Chapter 2.
Forecasting
Chapter 2: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
1
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
2
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
3
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
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Yasar A. Ozcan
4
Characteristics of a Good Forecast
Timely
Reliable
Accurate
Meaningful units ($$’s, visits, discharges, patient days, etc.)
Easy to use
Chapter 2: Quantitatve
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Yasar A. Ozcan
5
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
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Yasar A. Ozcan
6
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
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Management
Yasar A. Ozcan
7
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
8
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
9
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
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Yasar A. Ozcan
10
Forecasting Approaches, cont.

Associative Techniques
– Simple linear regression (y = a + bx)
– Scatter diagram-- plot data
– Correlations
Chapter 2: Quantitatve
Methods in Health Care
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Yasar A. Ozcan
11
Figure 2.1 Variation Characteristics
Seasonal
Variation
Seasonal
Variation
2005
2004
2003
Jan
Mar
May
Jul
Sep
Nov
Cycle
Random Variation
Chapter 2: Quantitatve
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Trend
Yasar A. Ozcan
12
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
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Yasar A. Ozcan
13
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
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Yasar A. Ozcan
14
Moving Averages
Forecast uses a number of the most recent actual
data values in generating a forecast
Ft  MAn
A


i
n
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
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Yasar A. Ozcan
15
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.
Chapter 2: Quantitatve
Methods in Health Care
Management
Period (t)
Age
Visits
1
5
15908
2
4
15504
3
3
14272
4
2
13174
5
1
10022
Yasar A. Ozcan
16
Moving Averages, cont.
Solution:
The three-period moving average (MA3) for period 6 is
F6 = MA3 = (14272+13174+10022) ÷ 3 = 12489.3
Period (t)
Age
Visits
1
5
15908
2
4
15504
3
3
14272
4
2
13174
15228
5
1
10022
14317
6
Chapter 2: Quantitatve
Methods in Health Care
Management
Forecast
12489
Yasar A. Ozcan
17
Moving Averages, cont.
The greater the number of periods in a moving
average, the greater the forecast will lag with changes
in the data
MA3
Data
MA5
1
2
Chapter 2: Quantitatve
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Management
3
4
5
Yasar A. Ozcan
6
7
8
9
18
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
19
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
1
5
15908
2
4
15504
3
3
14272
0.2
4
2
13174
0.3
5
1
10022
0.5
Ft  MAn   wi Ai
Chapter 2: Quantitatve
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Weights
6
Yasar A. Ozcan
20
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:
Period
(t)
Age
F6 = 14272*.2+13174*.3+10022*.5
F6 = 11818.
Chapter 2: Quantitatve
Methods in Health Care
Management
Weights
1
5
15908
2
4
15504
3
3
14272
0.2
4
2
13174
0.3
5
1
10022
0.5
6
Yasar A. Ozcan
Visits
Forecast
11818
21
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
22
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 = 15908 + .30(1550415908)
F3 = 15786.8
Chapter 2: Quantitatve
Methods in Health Care
Management
Smoothing constant α = 0.3
Error
(Actual – Forecast)
Period (t)
Actual (Visits)
Forecast
1
15908
--
2
15504
15908
-404.0
3
14272
15786.8
-1514.8
4
13174
15332.4
-2158.4
5
10022
14684.9
-4662.9
Yasar A. Ozcan
23
Exponential Smoothing, cont.
Example 2.5: Using
Smoothing constant α = 0.5
the data from Example
2.1, build forecasts with
smoothing constant
α = 0.5.
Solution:
Chapter 2: Quantitatve
Methods in Health Care
Management
Error
(Actual – Forecast)
Period(t)
Visits
Forecast
1
15908
--
2
15504
15908
-404.0
3
14272
15706.0
-1434.0
4
13174
14989.0
-1815.0
5
10022
14081.5
-4059.5
Yasar A. Ozcan
24
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:
α = 0.0
Period
(t)
Visits
Forecast
1
15908
--
2
15504
15908
3
14272
4
5
6
Chapter 2: Quantitatve
Methods in Health Care
Management
α = 1.0
Error
(Actual – Forecast)
Error
(Actual – Forecast)
Visits
Forecast
15908
--
-404.0
15504
15908
-404.0
15908.0
-1636.0
14272
15504.0
-1232.0
13174
15908.0
-2734.0
13174
14272.0
-1098.0
10022
15908.0
-5886.0
10022
13174.0
-3152.0
15908.0
10022.0
Yasar A. Ozcan
25
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(xy) - (x)(y)
b=
n(x2) - (x)2
Chapter 2: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
a = y - bx
n
26
Figure 2.9 Linear Regression
y
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
27
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
2
0.10
0.2
4
3
6
0.13
0.78
36
4
4
0.15
0.6
16
5
14
0.25
3.5
196
6
15
0.27
4.05
225
7
16
0.24
3.84
256
8
12
0.20
2.4
144
9
14
0.27
3.78
196
10
20
0.44
8.8
400
11
15
0.34
5.1
225
12
7
0.17
1.19
49
Total
132
2.71
35.29
1796
Chapter 2: Quantitatve
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Management
Yasar A. Ozcan
28
Solution:
After calculating
 x,  y,  xy,  x
2
substitute into the equations [2.5] for a and [2.6] for b, respectively.
xy)  ( x)( y ) 12(35.29)  132 (2.71)

b

 0.01593 .
12(1796 )  132 (132 )
n(  x )  (  x )
y  b x 2.71  0.01593(132)

a

 0.0506.
n(
2
2
n
12
Hence, the regression line is:
yx = 0.0506 + 0.01593x.
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 = 0.0506 + 0.01593(10) = .209903
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
29
Techniques for Trends
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(ty) - (t)(y)
b=
n(t2) - (t)2
Chapter 2: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
a=
y - bt
n
30
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
31
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
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Management
Yasar A. Ozcan
32
Techniques for Seasonality
Employing Seasonal Indices in Forecasts
Example 2.10: A forecast based on linear regression yields the following
trend equation
Demand (Yt) = 511.06 + 1.259 t.
The forecast of demand for periods 29 through 31 would be:
Y29 = 511.06 + 1.259 (29) = 547.6.
Y30 = 511.06 +1.259 (30) = 548.8.
Y31 = 511.06 + 1.259 (31) = 550.1.
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
1.036. Monthly adjustments to those forecasts are calculated
Monthly Adjusted Forecast (t): Forecast * Monthly Index
Period 29 (November): 547.6 (0.984) = 538.8.
Period 30 (December): 548.9 (0.973) = 534.0.
Period 31 (January) : 550.1 (1.036) = 569.9.
Chapter 2: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
33
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: 538.8 * (0.972) = 523.7.
Tuesday, November: 538.8 * (1.023) = 551.2.
Chapter 2: Quantitatve
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Management
Yasar A. Ozcan
34
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
35
Is your forecast accurate?
• Mean Absolute Deviation (MAD)
| Actual  Forecast |

MAD 
MAD weights all
errors evenly.
n
• Mean Absolute Percent Error (MAPE)
| Actual  Forecast |

MAPE 
 Actual
Seek lowest of MAD or MAPE for given set of data;
also examine historical performance versus
responsiveness to current situation.
Chapter 2: Quantitatve
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Management
Yasar A. Ozcan
MAPE avoids the
problem of
interpreting the
measure of accuracy
relative to the
magnitudes of the
actual and the
forecast values.
36
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
15908
-404
404
3
14272
15786.8
-1514.8
1515
4
13174
15332.4
-2158.4
2158
5
10022
14684.9
-4662.9
4662.9
6
Sum Σ
13286
52972
8740.1
Hence,
MAD = 8740.1 ÷ 4 = 2185.03, and
MAPE = 8740.1 ÷ 52972 = 0.165 or 16.5%.
Chapter 2: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
37
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
( Actual  Forecast )

Tracking signal 
MAD
Chapter 2: Quantitatve
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Management
Yasar A. Ozcan
38
Control Chart for Tracking Signal
6
Tracking signal
4
2
0
1
3
5
7
9
11
13
15
17
19
21
23
25
-2
27
Range of
Acceptable
Variation
-4
Need for
Corrective Action
-6
-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
39
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
40
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
41
The End
Chapter 2: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
42