Question

Consider a capital budgeting example with five projects from which to select. The firm needs to decide how to allocate its available capital based upon the combination of the five projects to maximize returns (based upon net present value (NPV)). The firm has 800 thousand dollars in capital to allocate.

• Project 1 costs 100 thousand dollars with NPV at 35 thousand dollars

• Project 2 costs 200 thousand dollars with NPV at 80 thousand dollars

• Project 3 costs 150 thousand dollars with NPV at 100 thousand dollars

• Project 4 costs 75 thousand dollars with NPV at 60 thousand dollars

• Project 5 costs 300 thousand dollars with NPV at 220 thousand dollars

To diversify the investments, there are some additional requirements as follows.

1) Choose no fewer than two projects.

2) If project 3 is chosen, project 4 must be chosen.

3) Projects 4 and 5 cannot be both selected.

The question is to : Formulate this problem as an integer programming model.

Answer 1

Decision Variables Projects pl p2 p3 p4 p5 Cost NPV Project 1 Project 2 Project 3 Project 4 Project 5 100 200 150 75 300 35 80 100 60 220 Objective Function maximize 35p1+80p2+100p3+60p4+220p5 Constraints Capital budget Contingency Mutually exclusive Multiple choice 100p1+200p2+150p3+75p4+300p5-2