1. Hospital Expansion Problem
Mt. Sinai Hospital
Hospital Expansion Problem
STRATEGIC
RESOURCE
ALLOCATION
and
PLANNING
MGMT E-5050

2. Mt. Sinai Hospital
Mt. Sinai Hospital is a 600-bed facility, complete with
laboratories, operating rooms, and x-ray equipment.
In seeking to increase revenues, the administration
has decided to make a 90-bed addition on a portion
of adjacent land currently used for staff parking.
The administration feels that the labs, operating
rooms, and x-ray department are not being fully uti-
lized at present and do not need to be expanded to
handle additional patients.
The addition of 90 beds, however, involves
deciding how many beds should be allocated to the
medical staff for medical patients and how many to
the surgical staff for surgical patients.

3. Mt. Sinai Hospital The hospital’s accounting and medical records
departments have provided the following perti-
nent information.
The average hospital stay for a medical patient
is 8 days, and the average medical patient gener-
ates $2, in revenues.
The average surgical patient is in the hospital 5
days, and receives a $1, bill.
The laboratory is capable of handling 15,000 tests
per year more than it is handling.
The average medical patient requires 3.1 lab tests
and the average surgical patient takes 2.6 lab tests.

4. Mt. Sinai Hospital
Furthermore, the average medical patient uses 1 x-ray,
whereas the average surgical patient requires 2 x-rays.
If the hospital were expanded by 90 beds, the x-ray de-
partment could handle up to 7,000 x-rays without signi-
ficant additional cost.
Finally, the administration estimates that up to 2,800
additional operations could be performed in existing
operating room facilities. Medical patients, of course,
do not require surgery, whereas each surgical patient
generally has one surgery performed.

5. Mt. Sinai Hospital REQUIREMENT:
Formulate this problem so as to determine
how many medical beds and how many
surgical beds should be added to maximize
revenues. Assume that the hospital is open
365 days a year.
Then solve the problem.

6. Solution Maximize revenue = $2,280.00 X1 + $1,515.00 X2
Let : X1 = number of medical patients
X2 = number of surgical patients
Maximize revenue = $2, X1 + $1, X2
subject to:
8X X2 =< 32,850 ( patient days available )
365 days x 90 new beds
3.1 X X2 =< 15,000 ( lab tests )
1 X X2 =< 7,000 ( x-rays )
X2 =< 2,800 ( operations / surgeries )
X1, X2 => 0

7. Solution X1 = 2,791 medical patients X2 = 2,105 surgical patients
Revenue = $9,551, per year
To convert X1 and X2 into the number of medical beds versus
surgical beds, find the total number of hospital days for each
type of patient:
Medical = ( 2,791 patients ) ( 8 days ) = 22,328 days
Surgical = ( 2,105 patients )( 5 days ) = 10,525 days
This represents 68% medical days and 32% surgical days,
which yields 61 medical beds and 29 surgical beds.