Methods Of Analysis For Business Operations • Unit III Artic

Methods of Analysis for Business Operations•Unit III Article Review

Calculate the likelihood of an event occurring a certain number of times within a given time frame using the Poisson distribution. The article “Routing and Staffing in Customer Service Chat Systems with Impatient Customers” by Tezcan and Zhang (2014) explores how to minimize overhead while satisfying customers who seek support via online chat systems. The focus is on understanding how wait times influence customer abandonment rates and agent productivity, and how Poisson distribution can help analyze these factors.

Customer service chat (CSC) systems facilitate real-time contact between customers and support representatives, offering benefits such as lower operational costs and collaborative troubleshooting capabilities. However, maintaining efficient staffing levels while ensuring satisfactory service remains challenging, especially when customer arrival rates are unpredictable. When agents handle multiple customers simultaneously, their productivity declines beyond a certain threshold, necessitating effective routing and staffing strategies.

The use of the Poisson distribution in this context is driven by the nature of customer arrivals at the CSC, which are independent, random, and vary over time. Poisson distribution is ideal because it models the number of independent events (customer messages) occurring within a fixed interval, given a constant average rate. Unlike other distributions, such as the normal distribution, Poisson is better suited here due to the discrete, count-based nature of customer arrivals that do not follow a fixed pattern over time.

Applying the Poisson model allows for estimation of key metrics such as the probability of a certain number of customer arrivals in a given period, the likelihood of agent overload, and the expected abandonment rate. For example, if an agent can effectively handle up to three customers simultaneously, Poisson calculations can predict the probability that four or more customers attempt service at once, revealing when routing adjustments are necessary. This information guides resource allocation to balance workload and maintain service levels.

In practice, Poisson distribution can be employed at various operational levels. At the macro level, it helps forecast daily, hourly, or minute-by-minute customer influx, enabling supervisors to adjust staffing schedules proactively. At the micro level, it informs real-time routing decisions to distribute workload evenly among agents, prevent bottlenecks, and minimize customer abandonment. The model also supports simulations to evaluate different staffing scenarios, aiming to optimize resource deployment for maximum efficiency and customer satisfaction.

At the New York City Military Entrance Processing Station (MEPS), the Poisson distribution demonstrates its practical utility. With daily enlistment numbers ranging from one to thirty-five individuals, the randomness of arrivals aligns with the Poisson assumptions of independent, variable events. This allows personnel to forecast the likelihood of high or low-to-moderate influx days, aiding in logistical planning and resource allocation. Such applications exemplify how understanding statistical principles enhances operational effectiveness in dynamic environments.

Conclusion

The integration of Poisson distribution analysis into business operations, especially in customer service systems like CSCs, provides valuable insights into managing unpredictable customer arrivals. By modeling arrivals as independent, random events, organizations can optimize staffing, improve routing algorithms, and reduce customer abandonment. The real-world example from NYC MEPS further illustrates its applicability beyond digital customer support, emphasizing the versatility and importance of statistical methods in operational decision-making.

References

  • Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. (2018). Quantitative analysis for management (13th ed.). Pearson.
  • Tezcan, T., & Zhang, J. (2014). Routing and staffing in customer service chat systems with impatient customers. Operations Research, 62(4), 943–956.
  • Barlow, R., & Proschan, F. (1996). Mathematical theory of reliability. SIAM.
  • Casella, G., & Berger, R. L. (2002). Statistical inference. Duxbury.
  • Kleinrock, L. (1975). Queueing systems, volume 1: Theory. Wiley-Interscience.
  • Ross, S. M. (2019). Introduction to probability models. Academic Press.
  • Gupta, P. K., & Kapoor, V. K. (2002). Fundamentals of mathematical statistics. Sultan Chand & Sons.
  • Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts.
  • Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & statistics for engineering and the sciences. Pearson.
  • Bishop, Y. M., Fienberg, S. E., & Holland, P. W. (2007). Discrete multivariate analysis: Theory and practice. Springer.

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