What is the arrival rate for each customer per hour

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Reference no: EM13544307

Case Study 1 - Abu Dhabi Equipment, Inc.

Abu Dhabi Equipment, Inc. (AEI) leases automatic mailing machines to business customers in Abu Dhabi, UAE. The company built its success on a reputation for providing timely maintenance and repair service. Each AEI service contract states that a service technician will come to a customer's business site within an average of three hours from the time that the customers informs AEI of an equipment problem.

Currently, AEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records shows that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer's office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for a service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, once the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer's office and an average of 1.5 hours to complete the repair service. The cost of one service technician is $80 per hour. The downtime (wait time and service time) for customer is $100 per hour.

AEI is planning to expand its business. Within a year, AEI projects that it will have 20 customers, and within two years, AEI projects that it will have 30 customers. Although AEI is satisfied that one service technician can handle the 10 existing customers, management is concerned about the ability of one technician to meet the average three-hour service guarantee when the AIE customer base expands.  In a recent planning meeting, the marketing manager made a proposal to add a second service technician when AEI reaches 20 customers and to add a third service technician when AEI reaches 30 customers. Before making a final decision, management would like an analysis of AEI service capabilities. AEI is particularly interested in meeting the average three-hour waiting time guarantee at the lowest possible total cost.

Required:

Develop a managerial report summarizing your analysis of the AEI service capabilities. Make recommendations regarding the number of technicians to be used when AEI reaches 20 customers and AEI reaches 30 customers. Include a discussion of the following in your report.

1. What is the arrival rate for each customer per hour?

2. Which queuing model will you use? What is arrival rate for each customer per hour?

3. What is the service rate in terms of the number of customers per hour? Note that the average travel time of 1 hour becomes part of the service time because the time that the service technician is busy handling a service call include the travel time plus the time required to complete the repair.

4. AEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information:

a. Probability that no customers are in the system

b. Average number of customers in the waiting line

c. Average number of customers in the system

d. Average time a customer waits until the service technician arrives

e. Average time a customer waits until the machine is back in operation

f.  The number of hours a week the technician is not making service calls. A technician works 40 hours a week.

g. The total cost per hour for the service operation

Do you agree with AEI management that one technician meet the average three-hour service call guarantee?(The average time a customer spends in the waiting line is the average time for the service technician to complete all previous service call commitments and be ready to travel to the new customer. Since the average travel time is 1 hour for the service technician to reach the new customer's office, the total customer waiting time is Wq + 1)

5. What is your recommendation for the number of service technicians to hire when AEI expands to 20 customers? Use the information that you developed in part (4) to justify your answer.

6. What is your recommendation for the number of service technicians to hire when AEI expands to 30 customers? Use the information that you developed in part (4) to justify your answer.

7. What are the annual savings of your recommendation in part (6) compared to the planning committee's proposal that 30 customers will require three service technicians? Assume 250 days of operation per year.

Reference no: EM13544307

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