331-14 - Chapter 6 Integer and Goal Programming Models...

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Chapter 6 Integer and Goal Programming Models (cont’d) (Using Binary constraints; Goal Programming)
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What is a BINARY Constraint? A special case of Integer constraint A “Binary” is an integer value that can be ONLY either 0 or 1 A Binary is most often used as a logical indicator where NO = 0 and YES = 1, or in corresponding terms 0 = Do not include and 1 = Include The Solver pull-down menu for the sign of a Constraint includes an option of: BIN for Binary
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Binary Integer Example: Portfolio Selection Choosing stocks to include in portfolio Decisions: Which of 7 stocks to include? We either buy a block of shares or not; we do not buy part of a block Objective: Maximize expected annual return (in $1000’s)
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Restrictions Invest up to $3 million Include at least 2 Texas companies Include no more than 1 foreign company Include exactly 1 California company If British Petro is included, then Trans-Texas Oil must also be included
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Decision Variables Use the first letter of each stock’s name Example for Trans-Texas Oil: T = 1 if Trans-Texas Oil is included T = 0 if not included This is an example of using Binary constraints to impose Logic conditions.
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Objective Function (in $1000’s return) Max 50T + 80B + 90D + 120H + 110L + 40S + 75C Subject to the constraints: Invest up to $3 Million 480T + 540B + 680D + 1000H + 700L + 510S + 900C < 3000 (Remember why we do not use “ = “ ?)
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The remaining constraints are all logic relationships that require the use of BINARY Include At Least 2 Texas Companies T + H + L > 2 Include No More Than 1 Foreign Company B + D < 1 Include Exactly 1 California Company S + C = 1
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How do we go from Logic relationship into a Binary Constraint Identify ALL the possible combinations Use trial and error to define the relationship that satisfies all these conditions. Which one of the following is valid for the Foreign Company constraint? (Not all possibilities are included.) B + D = 0 B + D = 1 B – D = etc… B + D ≥ 0 B + D ≥ 1 B + D 0 B + D ≤ 1
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“Include no more than one foreign company” D=0 D=1 B=0 ok ok B=1 ok NOT ok
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This note was uploaded on 08/29/2011 for the course ACCT 331 taught by Professor A during the Spring '11 term at Ohio State.

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331-14 - Chapter 6 Integer and Goal Programming Models...

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