A car wash has 10 available bays; however, the owners find that it is expensive

Question

A car wash has 10 available bays; however, the owners find that it is expensive to have too many bays open when utilization is low because there are costs associated with having a bay open, such as electricity for lighting and costs for cleaning. Thus, they would like to have only as many bays open as needed to ensure average customer wait time (in line) of no more than five minutes. (Corporate strategy emphasizes low cost over short wait time). Assuming a single waiting line where customers wait for the first available bay, an average arrival rate of 26 vehicles per hour (assume Poisson arrivals), and an average wash time of 16 minutes per vehicle, how many bays should they have open to meet their objectives?

Explanation / Answer

In 16 minutes 1 vehicle will be washed . If a customer will spend maximum 5 minutes in waiting, it will take 21 minutes as flow time. in 60 minutes 60/ 21=2.85 vehicle will be washed.  

26 vehicles arrive in 60 minutes so in 16 minutes 26/60*16=6.933 vehicle will be reached.

Number of bays to be opened =26/2.85=6.933=9 bays should be opened so that customer will not wait for more than 5 minutes.

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