
Place bag on conveyor 8 6 9 30b 35b 90
a) Compute the standard time for the bag-packing task.
b) How many observations are necessary for 99% confidence, within ± 5% accuracy?
E3 If Professor Laurie Macdonald takes 15 minutes to grade the first exam and follows an 80% learning curve, how long will it take her: a) to grade the 25th exam?
b) to grade the first 10 exams?
E5 Beth Zion Hospital has received initial certification from the state of California to become a center for liver transplants. The hospital, however, must complete its first 18 transplants under great scrutiny and at no cost to the patients. The very first transplant, just completed, required 30 hours. On the basis of research at the hospital, Beth Zion estimates that it will have an 80% learning curve. Estimate the time it will take to complete:
a) the 5th liver transplant.
b) all of the first 5 transplants.
c) the 18th transplant.
d) all 18 transplants
E6 Refer to Problem E.5. Beth Zion Hospital has just been informed that only the first 10 transplants must be performed at the hospital’s expense. The cost per hour of surgery is estimated to be $5,000. Again, the learning rate is 80% and the first surgery took 30 hours. a) How long will the 10th surgery take?
b) How much will the 10th surgery cost?
c) How much will all 10 cost the hospital?
