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Case 4.1 AMARCO, Inc. 207
C A S E
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 popula-
tion 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 tempera-
ture recorded at at-Turayf 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 explor-
ing. Thus, in 1937, the American Arabian Oil Com-
pany, Inc. (AMARCO), was formed as a joint venture
between Standard Oil Company of California
(SOCAL) and the Government of Saudi Arabia to ex-
plore, 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 accumu-
lation 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 re-
serves 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.
4.1 AMARCO, INC.10
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 produc-
tion 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 4.45, the three aviation gasolines, A,
B, and C, are made by blending four feedstocks:
Alkylate, Catalytic Cracked Gasoline, Straight Run
Gasoline, and Isopentane.
In Table 4.14,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 4.14 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.
10 This case was written by William D. Whisler, California StateUniversity, Hayward.
208 Chapter 4 Linear Programming Models
Assume that all feedstocks 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 4.15 gives the
AviationGas A
Refinery
Crude Oil
AviationGas C
Alkylate
CatalyticCrackedGasoline
StraightRun
GasolineIsopentane
AviationGas B
Figure 4.45
The Production of
Aviation Gasoline
Table 4.14 Stock Availabilitiesa
Feedstock
Catalytic StraightCracked Run
Characteristic Alkylate Gasoline Gasoline Isopentane
Reid Vapor Pressure 5 8 4 20Octane Number
If TEL is 0.5 94 83 74 95 If TEL is 4.0 107.5 93 87 108
Available (Bbl/day) 14,000 13,000 14,000 11,000 Value ($/Bbl) 17.00 14.50 13.50 14.00
aSome of the data in this case have been adapted from Walter W. Garvin, Introduction to Linear Programming (New York: McGraw-Hill, 1960), Chapter 5.
Table 4.15 Aviation Gasoline Data
Aviation Gasoline
Characteristic A B C
Minimum requirements (Bbl/day) 12,000 13,000 12,000Price ($/Bbl) 15.00 16.00 16.50
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.
Case 4.1 AMARCO, Inc. 209
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 formu-
lated in Question 1.
The following questions should be attempted only after
Questions 1 and 2 have been answered correctly.
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 opera-
tions? If, after current stocks are exhausted,
additional quantities must be obtained at
values double those given in Table 4.14, 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. AMARCO is considering trying to fill the avia-
tion gasoline shortage created by the new Iraqi
crisis by increasing its own production. If addi-
tional quantities of alkylate, catalytic cracked
gasoline, straight run gasoline, and isopentane
are available, should they be processed? If so,
how much of them should be processed, and
how do their values affect the situation?
6. Due to the uncertainty about both the U.S.
economy and the world economy resulting
from the Iraqi crisis, AMARCO’s economists
are considering doing a new market research
study to reestimate the minimum requirement
forecasts. With the economy continually
weakening, it is felt that demand will decrease,
possibly drastically, in the future. However,
because such marketing research is expensive,
management is wondering whether it would be
worthwhile. That is, do changes in the minimum
requirements have a significant effect on
AMARCO’s operations? What is the change in
profit from an increase or a decrease in the
minimum requirements? Over what ranges of
demand do these profit changes apply?
7. 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?
8. Suppose that the U.S. government is considering
mandating the elimination of lead from aviation
gasoline to decrease air pollution. This law
would be based on new technology that allows
jet engines to burn unleaded gasoline efficiently
at any octane level. Thus, there would no longer
be any need for constraints on octane level.
How would such a new law affect AMARCO?
9. The Environmental Protection Agency is propos-
ing regulations to decrease air pollution. It plans
to improve the quality of aviation gasolines by
decreasing the requirement on Reid Vapor
Pressure from 7 to 6. Management is concerned
about this regulation and wonders how it might
affect AMARCO’s profitability. Analyze and
make a recommendation.
10. The Marketing Department indicates that
AMARCO will be able to increase its share of
the market substantially with a new contract
being negotiated with a new customer. The
difficulty is that this contract will require that
the amount of aviation gas A plus the amount of
B must be at least as great as the amount of C
produced. Because aviation gasolines A and B are
least profitable of the three, this could cause a
big decrease in profit for the company. However,
marketing indicates that this is a short-run view,
because the “large” increase in market share
with the concomitant long-run profit increases
will more than offset the “temporary small
decrease” in profits because of the additional
restriction.What do you recommend? Why? �