Question

Consider a mini-market that has a single cashier who scans the purchased items and places them in bags. Customers have been complaining of the long waiting time. The mini-market 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 avvepted willingly to offer your services for free. First, you started collecting data on inter-arrival and departure times between succesive customers from and to the mini-market. Your analysis of the data revealed that the inter-arrival and service times are exponentially distributed random variables. You computed the cashier's service rate to be 22 customers per hour, and the customer's arrival rate to be 20 customers per hour. The hourly wage of the cashier is $12 per hour. While collecting the data, you conducted a survey to find how much customers are willing to tolerate waiting in the system. The survey revealed that customers are willing to tolerate a waiting time in the system of no more than ten minutes . You proposed three alternati e designs to the queing system in place. Design 1 is to keep the present design, that ism you suggest to the manager to 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 service rate of 25 customers per hour. The assistant's hourly wzge is $7 per hour. Design three suggests adding a second cashier with identical skills to the present cashier. Which design is most economical to implement? What should be the service rate of the present cashier so that the average waiting time in the system does not exceed ten minutes?

Answer 1

Answer:

Design 1 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. Hence, he need not employ additional assistant or new cashier to improve the efficiency. 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 minutes.