Amarco

Amarco

AMARCO, Inc.

William D. Whisler

California State University, Hayward

1. (a) There are two groups of variables: the amount of the four feedstocks (alkylate, catalytic cracked gasoline, straight run gasoline, and isopentane) used in producing the three types of gasoline (A, B, and C) and the amounts of the four feedstocks left over after production. Twelve variables are in the first group and four in the second, making a total of 16 variables.

Xi,j = amount of feedstock i used in gasoline j, in gallons

Xi = amount of feedstock i left over after production, in gallons

for i = feedstock A (Alkylate), CC (Catalytic Cracked gasoline), SR (Straight Run gasoline), I (Isopentane), and j = gasoline A, B, C. All of these variables must be nonnegative.

With the feedstocks available, the objective function maximizes the revenue from the gasoline produced and the feedstocks left over after production.

[pic]

where vi is the value of feedstock i, Xi.

There are five groups of conditions: (i) Reid Vapor Pressure, (ii) feedstock availability, (iii) minimum demand, (iv) octane level, and (v) the marketing condition. The first, third, and fourth groups have three restrictions each, the second has four, and there is one marketing condition. Thus, the total number of constraints is 14.

(i) Reid Vapor Pressure

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for j = gasoline A, B, C, where ri is the Reid Vapor Pressure of feedstock i and 7 is the maximum Reid Vapor Pressure. This gives three constraints

-2XA,j + XCC,j - 3XSR,j + 13XI,j < 0

for j = gasoline A, B, C.

(ii) The feedstock availability conditions are

[pic]

for i = A, CC, SR, I where Ai are the input stream availabilities from the case.

(iii) The minimum demand requirements are

[pic]

where Dj is the demand for gasoline j = gasoline A, B, C.

(iv) The octane number constraints are

for j = gasoline A, B, C, where oni is the octane...