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 ) :

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.

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?

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

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

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.

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.