Forecasting February 26, 2007. Laws of Forecasting Three Laws of Forecasting –Forecasts are always...
-
Upload
erin-shepherd -
Category
Documents
-
view
216 -
download
0
Transcript of Forecasting February 26, 2007. Laws of Forecasting Three Laws of Forecasting –Forecasts are always...
Forecasting
February 26, 2007
Laws of Forecasting
• Three Laws of Forecasting
– Forecasts are always wrong!
– Detailed forecasts are worse than aggregate forecasts!
– The further into the future, the less reliable the forecast will be!
Forecasting
• Starting point of all Production Planning systems
• Qualitative Forecasting techniques
• Quantitative Forecasting techniques
• Choice of technique varies with the Product Life Cycle
Product Development Stage
• Should we enter into this business? What segments?
• What are the alternative growth opportunities for product X?
• How have established products similar to X fared?
• How should we allocate R&D efforts and funds?• Where will be the market 5 years, 10 years from
now?
Preliminaries
• What is the purpose of forecast? How is it to be used?– Accuracy and power required by the techniques
• Requirements for entering a business vs. next year’s budget
– Impact of promotions and other marketing devices– Techniques vary with cost, scope and accuracy– Forecaster should fix the level of tolerance of
accuracy• Helps in managing the trade-offs• Accurate forecast reduces inventory (cost of inventory vs.
cost of forecasting)
Qualitative Forecasting
• Relies on expertise of people
• Data is scarce
• Usually used for technological forecasts (long term forecasts)
• Delphi Method, Market Research, Panel Consensus
Quantitative Forecasting
• Time Series models– Predict a future parameter as a function of past
values of that parameter (e.g., historical demand)– Systematic variation is captured (seasonality, trend)– Cyclic patterns– Growth (decline) rates of the trends– Assume future is like past (hence useful for short term
forecasts)– Managers need to look at the turning points in future
that change the past trends
Time Series Forecasting
• Time period i = 1,2,…..t (most recent data)• A(i): Actual observations• f(t+λ): Forecasts for t + λ, λ = 1,2,……,• F(t): smoothed estimate (current position of
the process under consideration)• T(t): smoothed trend
Time Series Model f(t+λ), λ =1,2,3,…,A(i), i =1,2,…t
Time Series Forecasting
• Moving-Average Model
• Exponential Smoothing Model
• Exponential Smoothing with a Linear Trend Model
• Winter’s Method (adds seasonal multipliers to the exponential smoothing with linear trend model)
Quantitative Forecasting
• Causal models– Most sophisticated – Predict a future parameter (e.g., demand for a
product) as a function of other parameters (e.g., interest rates, marketing strategy).
Causal Forecasting
• Opening a fast food restaurant– Demand forecast?– Predictable parameters
• Population in the vicinity• Competition
– Use statistics (e.g., regression) to estimate the parameters
• Y = b0 + b1x1 + b2X2
Components of an Observation
Observed demand (O) =
Systematic component (S) + Random component (R)
Level (current deseasonalized demand)
Trend (growth or decline in demand)
Seasonality (predictable seasonal fluctuation)
• Systematic component: Expected value of demand• Random component: The part of the forecast that deviates from the systematic component• Forecast error: difference between forecast and actual demand
Time Series ForecastingQuarter Demand Dt
II, 1998 8000III, 1998 13000IV, 1998 23000I, 1999 34000II, 1999 10000III, 1999 18000IV, 1999 23000I, 2000 38000II, 2000 12000III, 2000 13000IV, 2000 32000I, 2001 41000
Forecast demand for thenext four quarters.
Time Series Forecasting
0
10,000
20,000
30,000
40,000
50,000
97,2
97,3
97,4
98,1
98,2
98,3
98,4
99,1
99,2
99,3
99,4
00,1
Basic Approach toDemand Forecasting
• Understand the objectives of forecasting• Integrate demand planning and forecasting• Identify major factors that influence the demand
forecast• Understand and identify customer segments• Determine the appropriate forecasting technique• Establish performance and error measures for
the forecast
Patterns of DemandPatterns of DemandQ
ua
nti
tyQ
ua
nti
ty
TimeTime
(a) Horizontal: Data cluster about a horizontal line.(a) Horizontal: Data cluster about a horizontal line.
Patterns of DemandPatterns of DemandQ
ua
nti
tyQ
ua
nti
ty
TimeTime
(b) Trend: Data consistently increase or decrease.(b) Trend: Data consistently increase or decrease.
Patterns of DemandPatterns of DemandQ
ua
nti
tyQ
ua
nti
ty
| | | | | | | | | | | |JJ FF MM AA MM JJ JJ AA SS OO NN DD
MonthsMonths
(c) Seasonal: Data consistently show peaks and valleys.(c) Seasonal: Data consistently show peaks and valleys.
Year 1Year 1
Year 2Year 2
Patterns of DemandPatterns of DemandQ
ua
nti
tyQ
ua
nti
ty
| | | | | |11 22 33 44 55 66
YearsYears
(c) Cyclical: Data reveal gradual increases and (c) Cyclical: Data reveal gradual increases and decreases over extended periods.decreases over extended periods.
Demand Forecast ApplicationsDemand Forecast Applications DEMAND FORECAST APPLICATIONS
Time Horizon
Medium Term Long Term Short Term (3 months– (more than
Application (0–3 months) 2 years) 2 years)
Total salesGroups or familiesof products orservicesStaff planningProductionplanningMaster productionschedulingPurchasingDistribution
CausalJudgment
Forecast quantity Individualproducts orservices
Decision area InventorymanagementFinal assemblyschedulingWorkforceschedulingMaster productionscheduling
Forecasting Time seriestechnique Causal
Judgment
Total sales
Facility locationCapacityplanningProcessmanagement
CausalJudgment
Causal MethodsCausal MethodsLinear RegressionLinear Regression
Dep
end
ent
vari
able
Dep
end
ent
vari
able
Independent variableIndependent variableXX
YYEstimate ofEstimate ofY Y from fromregressionregressionequationequation
RegressionRegressionequation:equation:YY = = aa + + bXbX
ActualActualvaluevalueof of YY
Value of Value of X X used usedto estimate to estimate YY
Deviation,Deviation,or erroror error
{
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Sal
es (
tho
usa
nd
s o
f u
nit
s)
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Y = – 8.136 + 109.229X
Sal
es (
tho
usa
nd
s o
f u
nit
s)
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Y = – 8.136 + 109.229X
Sal
es (
tho
usa
nd
s o
f u
nit
s)
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Y = – 8.136 + 109.229X
Sal
es (
tho
usa
nd
s o
f u
nit
s)
Forecast for Month 6
X = $1750, Y = – 8.136 + 109.229(1.75)
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Y = – 8.136 + 109.229X
Sal
es (
tho
usa
nd
s o
f u
nit
s)
Forecast for Month 6
X = $1750, Y = 183.015, or 183,015 units
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Y = – 8.136 + 109.229X
Sal
es (
tho
usa
nd
s o
f u
nit
s)
Causal MethodsCausal MethodsLinear RegressionLinear Regression
SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)
11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0
aa = – 8.136= – 8.136bb = 109.229= 109.229XXrr = 0.98= 0.98rr22 = 0.96= 0.96ssyxyx = 15.61= 15.61
| | | |1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50
Y = – 8.136 + 109.229X
Sal
es (
tho
usa
nd
s o
f u
nit
s)
If current stock = 62,500 units,
Production = 183,015 – 62,500 = 120,015 units
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
FF44 = = 411 + 380 + 400411 + 380 + 40033
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
FF44 = 397.0 = 397.0
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
11 40040022 38038033 411411
FF44 = 397.0 = 397.0
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
22 38038033 41141144 415415
FF55 = = 415 + 411 + 380415 + 411 + 38033
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
Actual patientActual patientarrivalsarrivals
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
PatientPatientWeekWeek ArrivalsArrivals
22 38038033 41141144 415415
FF55 = 402.0 = 402.0
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsSimple Moving AveragesSimple Moving Averages
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Actual patientActual patientarrivalsarrivals
3-week MA3-week MAforecastforecast
6-week MA6-week MAforecastforecast
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
Exponential SmoothingExponential Smoothing = 0.10= 0.10
FFt +1t +1 = = FFtt + + (D(Dtt – – FFt t ))
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
Exponential SmoothingExponential Smoothing = 0.10= 0.10
FF44 = 0.10(411) + 0.90(390) = 0.10(411) + 0.90(390)
FF3 3 = (400 + 380)/2= (400 + 380)/2
DD33 = 411 = 411
Ft +1 = Ft + (Dt – Ft )
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
FF44 = 392.1 = 392.1
Exponential SmoothingExponential Smoothing = 0.10= 0.10
FF3 3 = (400 + 380)/2= (400 + 380)/2
DD33 = 411 = 411
FFt +1t +1 = = FFtt + + (D(Dtt – – FFt t ))
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
FF4 4 = 392.1= 392.1
DD44 = 415 = 415
Exponential SmoothingExponential Smoothing = 0.10= 0.10
FF44 = 392.1 = 392.1 FF55 = 394.4 = 394.4
FFt +1t +1 = = FFtt + + (D(Dtt – – FFt t ))
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
WeekWeek
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —
| | | | | |00 55 1010 1515 2020 2525 3030
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
Exponential Exponential smoothingsmoothing = 0.10= 0.10
Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing
450 450 —
430 430 —
410 410 —
390 390 —
370 370 —Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
| | | | | |00 55 1010 1515 2020 2525 3030
3-week MA3-week MAforecastforecast
6-week MA6-week MAforecastforecast
Exponential Exponential smoothingsmoothing = 0.10= 0.10
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Actual blood Actual blood test requeststest requests
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
5050 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Medanalysis, Inc.Medanalysis, Inc.Demand for blood analysisDemand for blood analysis
AAtt = = DDtt + (1 – + (1 – )()(AAtt-1-1 + + TTtt-1-1))
TTtt = = ((AAtt – – AAtt-1-1) + (1 – ) + (1 – ))TTtt-1-1
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
AA11 = 0.2(27) + 0.80(28 + 3) = 0.2(27) + 0.80(28 + 3)
TT11 = 0.2(30.2 - 28) + 0.80(3) = 0.2(30.2 - 28) + 0.80(3)
Medanalysis, Inc.Medanalysis, Inc.Demand for blood analysisDemand for blood analysis
AA00 = 28 patients = 28 patients TT00 = 3 patients = 3 patients
= 0.20 = 0.20 = 0.20 = 0.20
AAtt = = DDtt + (1 – + (1 – )()(AAtt-1-1 + + TTtt-1-1))
TTtt = = ((AAtt – – AAtt-1-1) + (1 – ) + (1 – ))TTtt-1-1
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
AA11 = 30.2 = 30.2
TT11 = 2.8 = 2.8
Medanalysis, Inc.Medanalysis, Inc.Demand for blood analysisDemand for blood analysis
AA00 = 28 patients = 28 patients TT00 = 3 patients = 3 patients
= 0.20 = 0.20 = 0.20 = 0.20
AAtt = = DDtt + (1 – + (1 – )()(AAtt-1-1 + + TTtt-1-1))
TTtt = = ((AAtt – – AAtt-1-1) + (1 – ) + (1 – ))TTtt-1-1
ForecastForecast22 = =
30.2 + 2.8 = 3330.2 + 2.8 = 33
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Medanalysis, Inc.Medanalysis, Inc.Demand for blood analysisDemand for blood analysis
AA22 = 30.2 = 30.2 DD22 = 44 = 44 TT11 = 2.8 = 2.8
= 0.20 = 0.20 = 0.20 = 0.20
AAtt = = DDtt + (1 – + (1 – )()(AAtt-1-1 + + TTtt-1-1))
TTtt = = ((AAtt – – AAtt-1-1) + (1 – ) + (1 – ))TTtt-1-1
AA22 = 0.2(44) + 0.80(30.2 + 2.8) = 0.2(44) + 0.80(30.2 + 2.8)
TT22 = 0.2(35.2 - 30.2) + 0.80(2.8) = 0.2(35.2 - 30.2) + 0.80(2.8)
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Medanalysis, Inc.Medanalysis, Inc.Demand for blood analysisDemand for blood analysis
AA22 = 30.2 = 30.2 DD22 = 44 = 44 TT11 = 2.8 = 2.8
= 0.20 = 0.20 = 0.20 = 0.20
AAtt = = DDtt + (1 – + (1 – )()(AAtt-1-1 + + TTtt-1-1))
TTtt = = ((AAtt – – AAtt-1-1) + (1 – ) + (1 – ))TTtt-1-1
AA22 = 35.2 = 35.2
TT22 = 3.2 = 3.2Forecast = Forecast =
35.2 + 3.2 = 38.435.2 + 3.2 = 38.4
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Actual blood Actual blood test requeststest requests
Trend-adjusted Trend-adjusted forecastforecast
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Trend-adjusted Trend-adjusted forecastforecast
Actual blood Actual blood test requeststest requests
Number of time periods 15.00Demand smoothing coefficient ( ) 0.20Initial demand value 28.00Trend-smoothing coefficient ( ) 0.20Estimate of trend 3.00
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 80 —
70 70 —
60 60 —
50 50 —
40 40 —
30 30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Trend-adjusted Trend-adjusted forecastforecast
Actual blood Actual blood test requeststest requests
0 28 28.00 3.00 0.00 0.00 1 27 30.20 2.84 31.00 –4.00 2 44 35.23 3.27 33.04 10.96 3 37 38.20 3.21 38.51 –1.51 4 35 40.14 2.96 41.42 –6.42 5 53 45.08 3.35 43.10 9.89 6 38 46.35 2.93 48.43 –10.43 7 57 50.83 3.24 49.29 7.71 8 61 55.46 3.52 54.08 6.92 9 39 54.99 2.72 58.98 –19.9810 55 57.17 2.61 57.71 –2.7111 54 58.63 2.38 59.78 –5.7812 52 59.21 2.02 61.01 –9.0113 60 60.99 1.97 61.23 –1.2314 60 62.37 1.85 62.96 –2.9615 75 66.38 2.28 64.22 10.77
TABLE 13.2 FORECASTS FOR MEDANALYSIS
Smoothed Trend ForecastWeek Arrivals Average Average Forecast Error
Time-Series MethodsTime-Series MethodsTrend-Adjusted Exponential SmoothingTrend-Adjusted Exponential Smoothing
|| || || || || || || || || || || || || || ||00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515
80 —80 —
70 —70 —
60 —60 —
50 —50 —
40 —40 —
30 —30 —
Pat
ien
t ar
riva
lsP
atie
nt
arri
vals
WeekWeek
Trend-adjusted Trend-adjusted forecastforecast
Actual blood Actual blood test requeststest requests
Smoothed Trend ForecastWeek Arrivals Average Average Forecast Error
0 28 28.00 3.00 0.00 0.00 1 27 30.20 2.84 31.00 –4.00 2 44 35.23 3.27 33.04 10.96 3 37 38.20 3.21 38.51 –1.51 4 35 40.14 2.96 41.42 –6.42 5 53 45.08 3.35 43.10 9.89 6 38 46.35 2.93 48.43 –10.43 7 57 50.83 3.24 49.29 7.71 8 61 55.46 3.52 54.08 6.92 9 39 54.99 2.72 58.98 –19.9810 55 57.17 2.61 57.71 –2.7111 54 58.63 2.38 59.78 –5.7812 52 59.21 2.02 61.01 –9.0113 60 60.99 1.97 61.23 –1.2314 60 62.37 1.85 62.96 –2.9615 75 66.38 2.28 64.22 10.77
SUMMARY
Average demand 49.80Mean square error 76.13Mean absolute deviation 7.35Forecast for week 16 68.66Forecast for week 17 70.95Forecast for week 18 73.24
QuarterQuarter Year 1Year 1 Year 2Year 2 Year 3Year 3 Year 4Year 4
11 4545 7070 100100 10010022 335335 370370 585585 72572533 520520 590590 830830 1160116044 100100 170170 285285 215215
TotalTotal 10001000 12001200 18001800 22002200
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Time-Series MethodsTime-Series MethodsSeasonal InfluencesSeasonal Influences
Seasonal Patterns
PeriodPeriod
De
ma
nd
De
ma
nd
| | | | | | | | | | | | | | | |00 22 44 55 88 1010 1212 1414 1616
(a) Multiplicative pattern(a) Multiplicative pattern
Seasonal PatternsSeasonal Patterns
PeriodPeriod
| | | | | | | | | | | | | | | |00 22 44 55 88 1010 1212 1414 1616
De
ma
nd
De
ma
nd
(b) Additive pattern(b) Additive pattern
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Measures of Forecast ErrorMeasures of Forecast Error
EEtt = = DDtt – – FFtt
||EEt t ||
nn
EEtt22
nn
CFE = CFE = EEtt
==MSE = MSE =
MAD = MAD = MAPE = MAPE = [[ ||EEt t | (100)| (100) ]] // DDtt
nn
((EEtt – E – E ))22
nn – 1– 1
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 -25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
Measures of Error
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
CFE = – 15
Measures of Error
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
CFE = – 15
Measures of Error
E = = – 1.875– 15
8
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
E = = – 1.875– 15
8
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
E = = – 1.875– 15
8
= 27.4
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
MAD = = 24.4195
8
E = = – 1.875– 15
8
= 27.4
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
MAD = = 24.4195
8
MAPE = = 10.2%81.3%
8
E = = – 1.875– 15
8
= 27.4
Choosing a MethodChoosing a MethodForecast ErrorForecast Error
Absolute Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%
MSE = = 659.45275
8
CFE = – 15
Measures of Error
MAD = = 24.4195
8
MAPE = = 10.2%81.3%
8
E = = – 1.875– 15
8
= 27.4
Summary of Learning Objectives
• What are the roles of forecasting for an enterprise and a supply chain?
• What are the components of a demand forecast?
• How is demand forecast given historical data using time series methodologies?
• How is a demand forecast analyzed to estimate forecast error?