Homework due Sep $25,202419$:$00+04$

Part $1$

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Brandon Washington is the operations manager for the call center $79-$Cents$-$Joke $--$ a call center that tells a random, high$-$quality joke to the caller for the very reasonable rate of $79$ cents $--$ has contacted you after hearing about your expertise in forecasting. Forecasting the number of incoming calls is crucial to the call center. With its current model, staffing is the single largest cost to the call center, and staffing levels are always set based on the forecasted number of calls. "For us$",$ the manager explains, "good forecasting is not a joke!"

Staffing levels can be adjusted every $4$ hours. The call center is operating from $6$ pm to $6$ am$,$ so there are three $4-$hour$-$blocks every day. The following data shows the number of incoming calls over these $4-$hour$-$blocks for seven days: Data.

Note that the first period in the data $($Period $1)$ is the $4-$hour block from $6$ pm to $10$ pm$.$

As you know from before, it is always a good idea to graph the data to get an understanding of possible patterns. Graph the historical number of incoming calls. What do you notice?

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There seems to be a slow decrease in the demand for jokes over the phone

The waiting time to hear a joke over the phone is more than $5$ minutes on average

Jokes over the phone seem to be more popular around midnight than early evening or early morning

There is no noticeable pattern in the data

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Part $2$

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Brandon Washington wants you to start with a simple model that can be easily extended.

Build a simple exponential smoothing model for the call center's incoming calls. Use an alpha value of $0\mathrm{.}25.$ Assume that the forecast for period $1$ is

$=939.$

What is your forecast for next $4-$hour block's $($for t$=22)$ number of incoming calls? $($Round your answer to the nearest whole number.$)$

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What is the Mean Absolute Percentage Error $($MAPE$)$ of the forecast for the given data, as measured from the forecast for period $1$ to the forecast made in period $21?$ Answer in percent without the percentage symbol, e$.$g$.$ if your answer is $24\mathrm{.}5\%$ write $24\mathrm{.}5.$

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Part $3$

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Brandon Washington now wants to know how including more factors may improve the forecast.

Build a level and trend exponential smoothing model for the incoming calls. Use an alpha of $0\mathrm{.}25,$ a beta of $0\mathrm{.}05,$ a level

of $939$ and a trend

of $6\mathrm{.}58.$ Assume that the forecast for period $1$ is the sum of the level and the trend, that is$,$

$=945\mathrm{.}58.$

What is your forecast for next $4-$hour block's $($for t$=22)$ number of incoming calls? $($Round your answer to the nearest whole number.$)$

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What is the Mean Absolute Percentage Error $($MAPE$)$ of the forecast for the given data, as measured from the forecast for period $1$ to the forecast made in period $21?$ Answer in percent without the percentage symbol, e$.$g$.$ if your answer is $24\mathrm{.}5\%$ write $24\mathrm{.}5.$

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Part $4$

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Brandon Washington suggests you also include a trend$-$dampening component,

$.$

Build a level and trend exponential smoothing model with damped trends for the incoming calls. Use an alpha of $0\mathrm{.}25,$ a beta of $0\mathrm{.}05,$ a level

of $939$ and a trend

of $6\mathrm{.}58.$

What is your forecast for next $4-$hour block's $($for t$=22)$ number of incoming calls? $($Round your answer to the nearest whole number.$)$

unanswered

What is the Mean Absolute Percentage Error $($MAPE$)$ of the forecast for the given data, as measured from the forecast for period $1$ to the forecast made in period $21?$ Answer in percent without the percentage symbol, e$.$g$.$ if your answer is $24\mathrm{.}5\%$ write $24\mathrm{.}5.$

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Part $5$

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The manager is surprised to learn that neither of the more complex forecast models in Part $3$ and Part $4$ provided a more accurate forecast $($a lower MAPE$)$ than the simple exponential forecast model in Part $2.$ He asks you why this is the case?

Which of the following statements do$,$ in part, explain why the more complex models have a higher MAPE?

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MAPE captures forecast bias, and the more complex models are biased upwards

None of the forecast models include a seasonal component, while the incoming calls displa

ime block $($t$)$ Arrivals $($x$($t$)$