WAITING LINE PROBLEM 1

Management is redesigning the customer service process in a large department store. Accomodating four customers is important. Customers arrive at the desk at the rate of two customers per hour. What is the probability that four customers will arrive during any hour?

What do you think should be the decision of the Manager of the Customer Service Desk regarding the space requirements of desk, waiting area and the seating capacity in the waiting area?

WAITING LINE PROBLEM 2

The Management of the large Department store in Problem 1 must determine whether more training is needed for the customer service clerk. The clerk at the customer service desk can serve an average of three customers per hour. What is the probability that a customer will require less than 10 minutes of service?

What do you think should be the Management’s decision to impart training for the customer service clerks ?

WAITING LINE PROBLEM 3

The manager of a grocery store in the retirement community of Sunnyville is interested in providing good service to senior citizens who shop in her store. Currently, the store has a separate check-out counter for senior citizens. On average, 30 senior citizens per hour arrive at the counter, according to a Poisson’s distribution, and are served at an average rate of 35 customers per hour, with exponential service times.

The manager of the Sunnyville grocery wants answers to the following questions :

a. What service rate would be required so that the customers averaged only 8 minutes in the system?

b. For that service rate, what is the probability of having more than four customers in the system?

c. What service rate would be required to have only a 10% chance of exceeding four customers in the system?

WAITING LINE PROBLEM 4

a. Manager of a Motor Vehicle licensing facility received complaints about the time people spend in the service facility. He estimated that 40 customers on average arrive per hour and the average number of customers being served at desk or in waiting is 30. Manager’s target is that not more than 30 minutes (on average) a customer should spend in the facility.

Would the Manager be required to add capacity or improve the work method or stay with the present arrangements?

b. In a manufacturing process, the average time a gear case (used for an outboard marine motor) spends at a machining center is 3 hours, and an average of 5 gearcases arrive at the machining center per hour. Average work in process (WIP) inventory of gearcases at the center should not exceed 12. Will the center need more capacity to be added ?

Attempt solving the above decision problems using Little’s Law.