You are in charge of quarry that supplies sand and stone aggregates to your company’s construction sites. Empty trucks from construction sites arrive at the quarry and wait to enter the filling station, which can load them with sand and stone aggregates. At the filling station the trucks are filled, weighed, checked, and then proceed to a construction site. Currently, nine empty trucks arrive per hour, on average. It takes six minutes (hint: how many trucks can be served per hour?) at the stations to fill, weigh and check the trucks.
Concerned that the trucks are spending too much time waiting and at the service stations, you are evaluating two alternatives to reduce the average time the trucks spend in the system.
The first alternative is to add side board to the truck beds (so that more material could be loaded) and to add two helpers at the loading station (so that overall filling time could be reduced). The arrival rate of trucks would change to six per hour (you need less trucks to transport the same amount of material due to larger truck beds), and the filling time would be reduced to four minutes.
The second alternative is to add another filling station (i.e. add a second server) identical to the current one. The trucks would wait in a common line and the truck at the front would proceed to the next available station.
Answer the following questions:
a) What is the average time a truck spends in the system (waiting and loading) under the current conditions?
b) What is the average time a truck would spend in the system (waiting and loading) if the first alternative would be chosen?
c) What is the average time a truck would spend in the system (waiting and loading) if the second alternative would be chosen?
d) Which alternative provides the biggest improvement regarding the time spent in the system?
e) What further cost information would be required/useful to make a business decision?
f) What other factors would influence your investment decision between the two alternatives?
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