Question

A hospital does many surgeries in a day. A standard hospital is open 24 hours with no breaks in a day. In examining patient flow and surgery process in a 2 hour period. Let us assume a long lineup of over 1000 people waiting for surgery. Surgery involves the following steps:
A. Check driver's licence, 60s on average exponential distribution.
B. Talk with patient about preexisting health problems, which is 90s.
C. Doing the surgery, which takes 180s or 3 minutes, again on average exponential distribution.
D. Patient, post operation, will rest immobile for 30 seconds.
Consider that there are 4 doctors with one doctor taking each step A, B, C, D. These doctors are not flexible and will only do the step they are assigned to. Each step can at most have 1 patient at a time. In a 120 minutes, how many patients can the clinic help operate? (2 hours). 20 marks/100 - Show your work.

Answer 1

Step A => 60 sec. Step B => 90 sec. Step C => 180 sec. Step D => 30 Sec

Total Processing time per patient = 360 sec = 4 minutes if done as a single operation. With a continuous inflow and 4 Doctors in a line, The cycle time reduces as follows. Step A takes 60 seconds post which patient moves to step B which takes 90 seconds. This implies that after 60 seconds the next patient coming from step A waits for 30 seconds before he moves to step B. Hence Total ime taken is 30 sec waiting plus 90 sec processing at B = 120 seconds. This needs to be added to the 60 sec processing at a to give 180 seconds for arrival at C. The arrival and departure rates at C therefore are same at 180 seconds. Add to this another 30 seconds of D gives us a total of 210 seconds = 3.5 minutes in which a patient is turned around. Hence in a 2 hour period we have 120/3.5 patients = approximately 34 patients.