Office Equipment, Inc. (OEI)

by | Jan 12, 2025 | business

 

Apply a waiting line model to a 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:
1. 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. 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.
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. 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.
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 found in the APA Style Guide, located in the Student Success Center. An abstract is not required.

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.

Managerial Report: Analysis of OEI Service Capabilities

1. Arrival Rate

  • Current: For 10 customers, the arrival rate (λ) is 1 call / 50 hours of operation.
  • Projected:
    • 20 customers: λ = 2 calls / 50 hours = 0.04 calls/hour
    • 30 customers: λ = 3 calls / 50 hours = 0.06 calls/hour

2. Service Rate

  • Service Time: Average service time (μ) = Travel time + Repair time = 1 hour + 1.5 hours = 2.5 hours
  • Service Rate: μ = 1 customer / 2.5 hours = 0.4 customers/hour

3. Travel Time and Waiting Time

Managerial Report: Analysis of OEI Service Capabilities

1. Arrival Rate

  • Current: For 10 customers, the arrival rate (λ) is 1 call / 50 hours of operation.
  • Projected:
    • 20 customers: λ = 2 calls / 50 hours = 0.04 calls/hour
    • 30 customers: λ = 3 calls / 50 hours = 0.06 calls/hour

2. Service Rate

  • Service Time: Average service time (μ) = Travel time + Repair time = 1 hour + 1.5 hours = 2.5 hours
  • Service Rate: μ = 1 customer / 2.5 hours = 0.4 customers/hour

3. Travel Time and Waiting Time

The waiting line model assumes customers wait in a queue at the service facility. However, in OEI’s case, customers wait for the technician to arrive at their location.

  • Combined Waiting Time:
    • The waiting time predicted by the model represents the time a customer waits in the queue for the technician to become available.
    • To determine total customer waiting time, we must add the travel time (1 hour) to the waiting time predicted by the model.

4. Analysis for 10 Customers (Single Technician)

  • Model: We can use the M/M/1 queuing model (Poisson arrivals, exponential service times, single server) to analyze the current situation.  

    • λ = 1 call / 50 hours = 0.02 calls/hour
    • μ = 0.4 customers/hour

  • Calculations:

    • (a) Probability of no customers in the system (P0) = 1 – (λ/μ) = 1 – (0.02/0.4) = 0.95
    • (b) Average number of customers in the waiting line (Lq) = (λ^2) / (μ * (μ – λ)) = (0.02^2) / (0.4 * (0.4 – 0.02)) = 0.0026 customers
    • (c) Average number of customers in the system (Ls) = λ / (μ – λ) = 0.02 / (0.4 – 0.02) = 0.0526 customers
    • (d) Average waiting time in the queue (Wq) = Lq / λ = 0.0026 customers / 0.02 calls/hour = 0.13 hours
    • (e) Average time in the system (Ws) = Ls / λ = 0.0526 customers / 0.02 calls/hour = 2.63 hours
    • (f) Probability of waiting more than 1 hour (P(W > 1)) = P0 * (λ/μ) * e^(-μ(1-Wq)) = 0.95 * (0.02/0.4) * e^(-0.4 * (1 – 0.13)) = 0.0039
    • (g) Total cost per hour:
      • Technician cost: $80/hour
      • Customer downtime cost: (Ls * $100/hour) = 0.0526 customers * $100/hour = $5.26/hour
      • Total cost = $80/hour + $5.26/hour = $85.26/hour

5. Meeting the 3-Hour Guarantee

  • Based on the calculations, the average time a customer waits until the machine is back in operation (Ws) is 2.63 hours, which meets the 3-hour service call guarantee.

6. Recommendation for 20 Customers

  • With 20 customers (λ = 0.04 calls/hour), maintaining a single technician may lead to increased waiting times and potentially exceed the 3-hour guarantee.
  • Recommendation:
    • Employ a second technician.
    • This will significantly improve service times and ensure customer satisfaction.
    • With two technicians, the system can handle higher arrival rates more effectively.

7. Recommendation for 30 Customers

  • With 30 customers (λ = 0.06 calls/hour), the service demands will likely increase substantially.
  • Recommendation:
    • Maintain two technicians.
    • While a third technician might seem necessary, it’s crucial to analyze the system performance with two technicians.
    • Overstaffing can lead to increased labor costs without significant improvements in service times.  

8. Annual Savings with Two Technicians (20 Customers)

  • Planning Committee Proposal:
    • At 20 customers, the committee proposes two technicians.
    • Cost: 2 technicians * $80/hour = $160/hour
  • Our Recommendation:
    • Two technicians: $160/hour
  • Annual Savings:
    • No significant savings compared to the committee’s proposal.

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