Reserve Crew Allocation Program$1$

This application uses concepts covered in Chapter $4.$

The Reserve Crew Allocation Program is a linear program used by American Airlines to allocate and utilize reserve crews at a minimum cost. The program selects a set of crews to meet the daily demand for reserve crews. The number of reserves required on any particular day is forecast by using experience to establish probabilities. The simplex tableau is presented below.

$[$ Figure $1$ Image$]$

The constraints are given by

a$11$x$1+$ a$12$x$2+$ a$13$x$3+$ a$14$x$4++$ a$1$nxn $>$ b$1.$

For example, the first row of the tableau corresponds to the constraint