Question

In: Statistics and Probability

The Europa Company has a large warehouse in Florida to store its inventory of goods until...

The Europa Company has a large warehouse in Florida to store its inventory of goods until they are needed by the company’s many furniture stores in that area. A single crew with four members is used to unload and/or load each truck that arrives at the loading dock of the warehouse. Management currently is downsizing to cut costs, so a decision needs to be made about the future size of this crew.

Trucks arrive randomly at the loading dock at a mean rate of 2 per hour. The time required by a crew to unload and/or load a truck has an exponential distribution with a mean given by (60/n) minutes where n is crew size. The cost of providing each member of the crew is $20 per hour. The cost that is attributable to having a truck not in use (i.e., a truck standing at the loading dock) is estimated to be $30 per hour.

  1. For the crew-size you determine in (b), calculate the following:
  1. Average utilization of crew
  2. Average number of trucks waiting to be unloaded
  3. Average time in queue
  4. Probablity at least 2 trucks will be waiting to be unloaded
  5. Probability a truck will have to wait at least 1 hour prior to unloading
  6. Probability that a truck will be in and out of the dock in 1 hour
  1. Using the same crew-size as in (a), assume that with the use of modern lifting equipment, the standard deviation of unloading time is reduced by 50%. This means service time no longer has an exponential distribution. Calculate:
    1. The average number of trucks waiting to be unloaded
    2. The average time in queue
    3. Compare your answers with those for part (c). What is the explanation for the difference?

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Expert Solution

orchestra answered 1 year ago
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