Large Scale Linear Program
A hospital must decide how many new nurses to hire and
train over the next T months. The number of nurse-hours required in month j = 1; 2; : : : ; T is known to
be Hj . A new nurse is trained during a month at the hospital before she/he can contribute nurse-hours to
the hospital. Therefore, a nurse that starts contributing nurse-hours in month j, must be hired in month
j 1 for j = 1, 2, 3, T. Each nurse that is being trained requires hs hours of supervision by experienced
nurses (i.e., nurses that have already gone through training), so that hs fewer hours are available by
experienced nurses in a month, for every nurse that is being trained. Each experienced nurse can work up
to hw hours per month, and the hospital has N experienced nurses available at the beginning of the rst
month. If in a given month j, the number of nurse-hours provided by experienced nurses is higher than
the number of nurse-hours Hj required by the hospital plus the hours required for training of new nurses,
then those hours are \lost". Any nurse that is hired cannot be laid o. However, at the end of each
month, a fraction r of the experienced nurses quit their jobs. An experience nurse costs ce per month and
a new nurse costs cn per month including salaries and benets (with ce > cn). Write an LP formulation
to nd the optimal hiring policy of the hospital (i.e., how many new nurses per month should be hired).
A hospital must decide how many new nurses to hire and
train over the next T months. The number of nurse-hours required in month j = 1; 2; : : : ; T is known to
be Hj . A new nurse is trained during a month at the hospital before she/he can contribute nurse-hours to
the hospital. Therefore, a nurse that starts contributing nurse-hours in month j, must be hired in month
j 1 for j = 1, 2, 3, T. Each nurse that is being trained requires hs hours of supervision by experienced
nurses (i.e., nurses that have already gone through training), so that hs fewer hours are available by
experienced nurses in a month, for every nurse that is being trained. Each experienced nurse can work up
to hw hours per month, and the hospital has N experienced nurses available at the beginning of the rst
month. If in a given month j, the number of nurse-hours provided by experienced nurses is higher than
the number of nurse-hours Hj required by the hospital plus the hours required for training of new nurses,
then those hours are \lost". Any nurse that is hired cannot be laid o. However, at the end of each
month, a fraction r of the experienced nurses quit their jobs. An experience nurse costs ce per month and
a new nurse costs cn per month including salaries and benets (with ce > cn). Write an LP formulation
to nd the optimal hiring policy of the hospital (i.e., how many new nurses per month should be hired).
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