Consider a large distribution centre (DC) that sees the arrival of, on average,

Question

Consider a large distribution centre (DC) that sees the arrival of, on average, 40 trucks per 8-hour workday (assume a Poisson distribution). The unloading of a truck at one of the unloading docks takes on average 45 minutes (assume exponential distribution). The docks operate for 8 hours per day. If a dock is not available, trucks wait in a common line for the next available dock. The truckers charge the DC $30 per hour (or portion thereof) for waiting (not including unloading). The cost to operate a dock is $50 per hour (assume this to be a fixed cost that does not depend on utilization of the dock). Determine the total average cost (dock costs plus truck waiting costs) per hour, if six docks are operated.

a. between $300 and $305 per hour

b. between $305 and $310 per hour

c. between $310 and $315 per hour

d. between $315 and $320 per hour e. more than $320 per hour

Explanation / Answer

Answer :    a)   between $ 300 and $305 per hour

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