Question

Based on the number of patients arriving at an emergency room in a local hospital, the scheduling manager determines that following number of nurses are needed for each day of a week:

Mon	Tue	Wed	Thur	Fri	Sat	Sun
5	7	9	8	10	9	5

The manager hires nursing graduates. Assume each hired graduate will work consecutively for 4 days followed by 3 days off.

Formulate the problem as an Linear Program to create a shift schedule for the scheduling manager to minimize her operating cost. Report those results.

Answer 1

The decision variables will be x1, x2,….x7 for the corresponding days of the week starting from Monday. These are the number of nurses who will start their workday on that particular day.

Objective function

Minimize x1 + x2 + x3 + x4 + x5 + x6 + x7

Subject to

x1                          + x5 + x6 + x7 >= 5

x1 + x2                          + x6 + x7 >= 7

x1 + x2 + x3                          + x7 >= 9

x1 + x2 + x3 + x4                          >= 8

       x2 + x3 + x4 + x5                 >= 10

                 x3 + x4 + x5 + x6           >= 9

                         x4 + x5 + x6 + x7   >= 5

x1, x2, x3, x4, x5, x6, x7 >= 0

The model is shown below

The formulas are shown below

The parameters are shown below

The result is shown below

We should start the following number of nurses on those days

Monday = 0

Tuesday = 4

Wednesday = 5

Thursday = 0

Friday = 1

Saturday = 4

Sunday = 0

Total staff = 14