Hello Professor and Class,
The manager of the fast-food store experiences difficulty staffing during hours when the average arrival rate is higher due to the inherent
characteristics of the Poisson distributions and its impact on workforce management.
The Poisson distribution models the number of events occurring within fixed intervals, given the average rate of occurrence. In this context, it
represents the arrival of customers per hour. When the average arrival rate is higher, the variability in the number of customers arriving within
a given hour increases. This heightened variability challenges the manager in predicting the exact staffing requirements.
Higher average arrival rates lead to a broader distribution, resulting in more significant fluctuations in customer arrivals from one hour to the
next. Consequently, the manager needs to be more sure about the number of servers required during these peak hours, making it challenging
to strike the right balance between providing efficient services and managing labor costs.
In contrast, if the average arrival rate were more significant and consistent, the Poisson distribution would exhibit less variability, allowing for
a more accurate prediction of customer flow. The manager could confidently schedule an appropriate number of servers, minimizing
overstaffing and understanding issues.
In summary, the challenges in staffing during peak hours with a higher average arrival rate stem from the increased variability inherent in the
Poisson distribution, making it harder for the manager to anticipate and meet customer service demands precisely.
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