JOB SCHEDULINGS
Problem 1.88
A big hospital has the following minimal daily requirements of doctors:
| Period | Clocktime (24 hours.) | No. of doctors required |
|---|---|---|
| 1 | 6 a.m. - 10 a.m. | 72 |
| 2 | 10 a.m. - 2 p.m. | 77 |
| 3 | 2 p.m. - 6 p.m. | 85 |
| 4 | 6 p.m. - 10 p.m. | 68 |
| 5 | 10 p.m. - 2 a.m. | 25 |
| 6 | 2 a.m. - 6 a.m. | 23 |
Doctors report to the hospital at the beginning of each period and work for 8 consecutive hours. Formulate this problem as a linear programming problem to minimise the total number of doctors to meet the needs of the hospital throughout the day.
Solution.
Let x1 represent the number of doctors required at starting period k (k = 1, 2, 6). Then the objective function and constraints can be written as:
Minimise (total number of doctors)
Z = x
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