Question

Inner City Health Center is a federally funded health clinic that serves the needs of the inner-city poor. Currently the center is at the end of third-year operation and is preparing its staffing plan for the upcoming year. The federal government requires that the center prepare a budget request each year. The request is based largely on the forecast of the # of Patient Visit for specific services during the next year.

The health center administrator has in the past tried using the last month’s # of Patient Visit and has also tried using the average of all historical data to predict the next period’s # of Patient Visit for the center. Neither of these two techniques has proven satisfactory due to complicated month to month data pattern. They are currently seeking outside helpers to forecast the # of patient visit for the upcoming January year 2016.

The # of patient visit each month in the preceding three years (including the current year) is available In the following Table.

Table. Emergency Service Demand for the Inner-city Health Center

Month	# of patient Visit
	Year 2013	Year 2014	Year 2015
Jan.	385	441	531
Feb.	368	464	654
Mar.	420	591	650
Apr.	502	645	755
May	505	612	758
June	633	718	790
July	546	717	770
Aug.	516	625	752
Sept.	492	659	752
Oct.	447	620	663
Nov.	441	552	699
Dec.	397	566	618

1. Forecast
   1. Use a 4- Month Simple Moving Average Method to forecast the # of the emergency visit from May 2013 to January 2016.
   2. Use a Linear Projection Forecast Method to forecast the # of the emergency visit from January 2013 to January 2016.
   3. Use an Exponential Smoothing Forecast Method, with a = 0.25, to forecast the # of the emergency visit from June 2013 to January 2016. Assume that initial forecast for May 2013 is 600.
2. Plot One (nice) Chart for Data Series over time (Jan 2013 to Jan 2016):
   1. the historical data series,
   2. the data series of forecasts obtained in 1a), 1b) and 1c).

1. Use one of forecast Error Measurements, either MAD, or MSE, or MAPE (you choose) to determine which of the forecasts from 1a), 1b) or 1c) provides the best (smallest) forecasting error summary from the given historical data set.
   1. It is important to point out that error comparison of different forecast methods should be done on a Consistent Base. That is, the forecast error comparison for different forecast methods is meaningful only when we compare the forecast error of the Same Range of forecasts.
2. For the Exponential Smoothing forecast obtained in 1c), use Tracking Signal to monitor the forecast results and draw a conclusion on whether or not the forecasts are Biased, assume C = 3, and -C = -3 to be the control limits of the tracking signal method.
3. Use the same Forecast Error Measurement you used in question 3), find the best smoothing parameter a (i.e. the a that leads to the smallest forecast error) of Exponential Smoothing Forecast Method.
4. For the given historical data set,
   1. Briefly discuss the potential weakness when applying each method in part 1a), 1b) and 1c).
   2. i) Propose a new Forecast Method that might be better than forecast methods 1a) - 1c). ii) Use your Forecast Method to do the forecasts and then iii) use the Same Forecast Error measurement you used in 3) to compare your forecast results with the results from forecast methods 1a), 1b) and 1c).

Answer 1

The calculated values are shown below for part a, b, and c.

The chart for data is shown below

The chart for forecasts are shown below

The MAD values are

4 period simple moving average (4SMA) = 75.92

Linear regression (LR) = 66.77

Exponential smoothing (ES) = 72.94

The best forecast method is linear regression as It minimizes the error measurement of MAD.