1. Chapter 2. Forecasting
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

2. Outline Why Forecast? Steps in the Forecasting Process
Forecasting Approaches
Judgmental
Time Series-- Historical Data
Techniques for Averaging
Techniques for Trend
Techniques for Seasonality
Associative
Accuracy and Control of Forecasts
Choosing a Forecasting Technique
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

3. Why forecasting is important?
Forecasts serve as a basis for planning
Enable health care managers to anticipate the future to plan the system and plan the use of that system
Forecasting is more than predicting demand
It is not an exact science; one must blend
experience, judgment, and technical expertise
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

4. All forecasts have common elements
Assumption that past continues into future
Errors occur-- actual differs from predicted; presence of randomness
Forecasts of group of items (aggregate) tends to be more accurate than individual items (i.e., departmental vs. whole hospital)
Forecast accuracy decreases as time horizon increases
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

5. Characteristics of a Good Forecast
Timely
Reliable
Accurate
Meaningful units ($$’s, visits, discharges, patient days, etc.)
Easy to use
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

6. Steps in the Forecasting Process
Step 1 Identify the goal of the forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Conduct the forecast (analyze data)
Step 5 Determine its accuracy
Step 6 Monitor the forecast
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

7. What approaches can we use?
Judgmental
Delphi method
Executive opinions
Contracts/insurance/HMO/PPO/POS estimates
Consumer surveys
Outside opinions
Opinions of managers/staff
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

8. Method of obtaining opinions of managers and staff
The Delphi Method
Method of obtaining opinions of managers and staff
Involves circulating a series of questionnaires, each developed from the previous one, to achieve a consensus on an issue (in this case, a forecast)
Useful for forecasting technological changes and their impacts
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

9. The Delphi Approach, cont.
Advantages
More individuals may be engaged than can effectively interact face-to-face
It is important to avoid bandwagon effect
Preserves anonymity of participants
Weaknesses
Questions may be ambiguous leading to false consensus
Panel members may change
Studies do not prove that Delphi forecasts are highly accurate
Preserving anonymity removes accountability
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

10. Forecasting Approaches, cont.
Time series-- identify the behavior of the series by using factors such as trend, seasonality, cycles, irregular variations, and random variations
Techniques for averaging
Naive forecasts
Moving averages (MA)
Exponential smoothing
Techniques for trend
Linear equations using regression (yt = a + bxt)
Trend adjusted exponential smoothing
Techniques for seasonality
Seasonal Variations
Indices Technique
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

11. Forecasting Approaches, cont.
Associative Techniques
Simple linear regression (y = a + bx)
Scatter diagram-- plot data
Correlations
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

12. Jan Mar May Jul Sep Nov Figure 2.1 Variation Characteristics Seasonal
2005
2004
2003
Jan Mar May Jul Sep Nov
Cycle
Random Variation
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan
Trend

13. Averaging Techniques
Smooth out fluctuations in time serious because individual highs and lows cancel each other out
So, would forecasts based on averages exhibit more or less variability?
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

14. Naive Forecasts
A naive forecast for any period equals the previous period’s actual value
Low cost, easy to prepare, easy to understand, but less accurate forecasts
Can be applied to seasonal or trend data
Examples:
If last week’s demand was 50 units, the naive forecast
for the coming week is 50 units.
If seasonal pattern exists, the naive forecast for next January
would equal the actual demand for January of this year.
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

15. Moving Averages
Forecast uses a number of the most recent actual data values in generating a forecast
where, i = “Age” of data (i=1,2,3. . .)
n = number of periods in moving average
Ai = actual value with age i
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

16. Moving Averages Example 2.1:
An OB/GYN clinic has the following yearly patient visits, and would like to predict the volume of business for the next year for budgeting purposes.
Period (t)
Age
Visits 1 5
15908 2 4
15504 3
14272
13174
10022
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

17. Moving Averages, cont. Solution:
The three-period moving average (MA3) for period 6 is
F6 = MA3 = ( ) ÷ 3 =
Period (t)
Age
Visits
Forecast 1 5
15908 2 4
15504 3
14272
13174
15228
10022
14317 6
12489
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

18. Moving Averages, cont. MA3 Data MA5 1 2 3 4 5 6 7 8 9
The greater the number of periods in a moving average, the greater the forecast will lag with changes in the data
MA3
Data
MA5
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

19. Moving Averages, cont.
Easy to compute and understand, but data storage requirements can be high and all values are weighted equally (i.e., in a ten year moving average, each value is given a weight of 1/10, adding up to 1).
A weighted average assigns more weight to recent values
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

20. Using Weighted Values
Example: Continuing with Example 2.1; since there is a downward trend in visits and in period 5 there is a sharp decline, a weight of .5 or even higher is justified by the healthcare manager to calculate a weighted average for period 6
Period
(t)
Age
Visits
Weights 1 5
15908 2 4
15504 3
14272
0.2
13174
0.3
10022
0.5 6
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

21. Using Weighted Values Solution:
In this analysis, a weighted average, using
formula [2.2], for the OB/GYN clinic for the
period 6 would be:
F6 = 14272* * *.5
F6 =
Period (t)
Age
Visits
Weights
Forecast 1 5
15908 2 4
15504 3
14272
0.2
13174
0.3
10022
0.5 6
11818
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

22. Simple Exponential Smoothing
Each new forecast is based on the previous forecast plus a percentage of the difference between that forecast the actual value of the series at that point
New forecast = Old forecast + α (Actual-Old forecast), where α is a percentage or
Ft = Ft-1 + α(At-1 - Ft-1),
where, Ft = Forecast for period t
Ft-1 = Forecast for period t-1
α = Smoothing constant
At-1 = Actual demand or sales in period t-1
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

23. Exponential Smoothing, cont.
Example 2.4: Using the data from Example 2.1, build forecasts with smoothing constant α = 0.3
Solution:
Following the previous example and formula [2.3], we can build forecasts for periods as data become available.
F3 = ( )
F3 =
Smoothing constant α = 0.3
Error
Period (t)
Actual (Visits)
Forecast
(Actual – Forecast) 1
15908 -- 2
15504
-404.0 3
14272 4
13174 5
10022
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

24. Exponential Smoothing, cont.
Smoothing constant α = 0.5
Error
Period(t)
Visits
Forecast
(Actual – Forecast) 1
15908 -- 2
15504
-404.0 3
14272 4
13174 5
10022
Example 2.5: Using the data from Example 2.1, build forecasts with smoothing constant
α = 0.5.
Solution:
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

25. Exponential Smoothing, cont.
Example 2.6: Using the data from Example 2.1, build forecasts with smoothing constants
α = 0.0 and α = 1.0.
Solution:
Period
(t)
α = 0.0
Error
α = 1.0
Visits
Forecast
(Actual – Forecast) 1
15908 -- 2
15504
-404.0 3
14272 4
13174 5
10022 6
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

26. Techniques for Trends
Least squares regression-- minimizes the sum of the squared errors
Least squares line:
y = a + bx, y = predicted (dependent) variable
x = predictor (independent) variable
b = slope of data line
a = value of y when x = 0
n(åxy) - (åx)(åy)
n(åx2) - (åx)2
b =
a =
åy - båx n
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

27. Figure 2.9 Linear Regressiony
y = a + bx
error
error Δy Δx
b =(Δy/Δx) , where b>0 a x
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

28. Multi Hospital System Revenues and Profits Data
Techniques for Trends
Example 2.7: A multi-hospital system (MHS) owns 12 hospitals. Revenues (x, or the independent variable) and profits (y, or the dependent variable) for each hospital are given below. Obtain a regression line for the data, and predict profits for a hospital with $10 million in revenues. All figures are in millions of dollars.
Multi Hospital System Revenues and Profits Data
Hospital
Revenue (x)
Profit (y)
x*y x2 1 7
0.15
1.05 49 2
0.10
0.2 4 3 6
0.13
0.78 36
0.6 16 5 14
0.25
3.5
196 15
0.27
4.05
225
0.24
3.84
256 8 12
0.20
2.4
144 9
3.78 10 20
0.44
8.8
400 11
0.34
5.1
0.17
1.19
Total
132
2.71
35.29
1796
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

29. Solution: After calculating yx = 0.0506 + 0.01593x.
substitute into the equations [2.5] for a and [2.6] for b, respectively.
Hence, the regression line is:
yx = x.
To predict the profits for a hospital with $10 million in revenue,
simply plug 10 in as the value of x in the regression equation:
Profit = (10) =
Multiplying this value by one million,
the profit level with $10 million in revenue is found to be $209,903.
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

30. Techniques for Trends n(åty) - (åt)(åy) n(åt2) - (åt)2 b = a =
Linear Regression as a Trend Line
y = a + b*t
y = predicted (dependent) variable
t = predictor (time) variable
b = slope of data line
a = value of y when x = 0
n(åty) - (åt)(åy)
n(åt2) - (åt)2
b =
a =
åy - båt n
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

31. Example 2.8: Referring back to the OB/GYN example, the health care manager can estimate the trend line using regression analysis.
Solution:
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

32. Techniques for Seasonality
Seasonal variations in a data set consistently repeat upward or downward movements of the data values that can be traced to recurrent events.
In the additive model, seasonality is expressed as a quantity (example: 5 units), which is added or subtracted from the series average in order to incorporate seasonality.
In the multiplicative model, seasonality is expressed as a percentage of the average amount (example: 1.15)
Quarterly, Monthly, Daily Indices Technique
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

33. Techniques for Seasonality
Employing Seasonal Indices in Forecasts
Example 2.10: A forecast based on linear regression yields the following trend equation
Demand (Yt) = t.
The forecast of demand for periods 29 through 31 would be:
Y29 = (29) =
Y30 = (30) =
Y31 = (31) =
Having forecast the next three months, the healthcare manager needs to incorporate seasonality back into those forecasts. The periods t = 29, 30 and 31 represent the months of November, December and January, respectively, with corresponding monthly indices 0.984, 0.973, and Monthly adjustments to those forecasts are calculated
Monthly Adjusted Forecast (t): Forecast * Monthly Index
Period 29 (November): (0.984) =
Period 30 (December): (0.973) =
Period 31 (January) : (1.036) =
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

34. Techniques for Seasonality
Employing Seasonal Indices in Forecasts
The next step in adjustment of the forecasted demand would be for daily fluctuations. As was shown in Table 2.4, Heal Me Hospital experiences daily variation in demand. Thus, the monthly index adjusted forecasts should be further adjusted for daily variations.
Daily Adjusted Forecast = Monthly Adjusted Forecast (t) * Daily Index
For example, for November (period 29), the adjusted forecasts for Monday and Tuesday are:
Monday, November: * (0.972) =
Tuesday, November: * (1.023) =
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

35. Errors may be caused by:
How accurate are we?
Forecast Error equals the actual value minus the forecasted value.
Error = Actual – Forecast
Errors may be caused by:
An inadequate forecasting model
Irregular variations due to severe weather, shortages or breakdowns, catastrophes, etc.
Forecasting technique may be used improperly
There may be random variations in the data
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

36. Is your forecast accurate?
Mean Absolute Deviation (MAD)
MAD weights all
errors evenly.
Mean Absolute Percent Error (MAPE)
MAPE avoids the problem of interpreting the measure of accuracy relative to the magnitudes of the actual and the forecast values.
Seek lowest of MAD or MAPE for given set of data; also examine historical performance versus responsiveness to current situation.
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

37. Is your forecast accurate?
Using data from Example 2.4, SES with α = 0.3, we observe the necessary error calculations in Table below.
Period t
Smoothing constant α = .3
Error
Absolute Error
Actual
Forecast
(Actual – Forecast)
|Actual – Forecast| 1
15908 -- 2
15504
-404
404 3
14272
1515 4
13174
2158 5
10022
4662.9 6
13286
Sum Σ
52972
8740.1
Hence,
MAD = ÷ 4 = , and
MAPE = ÷ = or 16.5%.
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

38. Is your forecast accurate?
Controlling forecasts-- set predetermined upper/lower limits for forecast errors
Forecasts can be monitored using either a tracking signal or control chart.
Tracking signals show cumulative errors
- Control Charts-- set upper and lower limits for individual forecast errors
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

39. Control Chart for Tracking Signal
Range of
Acceptable
Variation
Need for
Corrective Action
-During periods 12 through 15 the tracking signal went beyond the
acceptable control limits (down to -5.51), but recovered at period 16 and
stayed within acceptable limits after that.
-Until period 8 the predicted values were below the actual. That changed
from period 9 to period 20, when forecasts were higher than actual data.
-At the period 21 a return to under-forecast occurred.
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

40. So what technique should we use?
Factors of importance:
Frequency
Level of aggregation
Type of Model- Errors [MAD, MAPE]
Degree of managerial involvement
Cost per forecast
Time horizon considerations-- short, intermediate, or long
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

41. What makes a forecast a good one?
Timeliness
Accuracy
Meaningful Units ($$’s, visits, etc.)
In writing
Simple to understand and use
Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan

42. The End Chapter 2: Quantitatve Methods in Health Care Management
Yasar A. Ozcan