Maths Solutions 35

Schips Department Store operates a fleet of 10 trucks. The trucks arrive at random times throughout the day at the store- truck dock to be loaded with new deliveries or to have incoming shipments from the regional warehouse unloaded. Each truck returns to the truck dock for service two times per 8-hour day. Thus, the arrival rate per truck is 0.25 trucks per hour. The service rate is 4 trucks per hour. Using the Poisson arrivals and exponential service times model with a finite calling population of 10 trucks, determine the following operating characteristics:
a. The probability not trucks are at the truck dock
b. The average number of truck waiting for loading/unloading
c. The average number of trucks in the truck dock area
d. The average waiting time before loading/unloading begins
e. The average waiting time in the system
f. What is the hourly cost of operation if the cost is $50 per hour for each truck and $30 per hour for the truck dock?
g. Consider a two-channel truck dock operation where the second channel should be operated for an additional $30 per hour. How much would the average number of trucks waiting for loading/unloading have to be reduced to make the two-channel truck dock economically feasible?
h. Should the company consider expanding to the two-channel truck dock? Explain.