OPRE 6302 on 20 March 2008 - The University of Texas at Dallas

I understand that
<strong>OPRE</strong> <strong>6302</strong> on 20 March 2008
- This is a closed books/notes exam but I can use a calculator.
- A cheat sheet including complex formulas is provided so I will NOT bring my own.
- I will choose the most appropriate answer for the questions. I will NOT get any credit by marking
multiple choices for a single question. When changing my answers, I will erase the paper properly.
- I will NOT forget to define any variables I introduce.
- I will NOT use laptops, cellular phones, any cellular communication device, and I will turn off all
these devices before starting my exam.
- My conduct during the exam will reside entirely within the limits of the UTD regulations governing
scholastic honesty -detailed in the handbook of operating procedures Title V Chapter 49.
NAME (please print):
——————————————————————
Question Out of Points
0 30 30
1 20
2 30
3 20
Total 100
Q1. Put T before a statement if you think that statement is true. Otherwise put X.
1. ( ) The first come first served rule minimizes the average wait time for customers. X April Shepherd
2. ( ) Little’s Law fails when the last come first served rule is used. X Aubrey Stewart
3. ( ) In order to prevent starvation, we should reduce buffer sizes. X Jing Xian Xi
4. ( ) If the requested cycle time (RCT) is less than designed cycle time (DCT) then it is worth to balance
the production line to increase the capacity. T Moumita
5. ( ) A firm benefits from increasing the inventory turnover rate. T
6. ( ) Appointment systems are used to control the service times in queues. X
7. ( ) In a serial processing system with infinite amount of buffer space, no process starves. X
8. ( ) Erlang’s thruput loss formula gives losses due to impatient customers departing from the queue after
waiting in the queue for a while. X
9. ( ) By increasing the batch size on a non-bottleneck work center, we can increase the capacity of a system
including several work centers working in tandem (sequentially). X
10. ( ) A classroom lecture is an example of repetitive process. X

Q2: Choose the most appropriate answer and mark your answer on this paper.
1. If our production schedule was set to be a chase strategy with the weekly demand of Week 1: 5000; Week
2: 3000; Week 3: 6000; Week 4: 4000. The regular capacity is 4000 per week. What is the regular time
production schedule per week in weeks 1 to 4?
(a) 5000, 3000, 6000, 4000
(b) 4000, 3000, 4000, 4000
(c) 3000, 3000, 3000, 3000
(d) 4000, 4000, 4000, 4000
(e) None of the above
B Steven Yee
2. A process that is high volume, extremely standardized, very low cost, but not very flexible is an example of:
(a) Job Shop
(b) Continuous Processing
(c) Batch Processing
(d) Assembly Line
(e) Project
B Ashley Heis
3. In most cases, the fastest way to increase capacity to meet a short-term requirement is to:
(a) hire additional workers
(b) subcontract work
(c) acquire more equipment
(d) use overtime
(e) outsource
D Yao-Don Hung
4. Gary opened an office accessory store to supply cartridges of copy machines to UTD SOM which uses 8
cartridges a month. Gary charges $50 for a cartridge and $100 for a delivery. A SOM professor figured out
that the holding cost of a cartridge is $8 per year. How many times in a year does SOM order cartridges
from Gary?
(a) less than once
(b) once or more but less than twice
(c) twice or more but less than thrice
(d) thrice or more but less than four times
(e) four times or more
B, EOQ=48.9, Demand/EOQ=96/48.9, between 1 and 2, Gary Li
5. Mattel just received an unexpected high-priority order for 150 Cabbage Patch dolls that must be shipped
out as soon as possible. At this point there are no dolls in the assembly line. There are six different stations
that the dolls move through to be produced. Activity 1 takes 3 minutes, Activity 2 = 5 minutes, Activity 3
= 2 minutes, Activity 4 = 3 minutes, Activity 5 = 5 minutes, Activity 6 = 4 minutes. How long will it take
for Mattel to have the order ready for shipping?

(a) 12 hours 47 minutes
(b) 15 hours
(c) Less than 10 hours
(d) 55 hours
(e) Between 45 and 50 hours
A, 22+5*149=767 mins, Larissa
6. All hand-carry bags have to be X-rayed at airports. X-ray machines have conveyer belts transferring bags
to and through the X-ray machine. The portion of the belt outside the machine usually holds 4 bags at a
given time and it takes 12 seconds for a bag to reach the machine. Then an X-ray inspector looks at the
X-ray picture of the bag while it is on the belt but inside the X-Ray machine. Checking the picture takes
3 seconds per bag. Which of the following is the capacity in bags/minute of the entire X-raying operation
including bag transfers?
(a) 10
(b) 15
(c) 20
(d) 25
(e) None of the above
A, 10 per minute, six seconds for each bag. 3 sec in the machine. 3 seconds to the machine. Yi-Fan
7. Computers R Us has COGS of $18 B per year and keeps $450 M of inventory, what is the flowtime of an
average item in days (A month has 30 days, a year has 12 months)?
(a) 10
(b) 15
(c) 20
(d) 25
(e) None of the above
E 0.45/180=1/40 year=12/40 months=3/10 months=9 days. Liz Reeves
8. Which of the following is not a reason why companies plan to hold inventory?
(a) Due to pipeline inventory
(b) Unstable demand and supply
(c) Economies of scale
(d) To have buffers so disruption of an activity does not stop the whole process
(e) To accommodate the excess supply which exceeds the demand
E June Lee
9. In an assembly operation at a furniture factory, five workers assemble an average of 350 standard dining
chairs per 7-day week. What is the labor productivity of this operation?
(a) 50 chairs/(worker x week)
(b) 70 chairs/week
(c) 10 chairs/(worker x week)
(d) 50 chairs/day
(e) 70 chairs/(worker x day)

D
10. An instructor needs to prepare 20 multiple choice questions for a test in 2 hours, what is the requested cycle
time for this process?
(a) 20/120 questions per minute
(b) 10/60 questions per minute
(c) 20 questions per 120 minute
(d) 6 minutes
D
(e) 120 minutes

Use the following information to answer (11-14). PlaSkate is a skateboard manufacturer that supplies skateboard
decks to specialty skateboard stores. With skateboarding the fastest growing sport among children
aged 10-18, the company is experiencing demand that greatly exceeds capacity for these specialty boards.
The boards (=decks), are purchased from an outside supplier. PlaSkate first sands the decks (to make the
surface smoother) and second paints the decks using a painting machine. The decks are then loaded onto a
pallet and dried quickly using an ultraviolet lamp. The pallet is not placed under the lamp until all decks
in a batch have been painted. The lamp can dry up to 50 decks at one time. The company has 5 patterns
that are painted on the decks. The painting machine requires a set up, so decks are processed in batches
according to the pattern.
The activity times per deck are as follows. Sanding 3 minutes/deck. Painting: 15 minutes to set-up for a
batch and 2 minutes/deck. Drying: 30 minutes regardless of batch size. Suppose that sanding, painting,
and drying each have one operator.
11. What is the process capacity in decks per hour with a batch size of 50 decks (round to the nearest integer)?
(a) 10 decks/hour
(b) 16 decks/hour
(c) 20 decks/hour
(d) 26 decks/hour
(e) 50 decks/hour
(f) None of the above
C, In 60 mins: 20 at deck; (50/115) ∗ 60 ≈ 26 at painting; 100 at drying
12. What is the utilization in the drying area if the batch size is 50 decks?
(a) 10%
(b) 20%
(c) 50%
(d) 60%
(e) 80%
(f) None of the above
B, system does 20 per hour; drying does 100 per hour
13. What is the smallest batch size that can be used to minimize the inventory in the system without sacrificing
flow rate?
(a) 4 decks
(b) 7 decks
(c) 10 decks
(d) 15 decks
(e) 25 decks
(f) None of the above
D, solve for B from 15+2B=3B
14. PlaSkate is offered the opportunity to purchase another dryer. What should the company do?
(a) Purchase the new dryer because the flow rate will decrease.
(b) Purchase the new dryer because flow time will decrease.
(c) Purchase the new dryer because then the batch size can be doubled.
(d) Do not purchase the new dryer because additional capacity is not needed at the drying area.
(e) A cost-benefit analysis must be conducted to determine the financial benefit of a second dryer.
D, drying is not the bottleneck operation

15. In a single server queue, both the activity and interarrival times are exponentially distributed. The average
activity time is 4 minutes and the expected waiting time in the queue is 12 minutes, what is the utilization
of the server?
(a) Utilization cannot be found without CVa and CVp
(b) Utilization cannot be found without the expected interarrival time
(c) 50%
(d) 66%
(e) 75%
E u/(1 − u) = Tq/p = 3

Q3. RichChick is an east-Richardson company that produces two types of Chicken cutlets for sale to supermarkets.
Cutlets are called Silverlet and Brownlet. Each cutlet consists of white meat and dark meat. Silverlet sells for
$12/kg and must consist of at least 80% white meat. Brownlet sells for $10/kg and must consist of at least 40%
white meat. At most 300 kg of Silverlet and 500 kg of Brownlet can be sold in the next month. Three types of
chicken are used to manufacture the cutlets: Farm-grown chicken, Free Range chicken and Organic-fed chicken.
Each chicken’s cost, and its dark and white meat yield are below:
Chicken type Farm-grown Free-Range Organic-fed
Cost in $ 6 7 8
White meat yield in kg 1 2 2
Dark meat yield in kg 2 1 1
[4pts] a) To formulate a LP to maximize RichChick’s profit in the next month, define decision variables.
ANSWER: F, R, O: Number of Farm-grown, free-Range, Organic-fed chicken purchased. DS, DB: Kilograms of
Dark meat used in Silverlet, Brownlet. WS, WB: Kilograms of White meat used in Silverlet, Brownlet.
[4pts] b) Profit is revenue minus costs, express RichChick’s profit in terms of decision variables.
ANSWER: Max 12(WS + DS) + 10(WB + DB) − 6F − 7R − 8O
[4pts] c) Write constraints so that RichChick does not attempt to sell more cutlets than next month’s demand.
ANSWER: WS + DS ≤ 300 and WB + DB ≤ 500
[4pts] d) Write constraints so that RichChick does not attempt to use more white or dark meat than it buys in
the form of Farm-grown chicken, Free Range chicken and Organic-fed chicken.
ANSWER: WS + WB ≤ F + 2R + 2O and DS + DB ≤ 2F + R + O
[4pts] e) Finish your formulation by adding any constraints you find necessary.
ANSWER: Silverlet must have at leat 80% white meat:
Brownlet must have at least 40% white meat:
WS
WS + DS
WB
WB + DB
Nonnegativity constraints: F, R, O, WS, DS, WB, DB ≥ 0
≥ 0.8.
≥ 0.6.

Q3. UT Drill is a drill bit producer established by some UTD MBA students. UT Drill buys 5 cm long blank drill
bits and shapes them with drill patterns (like twist, masonry, lip, spur) by using a lathe. Then UT Drill packages
12 different drills in to a single box and sells them to the Lowe’s Home Improvement stores in Texas. UT Drill
requires 3000 blank drill bits every month and buys each bit at $0.05 and each box at $0.60. It costs $12 UTD
Drill to initiate an order from any of its suppliers. The holding costs are based on an annual interest rate of 12%.
[8pts] a) Determine the optimal number of drill bits that UT Drill should purchase and the time between these
purchases.
ANSWER: R= 3000/month. P = ∞. K=1200 cents. h = 5(0.01) = 0.05 cents. Then
2KR
EOQ =
h
=
2 · 1200 · 3000
=
0.05
√ 2 · 1200 · 3000 · 20 = √ 2 · 12 · 3 · 2 ∗ 1000 = 12, 000.
Time between orders is
Length of an Inventory Cycle = Q/R = 12000/3000 = 4 months.
[4pts] b) What is the annual holding and ordering cost for blank drill bits?
ANSWER:
Total monthly cost = C(Q = EOQ; P = ∞) =
1
EOQ h
2
+
KR
EOQ
Inventory holding cost per month Set up cost per month
= 1
1200 · 3000
12000 · 0.05 +
2 12000
= 300 + 300 = 600 cents,
or since optimal order is used, Total monthly cost= √ 2KRh = √ 2 · 1200 · 3000 · 0.05 = √ 1200 · 300 = √ 36 · 100 =
600. Then the annual cost is $72= 6 · 12.
[4pts] c) Determine the optimal number of package boxes that UT Drill should purchase.
ANSWER: R= 3000/12 per month. P = ∞. K=1200 cents. h = 60(0.01) = 12 · 0.05 cents. Then
EOQ =
2KR
h
=
2 · 1200 · 3000/12
12 · 0.05
= 1 √
2 · 1200 · 3000 · 20 =
12
1 √
2 · 12 · 3 · 2 ∗ 1000 = 1, 000.
12
[4pts] d) The forecaster at UT Drill has made a mistake in computing the monthly blank drill bit demand which
is actually 5000 per month. What is the annual holding and ordering cost for blank drill bits when the purchase
quantity in a) is used with the correct demand of 5000 per month? Basically, update your computations in b).
ANSWER:
Total monthly cost = C(Q = EOQ; P = ∞) =
1
EOQ h
2
+
KR
EOQ
Inventory holding cost per month Set up cost per month
= 1
1200 · 5000
12000 · 0.05 +
2 12000
= 300 + 500 = 800 cents.
Then the annual cost is $96= 8 · 12. Note that here we are computing the cost of ordering suboptimally in 12000
units. The formula √ 2KRh cannot be used when the order quantity is suboptimal.