Q1: A manufacturer’s average work-in-process inventory for a certain part is 1,000 units. The workstation produces this part at the rate of 200 units per day. What is the average time a unit spends at this workstation?
A unit spends an average time of 5 days at this workstation. Q2: The Wilcox Student Health Center has just implemented a new computer system and service process to “improve efficiency.” As pharmacy manager, you are concerned about waiting time and its potential impact on college students who “get no respect.” All prescriptions (Rxs) go through the following process: Drop-off ! Fill Rx ! Pick-up ! Cashier Assume that students arrive to drop-off Rxs at a steady rate of 2 Rxs per minute, with an average of one Rx per student. The average number of students in process (those who are waiting and those who are being served) at each station is:
Drop-off - 5 students
Pick-up - 3 students
Pay cashier - 6 students
On average, the Fill Rx station has 40 Rxs in process and waiting. Because of this perceived long wait, 95% of the students decide to come back later for pick-up. They come back an average of 3 hours later. If the students choose to stay, their name is called as soon as the Rx is filled and they then enter the pick-up line. Assume that the system is operating at a steady state.
a) The flow diagram for the entire process:
Flow paths for students
Flow paths for prescriptions
Table 1: Find Missing Data Using Little Law.
Average time in the pharmacy for those students who stay to pick-up their Rxs (see Table 1) = 2.5 + 20 + 1.5 + 3 = 27 minutes
c) Average time in the pharmacy for those students who pick-up 3 hours later (see Table 1) = 2.5 + 1.5 + 3 = 7 minutes
d) Average time that a student spends in the pharmacy (see Table 1) = 7*0.95 + 27*0.05 = 8 minutes
Q3: A hospital emergency room (ER) is currently organized so that all patients register through an initial check-in process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 50 people per hour arrive at the ER, 10% of whom are admitted to the hospital. On average, 30 people are waiting to be registered and 40 are registered and waiting to see a doctor. The registration process takes, on average, 2 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 5 minutes. Among those admitted to the hospital, average time is 30 minutes. On average, how long does a patient stay in the ER? On average, how many patients are being examined by doctors? On average, how many patients are in the ER? Waiting
Registration to see a
Table 2: Find Missing Data Using Little Law.
Average time that a patient stays in the ER (see Table 2)
Average number of patients examined by doctors (see Table 2) Average number of patients in the ER (see Table 2)
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