Question

The Wilcox Student Health Center has just implemented a new computer system and service process to "improve efficiency". The process flowchart and analysis framework is also provided. 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:
Assume that students arrive to drop off Rxs at a steady rate of two Rxs per minute, with an average of one Rx per student. The average number of students in process (assume waiting and being serviced) at each station is: drop-off — six students, pickup — four students, and pay cashier — eight students.

The fill Rx station typically has 50 Rxs in process and waiting, on average. Because of this perceived long wait, 85 percent of the students decide to come back later for pickup. They come back an average of four hours later. If the students choose to stay, each name is called as soon as the Rx is filled, and the student then enters the pickup line. Assume that the system is operating at a steady state.

What is the average time a student spends in the pharmacy if he or she stays to pick up the Rx? Round your answers to two decimal places.

    Drop-off   Fill Rx   Pickup   Cashier   Total
Flow Time (minutes)     




How many minutes does the student spend in the pharmacy if he or she picks-up the Rx four hours later (i.e., the student goes home after dropping the Rx off)? Round your answer to two decimal places.

minutes

What is the average time in minutes that all students spend in the pharmacy? Round your answer to two decimal places.

minutes

What is the average time in minutes that the Rx spends in the process? Count time from entering the drop-off line to completing payment. Round your answer to two decimal places.

minutes

Answer 1

Drop-off    Fill Rx       Pick-up     Cashier     Total Flow time
6 Rxs        50 Rxs      4 Rxs        8 Rxs

2 Rxs/min 2 Rxs/min 2 Rxs/min 2 Rxs/min

3 min        25 min      2 min        4 min 34 min/Rx

Table 1: Find Missing Data Using Little Law.

a) Average time in the pharmacy for those students who stay to pick-up their Rxs (see Table 1) = 3 + 25 + 2 + 4 = 34 minutes
b) Average time in the pharmacy for those students who pick-up 4 hours later (see Table 1) = 3 + 2 +4 = 9 minutes
c) Average time that a student spends in the pharmacy (see Table 1) = 9*0.85 + 34*0.15 = 7.65+5.10= 12.75 minutes

d) 34 minutes