Practice Exam
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Georgia Institute Of Technology *
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Course
3103
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
7
Uploaded by quinwaldrop
ISyE 3103-A Practice Final Exam
Spring 2020
J. Vande Vate
April 20, 2020
Instructions
You have
2 hours and 50 minutes
to complete the exam. Watch your time. If you are having
difficulty with a question, you might wish to “peel the onion”: outline the main ideas and explain
what you would calculate (so I can award partial credit) or pass over it entirely (but there’s no
partial credit) and return to it later if you have time at the end of the exam.
•
Show your work and be sure to upload it in the places provided
•
Make sure your work is reasonably well organized and clearly explained so I can understand
your thinking well enough to award partial credic.
The exam is open-book, open-notes: you may use any notes or text material. You may use a
computer or calculator
The exam is to be done
individually, without collaboration
with anyone else.
You may
NOT
search the internet or communicate electronically with anyone else during the exam.
By
submitting your exam, you attest that you have not collaborated on this exam.
1
Question 1
Fairmount Bagels in Montreal starts the day with a large production run. Throughout the morning,
additional bagels are produced as needed. The last bake is completed at 3 PM and the store closes
at 8 PM. Production costs are approximately
$
0.40 per bagel. Fresh bagels sell for
$
1.40 each and
bagels not sold by the end of the day are sold the next day as “day old” bagels in bags of six for
$
0.99 a bag.
About 2/3
rds
of the day-old bagels are sold; the remainder are just thrown away.
The store manager estimates that demand for cinnamon raisin bagels from 3 PM until closing is
normally distributed with mean of 100 and standard deviation of 40.
a. How many cinnamon raisin bagels should the store have at 3 PM (after the last bake comes
out) to maximize the expected profit from sales between 3 PM until closing?
Answer:
Fairmount should target a stock of
cinnamon raisin bagels at 3PM
b.
Suppose that the store manager is concerned that stockouts might cause a loss of future
business. The store manager estimates that it is appropriate to assign a stockout cost of
$
5
per bagel that is demanded but not available. Given the additional stockout cost, how many
cinnamon raisin bagels should the store have at 3 PM (after the last bake)?
Answer:
With the
$
5 stockout fee, Fairmount should target a stock of
cin-
namon raisin bagels at 3PM
c. If the store manager incorporates the
$
5 stockout cost into her calculations and successfully
hits the target stocking level at 3 PM (after the last bake), how many cinnamon raisin bagels
should she expect to throw away each day?
Answer:
With the
$
5 stockout fee, Fairmount should expect to throw way
cinammon raisin bagels each day
2
d. Fairmount’s automated bagel process makes production lots of 100 bagels at a time. It has the
capability to make mixed lots consisting of bagels of different flavors, but only makes
exactly
100 bagels at a time, no more, no fewer. For simplicity, we will ignore the time required to
make a lot and focus on both the number of lots and their compositions to approximate the
target 3PM stock levels. The store manager estimates demand for each of the four flavors of
bagel (Cinnamon Raisin, Sesame Seed, Poppy Seed and Plain) from 3 PM until closing to be
Normally distributed with mean 80 and standard deviation 50. She has 100 of each flavor in
stock just prior to beginning the final run of the day – to complete at 3 PM (ignore the fact
that the run takes time to complete).
Given this information, how many lots should Fairmount produce and how many bagels of
each flavor should Fairmount make in its final production run of the day in order to maximize
expected profits, while considering the
$
5/bagel stockout cost? Note: All bagels enjoy the
same costs and selling prices and show no measurable differences in how they sell as “day old
bagels”.
Answer:
The manager should produce
lots in the last production run.
Answer:
Those lots should produce:
Cinnamon Raisin bagels,
Sesame bagels,
Poppy Seed bagels and
Plain bagels.
Answer:
Briefly explain your reasoning
3
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Question 2
(Refers to the story in Question 1) To improve her estimates of late afternoon demand, the Fair-
mount manager developed a forecasting process and kept track of the forecast, actual sales and
stock at the end of the day by flavor. Table 1 shows the results for cinnamon raisin bagels after
the first month. (For your convenience, you can download this table from
Exam Table.xls
)
Table 1: Forecast of sales and actual sales between 3PM and closing along with stock at the end
of the day for cinnamon raisin bagels during the the month of November.
End-of-Day
Date
Forecast
Sales
Stock
11/1/19
100
86
54
11/2/19
250
140
0
11/3/19
225
140
0
11/4/19
200
140
0
11/5/19
74
72
68
11/6/19
42
63
77
11/7/19
53
86
54
11/8/19
100
115
25
11/9/19
250
140
0
11/10/19
225
140
0
11/11/19
149
112
28
11/12/19
74
74
66
11/13/19
42
50
90
11/14/19
53
55
85
11/15/19
100
103
37
11/16/19
250
140
0
11/17/19
158
120
20
11/18/19
149
90
50
11/19/19
74
115
25
11/20/19
42
60
80
11/21/19
53
85
55
11/22/19
100
65
75
11/23/19
250
140
0
11/24/19
158
139
1
11/25/19
149
130
10
11/26/19
74
87
53
11/27/19
42
45
95
11/28/19
53
87
53
11/29/19
100
70
70
11/30/19
250
140
0
4
a. Based on this limited data, does the manager tend to over estimate demand or underestimate
demand for cinnamon raisin bagels after 3PM (Circle the appropriate answer)? By how much
does she typically over- or under-estimate actual demand? Briefly explain your assessment.
Answer:
The store manager
over-estimates
under-estimates
actual demand.
(Circle one)
Answer:
By
%
Answer:
Briefly explain your reasoning:
b. The store manager’s forecast for demand of cinnamon raisin bagels between 3PM and closing
on December 11, 2019 is 149. If the store manager incorporates the
$
5 stockout cost into her
calculations and assumes a Normal Distribution with mean and standard deviation derived
from past forecasting performance, how many cinnamon raisin bagels should she target to
have on hand after the 3PM production run (ignoring any issues associated with the lot size)?
Answer:
The ideal target stock is:
cinnamon raisin bagels
c. Given the store manager’s forecast of 149 cinnamon raisin bagels (and the associated Nor-
mal Distribution for demand) and assuming she hits her 3PM stocking target, what fill rate
should she expect to achieve for cinnamon raisin bagels that afternoon (i.e. between 3PM and
closing)?
Answer:
The store manager should expect a fill-rate of
% on cinnamon raisin
bagels for the day.
5
Question 3
A manufacturer orders parts from Asia.
Average daily demand is 200 units with a standard
deviation of 50 units.
Due to the carrier’s fixed shipment cost of
$
500 per shipment (no matter
the quantity in the order), the manufacturer currently orders from its supplier on a weekly basis.
The manufacturer is also concerned about the costs of inventory. It recognizes that its inventory is
lowest at the end of the week (or more generally at the end of the order period) but prefers a more
realistic estimate of its average inventory.
In particular, the manufacturer estimates its average
inventory to be its average inventory just before an order arrives plus half of its average order
quantity.
The holding cost the manufacturer incurs on that average inventory is
$
0.10 per unit
per week. The supplier ships immediately but the carrier reliably requires two weeks to deliver.
Assume 52 weeks per year, five days per week.
a. The manufacturer wishes to maintain a 99 % in-stock probability. If it does so, what is its
annual inventory holding cost?
Answer:
Annual Inventory holding cost of
$
b. What is the manufacturer’s annual shipping cost?
Answer:
Annual shipping cost of
$
c. Should the manufacturer consider ordering less frequently, say, every two weeks?
Briefly
explain your answer.
Answer:
The manufacturer
should
should not
order every two weeks instead
of weekly (Circle the appropriate choice).
Answer:
Briefly explain your answer.
6
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d. The manufacturer has found an alternative carrier that charges less per shipment
$
400, but
is also less reliable – with a standard deviation in transit time of 4 days. Should the manu-
facturer change to the new carrier if they order every other week? Briefly explain your answer.
Answer:
The manufacturer
should
should not
change to the new carrier (Cir-
cle the appropriate choice).
Answer:
Briefly explain your answer.
7