Question: Trucks arrive at a warehouse according to a Poisson process
Trucks arrive at a warehouse according to a Poisson process with a mean rate of 4 per hour. Only one truck can be loaded at a time. The time required to load a truck has an exponential distribution with a mean of 10/n minutes, where n is the number of loaders (n = 1, 2, 3, . . .). The costs are (i) $18 per hour for each loader and (ii) $20 per hour for each truck being loaded or waiting in line to be loaded. Determine the number of loaders that minimizes the expected hourly cost.
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