You manage a drive-through restaurant. There are 4 order-booths but all of them are served by a single queue. You know that customers arrive at an average rate of 30 per hour. At present, an order takes an average of 6 minutes to process. You are contemplating on purchasing some technology that will allow you to improve processing time to an average of 4 minutes per order. This technology will need to be rented at the cost of $30 per hour. Assume inter-arrival and processing times are exponentially distributed.
a) If you expect the customer’s waiting time in queue to be worth $20 per customer per hour (lost sales, dissatisfaction etc.), is renting of the new technology economically justifiable?
b) How good would the new technology need to be (how low should it make the average processing time) to ensure an average flow time of 8 minutes for the customer.