A building-materials firm loads trucks with two pay loader tractors. The distrib

Question

A building-materials firm loads trucks with two pay loader tractors. The distribution of truck-loading times has been found to be exponential with a mean loading time of 6 minutes. The truck interarrival time is exponentially distributed with an arrival rate of 16 per hour. The waiting time of a truck and driver is estimated to cost $50 per hour. How much (if any) could the firm save (per 10 hour day) if an overhead hopper system that would fill any truck in a constant time of 2 minutes is installed? (Assume that the present tractors could and would adequately service the conveyors loading the hoppers.)

Explanation / Answer

Earlier, every truck used to wait 6 minutes. total wait time = total hours*no. of trucks in one hour*6 minutes=10*16*6= 1056 minutes

Waiting time paid by the company = (total wait time in minutes/60)*$50= (1056/60)*$50=$880

After installing hopper,  total wait time = total hours*no. of trucks in one hour*2= 10*16*2=320 minutes=5.33 hours

Waiting time paid by the company = (total wait time)*$50=5.33*$50=$266.67

Money saved by firm After installing hopper = 880-266.67= $613.33.

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