# MATH 543 Case Study 1 Forecasting

Case Study 1: Forecasting

MAT 543: Quantitative Methods for Health Services

August 1, 2015

Extrapolation Based upon Average Change examines the month-to-month change that occurs in the data. This data is calculated in whole terms not absolute value. Once we have the average for the change month-to-month, then we can get a forecast for the month asking. The equation used is:

1. Explain each step in the forecasting process for each method.

In order to use this equation first we have to find the change from the previous month and find the total for visits to health services. I first found the total of all the visits in 2008 by adding all the visits up from January to October. That total came to be 343. I then found the changes from month to month. To find the change from January to February I subtracted January visits from February, which gave me a difference of 2. I did this for each month up until October. I then added the changes up and got 0. I then had to find the averages of both the visits to health services and changes from previous months. To do so I took the total of the visits (343) and divided it by the number of months (10), which gave me an average of 34.3. Due to the fact that my total change was 0 the average would be the same because 0 divided anything will be 0. I then found the midpoint by using the equation (n+1)/2, with n being the number of months (10). The midpoint is 5.5. Now that I have all the information for my forecast equation, I just plug in the info.

The forecast for November is 34.3 using the Average Change method.

Month (2008) January Visits to Health Services Change from previous month 39 41 2 34 -7 39 5 38 -1 19 -19 28 9 29 1 37 8 39 2 343 0 34.3 0 5.5 34.3+(5.5×0)=34.3 35

Extrapolation based upon using average percent change builds is based on calculating the percent change from month to month. To find the percent change I had to use the equation (future-past/past). So for the percent change from February to January the equation looked like so: (41-39/39). Once I have the solution for that equation I would then have to multiply it by 100 to get a percentage figure. Once all the percent changes have been found I would then find the total and average to find the forecast month for November. To do so we use the following equation:

 Month (2008) Change from previous month % Change January February 2 5.12% March -7 -17.07% April 5 14.71% May -1 -2.56% June -19 -50.00% July 9 47.37% August 1 3.57% September 8 27.57% October 2 5.41% Sum 0 34.12% Ave 3.41% Forecast for November 39 + (39 x .0541) = 41.11 42

Extrapolation based on a confidence interval uses a confidence level of 95% because it gives us a 95% chance that the actual number will be within the parameters. When using the 95% confidence interval it is important to remember that the standard deviation is 1.96 above and below the mean.Confidence intervals become helpful to managers in many ways with one being when precision is not the primary motivation. To use this forecasting method you have to use the standard deviation and/or standard error. You use the standard deviation when the data is representing a population not a sample. The standard error is used when the data is representing a sample and that can be found by dividing the standard deviation by n.

Month (2008) January February Visits to Health Services 39 Average 34.3 41 Std. Dev. 6.95 34 95% C.I. 39 Upper= 34.3 + (1.96 x 6.95)47.92 38 Lower = 34.3 + (1.95×6.95)20.68 19 28 29 37 39 343

The forecast for the month of November using the confidence interval method is between 20 and 48.

Forecasting based on a moving (time period to time period) average provides a method to examine the variability in data and use the pattern to construct a forecast. To calculate a moving average you first have to choose a time period and let n represent a number of time periods. For example for month 2 n=2, for month 3 n=3 and so on and so on. Now that we have that figured out, we then have to select an. Once the n is selected you calculate the n-period moving average by starting with the oldest data and working forward. For example, we are forecasting for November so we would start with (September + October)/2.

The forecast using moving average for November 2008 is 38.

Forecasting using exponential smoothing provides a technique to minimize the effect of fluctuation in the forecast. The equation for exponential smooth is: SC represents the smoothing constant (a number between 1 and0). F represents forecast for the next period in the future. O represents the observed value for the last or most recent period. Ft-1 represents the forecasted value for the last or most recent historical period. The first step is to choose a smoothing constant, which is a number between 0 and 1. After using the formula to calculate the forecast, it is important to figure out the forecast error in order to ensure that the information is as accurate as possible. When calculating the smoothing constant, in order to determine the best constant to use, we have to calculate different ones to see which one yields the least MAD possible.

The forecast for November 2008 is 37.

2. Provide a brief summary of your researched health services organizations implementing the forecasting methods.

The article Healthcare providers increase reliance on demand forecasting discusses how New York’s Long Beach Medical Center after Hurricane Sandy in 2012 was destroyed and never reopened as a full-service hospital. The medical center went bankrupt and had to sale to South Nassau Communities Hospital. Due to the sale of the medical center there is no access to emergency services for those who actually live on the beach. The residents are calling for a medical center right there at the beach, but the CFO and senior vice president of finance, Mark Bogen, disagrees.

The organization used demand forecasting to help make the decision to not put a medical center right on the beach. Their research showed that before Hurricane Sandy only “about 50 percent of residents used the emergency department,” and “only about 35 percent sought inpatient care there and less than 10 percent used the hospital when needing surgery of any kind.” The hospital’s revenue before Sandy was \$55 million that was not enough to cover the \$59 million in expenses. Also, the community shrunk from being more than 30,000 full-time residents because nearly one-quarter of residents never returned deciding to stay in the South.

The organization worked with Adam Powell, consultant and president of Payer+Provider Syndicate, to determine a staff development planed based on potential demand in 2014 and 2019. The demand for the medical center isn’t there and isn’t financially responsible for the community. With all these factors there is really no demand for the medical center to be back in the community, but this can all change if the number of full-time residents increased dramatically and the use for the medical center increased.

3. Provide a forecast on the number of clinic visits for November 2008 using each method of the forecasting process

Extrapolation based on Average change 34.3 ≈ 35
Extrapolation based upon using average percent change 41.11 ≈ 42
Extrapolation based on a confidence interval 20-48
Forecasting based on moving average 38
Forecasting using exponential smoothing 36.82 ≈ 37

4. Conclude which forecasting method provides the best forecast, and provide a rationale for your reasoning.

The forecasting model using exponential smoothing provides the best forecast. This model provides the lowest standard error and it’s a weighted measurement. It also provides the lowest standard error. The smoothing model has the best prediction of the past, which is an indicator that it will also provide the best prediction of the future value. The other models offered the information necessary to help assess the range of the forecast and allowed me to see that the forecast using weighted standard measurement actually fell right within those numbers.