You manage a drive-through restaurant. There are 4 order-booths but all of them

Question

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.

Explanation / Answer

a-Customers arrive in an hour=30, time required for processing of an order=6 minutes hence in an hour 60/6=10 orders can be processed.A customer wait for 6 minutes for processing order. 30 customers wait for 30*6=180 minutes that is 180/60=3 hours.Customers waiting time is worth $30 per hour.By improving the processing $30 per hour is needed.Now customer will be wait for 4 minutes hence saving in each processing=6-4=2 minutes.For 30 orders saving is 60minutes.So cost=$30 and benefit=$20. So economically it is not justifiable.

b-The new technology need to be processed 30 customers in one hour so it should take 2 minutes per order, so that average flow time will be 6minutes+2minutes=8minutes.

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