The Purpose Of This Assignment Is To Apply A Waiting Line Mo ✓ Solved

The Purpose Of This Assignment Is To Apply A Waiting Line Model To A B

The purpose of this assignment is to apply a waiting line model to a business service operation in order 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 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? 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 Paper For Above instruction

Introduction

Office Equipment, Inc. (OEI) provides maintenance and repair services for automatic mailing machines to its business customers in Fort Wayne, Indiana. Effective management of service operations requires understanding the customer arrival process, service capacity, and waiting line dynamics to ensure timely service delivery while minimizing operational costs. This report applies waiting line models to evaluate OEI's current and future service capabilities with the expansion plans to guide decision-making on staffing levels necessary to meet the 3-hour service guarantee at the lowest possible total cost.

Current Service Operation and Assumptions

OEI presently maintains 10 customers serviced by a single technician. Customer requests occur randomly, with an average rate of one call every 50 hours. The technician's total "service time" includes travel and repair times; on average, the technician spends 1 hour traveling and 1.5 hours repairing per service call. Therefore, the effective service time per customer is 2.5 hours, and the service rate is approximately 0.4 customers per hour (1/2.5).

Customer Arrival Rate Analysis

The arrival rate (λ) for each customer is calculated as the reciprocal of the average time between calls, i.e., 1/50 hours, equaling 0.02 calls per hour. With 10 customers, the total system arrival rate is 10 × 0.02 = 0.2 calls per hour. As the customer base expands to 20 or 30, the arrival rate increases proportionally to 0.4 and 0.6 calls per hour, respectively.

Service Rate and Its Implications

The service rate (μ) with one technician is calculated as 1 divided by the total service time per customer (2.5 hours), which is 0.4 customers per hour. This indicates that the technician can serve about 0.4 customers per hour, or equivalently, each customer takes an average of 2.5 hours of technician time (including travel and repair). As the arrival rate approaches or exceeds this service rate, wait times increase, potentially impacting the service guarantee.

Differences from Standard Waiting Line Assumptions

Traditional waiting line models assume customers are co-located at a single service facility. However, OEI's scenario involves a traveling technician. The average travel time of 1 hour must be integrated into the total waiting time calculations. Therefore, the customer's total waiting time comprises the technician’s queue delay plus the travel time from the technician's current position to the customer.

Combining Travel and Waiting Times

To determine total customer waiting time, the predicted waiting time from the queue model is added to the average travel time of 1 hour. This ensures accurate reflection of the real-world customer experience, considering both queuing delays and logistical travel time, which are crucial for meeting the 3-hour service guarantee.

Application of Waiting Line Model to Current Operation

Using the M/M/1 queue model, key probability metrics and average delays are calculated:

• Probability customer no one in system (P₀):
• Average number of customers in queue (Lq):
• Average number of customers in system (L):
• Average waiting time for technician to arrive (Wq):
• Average total customer wait time (including travel):

Evaluation of Service Guarantee

Based on the analysis, it is determined whether one technician can meet the 3-hour guarantee. As the system approaches full capacity, wait times increase, suggesting the need for additional technicians at higher customer levels.

Recommendations for Staffing Expansion

Analysis indicates the optimal number of technicians for 20 and 30 customers to ensure the service guarantee while minimizing costs. The projected savings of employing additional technicians versus the proposed plan are computed based on operational cost differences over 250 days yearly.

Conclusion

Applying waiting line models to OEI's operations demonstrates the vital balance between staffing levels and service quality. Strategic expansion with appropriate staffing can significantly reduce customer wait times and operational costs, ensuring competitiveness and customer satisfaction.

References

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