Question

roblem No.3 (30%): Consider a mini-market that has a single sashier who scans the places them in bags. Customers have been complaining about the long waiting time. 1 manager is worried that this may lead to losing customers and subsequently their business. The manager approached you to find an economical solution to this problem. You accepted willingly to offer y services for free. First, customers from and to the mini-market. Your results showed that arrivals and-departures Markovian process. You computed the cashier service rate to be 22 customers per hour,and the arrival rate to be 20 customers per hour. Second, you estimated the hourly S10 per customer. The hourly wage of the cashier is S12. While collecting the data, you conducted a survey and found that customers would tolerate a waiting time in the system of no proposed three alternative designs to the queuing system in place. Design 1 suggests keeping the present design, i.e., do nothing. Design 2 suggests adding an assistant whose task is to place the purchased items in bags. Working as a team, the cashier and the assistant have a combined service rate of 25 customers hour. The assistant's hourly wage is $7. Design 3 suggests adding a second cashier with identical skills to the present cashier. Which design should you recommend to the manager? What should be the service rate of the present cashier so that the average waiting time in the system does not exceed 10 minutes? our data on inter-arrival and departures times between successive you started collecting follow a ting in queue to be more than 10 minutes. You per

Answer 1

According to given data implies the design I would be most economical It is better to continue with the present cashier as he already serving 22 customers per hour however the average customers arrival rate is only 20 customers per hour implies Hence he need not employ additional assistant or new cashier to improve the efficiency implies The existing cashier would be able to manage the load as he is already serving the customers the existing service rate could continue to ensure that the waiting time is less than 10 min