Managerial Report: Office Equipment, Inc. (OEI) Service Capabilities
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’s business site within an average of 3 hours from the time that the customer 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 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 service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, after 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 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, OEI projects that it will have 20 customers, and within 2 years, OEI projects that it will have 30 customers. Although OEI 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 3-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 3-hour waiting time guarantee at the lowest possible total cost.
Managerial Report
Develop a managerial report (1,000-1,250 words) summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 and then 30 customers, and justify your response. Include a discussion of the following issues in your report:
What is the arrival rate for each customer?
What is the service rate in terms of the number of customers per hour? (Remember that the average travel time of 1 hour is counted as service time because the time that the service technician is busy handling a service call includes the travel time in addition to the time required to complete the repair.)
Waiting line models generally assume that the arriving customers are in the same location as the service facility. Consider how OEI is different in this regard, given that a service technician travels an average of 1 hour to reach each customer. How should the travel time and the waiting time predicted by the waiting line model be combined to determine the total customer waiting time? Explain.
OEI 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) probability that a customer will have to wait more than one hour for the service technician to arrive, and (g) the total cost per hour for the service operation.
Do you agree with OEI management that one technician can meet the average 3-hour service call guarantee? Why or why not?
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 Question 4 (above) to justify your answer.
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 Question 4 (above) to justify your answer.
What are the annual savings of your recommendation in Question 6 (above) compared to the planning committee's proposal that 30 customers will require three service technicians? (Assume 250 days of operation per year.) How was this determination reached?
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Benchmark Information
This benchmark assignment assesses the following programmatic competency:
Data Analysis - OEI Service Capabilities
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Data Analysis - OEI Service Capabilities Introduction Office Equipment, Inc. (OEI) is a company that specializes in leasing automatic mailing machines to its customer base in Indiana. As such, the company has built its brand on excellent customer service when providing maintenance and repair services of equipment. On average, OEI arrives within 3 hours after a customer places a request for a service. However, with the potential increase in its customer base, there are rising concerns on the ability of the single technician employed by the company to handle the customer requests based on the company’s 3-hour guarantee (Anderson, 2019). Consequently, this report analyzes OEI’s current service capabilities with the aim of providing relevant recommendations at the most affordable rates. Analysis Customer Arrival Rate The historical data on OEI customer service requests shows an average of one call per 50 hours of operation. Based on queuing formulas, the arrival rate is calculated by getting the inverse of the average time between service calls (Anderson, 2019). In this case, the rate will be calculated as: λ = 1/50 = 0.02 calls per hour Customer Service Rate The service rate is calculated by taking the total time taken to perform services for a customer per hour. In this case, the travel time and time taken to complete the service/repair add up to 2.5 hours (1 hour travel + 1.5 hours for service) (Singhal et al., 2019). The customer service rate therefore is calculated as: µ = 1/2.5 = 0.4 customers per hour Predicting the Waiting Time In OEI’s case, the customers are not in the general area of the company, forcing technicians to travel an average of 1 hour to reach them for services and repair. Consequently, to determine the total customer waiting time there is a need to combine the travel time and waiting time as predicted form the model. Therefore, by dividing the waiting time by the arrival rate and adding the 1-hour travel time taken by the technician will provide the total customer waiting time. Waiting Line Model In this case, we assume that the waiting line model is referred to as an M/M/1 model with a finite calling population. Based on OEI’s standards that 1 service technician can handle the 10 existing customers, the following aspects were calculated. a) Probability that no customers are in the system P0 = 1/[N!/ (N-n)!* (λ/µ)n] = 1 / 1.8537 = 0.537 b) Average number of customers in the waiting line (Lq) = N – [(λ + µ)/ λ](1-P0) = 10 – [(0.02+0.4)/0.02](1-0.537) = 0.277 c) Average number of customers in the system (L) = Lq + 1 – P0 = 0.227 + (1-0.537) = 0.69 d) Average time a customer waits until the service technician arrives (Wq) = Lq / (N-L) λ = 0.227 / (10-0.69)0.02 = 1.219 Adding the 1-hour travel time, the customer is expected to wait for 2.219 hours before the technician arrives for a service call. e) Average time a customer waits until the machine is back in operation (W) = Wq + 1/ µ = 2.219 / (1/0.4) = 0.85 hours f) Probability that a customer will have to wait more than one hour for the service technician to arrive P(W) = 1- P0 = 1- 0.537 = 0.463 g) Total cost per hour for the service operation TC = CwL...