Call Center Staffing

The operations manager for the call center One-Dollar-Joke -- a call center that tells a random, high-quality joke to the caller for the very reasonable rate of one dollar -- 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.

Part 1
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?
Select the best answer
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

Part 2
The manager 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 0.25. Assume that the forecast for period 1 is = 939.

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

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 for period 21? Answer in percent without the percentage symbol, e.g. if your answer is 24.5% write 24.5.

Part 3
The manager 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 0.25, a beta of 0.05, a level of 939 and a trend of 6.58. Assume that the forecast for period 1 is the sum of the level and the trend, that is, = 946.

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

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 for period 21? Answer in percent without the percentage symbol, e.g. if your answer is 24.5% write 24.5.

Part 4
The manager 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 0.25, a beta of 0.05, a level of 939 and a trend of 6.58.

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

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 for period 21? Answer in percent without the percentage symbol, e.g. if your answer is 24.5% write 24.5.

Part 5
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?
Select the best answer
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 display strong seasonality
If the training data set was larger, the more complex models would be more accurate
None of the above

Call Center Staffing The operations manager for the call center...