Name:______ID:______
Operations Management II 73-431 Fall 2002
Odette School of Business
University of Windsor
Final Exam Solution
Saturday, December 7, 3:30 – 6:30 pm OB B02
Instructor: Mohammed Fazle Baki
Aids Permitted: Calculator, straightedge, and 3 one-sided formula sheet.
Time available: 3 hours
Instructions:
· This exam has 28 pages including this cover page, 2 blank pages and 6 pages of table
· Please be sure to put your name and student ID number on each odd numbered page
· It is not necessary to return the tables
· Show your work
Marking Scheme:
Question / Score / Question / Score1 / /15 / 2 / /6
3 / /4 / 4 / /8
5 / /8 / 6 / /14
7 / /4 / 8 / /10
9 / /11 / 10 / /2
11 / /5 / 12 / /4
13 / /5 / 14 / /4
Total / /100
Question 1: (15 points) Circle Best Answer
1.1 The following is a characteristic of the process layout
a. standard products
b. high volume of production
c. wide aisles
d. special purpose equipment
e. stable demand
f. limited skills of workers
1.2 Flexible manufacturing systems include
a. automated machining operations
b. automated material handling
c. automated tool changers
d. computerized controlled system
e. all of the above
f. none of the above
1.3 Following is a disadvantage of cellular layouts
a. increased setup time
b. increased material handling and transit time
c. increased work-in process inventory
d. increased capital investment
e. difficult to automate
f. difficult to control
1.4 A suitable goal for the following facility location problem is to minimize maximum Euclidean distance
a. facilities used by many people e.g., computer center
b. transmission towers e.g., radio towers
c. emergency facilities e.g., fire station
d. utilities e.g., phone cable
e. all of the above
f. none of the above
1.5 Choose the best of the following
a. ALDEP is a layout improvement procedure
b. ALDEP is a layout construction procedure
c. CRAFT is a layout improvement procedure
d. CRAFT is a layout construction procedure
e. a and d
f. b and c
1.6 According to CRAFT, a pairwise interchange is feasible if two departments are
a. adjacent
b. not adjacent
c. of equal size
d. of unequal size
e. a or c
f. b or d
1.7 Minimization of which of the following measure is the gravity problem?
a. weighted sum of the squares of the Euclidean distances
b. weighted sum of the squares of the rectilinear distances
c. weighted sum of the Euclidean distances
d. weighted sum of the rectilinear distances
e. maximum Euclidean distances
f. maximum rectilinear distances
1.8 What is ?
a. 0.4821
b. 0.9821
c. 0.0179
d. 0.5179
e. 0.50
f. 1.00
1.9 What is ?
a. 0.3643
b. 0.8643
c. 0.1357
d. 0.6357
e. 0.50
f. 1.00
1.10 Choose the best of the following
a. Type I error occurs when the process mean shifts, but the sample mean lies inside the control limits
b. Type I error occurs when the process mean does not shift, but the sample mean lies outside the control limits
c. Type II error occurs when the process mean shifts, but the sample mean lies inside the control limits
d. Type II error occurs when the process mean does not shift, but the sample mean lies outside the control limits
e. a and d
f. b and c
1.11 If wider control limits are chosen
a. Type I error increases
b. Type II error decreases
c. sampling cost increases
d. searching cost decreases
e. cost of operating in out-of-control condition decreases
f. all of the above
1.12 If a lot is rejected
a. the entire lot is inspected one by one
b. all the defective items in the lot are fixed and sold at a reduced price
c. no transaction takes place
d. only good items in the lot are purchased
e. the supplier is sued
f. the items are purchased from a different supplier
1.13 Reliability increases if the components are in
a. series and the number of components increase
b. series and the number of components decrease
c. parallel and the number of components increase
d. parallel and the number of components decrease
e. a and d
f. b and c
1.14 Which of the following is not a part of the cost of operating out of control?
a. Scrap cost
b. Cost of fixing the system problem
c. Cost of warranty claims
d. Cost of liability suits
e. Overall customer dissatisfaction
f. All of the above is a part of the of the cost of operating out of control
1.15 Failure rate
a. increases in the beginning
b. is constant in the end
c. decreases in the normal operating period
d. is the inverse of the average life
e. all of the above
f. none of the above
Question 2: (6 points)
An amplifier has a constant failure rate of 5% per 1,000 hour.
a. (2 points) What is the probability that the amplifier will survive 4,000 hours?
b. (2 points) What is the average life in hour?
in 000 hours = 20,000 hours
c. (2 points) What failure rate is required to have a probability of survival of 90% at 4,000 hour?
Question 3: (4 points)
Two components A and B are used to make a subassembly in a circuit board. The reliabilities of A and B are 0.80 and 0.90 respectively.
a. (2 points) Find the reliability of the subassembly, if the components are in parallel.
b. (2 points) Find the reliability of the subassembly, if the components are in series.
Question 4: (8 points)
The next-door neighbours are currently installing a new cistern that will provide water for their household. The different components for the system and their reliability are described in the diagram below. Determine the reliability of the system.
Consider the following subsystems:
Question 5: (8 points)
In one of the acceptance sampling plans, 20 items were to be tested for 150 hours with replacement and with an acceptance number of 3. Plot an Operating Characteristic curve showing probability of acceptance as function of average life. Consider average life, q = 500, 750, 1000, 1500, and 3000 hours. For each average life compute and plot the probability of acceptance.
500 / 0.00200 / 3000(0.00200)
=6 /
750 / 0.00133 / 3000
(0.00133)
=4 /
1000 / 0.00100 / 3000
(0.00100)
=3 /
1500 / 0.00067 / 3000
(0.00067)
=2 /
3000 / 0.00033 / 3000
(0.00033)
=1 /
Question 6: (14 points)
A film processing service monitors the quality of the developing process with light-sensitive equipment. The accuracy measure is a number with a target value of zero. Suppose that a chart with subgroup of size four is used to monitor the process and the control limits are UCL = 0.675 and LCL = -0.675. Assume that the process mean is zero and the process standard deviation is 0.60.
a. (2 points) What is the Type I error probability, a for this control chart?
b. (2 points) Suppose that the process mean shifts to 0.525. What is the Type II error probability, b?
c. (2 points) What is the probability that the shift is detected on the first subgroup after the shift occurs? What is the probability that the shift is detected on the first two subgroups after the shift occurs?
d. (2 points) Suppose that there is a probability of 0.04 that the process shifts from an in-control state to an out-of-control state in any period. What is the expected number of periods per cycle that the process remains in control? Assuming each search costs $20, compute the expected searching cost per cycle.
e. (2 points) Assume that when the process shifts out of control, the process mean shifts to ±0.525. What is the expected number of periods per cycle that the process remains in an out-of-control state until a detection is made? If the cost of operating in an out-of-control state is $200 per period, what is the expected cost of operating in out-of-control state per cycle?
Cost of operating in out-of-control state per cycle =
f. (2 points) What is the expected number of periods per cycle? If the cost of sampling is $5 per unit, what is expected cost of sampling per cycle? What is the expected total cost of sampling, searching, and operating in out-of-control state per period?
g. (2 points) Find the UCL and LCL based on three-sigma control limits.
Question 7: (4 points)
An chart is used to monitor the variation in the weights of packages of chocolate chip cookies produced by a large national producer of baked goods. An analyst has collected a baseline of 150 observations to construct the chart. Suppose the computed value of is 4.2.
a. (2 point) If subgroups of size five are to be used, compute the value of three-sigma limits for the chart.
b. (2 points) If an chart based on three-sigma limits is used, what is the difference between UCL and the LCL? (You can compute without knowing )
Question 8: (10 points)
Consider a single sampling plan with , , AQL=0.05, and LTPD=0.2.
a. (2 points) Compute producer’s risk . Use Poisson probability table.
Producer’s risk =
=
= = 0.0190
(Table A-3 gives Poisson cumulative probabilities for or more defectives. The value 0.0190 is obtained from )
b. (3 points) Compute consumer’s risk . Use Normal probability table.
Consumer’s risk =
=
=
= (continuity correction)
» 0.50 - 0.1103 (From Table A-1) = 0.3897
c. (4 points) Compute the probability of acceptance, at proportion of defective, . Use Binomial probability formula.
=
= + + +
=+++
=++ +
=+++
=+++
=0.000798+0.0006839+0.027845873+0.0715942
= 0.1070697
d. (1 point) Use the result of part c. Compute AOQ at if the lot size, is 600.
Question 9: (11 points)
Consider the activity relationship chart shown on the right.
a. (1 point) According to ALDEP, what is the order of placement that starts with department C?
C-A-B
Suppose that departments A, B and C consume respectively 8, 6 and 10 squares. Based on a sweep width of 2 and a facility layout size of 6 (horizontal) by 4 (vertical), use the technique employed by ALDEP to find a layout.
b. (2 points) Show the layout obtained by ALDEP when the departments are placed in the order obtained in Part a. Compute the layout evaluation score.
Adjacent departments / Rel Chart Score / Numeric ScoreC-A / E / 16
A-B / A / 64
B-C / I / 4
Total / 84
c. (2 points) Show the layout obtained by ALDEP when the departments are placed in the order B, A, C. Compute the layout evaluation score.
Adjacent departments / Rel Chart Score / Numeric ScoreB-A / A / 64
A-C / E / 16
C-B / I / 4
Total / 84
d. (1 point) According to ALDEP, which of the two layouts obtained in parts b and c is better?
The layout evaluation score is 84 for both layouts. Hence, both layouts are equally good.
Consider the better layout obtained part d. Suppose that the facility is 12 feet horizontal and 8 feet vertical. So, every square represents an area of 2 feet by 2 feet.
e. (1 point) Compute the centroid of Department B.
Both layouts are equally good.
The solution considers the layout obtained in part c.
The centroid of department B is (2,5).
f. (2 points) Compute the centroid of Department A.
A1 à Area = 4(2) = 8, centroid = (2,1)
A2 à Area = 6(4) = 24, centroid = (6,3)
,
g. (1 point) What is the rectilinear distance between A and B?
Rectilinear distance =
h. (1 point) According to CRAFT, what are the feasible interchanges?
· A-B
· B-C
· C-A
Question 10: (2 points)
Activities of a project and their immediate predecessors are shown below:
Activity / Time (Weeks) / Immediate PredecessorsA / 7 / ---
B / 4 / ---
C / 5 / A
D / 3 / A, B
E / 6 / A, B
Construct a network for the project. Use activity on arc methods.
Question 11: (5 points)
Following network shows PERT time estimates (a,m,b) in weeks:
a. (3 points) Determine a critical path based on most likely times. What is the mean and standard deviation of the length of the critical path?
There are only a few paths from start node 1 to end node 7:
A-C-E-G: length = 5+7+8+4 = 24 weeks
A-B-E-G: length = 5+13+8+4 = 30 weeks
A-B-D-G: length = 5+13+11+4 = 33 weeks (longest, so critical)
A-B-F-H: length = 5+13+6+6 = 30 weeks
Activity / /A / /
B / /
D / /
G / /
Total / 33.677 / 4.39
b. (2 points) Assuming that the critical path is the one identified in a, find the probability that the project will be completed in 36 days.
Question 12: (4 points)
Three trucks, 1, 2 and 3 will be unloaded at a loading dock at XYZ Company that has only a single service bay. The trucks are labelled in the order that they are scheduled to arrive at the dock. Assume that the current time is 2:00 pm. The times required to unload each truck and the times that the goods they contain are due in the plant are given in the table below: