CASE #2: CLASSIC MODELS Name(s): Burger Dome fast-food restaurant. Burger Dome sells hamburgers, cheeseburgers, french fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selec- tions. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Burger Dome is concerned that the methods currently used to serve customers are resulting in excessive waiting times and a possible loss of sales. Management wants to conduct a waiting line study to help determine the best approach to reduce waiting times and improve service. In the current Burger Dome operation, an employee takes a customer's order, determines the total cost of the order, receives payment from the customer, and then fills the order. Once the first customer's order is filled, the employee takes the order of the next customer waiting for service. This operation is an example of a single-server waiting line. Each customer entering the Burger Dome restaurant is served by a single order-filling station that handles order placement, bill payment, and food delivery. When more customers arrive than can be served immediately, they form a waiting line and wait for the order-filling station to become available. Suppose that Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 45 customers per hour and that the time between arrivals is independent for each customer. Also, though at Burger Dome, the number of items ordered and the mix of items ordered vary considerably from one customer to the next. Small orders can be handled in a matter of seconds, but large orders may require more than two minutes.Burger Dome studied the order-filling process and found that a single employee can process an average of 60 customer orders per hour and the serving times are independent and memoryless. (a) Calculate all the queuing metrics for Burger Dome. After reviewing the operating characteristics provided by the waiting line model, Burger Dome's management concluded that improvements designed to reduce waiting times were de- sirable. To make improvements in the waiting line operation, Burger Dome's analysts suggest two ways to improve the service rate. 1. Increase the service rate by letting customers introduce their order themselves in a tablet attached to the counter and proceed directly to payment. With this design the service rate can increase from 60 to 75 customers per hour. 2. Add one server so that more customers can be served simultaneously. (b) Calculate the queuing metrics for both models and compare them. Burger Dome's managers have realized that these changes will considerably improve the service but also the operating costs. Suppose that BD has estimated the following costs: Service cost: This includes the server's wages, benefits and any other direct costs asso- ciated with operation the channel. In this case, this cost is $12 per channel. Waiting time cost: This one is harder to evaluate, but Burger Dome has estimated a cost of $15 per hour for customer waiting. 1 (c) Compare the cost of the single channel and two channel models (ignore the option of the tablet, since this one would have a fixed cost of the purchase and installation of the tablet and this can't be compared with the per hour costs of the other two models). (d) Since the estimation of the Waiting Time cost is so hard, BD is worried that if they overestimated it, their decision will be wrong and decide to do a little sensitivity analysis. What is the minimum waiting time cost that would lead BD to implement the two-channel model. Comment. (e) Considering all the analysis done, what would be your recommendation for Burger Dome?