A warehouse has 1 loading dock and 3 persons for loading operations

Q. A warehouse has 1 loading dock and 3 persons for loading operations. The arrival rate of trucks follows Poisson distribution with a mean of 4 trucks/hour. The average loading time (by three persons together) per truck is exponentially distributed with a mean of 10 minutes. The charge of the trucks per hour and loading charges per person per hour are Rs.20 and Rs.6, respectively. The total cost (in Rs./hour) is    

Ans: 57 – 59

Sol:

Total cost in one hour = Loading crew cost + Cost of waiting time

Loading crew cost = Number of loaders × Hourly wage rate

Cost of waiting time = Ws × λ × (truck charge per hour)