Chapter 2 Section 3

Excel Companion Chapter 2 --- Integer LP
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Integer Linear Programming (ILP)	*Rlestate.xls*

Open the workbook Rlestate.xls and click the sheet Graph 1.

Realty Investment Group, RIG, currently has $416,000 available for new property investments. The group has narrowed the alternatives to a combination of condominiums and apartment buildings. The condos can be purchased with down payments of $12,000 each and the apartment buildings for down payments of $64,000 each. At this point in time, at most four condos are available. RIG’s property manager can devote up to 60 hours per month to oversee these investments. Each condo will require 10 hours per month of the property manager’s time and each apartment building will require 6 hours per month. After deducting mortgage payments and operating expenses, the yearly cash flow is estimated to be $1,000 per condo and $10,000 per apartment building. RIG wants to allocate its new property investments to maximize yearly cash flow.

Rlestate.xls - Graph 1.

A common approach to this problem is to initially ignore the condition that the decision variables must be integers. Treating decision variables in an ILP problem as if they were continuous quantities (like the Vitamins and Machine models) is referred to as solving the "LP Relaxation" of the original problem. A very common error is to find the optimum solution to the "relaxed" or "related" problem and then to round-off non-integer coordinates to the nearest integer. As we will discover, this assumption cannot be justified.

QUESTIONS

The most obvious corner points to the "relaxed" problem are
(0,0), (0, 6.5), and (4,0). What are the other two corner points?

x	y

a) Verify that the optimum solution to the "relaxed" problem occurs at the point (0, 6.5). Could the optimal cash flow to the ILP problem be greater than $65,000? Explain.

Which of the following feasible points with integer coordinates gives the highest cash flow (0,6), (3,5), (4,4), or (2,6)?

x	y

From the Answer Report to the solution with integer constraints, how many dollars were actually invested and how many hours per month were actually used for management.

Suppose the investment group learns that they can invest at most $360,000 (no changes are to be made to the other constraints). How does this impact the optimum solution?

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