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? �