F23_Final Exam Prep
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School
University of Texas, Dallas *
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Course
3310
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
6
Uploaded by abdulatoum
OPRE 3310 Practice Problems for Test 2
Q1. Project Management
(a)
For the network shown below, determine the critical path and the early completion time for the
project. (All durations shown are in weeks).
A
(5)
B
(10)
F
(4)
E
(7)
D
(6)
G
(4)
C
(8)
(b)
For the project in Q1(a), we need to reduce the project completion time by 3 weeks. Using the
data given below and assuming a linear cost of crashing, determine, step by step, how you
would achieve the reduction.
Activity
Normal Duration
Normal Cost
Crash Time
Crash Cost
A
5
$ 7,000
3
$ 13,000
B
10
$ 12,000
7
$ 18,000
C
8
$ 5,000
7
$ 7,000
D
6
$ 4,000
5
$ 5,000
E
7
$ 3,000
6
$ 6,000
F
4
$ 6,000
3
$ 7,000
G
4
$ 7,000
3
$ 9,000
(c)
Using the diagram in Q1(a), assume that
no crashing
has happened, and all activities are
scheduled to start as
early
as possible. After 8 weeks into the project, an inspection is
performed and the following are found: Activity A is 100% completed, activity B is 20%
completed, while activity C is 50% completed. The actual costs incurred for A, B and C are shown
in the following table. Fill in the empty cells in the table.
A
B
C
Planned Value
Earned Value
Actual Cost
$8,000
$4,000
$1,500
Based on the information, how do you evaluate the current progress of
activity B
? In other
words, is activity B early or late, and is it under budget or over budget?
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Q2. Inventory Management
An allergy products superstore sells 500 of their most popular model of air filters on average each
month. The wholesale price for each filter is $30. The cost of ordering and receiving shipments is $20 per
order.
Accounting estimates that annual inventory holding cost is 20% of the purchase cost. The store
operates 240 days per year (operating days), i.e., the operating days in each month is 20 days. The
supplier lead time is 3 operating days. Each order is received from the supplier in a single delivery. There
are no quantity discounts.
1. What quantity should the store order with each order?
2.How many times per year will the store order?
3. How many operating days will elapse between two consecutive orders?
4.
What is the store’s minimum total annual co
st of placing orders & carrying inventory (cycle stock)?
5. What is the annual inventory holding cost for the safety stock if the company wishes to carry a safety
stock of 10 filters?
6. What is the reorder point if the company wishes to carry a safety stock of 10 filters?
Q3. Newsvendor Problems
(a) You manage a hotel with 200 rooms in Houston. The NCAA Championship Game is coming up. Sports
fans either book a room in advance or wait until the last minute. Here are the prices you charge for the
two cases:
Advance booking:
$200/night
Late booking:
$500/night
Suppose you can easily get 200 advance reservations, and fill up your hotel. The number of last minute
customers is uniformly distributed between 25 and 50. How many rooms should be set aside for last-
minute customers?
(b) Suppose you are a wholesaler for newspapers. Your cost is 20 cents per newspaper and you charge
the retailer 80 cents per newspaper. The retailer sells to customers at $1 per newspaper. Demand for
newspapers is uniformly distributed between 10 and 100. How many newspapers should the retailer
stock?
(c) You would like to “induce” retailer to purchase more newspapers. Therefore, you agree to “buy
-
back”
unsold newspapers at price $60 cents per newspaper. How many newspapers will the retailer purchase?
What buy-back price should you offer to induce the retailer to buy the quantity that maximizes the
combined profit of you and the retailer?
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