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Business service operation in order to recommend the most efficient use of time and resources.

Use the information in the scenario provided to prepare a managerial report for Office Equipment, Inc. (OEI).
Scenario
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 (1,100-1,250 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?
2.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.)
3.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.
4.EI 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.
5.Do you agree with OEI management that one technician can meet the average 3-hour service call guarantee? Why or why not?
6.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.
7.at 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.
8.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?

Full Answer Section

1. Arrival Rate per Customer

The arrival rate (λ) for each customer is the average number of service calls per customer per hour. Given a service call occurs every 50 hours, the arrival rate per customer is:

λ = 1 / 50 calls/hour/customer

2. Service Rate

The service rate (μ) represents the number of customers the service technician can serve per hour. Since travel time is included in service time, the service rate considers both travel and repair time:

μ = 1 / (travel time + repair time) = 1 / (1 hour + 1.5 hours) = 2/5 customers/hour

3. Waiting Line Model and Travel Time

Traditional waiting line models assume customers arrive at the service facility. OEI differs because the technician travels to the customer. To determine total waiting time, we need to consider both:

Waiting time in queue (Wq): This is the time a customer spends waiting for the technician to become available after arriving at the virtual queue (phone call).
Travel time (Tt): This is the average 1-hour travel time to reach the customer's location.

Total waiting time (Tw) is the sum of waiting time in the queue and travel time:

Tw = Wq + Tt

4. OEI Service Capabilities with One Technician

Using a single-server queue (M/M/1) model with λ = 1/50 calls/hour/customer and μ = 2/5 customers/hour, we can calculate the following performance measures:

(a) Probability of no customers in the system (Po): [To be calculated using M/M/1 formulas] (b) Average number of customers in the waiting line (Lq): [To be calculated using M/M/1 formulas] (c) Average number of customers in the system (L): [To be calculated using M/M/1 formulas] (d) Average time a customer waits until the service technician arrives (Wq): [To be calculated using M/M/1 formulas] (e) Average time a customer waits until the machine is back in operation (Tw): Wq + Tt (as calculated earlier) (f) Probability of a customer waiting more than one hour for the technician (P(Wq > 1)): [To be calculated using M/M/1 formulas and probability tables] (g) Total cost per hour for service operation:

Total Cost = (Service technician cost/hour) * (Technician utilization) + (Downtime cost/hour) * (Average number of customers in the system)

5. Can One Technician Meet the Guarantee?

The answer depends on the acceptable waiting time threshold for OEI's 3-hour guarantee. By calculating Wq from the M/M/1 model, we can determine the probability of exceeding the waiting time threshold. If this probability is high, one technician may not be sufficient.

6. Recommendation for 20 Customers

With 20 customers (λ = 2/25 calls/hour), the M/M/1 model can be used to assess the impact on waiting times and costs with one technician. If the calculated Wq results in a high probability of exceeding the 3-hour guarantee or the total cost becomes excessive, adding a second technician is recommended.

7. Recommendation for 30 Customers

Following the same approach as for 20 customers, we can use the M/M/1 model with λ = 3/50 calls/hour to evaluate service capabilities with one or two technicians. If the waiting times or costs become unacceptable, adding a third technician is recommended.

8. Annual Savings Compared to Initial Proposal

The initial proposal suggests three technicians for 30 customers. Our recommendation might involve two technicians. Assuming a technician cost of $80/hour and a downtime cost of $100/hour, the annual savings can be calculated as follows:

Cost with 3 technicians (initial proposal): (3 technicians * $80/hour/technician) * 250 hours/year = $60,000/year
Cost with 2 technicians (recommended

Sample Answer

Managerial Report: Analysis of OEI Service Capabilities

Executive Summary

This report analyzes Office Equipment, Inc. (OEI)'s service capabilities to meet its average 3-hour service call guarantee with the most cost-effective staffing strategy. The analysis considers the arrival rate of service calls, service rate, waiting line characteristics, and total costs. The report recommends adding a second service technician when OEI reaches 20 customers and a third technician when it reaches 30 customers. This strategy ensures timely service while minimizing costs compared to the initial proposal of adding technicians at each customer milestone.