Joe Fix Plans the Repair Schedules Each Day for the Freeway

Essay

Joe Fix plans the repair schedules each day for the Freeway Airline. Joe has 3 planes in need of repair and 5 repair personnel at his disposal. Each plane requires a single repairperson, except plane 3, which needs 2 personnel. Anyone not assigned to maintaining an airplane works in the maintenance shop for the day (not modeled). Each repairperson has different likes and dislikes regarding the types of repairs they prefer. For each plane, Joe has pulled the expected maintenance and determined the total preference matrix for his repair personnel. The preference matrix is:
$\begin{array}{lccc}&\text {Plane 1}&\text {Plane 2}&\text {Plane 3}\\ \hline \text { Repair Person 1 } & 11 & 9 & 21 \\\text { Repair Person 2 } & 17 & 7 & 13 \\\text { Repair Person 3 } & 9 & 12 & 17 \\\text { Repair Person 4 } & 14 & 8 & 28 \\\text { Repair Person 5 } & 12 & 5 & 12\end{array}$
Draw the balanced network flow for this assignment problem assuming Joe would like to maximize the total preference in his worker-to-aircraft schedule.