Real Estate Developer A real estate developer is considering three possible projects: a small apartment complex, a small shopping center, and a mini-warehouse.

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Presentation transcript:

Real Estate Developer A real estate developer is considering three possible projects: a small apartment complex, a small shopping center, and a mini-warehouse. Each of these requires different funding over the next two years, and the net present value of the investments also varies. The following table provides the required investment amounts ( in $1,000s ) and the net present value (NPV) of each ( also expressed in $1,000s ) :

Real Estate Developer NPV Year 1 Year 2 18 40 30 15 20 14 Apartment Shopping Center 15 20 Mini-warehouse 14 The company has $80,000.00 to invest in year 1 and $50,000.00 to invest in year 2.

Real Estate Developer REQUIREMENT: Develop an integer programming model to maximize the NPV in this situation. Solve the problem using computer software. Which of the three projects would be undertaken if NPV is maximized? 4. How much money would be used each year?

Real 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

Real Estate Developer Solution : X1 = 1 NPV = 33 This means that both the apartment project and the shopping center project will be undertaken. The amount of money spent in year 1 would be $70,000.00 and in year 2 would be $50,000.00

Real Estate Developer Suppose that the shopping center and the apartment would be on adjacent properties, and the shopping center would only be considered if the apartment were also built. REQUIREMENT: Formulate the constraint that would stipulate this. Formulate a constraint that would force exactly two of the three projects to be undertaken.

Real 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.