Forecasting

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 ObservationObserved 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

uant

ityQ

uant

ity

TimeTime

(a) Horizontal: Data cluster about a horizontal line.(a) Horizontal: Data cluster about a horizontal line.


uant

ityQ

uant

ity

TimeTime

(b) Trend: Data consistently increase or decrease.(b) Trend: Data consistently increase or decrease.


uant

ityQ

uant

ity

| | | | | | | | | | | |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


uant

ityQ

uant

ity

| | | | | |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

ende

nt v

aria

ble

Dep

ende

nt v

aria

ble

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

{


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



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

Sale

s (th

ousa

nds

of u

nits

)



11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0


| | | |1.0 1.5 2.0 2.5


300 —

250 —

200 —

150 —

100 —

50

Y = – 8.136 + 109.229X

Sale

s (th

ousa

nds

of u

nits

)



11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0


| | | |1.0 1.5 2.0 2.5


300 —

250 —

200 —

150 —

100 —

50

Y = – 8.136 + 109.229X

Sale

s (th

ousa

nds

of u

nits

)

Forecast for Month 6X = $1750, Y = – 8.136 + 109.229(1.75)



11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0


| | | |1.0 1.5 2.0 2.5


300 —

250 —

200 —

150 —

100 —

50

Y = – 8.136 + 109.229X

Sale

s (th

ousa

nds

of u

nits

)

Forecast for Month 6X = $1750, Y = 183.015, or 183,015 units



11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0


| | | |1.0 1.5 2.0 2.5


300 —

250 —

200 —

150 —

100 —

50

Y = – 8.136 + 109.229X

Sale

s (th

ousa

nds

of u

nits

)



11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0


| | | |1.0 1.5 2.0 2.5


300 —

250 —

200 —

150 —

100 —

50

Y = – 8.136 + 109.229X

Sale

s (th

ousa

nds

of u

nits

)

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

Patie

nt a

rriv

als

Patie

nt a

rriv

als

Actual patientActual patientarrivalsarrivals



450 450 —

430 430 —

410 410 —

390 390 —

370 370 —

WeekWeek

| | | | | |00 55 1010 1515 2020 2525 3030

Patie

nt a

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als

Patie

nt a

rriv

als




450 450 —

430 430 —

410 410 —

390 390 —

370 370 —

WeekWeek

| | | | | |00 55 1010 1515 2020 2525 3030

PatientPatientWeekWeek ArrivalsArrivals

11 40040022 38038033 411411

Patie

nt a

rriv

als

Patie

nt a

rriv

als



WeekWeek

450 450 —

430 430 —

410 410 —

390 390 —

370 370 —

| | | | | |00 55 1010 1515 2020 2525 3030


11 40040022 38038033 411411

FF44 = = 411 + 380 + 400411 + 380 + 40033Pa

tient

arr

ival

sPa

tient

arr

ival

s



450 450 —

430 430 —

410 410 —

390 390 —

370 370 —

WeekWeek

| | | | | |00 55 1010 1515 2020 2525 3030


11 40040022 38038033 411411

FF44 = 397.0 = 397.0

Patie

nt a

rriv

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Patie

nt a

rriv

als



WeekWeek

450 450 —

430 430 —

410 410 —

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| | | | | |00 55 1010 1515 2020 2525 3030


22 38038033 41141144 415415

FF55 = = 415 + 411 + 380415 + 411 + 38033

Patie

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Patie

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als



450 450 —

430 430 —

410 410 —

390 390 —

370 370 —

WeekWeek

| | | | | |00 55 1010 1515 2020 2525 3030


22 38038033 41141144 415415

FF55 = 402.0 = 402.0

Patie

nt a

rriv

als

Patie

nt a

rriv

als


WeekWeek

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3-week MA3-week MAforecastforecast


Time-Series MethodsTime-Series MethodsExponential SmoothingExponential Smoothing

450 450 —

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410 410 —

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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 ))

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370 370 —

WeekWeek

| | | | | |00 55 1010 1515 2020 2525 3030


FF44 = 0.10(411) + 0.90(390) = 0.10(411) + 0.90(390)

FF3 3 = (400 + 380)/2= (400 + 380)/2DD33 = 411 = 411

Ft +1 = Ft + (Dt – Ft )

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450 450 —

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WeekWeek

| | | | | |00 55 1010 1515 2020 2525 3030

FF44 = 392.1 = 392.1


FF3 3 = (400 + 380)/2= (400 + 380)/2DD33 = 411 = 411


Patie

nt a

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WeekWeek

450 450 —

430 430 —

410 410 —

390 390 —

370 370 —

| | | | | |00 55 1010 1515 2020 2525 3030

FF4 4 = 392.1= 392.1DD44 = 415 = 415


FF44 = 392.1 = 392.1 FF55 = 394.4 = 394.4


Patie

nt a

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Patie

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WeekWeek

450 450 —

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| | | | | |00 55 1010 1515 2020 2525 3030

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450 450 —

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370 370 —Patie

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Exponential Exponential smoothingsmoothing = 0.10= 0.10


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410 410 —

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370 370 —Patie

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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

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WeekWeek

Actual blood Actual blood test requeststest requests


| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515

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70 70 —

60 60 —

5050 —

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30 30 —

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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


| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515

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30 30 —

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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)


AA00 = 28 patients = 28 patients TT00 = 3 patients = 3 patients = 0.20 = 0.20 = 0.20 = 0.20



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WeekWeek

AA11 = 30.2 = 30.2TT11 = 2.8 = 2.8


AA00 = 28 patients = 28 patients TT00 = 3 patients = 3 patients = 0.20 = 0.20 = 0.20 = 0.20


ForecastForecast22 = = 30.2 + 2.8 = 3330.2 + 2.8 = 33


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AA22 = 30.2 = 30.2 DD22 = 44 = 44 TT11 = 2.8 = 2.8 = 0.20 = 0.20 = 0.20 = 0.20


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)


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WeekWeek


AA22 = 30.2 = 30.2 DD22 = 44 = 44 TT11 = 2.8 = 2.8 = 0.20 = 0.20 = 0.20 = 0.20


AA22 = 35.2 = 35.2TT22 = 3.2 = 3.2

Forecast = Forecast = 35.2 + 3.2 = 38.435.2 + 3.2 = 38.4


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Trend-adjusted Trend-adjusted forecastforecast


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Number of time periods 15.00Demand smoothing coefficient ( ) 0.20Initial demand value 28.00Trend-smoothing coefficient ( ) 0.20Estimate of trend 3.00


| | | | | | | | | | | | | | |00 11 22 33 44 55 66 77 88 99 1010 1111 1212 1313 1414 1515

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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


|| || || || || || || || || || || || || || ||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 —

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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

SUMMARYAverage 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 411 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

Seasonal Patterns

PeriodPeriod

Dem

and

Dem

and

| | | | | | | | | | | | | | | |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

Dem

and

Dem

and

(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%





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




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




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




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




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




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 = = 24.41958

E = = – 1.875– 15 8

= 27.4




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 = = 24.41958

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?

Forecasting

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