1. In a multi-speciality hospital, nurses report to duty at the end of every 4
hours as shown in table 1. Each nurse, after reporting, will work for 8 hours
continuously. The minimum number of nurses required during various
periods are summarised in Table below. Develop a mathematical model to
determine the number of nurses to report at the beginning of each period
such that the total number of nurses who have to report to duty in a day is
minimised.
Interval Time Period Minimum
number
number of
From
nurses
required
12
4 am.
midnight
4 a.m.
8a.m
25
8 a.m.
12 noon 35
12 noon 4p.m.
32
4 p.m.
8 p.m.
22
8 p.m.
12
15
midnight
Answers
Step-by-step explanation:
Given In a multi-speciality hospital, nurses report to duty at the end of every 4 hours as shown in table 1. Each nurse, after reporting, will work for 8 hours continuously. The minimum number of nurses required during various periods are summarised in Table below. Develop a mathematical model to determine the number of nurses to report at the beginning of each period such that the total number of nurses who have to report to duty in a day is minimised.
Interval Time Period Minimum
Now we have a table of time period.
Time period
Interval From To Minimum number of nurses required.
1 12 midnight 4 am 20
2 4 am 8 am 25
3 8 am 12 noon 35
4 12 noon 4 pm 32
5 4 pm 8 pm 22
6 8 pm 12 midnight 15
Let xj be the number of nurses to report for duty at the start of jth period where j varies from 1 to 6.
Now Z (Minimise) = x1 + x2 + x3 + x4 + x5 + x6 .
So x6 + x1 >= 20
x 1 + x2 > = 25
x2 + x3 > = 35
x3 + x4 > = 32
x4 + x5 > = 22
x5 + x6 > = 15
x1, x2, x3, x4, x5, x6 is greater than or equal to 0