Reference no: EM132817575
Noticing the vaccine roll-out and considering that most people spent the last year in their pajamas, you and your colleagues expect a return of fancy events in the Spring. As a result, you launch GTUX a small company specialized in renting tuxedos to college students.
GTUX's operating model is as follows. When a customer finds a tuxedo on GTUX's website and decides to rent it, they put it in a virtual shopping cart. If a tuxedo is available, it is shipped directly to the customer (assume it can be shipped during weekends and holidays too). If not available, the customer enters a queue and waits until a tuxedo is available. When a tuxedo is returned to GTUX, it is shipped to the customer next in line to receive it. GTUX manages this queue such that a returned tuxedo is shipped to the first customer in the queue (which is the customer that has been waiting for the longest).
Since you are currently experimenting with the business model, GTUX only owns one tuxedo. The average time between requests for the tuxedo is 10 days, with a coefficient of variation of 1.
On average, a customer keeps the tuxedo for 6 days before returning it. It also takes 1 day to ship the tuxedo to the customer and 1 day to ship it from the customer back to GTUX. Thus, it takes 8 days on average between GTUX shipping the tuxedo to a customer and receiving it back. The standard deviation of the time between shipping the tuxedo to a customer from GTUX and receiving it back in 8 days (thus the coefficient of variation is 1).
Question 2
On average, how many customers are in GTUX's internal queue for a tuxedo? Assume customers do not cancel their items in their shopping carts.
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