Mt. Sinai HospitalMt. Sinai HospitalHospital Expansion ProblemHospital Expansion Problem

STRATEGICRESOURCE

ALLOCATIONand

PLANNING

MGMT E-5050

Mt. Sinai HospitalMt. 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.

Mt. Sinai HospitalMt. Sinai Hospital

The hospital’s accounting and medical recordsdepartments have provided the following perti-nent information. The average hospital stay for a medical patientis 8 days, and the average medical patient gener-ates $2,280.00 in revenues. The average surgical patient is in the hospital 5 days, and receives a $1,515.00 bill. The laboratory is capable of handling 15,000 testsper year more than it is handling. The average medical patient requires 3.1 lab testsand the average surgical patient takes 2.6 lab tests.

Mt. Sinai HospitalMt. 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 2,800additional operations could be performed in existingoperating room facilities. Medical patients, of course,do not require surgery, whereas each surgical patientgenerally has one surgery performed.

Mt. Sinai HospitalMt. Sinai Hospital

REQUIREMENT:

1. 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.

SolutionSolution

Let : X1 = number of medical patients

X2 = number of surgical patients

Maximize revenue = $2,280.00 X1 + $1,515.00 X2

subject to:

8X1 + 5X2 =< 32,850 ( patient days available ) 365 days x 90 new beds

3.1 X1 + 2.6 X2 =< 15,000 ( lab tests )

1 X1 + 2 X2 =< 7,000 ( x-rays )

X2 =< 2,800 ( operations / surgeries )

X1, X2 => 0

SolutionSolution

X1 = 2,791 medical patients

X2 = 2,105 surgical patients

Revenue = $9,551,659.00 per year

To convert X1 and X2 into the number of medical beds versussurgical beds, find the total number of hospital days for eachtype 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.