Assignment task:
You are in charge of a quarry that supplies sand and stone aggregates to your company's construction sites. Empty trucks from construction sites arrive at the quarry's huge piles of sand and stone aggregates and wait in line to enter the station, which can load either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceeded to a construction site. Currently, 9 empty trucks arrive per hour, on average. Once a truck has entered a loading station, it takes 6 minutes for it to be filled, weighed, and checked out. Concerned that trucks are spending too much time waiting and being filled, you are evaluating two alternatives to reduce the average time the trucks spend in the system. The first alternative is to add side boards to the trucks (so that more material could be loaded) and a helper at the loading station (so that filling time could be reduced) at a total cost of $50,000. The arrival rate of trucks would change to six per hour, and the filling time would be reduced to 4 minutes.
The second alternative is to add another loading station identical to the current one (second server model) at a cost of $80,000. The trucks would wait in a common line and the truck at the front of the line would move to the next available station. You realized adding another loading station is a 2 server model! Thus, you calculated the average waiting time in the system using Solver and the result is W= 0.1254 hour or 7.52 minutes!
a. What is the average time a truck waits in the system with current setup?
b. What is the average time a truck waits in the system if you apply the first alternative?
c. Which alternative would you recommend if you want to reduce the current average time the trucks spend in the system, including service?