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At a single-phase, multiple-channel service facility, customers arrive randomly. Statistical analysis of past data shows that the interarrival time has a mean of 20 minutes and a standard deviation of 4 minutes. The service time per customer has a mean of 15 minutes and a standard deviation of 5 minutes. The waiting cost is $200 per customer per hour. The server cost is $25 per server per hour. Assume general probability distribution and no buffer capacity restriction.
a. Find the optimal number of servers to be employed to minimize the total of waiting and server costs. (Ans: Cost per hour with one server=$59.00; Cost with 2 servers = $52.19; Cost with 3 servers = $75.40: So two servers are optimal.)
b. Find the average waiting time and the average total time through the system for the optimal case. (waiting: 0.2188 min; Total: 15.2118 min)
c. Find the cost per hour, average waiting time, and average flow time for one server if the probability distributions for the interarrival time and service time are assumed to be exponential and the mean values remain the same. The cost data remain the same. Use manual calculations. (Ans: Cost per hour=$475.00, Waiting time=45.00 min, Flow time=60.00 min).
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