You are in charge of a quarry that supplies sand and stone a

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 lad either sand or aggregate. At the station, they are filled with material, weighed, checked out, and proceed to a construction site. Currently, nine (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 to add 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 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.

Which alternative would you recommend if you want to reduce the current average time the trucks spend in the system, including service? Show answer.

Solution

Empty trucks arrive 9 per hour and it takes 6 minutes to be filled, weighed and check out. Therefore we can say that the arrival rate is 9/hr and service rate is 10/hr in terms of queuong system.

The average time spent by a truck in the existing queue system = 1/ (service rate-arrival rate) = 1/(10-9) = 1 hour

Under the first alternative by hiring a helper, the arrival rate would be 6 per hour and filling time 4 minutes. In other words arrival rate would be 6/hr and service rate would be 15/hr and thus average time spend would be 1/(15-6) hr.

Ultimate conclusion under first alternative is savings of 8/9 hr (1-(1/9)) in average time spent in the system with a total cost of $50,000.

Second alternative is to have another loading station identical to earlier one at additional cost of $80,000. There will be reduction in the average time spent by 50%. In other words on the average saving of 1/2 hr at cost of $80,000.

On comparing, costs for saving average time spend by a truck in the system, it is preferred to have First Alternative.