Waiting Line Models

Order Details
Office Equipment, Inc (OEI), leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer business site within an average of three hours from the time that the customers notifies OEI of an equipment problem.
Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates 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 travel time to reach the customer 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 service, the technician completes the current service 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 commitment, the technician takes an average of 1 hour travel time to reach the new customer office and an average of 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. The downtime cost (wait time and service time) for customers is $100 per hour.
OEI is planning to expand its business. Within one year, OEI projects that it will have 20 customers and within two years, OEI projects that it will have 30 customers. Although OEI is satisfied that one service technician can handle the 10 existing customer, management is concerned about the ability of one technician to meet the average three-hour service call guarantee when the OEI customer base expands. In a recent planning meeting, the marketing manager made a proposal to add a second service technician when OEI reaches 20 customers and to add a third service technician when OEI reaches 30 customers. Before making a final decision, management would like an analysis of OEI service capabilities. OEI is particularly interested in meeting the average three-hour waiting time guarantee at the lowest possible total cost.
Develop a managerial report summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 customers and when OEI reaches 30 customers. Include a discussion of the following issues in your report:
1. What is the arrival rate for each customer per hour?
2. What is the service rate in terms of the number of customer 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 all includes the travel time plus the time required to complete the repair.
3. Waiting line models generally assume that the arriving customers are in the same location as the service facility. Discuss the OEI situation in light of the fact that a service technician travels an average of 1 hour to reach each customer. How should the travel time and the waiting time predicated by the waiting line middle be combined to determine the total customer waiting time?
4. OEI is satisfied that one service technician can handle 10 existing customers. Use a waiting line model to determine the following information:
– Probability that no customers are in the system
– Average number of customers in the waiting line
– Average number of customer in the system
– Average time a customer waits until the service technician arrives
– Average time a customer waits until the machine is back in operation
– Probability that a customer will have to wait more than one hour for the service technician to arrive
– The number of hours a week the technician is not making service calls
– The total cost per hour for the service operation
Do you agree with the OEI management that one technician can meet the average three-hour service cal guarantee? Explain
5. What is your recommendation for the number of service technicians to hire when OEI 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 OEI expands to 30 customers? Use the information that you developed in part 4 to justify your answer
7. When are the annual savings of your recommendation in part 6 compared to the planning committee proposal that 30 customers will require three service technicians? Assume 250 days of operation per year