Question: Truckloads of seasonal merchandise arrive to a distribution center within a 2 week span. Because of this, merchandised-filled trucks waiting to unload have been known to back up for a block at the receiving dock. The increased cost by unloading delays including truck rental and idle driver time is of significant concern to the company. The estimated cost of waiting and unloading for truck and driver is $18 per hour. During the 2 week delivery time, the receiving dock is opened 16 h/day, 7 days/week, and can on average unload 35 trucks/h according. The unloading times closely follow an exponential distribution. Full trucks arrive during the time the dock is opened at a mean rate of 30 per hour, with interarrival times following an exponential distribution. To help the company get a handle on the problem of lost time while trucks are waiting in line or unloading at the dock, find the following measures of performance:
a. The average number of trucks in the unloading process.
b. The average cycle time.
c. The probability that there are more than three trucks in the process at any given time.
d. The expected total daily cost of having the trucks tied up in the unloading process.
e. It has been estimated that if the storage area were to be enlarged, the sum of waiting and unloading costs would be cut in half next year. If it costs $9000 to enlarge the storage area, would it be worth the expense to enlarge it?