Office Equipment, Inc. (OEI) leases automatic mailing machinesto business customers in Fort Wayne, Indiana. The company built itssuccess on a reputation of providing timely maintenance and repairservice. Each OEI service contract states that a service technicianwill arrive at a customer’s business site within an average of 3hours from the time that the customer notifies OEI of an equipmentproblem.

Currently, OEI has 10 customers with service contracts. Oneservice technician is responsible for handling all service calls. Astatistical analysis of historical service records indicates that acustomer requests a service call at an average rate of one call per50 hours of operation. If the service technician is available whena customer calls for service, it takes the technician an average of1 hour of travel time to reach the customer’s office and an averageof 1.5 hours to complete the repair service. However, if theservice technician is busy with another customer when a newcustomer calls for service, the technician completes the currentservice call and any other waiting service calls before respondingto the new service call. In such cases, after the technician isfree from all existing service commitments, the technician takes anaverage of 1 hour of travel time to reach the new customer’s officeand an average of 1.5 hours to complete the repair service. Thecost 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 1 year, OEIprojects that it will have 20 customers, and within 2 years, OEIprojects that it will have 30 customers. Although OEI is satisfiedthat one service technician can handle the 10 existing customers,management is concerned about the ability of one technician to meetthe average 3-hour service call guarantee when the OEI customerbase expands. In a recent planning meeting, the marketing managermade a proposal to add a second service technician when OEI reaches20 customers and to add a third service technician when OEI reaches30 customers. Before making a final decision, management would likean analysis of OEI service capabilities. OEI is particularlyinterested in meeting the average 3-hour waiting time guarantee atthe lowest possible total cost.

Managerial Report

Develop a managerial report (1,000-1,250 words) summarizing youranalysis of the OEI service capabilities. Make recommendationsregarding the number of technicians to be used when OEI reaches 20and then 30 customers, and justify your response. Include adiscussion of the following issues in your report:

1. What is the arrival rate for each customer?
2. What is the service rate in terms of the number of customersper hour? (Remember that the average travel time of 1 hour iscounted as service time because the time that the servicetechnician is busy handling a service call includes the travel timein addition to the time required to complete the repair.)
3. Waiting line models generally assume that the arrivingcustomers are in the same location as the service facility.Consider how OEI is different in this regard, given that a servicetechnician travels an average of 1 hour to reach each customer. Howshould the travel time and the waiting time predicted by thewaiting line model be combined to determine the total customerwaiting time? Explain.
4. OEI is satisfied that one service technician can handle the 10existing customers. Use a waiting line model to determine thefollowing information: (a) probability that no customers are in thesystem, (b) average number of customers in the waiting line, (c)average number of customers in the system, (d) average time acustomer waits until the service technician arrives, (e) averagetime a customer waits until the machine is back in operation, (f)probability that a customer will have to wait more than one hourfor the service technician to arrive, and (g) the total cost perhour for the service operation.
5. Do you agree with OEI management that one technician can meetthe average 3-hour service call guarantee? Why or why not?
6. What is your recommendation for the number of servicetechnicians to hire when OEI expands to 20 customers? Use theinformation that you developed in Question 4 (above) to justifyyour answer.
7. What is your recommendation for the number of servicetechnicians to hire when OEI expands to 30 customers? Use theinformation that you developed in Question 4 (above) to justifyyour answer.
8. What are the annual savings of your recommendation in Question6 (above) compared to the planning committee's proposal that 30customers will require three service technicians? (Assume 250 daysof operation per year.) How was this determination reached?