The University of Wisconsin – Milwaukee
Business Administration 478-Supply Chain Analytics
Case Assignment 01 – Oct. 13 at 5:30 PM
Note 1: There are three case studies in this assignment. Each group should select
only one case study. Also, each group is required to submit a written report in doc
file along with Excel file to D2L dropbox that is assigned to the project.
Note 2: These case studies can be done in self-selected of groups of at most 5 people.
A single grade will be assigned to the group. It is expected that all group members
do the fair amount of work and equal contribution.
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CASE ONE
Sonoma Valley Wines1
After graduating from business school, George Clark went to work for a Big Six
accounting firm in San Francisco. Because his hobby has always been wine making,
when he had the opportunity a few years later, he purchased 5 acres plus an option to buy
35 additional acres of land in Sonoma Valley in Northern California. He plans eventually
to grow grapes on that land and make wine with them. George knows that this is a big
undertaking and that it will require more capital than he has at the present. However, he
figures that, if he persists, he will be able to leave accounting and live full-time from his
winery earnings by the time he is 40.
Because wine making is capital-intensive and growing commercial-quality grapes
with a full yield of 5 tons per acre takes at least 8 years, George is planning to start small.
This is necessitated by both his lack of capital and his inexperience in wine making on a
large scale, although he has long made wine at home. His plan is first to plant the grapes
on his land to get the vines started. Then he needs to set up a small trailer where he can
live on weekends while he installs the irrigation system and does the required work to the
vines, such as pruning and fertilizing. To help maintain a positive cash flow during the
first few years, he also plans to buy grapes from other nearby growers so he can make his
own label wine. He proposes to market it through a small tasting room that he will build
on his land and keep open on weekends during the spring–summer season.
To begin, George is going to use $10,000 in savings to finance the initial purchase
of grapes from which he will make his first batch of wine. He is also thinking about going
to the Bank of Sonoma and asking for a loan. He knows that if he goes to the bank, the
loan officer will ask for a business plan; so he is trying to pull together some numbers for
himself first. This way he will have a rough notion of the profitability and cash flows
associated with his ideas before he develops a formal plan with a proforma income
statement and balance sheet. He has decided to make the preliminary planning horizon
two years and would like to estimate the profit over that period. His most immediate task
is to decide how much of the $10,000 should be allocated to purchasing grapes for the
first year and how much to purchasing grapes for the second year. In addition, each year
he must decide how much he should allocate to purchasing grapes to make his favorite
Petite Syrah and how much to purchasing grapes to make the more popular Sauvignon
Blanc that seems to have been capturing the attention of a wider market during the past
few years in California.
In the first year, each bottle of Petite Sirah requires $0.80 worth of grapes and
each bottle of Sauvignon Blanc uses $0.70 worth of grapes. For the second year, the costs
of the grapes per bottle are $0.75 and $0.85, respectively.
George anticipates that his Petite Sirah will sell for $8.00 a bottle in the first year
and for $8.25 in the second year, whereas his Sauvignon Blanc’s price remains the same
in both years at $7.00 a bottle.
Besides the decisions about the amounts of grapes purchased in the 2 years,
George must make estimates of the sales levels for the two wines during the 2 years. The
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This case is written by William D. Whisler from California State University-East Bay.
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local wine-making association has told him that marketing is the key to success in any
wine business; generally, demand is directly proportional to the amount of effort spent on
marketing. Thus, because George cannot afford to do any market research about sales
levels due to his lack of capital, he is pondering how much money he should spend to
promote each wine each year. The wine-making association has given him a rule of
thumb that relates estimated demand to the amount of money spent on advertising. For
instance, they estimate that, for each dollar spent in the first year promoting the Petite
Sirah, a demand for 5 bottles will be created; and for each dollar spent in the second year,
a demand for 6 bottles will result. Similarly, for each dollar spent on advertising for the
Sauvignon Blanc in the first year, up to 8 bottles can be sold; and for each dollar spent in
the second year, up to 10 bottles can be sold.
The initial funds for the advertising will come from the $10,000 savings. Assume
that the cash earned from wine sales in the first year is available in the second year. A
personal concern George has is that he maintain a proper balance of wine products so that
he will be well positioned to expand his marketing capabilities when he moves to the
winery and makes it his full-time job. Thus, in his mind, it is important to ensure that the
number of bottles of Petite Sirah sold each year falls in the range between 40% and 70%
of the overall number of bottles sold.
Questions:
1) George needs help to decide how many grapes to buy, how much money to spend
on advertising, how many bottles of wine to sell, and how much profit he can
expect to earn over the 2-year period. Develop a spreadsheet LP model to help
him.
2) Solve the linear programming formulated in question 1.
3) Another comment the loan officer of the Bank of Sonoma has after reviewing the
business plan is: “I see that you do have an allowance in your calculations for the
carryover of inventory of unsold wine from the first year to the second year, but
you do not have any cost associated with this. All companies must charge
something for holding inventory, so you should redo your plans to allow for this.”
If the holding charges are $0.10 per bottle per year, how much, if any, does
George’s plan change?
4) The president of the local grape growers’ association mentions to George that
there is likely to be a strike soon over the unionization of the grape workers
(currently they are not represented by any union). This means that the costs of the
grapes might go up by anywhere from 50% to 100%. How might this affect
George’s plan?
5) Suppose that the Bank of Sonoma is so excited about the prospects of George’s
wine-growing business that they offer to lend him an extra $10,000 at their best
small business rate—28% plus a 10% compensating balance.17 Should he accept
the bank’s offer? Why or why not?
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CASE TWO
AMARCO, INC.2
Saudi Arabia is a kingdom in the Middle East with an area of 865,000 square miles,
occupying about four-fifths of the Arabian Peninsula. With a population of about 10
million, this Muslim and Arab state is generally recognized as being formed in 1927
when Ibn Sa’ud united the country and was acknowledged as the sovereign independent
ruler. Summer heat is intense in the interior, reaching 124°F, but it is dry and tolerable in
contrast to coastal regions and some highlands, which have high humidity during the
summer. Winters (December through February) are cool, with the coldest weather
occurring at high altitudes and in the far north. A minimum temperature recorded at atTurayf in 1950 was 10°F, and it was accompanied by several inches of snow and an inch
of ice on ponds. Average winter temperatures are 74°F at Jidda and 58°F at Riyadh (the
capital city), which has an annual precipitation of 2.5 to 3 inches.
After oil was discovered in Bahrain in 1932, many companies turned to Saudi
Arabia and started exploring. Thus, in 1937, the American Arabian Oil Company, Inc.
(AMARCO), was formed as a joint venture between Standard Oil Company of California
(SOCAL) and the Government of Saudi Arabia to explore, produce, and market any
petroleum found in the country. The year before, a geologist from SOCAL had
discovered a small quantity of oil in the Eastern Province at Dammam Dome, on which
the oil company town of Dhahran is now built. It was just beginning to be developed
when another discovery was made—of what was to prove to be the largest oil field in the
world. Called the Ghamar field, it would start Saudi Arabia on the road to becoming a
highly developed country in just a generation. Located about 50 miles inland from the
western shores of the Persian Gulf, the Ghamar field is a structural accumulation along
140 miles of a north–south anticline. The productive area covers approximately 900
square miles, and the vertical oil column is about 1,300 feet. It is generally considered to
have recoverable reserves of about 75 billion barrels of oil. Total proven reserves in
Saudi Arabia are estimated at more than 500 billion barrels, enough for more than a
hundred years of production. 4
Figure 2.1
2
This case was written by William D. Whisler from California State University-East Bay.
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.1 AMARCO,
Since 1950, Saudi Arabia has experienced greater and more rapid changes than it
had in the several preceding centuries. For example, during this time, as skilled nationals
became available, more and more of the exploration, drilling, refining, and other
production activities came under the control of the country. SOCAL was left primarily
with the marketing and transportation functions outside the country.
During the 1960s, AMARCO increased its profitability substantially by hiring Dr.
George Dantzig, then of the University of California, as a consultant. He supervised the
development and implementation of LP models to optimize the production of different
types of crude oils, their refining, and the marketing of some of their principal products.
As a result of this effort, an operations research (OR) department was started in the
company with the responsibility of continuing to review the firm’s operations to find
other areas where costs might be decreased or profits increased by applications of OR.
Now attention is being focused on another aspect of one of the company’s small
California refinery operations: the production of three types of aviation gasoline from the
Saudi Arabian crude oil available. Recently, the marketing of petroleum products to the
airline industry has become a rather substantial portion of AMARCO’s business. As
shown in Figure 2.1, the three aviation gasolines, A, B, and C, are made by blending four
feedstocks: Alkylate, Catalytic Cracked Gasoline, Straight Run Gasoline, and Isopentane.
Table 2.1 Stock availability
Characteristics
Reid vapor pressure
Octane number
IF TEL is 0.5
IF TEL is 0.4
Available (Bbl/day)
Value ($/Bbl)
Alkylate
5
94
107.5
14,000
17.00
Feedstock
Catalytic
Straight
Cracked
Run
Gasoline
Gasoline
8
4
83
93
13,000
14.50
74
87
14,000
13.50
Isopentance
20
95
108
11,000
14.00
In Table 2.1, TEL stands for tetraethyl lead, which is measured in units of
milliliters per gallon (ml/gal). Thus, a TEL of 0.5 means there is 0.5 milliliter of
tetraethyl lead per gallon of feedstock. Table 2.1 shows that TEL does influence the
octane number but does not influence the Reid Vapor Pressure.
Each type of aviation gasoline has a maximum permissible Reid Vapor Pressure
of 7. Aviation gasoline A has a TEL level of 0.5 ml/gal and has a minimum octane
number of 80. The TEL level of aviation gasolines B and C is 4 ml/gal, but the former
has a minimum octane number of 91, whereas the latter has a minimum of 100.
Assume that all feed stocks going into aviation gasoline A are leaded at a TEL
level of 0.5 ml/gal and that those going into aviation gasolines B and C are leaded at a
TEL level of 4 ml/gal. Table 2.2 gives the aviation gasoline data. A final condition is that
marketing requires that the amount of aviation gas A produced be at least as great as the
amount of aviation gas B.
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Characteristic
Minimum requirement (Bbl/day)
Price ($/Bbl)
A
12,000
15.00
Aviation Gasoline
B
13,000
16.00
C
12,000
16.50
Questions
1) AMARCO’s planners want to determine how the three grades of aviation gasoline
should be blended from the available input streams so that the specifications are
met and the income is maximized. Develop an LP spreadsheet model of the
company’s problem.
2) Solve the linear programming model formulated in Question 1.
3) Suppose that a potential supply shortage of Saudi Arabian petroleum products
exists in the near future due to possible damage to AMARCO’s oil production
facilities from Iraqi attacks. This could cause the prices of the three types of
aviation gasolines to double (while the values of the stocks remain the same,
because they are currently on hand). How would this affect the refinery’s
operations? If, after current stocks are exhausted, additional quantities must be
obtained at values double those given in Table 2.1, how might AMARCO’s plans
be affected?
4) Suppose that because of the new Iraqi crisis, the supply of alkylate is decreased
by 1,800 bbl/day, catalytic cracked gas is decreased by 2,000 bbl/day, and straight
run gasoline is decreased by 5,000 bbl/day. How does this affect AMARCO’s
operations?
5) Suppose that the Middle East crisis ends and a flood of oil fills the marketplace,
causing the prices of aviation gasoline to drop to $10.00, $11.00, and $11.50,
respectively, for A, B, and C. How would this affect the company’s plans?
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CASE THREE
International Textile Company, LTD.3
International Textile Company, Ltd., is a Hong Kong–based firm that distributes textiles
worldwide. The company is owned by the Lao family. Present plans are to remain in
Hong Kong through the transition in governments. Should the People’s Republic of
China continue its economic renaissance, the company hopes to use its current base to
expand operations to the mainland. International Textile has mills in the Bahamas, Hong
Kong, Korea, Nigeria, and Venezuela, each weaving fabrics out of two or more raw
fibers: cotton, polyester, and/or silk. The mills service eight company distribution centers
located near the customers’ geographical centers of activity.
Because transportation costs historically have been less than 10% of total
expenses, management has paid little attention to extracting savings through judicious
routing of shipments. Ching Lao is returning from the United States, where he has just
completed his bachelor’s degree in marketing. He believes that each year he can save
International Textile hundreds of thousands of dollars—perhaps millions—just by better
routing of fabrics from mills to distribution centers. One glaring example of poor routing
is the current assignment of fabric output to the Mexico City distribution center from
Nigeria instead of from Venezuela, less than a third the distance. Similarly, the Manila
center now gets most of its textiles from Nigeria and Venezuela, although the mills in
Hong Kong itself are much closer.
Of course, the cost of shipping a bolt of cloth does not depend on distance alone.
Table 3.1 provides the actual costs supplied to Lao from company headquarters.
Distribution center demands are seasonal, so a new shipment plan must be made each
month. Table 3.2 provides the fabric requirements for the month of March. International
Textile’s mills have varying capacities for producing the various types of cloth. Table 3.3
provides the quantities that apply during March.
Table 3.1 Shipping cost data ($/bolt)
Mill
Bahamas
Hong Kong
Korea
Nigeria
Venezuela
Los Angles
2
6
5
14
4
Chicago
2
7
6
12
3
London
3
8
8
6
5
Distribution Center
Mexico City Manila
3
7
10
2
11
4
9
11
1
9
Rome
4
9
9
7
6
Tokyo
7
4
1
5
11
New York
1
8
7
10
4
Table 3.2 Fabric demand for March (bolt)
Fabric
Cotton
Polyester
Silk
3
Los Angles
500
1000
100
Chicago
800
2000
100
London
900
3000
200
Distribution Center
Mexico City Manila
900
800
1500
400
50
400
Rome
100
700
200
This case was written by Lawrence L. Laplin, from San Jose State University.
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Tokyo
200
900
700
New York
700
2500
200
Lao wants to schedule production and shipments in such a way that the most
costly customers are shorted when there is insufficient capacity, and the least-efficient
plants operate at less than full capacity when demand falls below maximum production
capacity. You have been retained by International to assist Lao.
Table 3.3 March production capacity (bolt)
Production Capacity
Mill
Cotton Polyester Silk
Bahamas
1000
3000
0
Hong Kong 2000
2500
1000
Korea
1000
3500
500
Nigeria
2000
0
0
Venezuela
1000
2000
0
Questions
1) Find the optimal March shipment schedule and its total transportation cost for
each of the following:
a. cotton
b. polyester cloth
c. silk
2) The company will be opening a silk-making department in the Nigeria mill.
Although it will not be completed for several months, a current capacity of 1,000
bolts for that fabric might be used during March for an added onetime cost of
$2,000. Find the new optimal shipment schedule and the total cost for that fabric.
Should the Nigeria mill process silk in March?
3) Lao learns that changes might have to be made to the March plans. If a new
customer is obtained, the cotton demand in Manila and in Mexico City will
increase by 10% at each location. Meanwhile, a big New York customer might
cut back, which would reduce polyester demand by 10% in both New York and
Chicago. Find the contingent optimal schedules and total costs (a) for cotton and
(b) for polyester.
Table 3.4 Overtime production cost ($)
Production Capacity
Mill
Cotton Polyester Silk
Bahamas
10
10
N.A.
Hong Kong
15
12
25
Korea
5
8
22
Nigeria
6
N.A.
N.A.
Venezuela
7
6
N.A.
4) International Textile loses a profit of $10 for each bolt of cotton it falls short of
meeting the distribution center’s demand. For polyester, the loss is $20 per bolt;
for silk, it is a whopping $50 per bolt. By running the mills on overtime, the
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company can produce additional bolts at the additional costs shown in Table 3.4.
Using only the original data from Tables 5.14 through 5.16 and the information in
Table 3.4, determine new production schedules to maximize overall profit for
successively (a) cotton, (b) polyester, and (c) silk. Which fabrics and locations
involve overtime production, and what are the overtime quantities?
5) Without making any calculation, what suggestion do you offer Lao to further
reduce transportation cost?
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