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Chapter 2. Forecasting. 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 - PowerPoint PPT Presentation
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Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 11
Chapter 2. Chapter 2. ForecastingForecasting
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 22
OutlineOutline Why Forecast?Why Forecast? Steps in the Forecasting ProcessSteps in the Forecasting Process Forecasting ApproachesForecasting Approaches
– JudgmentalJudgmental– Time Series-- Historical DataTime Series-- Historical Data– Techniques for AveragingTechniques for Averaging– Techniques for TrendTechniques for Trend– Techniques for SeasonalityTechniques for Seasonality– AssociativeAssociative
Accuracy and Control of ForecastsAccuracy and Control of Forecasts Choosing a Forecasting TechniqueChoosing a Forecasting Technique
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 33
Why forecasting is important?Why forecasting is important?
Forecasts serve as a basis for planningForecasts serve as a basis for planning Enable health care managers to anticipate the Enable health care managers to anticipate the
future to plan the system and plan the use of future to plan the system and plan the use of that systemthat system
Forecasting is more than predicting demandForecasting is more than predicting demand It is not an exact science; one must blendIt is not an exact science; one must blend experience, judgment, and technical expertiseexperience, judgment, and technical expertise
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 44
All forecasts have common elementsAll forecasts have common elements
Assumption that past continues into futureAssumption that past continues into future Errors occur-- actual differs from Errors occur-- actual differs from
predicted; presence of randomnesspredicted; presence of randomness Forecasts of group of items (aggregate) Forecasts of group of items (aggregate)
tends to be more accurate than individual tends to be more accurate than individual items (i.e., departmental vs. whole items (i.e., departmental vs. whole hospital)hospital)
Forecast accuracy decreases as time Forecast accuracy decreases as time horizon increaseshorizon increases
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Characteristics of a Good ForecastCharacteristics of a Good Forecast
Timely
Reliable
Accurate
Meaningful units ($$’s, visits, discharges, patient days, etc.)
Easy to use
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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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
Steps in the Forecasting ProcessSteps in the Forecasting Process
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 77
What approaches can we use?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 MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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The Delphi MethodThe Delphi Method Method of obtaining opinions of Method of obtaining opinions of
managers and staffmanagers and staff Involves circulating a series of Involves circulating a series of
questionnaires, each developed from the questionnaires, each developed from the previous one, to achieve a consensus on previous one, to achieve a consensus on an issue (in this case, a forecast)an issue (in this case, a forecast)
Useful for forecasting technological Useful for forecasting technological changes and their impactschanges and their impacts
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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The Delphi Approach, cont.The Delphi Approach, cont. AdvantagesAdvantages
– More individuals may be engaged than can effectively More individuals may be engaged than can effectively interact face-to-faceinteract face-to-face
– It is important to avoid bandwagon effectIt is important to avoid bandwagon effect– Preserves anonymity of participantsPreserves anonymity of participants
WeaknessesWeaknesses– Questions may be ambiguous leading to false Questions may be ambiguous leading to false
consensusconsensus– Panel members may changePanel members may change– Studies do not prove that Delphi forecasts are highly Studies do not prove that Delphi forecasts are highly
accurateaccurate– Preserving anonymity removes accountabilityPreserving anonymity removes accountability
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Forecasting Approaches, cont.Forecasting Approaches, cont. Time series-- Time series-- identify the behavior of the series by using identify the behavior of the series by using
factors such as trend, seasonality, cycles, irregular factors such as trend, seasonality, cycles, irregular variations, and random variationsvariations, and random variations
Techniques for Techniques for averagingaveraging Naive forecastsNaive forecasts Moving averages (MA)Moving averages (MA) Exponential smoothingExponential smoothing
– Techniques for Techniques for trendtrend Linear equations using regression (yLinear equations using regression (ytt = a + bx = a + bxtt)) Trend adjusted exponential smoothing Trend adjusted exponential smoothing
– Techniques for Techniques for seasonalityseasonality Seasonal Variations Seasonal Variations Indices TechniqueIndices Technique
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Forecasting Approaches, cont.Forecasting Approaches, cont.
Associative TechniquesAssociative Techniques– Simple linear regression (y = a + bx)Simple linear regression (y = a + bx)– Scatter diagram-- plot dataScatter diagram-- plot data– CorrelationsCorrelations
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Jan Mar May Jul Sep Nov
SeasonalVariation
2005
2004
2003
SeasonalVariation
CycleRandom Variation
Trend
Figure 2.1 Variation Characteristics
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Averaging TechniquesAveraging Techniques Smooth out fluctuations in time serious Smooth out fluctuations in time serious
because individual highs and lows cancel because individual highs and lows cancel each other outeach other out
So, would forecasts based on averages So, would forecasts based on averages exhibit more or less variability?exhibit more or less variability?
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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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
dataExamples: If last week’s demand was 50 units, the naive forecastfor 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 MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Moving AveragesMoving Averages
where, i = “Age” of data (i=1,2,3. . .) n = number of periods in moving average Ai = actual value with age i
n
AMAF i
nt
Forecast uses a number of the most recent actual data values in generating a forecast
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Moving AveragesMoving AveragesExample 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 3 14272
4 2 13174
5 1 10022
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Moving Averages, cont.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 Forecast
1 5 15908
2 4 15504
3 3 14272
4 2 13174 15228
5 1 10022 14317
6 12489
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Moving Averages, cont.Moving Averages, cont.
1 2 3 4 5 6 7 8 9
Data
MA5
MA3
The greater the number of periods in a moving average, the greater the forecast will lag with changes in the data
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Moving Averages, cont.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 MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 2020
Using Weighted ValuesUsing Weighted ValuesExample:Example: Continuing Continuing
with Example 2.1; since with Example 2.1; since there is a downward there is a downward trend in visits and in trend in visits and in period 5 there is a sharp period 5 there is a sharp decline, a weight of .5 or decline, a weight of .5 or even higher is justified even higher is justified by the healthcare by the healthcare manager to calculate a manager to calculate a weighted average for weighted average for period 6 period 6
Period (t) Age Visits Weights
1 5 15908
2 4 15504
3 3 14272 0.2
4 2 13174 0.3
5 1 10022 0.5
6
iint AwMAF
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
Yasar A. OzcanYasar A. Ozcan 2121
Using Weighted ValuesUsing Weighted ValuesSolution: Solution:
In this analysis, a weighted average, using In this analysis, a weighted average, using formula [2.2], for the OB/GYN clinic for the formula [2.2], for the OB/GYN clinic for the period 6 would be: period 6 would be: FF66 = 14272*.2+13174*.3+10022*.5 = 14272*.2+13174*.3+10022*.5FF66 = 11818. = 11818.
Period (t) Age Visits Weights Forecast
1 5 15908
2 4 15504
3 3 14272 0.2
4 2 13174 0.3
5 1 10022 0.5
6 11818
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Simple Exponential SmoothingSimple Exponential Smoothing Each new forecast is based on the previous forecast plus a Each new forecast is based on the previous forecast plus a
percentage of the difference between that forecast the actual percentage of the difference between that forecast the actual value of the series at that pointvalue of the series at that point
New forecast = Old forecast + New forecast = Old forecast + αα(Actual-Old forecast), where (Actual-Old forecast), where αα is a percentage or is a percentage or
FFtt = F = Ft-1 t-1 + + αα(A(At-1 t-1 - F- Ft-1t-1),),
where, Fwhere, Ftt = Forecast for period t = Forecast for period t FFt-1t-1 = Forecast for period t-1 = Forecast for period t-1 αα = Smoothing constant = Smoothing constant AAt-1 t-1 = Actual demand or sales in period t-1= Actual demand or sales in period t-1
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Exponential Smoothing, cont.Exponential Smoothing, cont.Example 2.4:Example 2.4: Using the data Using the data
from Example 2.1, build from Example 2.1, build forecasts with smoothing forecasts with smoothing constant α = 0.3constant α = 0.3
Solution: Solution: Following the previous Following the previous example and formula [2.3], example and formula [2.3], we can build forecasts for we can build forecasts for periods as data become periods as data become available. available.
FF33 = 15908 + .30(15504- = 15908 + .30(15504-15908)15908)
FF33 = 15786.8 = 15786.8
Smoothing constant α = 0.3 Error
Period (t) Actual (Visits) Forecast (Actual – 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
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Smoothing constant Smoothing constant αα = 0.5 = 0.5 ErrorError
Period(t)Period(t) VisitsVisits ForecastForecast (Actual – Forecast)(Actual – Forecast)
11 1590815908 ----
22 1550415504 1590815908 -404.0-404.0
33 1427214272 15706.015706.0 -1434.0-1434.0
44 1317413174 14989.014989.0 -1815.0-1815.0
55 1002210022 14081.514081.5 -4059.5-4059.5
Example 2.5:Example 2.5: Using the Using the data from data from Example 2.1Example 2.1, build , build forecasts with smoothing forecasts with smoothing constantconstant
αα = 0.5. = 0.5.
Solution:Solution:
Exponential Smoothing, cont.Exponential Smoothing, cont.
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Example 2.6:Example 2.6: Using the data Using the data from from Example 2.1Example 2.1, build forecasts , build forecasts with smoothing constants with smoothing constants
αα = 0.0 and = 0.0 and αα = 1.0. = 1.0. Solution:Solution:
Exponential Smoothing, cont.Exponential Smoothing, cont.
Period(t)
α = 0.0 Error α = 1.0 Error
Visits Forecast (Actual – Forecast) Visits Forecast (Actual – Forecast)
1 15908 -- 15908 --
2 15504 15908 -404.0 15504 15908 -404.0
3 14272 15908.0 -1636.0 14272 15504.0 -1232.0
4 13174 15908.0 -2734.0 13174 14272.0 -1098.0
5 10022 15908.0 -5886.0 10022 13174.0 -3152.0
6 15908.0 10022.0
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Techniques for TrendsTechniques for Trends
Least squares regressionLeast squares regression-- minimizes the sum -- minimizes the sum of the squared errorsof the squared errors
Least squares lineLeast squares line::y = a + bxy = a + bx, y = predicted (dependent) variable, y = predicted (dependent) variable
x = predictor (independent) x = predictor (independent) variablevariable
b = slope of data lineb = slope of data linea = value of y when x = 0a = value of y when x = 0
n(xy) - (x)(y)n(x2) - (x)2b = a = y - bx
n
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Figure 2.9 Linear RegressionFigure 2.9 Linear Regression
y
x
y = a + bx
a
errorerror
Δy
Δx b =(Δy/Δx) , where b>0
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Techniques for TrendsTechniques for Trends
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
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.
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Solution:Solution:After calculating
x y xy x, , , 2substitute into the equations [2.5] for a and [2.6] for b, respectively.
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.
.01593.0)132(132)1796(12)71.2(132)29.35(12
)()(
))(()(22
xxn
yxxynb
.0506.012
)132(01593.071.2
nxby
a
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Techniques for TrendsTechniques for Trends
Linear Regression as a Trend Line
y = a + b*t y = predicted (dependent) variablet = predictor (time) variableb = slope of data linea = value of y when x = 0
n(ty) - (t)(y)n(t2) - (t)2b = a = y - bt
n
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Example 2.8:Example 2.8: Referring back to the OB/GYN example, the health care manager can Referring back to the OB/GYN example, the health care manager can estimate the trend line using regression analysis. estimate the trend line using regression analysis.
Solution:Solution:
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Techniques for SeasonalityTechniques for SeasonalitySeasonal variationsSeasonal variations in a data set consistently repeat upward in a data set consistently repeat upward
or downward movements of the data values that can be or downward movements of the data values that can be traced to recurrent events. traced to recurrent events.
In the In the additiveadditive model model, seasonality is expressed as a quantity , seasonality is expressed as a quantity (example: 5 units), which is added or subtracted from the (example: 5 units), which is added or subtracted from the series average in order to incorporate seasonality. series average in order to incorporate seasonality.
In the In the multiplicativemultiplicative model model, seasonality is expressed as a , seasonality is expressed as a percentage of the average amount (example: 1.15) percentage of the average amount (example: 1.15)
Quarterly, Monthly, Daily Indices TechniqueQuarterly, Monthly, Daily Indices Technique
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Techniques for SeasonalityTechniques for SeasonalityEmploying Seasonal Indices in ForecastsExample 2.10: A forecast based on linear regression yields the following
trend equationDemand (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 IndexPeriod 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 MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Techniques for SeasonalityTechniques for SeasonalityEmploying Seasonal Indices in ForecastsEmploying Seasonal Indices in Forecasts
The next step in adjustment of the forecasted The next step in adjustment of the forecasted demand would be for daily fluctuations. As was demand would be for daily fluctuations. As was shown in Table 2.4, Heal Me Hospital experiences shown in Table 2.4, Heal Me Hospital experiences daily variation in demand. Thus, the monthly index daily variation in demand. Thus, the monthly index adjusted forecasts should be further adjusted for adjusted forecasts should be further adjusted for daily variations.daily variations.
Daily Adjusted Forecast = Monthly Adjusted Forecast (t) * Daily Adjusted Forecast = Monthly Adjusted Forecast (t) * Daily IndexDaily Index
For example, for November (period 29), the For example, for November (period 29), the adjusted forecasts for Monday and Tuesday are:adjusted forecasts for Monday and Tuesday are:Monday, November: 538.8 * (0.972) = 523.7.Monday, November: 538.8 * (0.972) = 523.7.Tuesday, November: 538.8 * (1.023) = 551.2.Tuesday, November: 538.8 * (1.023) = 551.2.
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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How accurate are we?How accurate are we?
Errors may be caused by:Errors may be caused by:– An inadequate forecasting modelAn inadequate forecasting model– Irregular variations due to severe weather, Irregular variations due to severe weather,
shortages or breakdowns, catastrophes, etc.shortages or breakdowns, catastrophes, etc.– Forecasting technique may be used Forecasting technique may be used
improperlyimproperly– There may be random variations in the dataThere may be random variations in the data
Forecast Error equals the actual value minus the forecasted value.Error = Actual – Forecast
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Is your forecast accurate?Is your forecast accurate?
• Mean Absolute Deviation (MAD)
Seek lowest of MAD or MAPE for given set of data; also examine historical performance versus responsiveness to current situation.
MAD weights allerrors evenly.
MAPE avoids the problem of interpreting the measure of accuracy relative to the magnitudes of the actual and the forecast values.
nForecastActual
MAD
||
ActualForecastActual
MAPE||
• Mean Absolute Percent Error (MAPE)
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Periodt
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 13286
Sum Σ 52972 8740.1
Is your forecast accurate?Is your forecast accurate?Using data from Example 2.4, SES with α = 0.3, we observe the necessary error calculations in Table below.
Hence,MAD = 8740.1 ÷ 4 = 2185.03, andMAPE = 8740.1 ÷ 52972 = 0.165 or 16.5%.
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Is your forecast accurate?Is your forecast accurate? Controlling forecasts-- set predetermined upper/lower Controlling forecasts-- set predetermined upper/lower
limits for forecast errorslimits for forecast errors Forecasts can be monitored using either a Forecasts can be monitored using either a tracking tracking
signal signal or or control chartcontrol chart..– Tracking signals show cumulative errorsTracking signals show cumulative errors- Control Charts-- set upper and lower limits for - Control Charts-- set upper and lower limits for
individual forecast errorsindividual forecast errors
MADForecastActual
signalTracking
)(
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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Control Chart for Tracking SignalControl Chart for Tracking Signal
Range ofAcceptableVariation
Need for Corrective Action
-6
-4
-2
0
2
4
6
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Trac
king
sig
nal
-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 MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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So what technique should we use?So what technique should we use?
Factors of importance:Factors of importance:– FrequencyFrequency– Level of aggregationLevel of aggregation– Type of Model- Errors [MAD, MAPE]Type of Model- Errors [MAD, MAPE]– Degree of managerial involvementDegree of managerial involvement– Cost per forecastCost per forecast
Time horizon considerations-- short, Time horizon considerations-- short, intermediate, or longintermediate, or long
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What makes a forecast a good one?What makes a forecast a good one?
TimelinessTimeliness AccuracyAccuracy Meaningful Units ($$’s, visits, etc.)Meaningful Units ($$’s, visits, etc.) In writingIn writing Simple to understand and useSimple to understand and use
Chapter 2: Quantitatve MChapter 2: Quantitatve Methods in Health Care Maethods in Health Care Managementnagement
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The End
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