Problem Questions
1. Thermostats are subjected to rigorous testing before they are shipped to air
conditioning technicians around the world. Results from the last five samples
are shown in the table. Draw and R Chart and an x-bar chart. Based on the
charts, is the process under control? (20 Points)
Sample
1
2
3
4
5
1
73.5
71.3
70.0
71.1
70.8
Observations
2
3
4
70.8
72.2
73.6
71.0
73.1
72.7
72.6
71.9
72.4
70.6
70.3
74.2
70.7
70.7
73.5
5
71.0
72.2
73.3
73.6
71.1
Answer 1:
2. A professor records the number of students who complain each week throughout
the semester. If the class size is forty students, what are 3-sigma control limits for
this class? Construct a control p-chart and interpret the data. Is the process in
control? (20 points)
Week
number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Complaints
5
2
7
1
3
2
8
1
3
5
4
6
3
1
4
Answer 2:
3. A department store chain is designing a layout for a new store. The store
manager wants to provide as much convenience as possible for her
customers. Based on historical data, the number of trips between
departments per hour is given in the following closeness matrix. A block plan
showing a preliminary layout is also shown.
Closeness Factors (Trips per hour)
1/O 2/S
3/H 4/T
5/A
6/E
1. Office Supplies (O)
2. Sporting Goods (S)
3. Hardware (H)
4. Toys (T)
5. Automotive (A)
6. Electronics (E)
1. OFFICE
SUPPLIES
4. TOYS
---
40
---
2. SPORTING
GOODS
5. AUTOMOTIVE
100
100
---
50
80
70
---
20
60
100
70
---
10
80
50
90
60
---
3. HARDWARE
6. ELECTRO
NICS
Customer travel between departments is restricted to the aisles shown in the
block plan as dotted lines.
CALCULATIONS TABLE:
Dept. Pair Closeness
Factor (w)
Original
Distance
(dO)
w × dO
Revision #1
Distance
(d1)
w × d1
12
13
14
15
16
23
24
25
26
34
35
36
45
46
56
TOTAL
Complete the calculations and fill in the table above. Based on the table above
answer the following questions.
a) What is the total expected weighted-distance score between Office Supplies
and Hardware? (4 points)
b) What is the total weighted-distance score between Hardware and Toys? (4
points)
c) What is the total weighted-distance score for the entire store? (4 points)
d) A suggestion has been made to switch Hardware and Automotive. What
would the total weighted-distance score for the entire store if these two
departments were switched? (4 points)
e)
Based on your calculations, would you recommend that Hardware and
Automotive be switched? (4 points)
Answer 3:
4. Balance the assembly line for the tasks contained in the table. The desired
output is 240 units per day. Available production time per day is 480 minutes.
Work
Element
A
B
C
D
E
F
G
Time
(Sec.)
40
45
55
55
65
40
25
Immediate
Predecessor(s)
----A
B
B
C,D
D,E
a) What is the desired Cycle time in seconds? (4 points)
b) What is the theoretical minimum number of stations? (4 points)
c) Use trial and error to work out a solution in the table below. Your efficiency
should be at least 90%. (10 Points)
Station
Candidates
Choice
WorkElement
Time (Sec)
d) Calculate the efficiency of your solution. (2 points)
Answer 4:
Cumulative
Time (Sec)
Idle Time
5. A manufacturers research and development center must expand by building
a new facility. The search has been narrowed to five locations, all of which are
acceptable to management. The assessment of these sites is being made on
the basis of the five subjective location factors that follow. Management has
agreed to use a five-point scale (Excellent = 5, and Poor = 1) to quantify and
compare their subjective opinions about the relative goodness of the sites.
The weight reflects the importance of each factor in the decision.
Factor
Labor climate
Proximity to markets
Quality of life
Proximity to suppliers
Taxes
Locations
Weight
0.30
0.30
0.15
0.15
0.10
A
4
5
1
2
4
B
2
3
3
5
4
C
1
3
2
3
4
D
4
4
1
4
1
E
2
4
5
3
3
Calculate the weighted score for each alternative. Which location would
you recommend? (15 points)
Answer 5:
6. Complete the following MPS Record (15 points)
Lot
130
Size
Lea 1
d
Tim
e
Qua 45
ntity
on
1
Han
d
Forecast
Customer Orders
(booked)
Projected On-Hand
Inventory
MPS Quantity
MPS start
2
3
4
5
6
25
25
25
25
30
20
5
8
50
7
50
2
8
50
9
50
10
40
20
Available to Promise
Inventory
Answer 6:
7. Use the bill of materials and inventory records to determine the quantity of
purchased items necessary to assemble 20 end items if the manufacturer
uses lot-for-lot ordering. There are no end items currently on hand, and none
of the components have any scheduled receipts. (20 points)
Component On-hand
A
5
B
75
C
10
Answer 7:
Component On-hand
D
15
E
3
F
20
8. Use the table below to answer the following questions.
a) Use the information in the Table above, what is the throughput time for the
process, assuming that the Call Center is always busy and has customers
waiting to be processed? (5 points)
b) Use the information in Table above, what is the process bottleneck? (5 points)
c) Use the information in Table above, what is the 8-hour capacity for the
process? (5 points)
d) Use the information in Table above, where would you expect customer wait
times to occur? (5 points)
Answer 8:
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