A triage system is proposed for a hospital emergency room (ER). On average, 250 patients per hour arrive at the ER and the same number of patients leave the ER every hour. Under the proposed triage plan, entering patients will be registered first. The registration (stage 2) for each patient takes an average of 2 minutes. They will be in stage 3 for waiting, then be quickly examined by a nurse practitioner (stage 4) who will classify them as Simple Prescriptions (SP) or Potential Admits (PA). While Simple Prescriptions will move on to an area staffed for regular care, Potential Admits will be taken to the urgent area. Planners expect that, on average, 5 patients will be waiting to register (stage 1) and 3 patients will be waiting to be seen by the triage nurse (stage 3 in the flowchart). For each patient, the triage nurse is expected to take an average of 5 minute of examination time (stage 4). Planners expect that the Simple Prescriptions area to have, on average, 6 patients waiting to be seen (stage 5). Once a patient's turn comes, each will take 6 minutes of a doctor's time (stage 6). The hospital anticipates that, on average, the urgent area will have only 2 patients waiting to be seen (stage 7). Once one patient's turn comes, he or she will take 20 minutes of a doctor's time (stage 8). Assume that, 80% of all patients are Simple Prescriptions and the remaining 20% are Potential Admits. Also assume that the triage nurse is 100% accurate in making classifications. Assume the process to be stable; that is, average inflow rate equals average outflow rate. (Hint: For each of the 8 stages, find the given performance measures such as I, R and T (two measures are given, one is unknown). Apply Little's law to all 8 stages of the process. Keep at least one decimal place when calculating process measures). Under the proposed plan, answer the following questions:
a. What is your process flow rate? What are the flow rates for all eight stages?
b. For all eight stages, what other measure do you still know (for example, flow time or inventory for that stage)? List them below.
c. Can you calculate the third unknown measures for all 8 stages? (using Little's law)
d. On average, how many patients will be in the ER (including 8 stages)?
e. How long, on average, will a patient spend in the ER? Use the long way and short way to confirm your answers.
f. On average, how long will a Potential Admit spend in the ER?