Office Equipment Inc Managerial Report

Office Equipment Inc Managerial Report

Office Equipment Inc. (OEI) is a company that leases automatic mailing machines to customers conducting various businesses in Fort Wayne, Indiana. The company boasts a positive reputation for providing timely repair and maintenance services to its clients (Anderson et al., 2013). The company plans to expand its business and projects that it will have 20 customers within one year and 30 customers within the next two years. Although the firm is satisfied that one service technician can handle the current ten customers, there is a concern about whether the technician can take the guaranteed three-hour service call upon expanding the customer base. In a recent planned meeting, the marketing manager proposed adding a second technician when the customer base reaches 20 customers and three service technicians when the customer base reaches 30 customers (Anderson et al., 2013). Therefore, the current managerial report analyses the OEI service capabilities to determine how the company can meet the guaranteed three-hour average waiting time under minimal costs.

The hourly arrival rate for each customer

It is crucial to obtain the arrival rate for each customer. The current average velocity of customer requests for service is one for every 50 hours of operation. Therefore, the arrival rate can be obtained as follows;

Let arrival rate be λ, then λ= 1call/50 hours= 0.002 calls/hour

Therefore, the arrival rate for each customer is 0.02 calls per hour.

The service rate in terms of the number of customers per hour

It is important to note that the average travel time is counted as the service time since the time a technician takes to handle a service call and the time required to complete the repair. Therefore, the average service time becomes;

Time taken in travel + time taken in repair= 1+ 1.5= 2.5hours

Then, μ= 1/ 2.5 hours= 0.4 customers per hour.

The service rate in terms of customers per hour is 0.4.

I am predicting the waiting and travel times using the waiting line model to combine the two variables and determine the total customer waiting time.

The waiting time and the travel time can be combined to determine the total waiting time for a customer. In this combination, it is essential to note that the one hour the technician takes to travel is to be included as part of the service time. Since the customer has to wait for the technician to arrive for 1 hour, the travel must be included in the waiting line model in determining the total waiting time for the customer. This way, although waiting line models assume that the customer is at the exact location of the service facility when they are not, accounting for the time taken by the technician to reach the area makes the model more accurate.

4. I am using the waiting line model in determining the following factors. Currently, the OEI has ten clients and one service technician. Applying the M/M/1 model in Excel-QM gives the values as follows;
5. The probability that there are no customers in the system= P₀= 0.5380
6. The average number of customers in the waiting line= L_q= 2972
7. To obtain the Average number of customers in the system= L=1-0.2972= 0.7593
8. The average time a customer should wait in the queue for the service technician to arrive= W_total= Travel time + waiting time= 1 + 1.6082 = 2.6082 hours
9. The average time the customer should wait until the machine is back in operation= W= 2.6082+ 1.5= 4.1082 hours
10. To obtain the probability that the customer has to wait for more than 1 hour before the service technician arrives is, P= 0.4620
11. Total cost per hour for the service operation= TC= $80 + $100(0.7593) = $155.93 Per hour.
12. Whether one technician can meet the average 3-hour service call guarantee as OEI management suggests.

The analysis implies that the service technician can meet the 3-hour service call guarantee since the average waiting time until a technician arrives is 2.6082 hours. If the average waiting time could exceed 3 hours, then the service technician cannot meet the average service call guarantee. The total cost for the service is $155.93 per hour.

A recommendation for the average number of service technicians that OEI should hire when the customer base expands to 20 customers.

Using the m/m/1 Model for 20 customers,

The probability that there are no customers in the system is 0.3525

The average number of customers in the waiting line: 0.2104

The average number of customers in the system is 1.1527

Customer’s average waiting time until a technician arrives= 0.5581 hours

Average waiting time until the machine is back in operation= 3.0581 hours

Probability that a customer waits for more than one 1hour before the technician arrives = 0.2949

Total cost per hour of the service operation

The number of hours the service technician is not making calls each week;

P0= 0.3525 x 2 x 40 hours= 28.2 hours

P1=0.3525 x 1 x 40 hours = 14.1 hours

Total = 42.3 hours

Since the average time in the waiting line increases to 6.9454 + 1 hour = 7.9454 hours when the customer base extends to 20 customers, one technician cannot meet the average waiting time, which is too long. This necessitates a second service technician. The average cost of service per hour also increases to $275.27 per hour.

A recommendation for the number of service technicians when the OEI customer base expands to 30 customers.

The probability that there are no customers in the system is 0.1760

The average number of customers in the waiting line is 0.9353

The average number of customers in the system = 2.3194

Average waiting time for the customer before the service technician arrives = 1.6895 hours

Average waiting time until the machine is back in operation= 4.1895

The probability that a customer waits for more than an hour before the service technician arrives= 1.6895 hours

The average time taken before the machine is back in operation= 4.1895

The probability that a customer waits more than 1 hour before the service technician arrives= 0.5600

P₀= 0.1760(0.1760) x 2technicians x 40 hours = 14.08 hours

P₁= 0.2640(0.2640) x 1technician x 40 hours = 10.56 hours

Total hours = 14.08 + 10.56= 26.64 hours

Total cost per hour of service operation= $391.94

When the customer base expands to 30, the average waiting time online increases to 2.6895. The average cost per service hour for two technicians is $391.94, which is $397.08 per hour for three technicians. Although the waiting time for the service technicians is shorter, they can finish the work within three hours and at a lower cost. This implies that the two technicians can still serve the customer base when it expands to 30 customers.

A recommendation for the annual savings compared to the committee’s initial proposal of 3 service technicians to serve 30 customers. (Assuming 250 days of operation per year)

This requires a comparison of savings when operating with two technicians and working with three technicians. The cost of service per hour for the proposed three technicians for 30 customers is $397.08 per hour. For the recommended two technicians, the spending is $391.94 per hour. The total savings per year becomes;

Total cost saved= ($397.08 – $391.94) x 8 hours a day x 250 days a year = $10,280 per year

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, A. J., Fry, M. J., & Ohlmann, J. W. (2013). Quantitative Methods for Business. (13.Ed.). South-Western, Cengage Learning.

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To recommend the most efficient use of time and resources.

(This assignment has been adapted from Case Problem 2 in Chapter 15 of the textbook.)

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 Fort Wayne, Indiana business customers. The company built its success on its reputation for 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 when the customer notifies OEI of an equipment problem.

Currently, OEI has ten 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. Suppose the service technician is available when a customer calls for service. In that case, it takes the technician an average of 1 hour of travel time to reach the customer’s office and 1.5 hours to complete the repair service. However, suppose the service technician is busy with another customer when a new customer calls for service. In that case, the technician completes the current service and any other waiting service before responding to the recent service call. In such cases, after the technician is free from all existing service commitments, the technician takes 1 hour of travel time to reach the new customer’s office and 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. Customers’ downtime costs (wait and service time) are $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, it will have 30 customers. Although OEI is satisfied that one service technician can handle the ten 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 proposed adding a service technician when OEI reaches 20 customers and adding a service tech has called 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:

1. What is the arrival rate for each customer?
2. What is the service rate regarding the number of customers per hour? (Remember that the average travel time of 1 hour is counted as service time because the service technician is busy handling a service call, including the travel time and the time required to complete the repair.)
3. Waiting line models generally assume that the arriving customers are in the exact location of 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. OEI is satisfied that one service technician can handle the ten 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 you developed in Question 4 (above) to justify your answer.
7. What is your recommendation for the number of service technicians to hire when OEI expands to 30 customers? Use the information 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?

Prepare this assignment according to the guidelines in the APA Style Guide in the Student Success Center. An abstract is not required.