To provide adequate medical service to its constituents at a reasonable cost, hospital administrators must constantly seek ways to hold staff levels as low as possible while maintaining sufficient staffing to provide satisfactory levels of health care.
A university hospital has three departments; the emergency room (department 1), the neonatal intensive care (department 2), and the orthopedics (department 3). The hospital has three work shifts, each with different levels of necessary staffing for interns. The hospital would like to identify the minimum number of interns required to meet the following three constraints.
1. The hospital must allocate at least 13, 32, and 22 interns to the three departments (over all shifts).
2. The hospital must assign at least 26, 24, and 19 interns to the three shifts (over ail departments).
3. The minimum and maximum number of interns allocated to each department in a specific shift must satisfy the following limits:
|
|
Departments
|
|
|
1
|
2
|
3
|
|
|
1
|
(6,8)
|
(11,12)
|
(7,12)
|
|
Shifts
|
2
|
(4,6)
|
(11,12)
|
(7,12)
|
|
|
3
|
(2,4)
|
(10,12)
|
(5,7)
|
Formulate this problem as a maximum flow problem (by identifying every node, including the source and sink, as well as every arc and the attributes of the arcs) where the objective is to identify- the minimum number of interns required to satisfy- the given constraints.
Draw the network and solve the problem.