real estate developer a real estate developer is considering three possible projects: a small...
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Real Estate DeveloperReal Estate Developer
A real estate developer is considering three possibleprojects: a small apartment complex, a small shoppingcenter, and a mini-warehouse.Each of these requires different funding over the nexttwo years, and the net present value of the investmentsalso varies. The following table provides the required investmentamounts ( in $1,000s ) and the net present value (NPV)of each ( also expressed in $1,000s ) :
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Real Estate DeveloperReal Estate Developer
NPV Year 1 Year 2
Apartment 18 40 30
Shopping Center 15 30 20
Mini-warehouse 14 20 20
The company hasThe company has $80,000.00$80,000.00
to invest in year 1 andto invest in year 1 and$50,000.00 $50,000.00
to invest in year 2.to invest in year 2.
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Real Estate DeveloperReal Estate Developer
REQUIREMENT:
1. Develop an integer programming model to maximize the NPV in this situation.
2. Solve the problem using computer software.
3. Which of the three projects would be under- taken if NPV is maximized?
4. How much money would be used each year?
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Real Estate DeveloperReal Estate Developer
Let X1 = 1 if apartment project is undertaken; 0 otherwise.
Let X2 = 1 if shopping center project is undertaken; 0 otherwise.
Let X3 = 1 if mini-warehouse project is undertaken; 0 otherwise.
Maximize NPV = 18X1 + 15X2 + 14X3
subject to:
40X1 + 30X2 + 20X3 =< 80
30X1 + 20X2 + 20X3 =< 50
X1, X2, X3 = 1 or 0
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Real Estate DeveloperReal Estate Developer
Solution :
X1 = 1
X2 = 1
X3 = 0
NPV = 33
This means that both the apartmentproject and the shopping center
project will be undertaken.The amount of money spent in year1 would be $70,000.00 and in year 2
would be $50,000.00
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Real Estate DeveloperReal Estate Developer
Suppose that the shopping center and the apartmentwould be on adjacent properties, and the shoppingcenter would only be considered if the apartment werealso built.
REQUIREMENT:
1. Formulate the constraint that would stipulate this.
2. Formulate a constraint that would force exactly two of the three projects to be undertaken.
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Real Estate DeveloperReal Estate Developer
X1 => X2
This means that if the apartment is not built ( X1 = 0 ) the shopping center cannot be built ( X2 must equal 0 ) .
X1 + X2 + X3 = 2
This forces two of the three projects to be undertaken.
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