Assignment task: My Wardrobe
My Wardrobe is an Internet-based designer fashion rental business specializing in vintage high-end fashion clothing and accessories. Its operating model is as follows. When a customer finds a piece of clothing on the My Wardrobe Web site and decides to rent it, she puts it in the virtual shopping cart. If a piece of clothing is available, it is shipped immediately (assume it can be shipped during weekends and holidays, too). If not available, the piece remains in the customer's shopping cart until a rented item is returned to My Wardrobe, at which point it is shipped to the customer if she is next in line to receive it. My Wardrobe maintains an internal queue for each piece of clothing and a returned item is shipped to the first customer in the queue (first-in, first-out).
My Wardrobe has a vintage Fendi Baguette which is always in high demand. The average time between requests for the bag is 8 days, with a coefficient of variation of 1.1. On average, a customer keeps the bag for 5 days before returning it. It also takes 1 day to ship the bag to the customer and 1 day to ship it from the customer back to My Wardrobe (i.e., it takes on average 7 days to (a) ship it, (b) have it with the customer, and (c) ship it back). The standard deviation of the time between shipping the bag out from My Wardrobe and receiving it back is also 7 days; hence, the coefficient of variation of this time is 1.
Q.1 - On average, how many customers are in My Wardrobe's internal queue for the Fendi Baguette bag? Assume customers do not cancel their items in their shopping carts.
Q.2 - What is the average time that a customer has to wait to receive the bag after the request? Recall it takes 1 day for a shipped item to arrive at a customer address (i.e., in your answer, you have to include the 1-day shipping time).
Q.3 - My Wardrobe is considering acquiring a second Fendi vintage baguette bag. If My Wardrobe owns a total of two bags (whether in My Wardrobe internal stock, in customer's possession or in transit), what will be the new average time that a customer has to wait to receive the bag after the request?