Question: 05 (Algorithmic)

The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $450 per order to cover the expenses of delivering and transferring the fuel to MBC's storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.07 per month, or $0.84 per year; and annual fuel usage is 210,000 gallons. MBC buses operate 210 days a year.

1. What is the optimal order quantity for MBC?
   
   Q* =
2. How frequently should MBC order to replenish the gasoline supply?
   
   orders per year
3. The MBC storage tanks have a capacity of 15,000 gallons. Should MBC consider expending the capacity of its storage tanks?
   
   Metropolitan Bus Company does not need to expand the capacity of its storage tanks.
4. What is the reorder point?

(a) Q* = 15,000

(b) 14 orders per year

(c) Does not need to expand

(d) Reorder Point = 10,000 units

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour.

1. What is the probability that no requests for assistance are in the system? If required, round your answer to four decimal places.
   
   P ₀ =
2. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.
   
   L _q =
3. What is the average waiting time in minutes before service begins? If required, round your answer to nearest whole number.
   
   W _q = min
4. What is the average time at the reference desk in minutes (waiting time plus service time)? If required, round your answer to nearest whole number.
   
   W = min
5. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.
   
   P _w =

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