Linear programming Case Study

MAT540 Assignment
Linear programming Case Study
Name of the Student
Name of the University
Author Note

Table of Contents
Background of the problem:..................................................................................................................3
Case details:...........................................................................................................................................3
LP Problem Formulation:.......................................................................................................................3
Excel solver output:...............................................................................................................................4
Conclusion:............................................................................................................................................5
Bibliography...........................................................................................................................................6

Background of the problem:
It has seen that emergency room in any hospital plays crucial role in hospital
operation. Depending on the demand, the emergency room operates 24*7 and
hence nurses who are doing shifts in emergency room works in different shifts. Now,
due to odd time factor, the hospital has to pay additional monetary benefits. Under
such circumstances, the management of the hospital needs to manage the shift
timing of individual nurses so that individual nurse can fulfill their usual shift timing
with minimum salary. Thus, this will be a minimization problem.
Case details:
The emergency room operates for 24 hours and have the following number of cases
during the indicated time slots:
Times 08-12 12-16 16-20 20-24 24-04 04-08
Cases/hr 3 12 8 11 4 3
There are three shifts starting at 8:00, 16:00 and 24:00. All nurses that start at these
times can handle 3 cases per hour and work 8 consecutive hours. Some nurses ask to
start at 12:00 or 20:00 and claim that they can work more productively handling 4
cases per hour if they let to start at 12:00 or 20:00 and work 8consecutive hours. The
emergency room pays equal salary to all nurses except for those working 24:00-
08:00shift, who earn 25% more. Salary for normal shift hours is $45
LP Problem Formulation:
Let x1, x2, x3, x4 and x5 will be the number of nurses starting at 08:00, 12:00, 16:00,
20:00 and 24:00 hours respectively. There will be no nurse who can start their shift at
04:00.
Hence, the objective function is:
Min Z = 45x1 + 45x2 + 45x3 + 45x4 + 56.25x5
The constraints are as follows:
3x1 >= 3
3x1 + 4x2 >= 12
4x2 + 3x3 >= 8
3x3 + 4x4 >= 11
4x4 + 3x5 >= 4
3x5 >= 3