Predictive and Prescriptive Analytics: NPV and $0-1$ Integer

Assume you are to consider $5$ projects with the expectation that you are to move forward with $3$ of the best projects under review. Each project has its own unique risk characteristics which is reflected in the assigned required rate of return for each project. Original Data Set

Discounting Model

$0-1$ Integer Model

Maximize $Z=NPV{x}_1+NPV{x}_2+NPV{x}_3+NPV{x}_4+NPV{x}_5$

Subject to:

$55x_1+45x_2+60x_3+50x_4+30x_{5}150$

$40x_1+35x_2+25x_3+35x_4+30x_5<mn\; id="EditorElement\_3546872">1</mn><mn\; id="EditorElement\_3546873">1</mn><mn\; id="EditorElement\_3546874">0</mn>$

$25x_1+20x_2+30x_4$~~$60$

$x_3+x_4<mn\; id="EditorElement\_3546949">1</mn>$

$x_1=0or1$

Total Retum:Management has learned that additional "hidden costs" may exist in the start up of each project and have provided estimated costs in terms of phase $1,$ phase $2,$ and phase $3$ of the project start up$.$

Management has budged a total of $$150,000$ for phase $1,$$$110,000$ for phase $2,$ and $$60,000$ for

phase $3.$ The budgeted costs reflect the total amount spent for all accepted projects in phase $1,2,$and $3$ In addition, management has decided that projects $3$ and $4$ are mutually exclusive but is not opposedto foregoing investment in either of these projects if the analysis supports such a recommendation.

Objective: Determine the projects for selection under the NPV approach. Maximize the total return given the start up phase $1,2,$ and $3$ costs and management's discretion regarding project $3$ and $4.$Use a $5-$year timeline with the initial investment outlay $($period $0)$ occurring in $2024.$