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Chapter 12 Forecasting
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OBJECTIVES
• Demand Management • Qualitative Forecasting Methods • Simple & Weighted Moving Average Forecasts • Exponential Smoothing • Simple Linear Regression • Web-Based Forecasting
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Demand Management Independent Demand: Finished Goods Dependent Demand: Raw Materials, Component parts, Sub-assemblies, etc.
A
C(2)
B(4)
D(2)
E(1)
D(3)
F(2)
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Independent Demand: What a firm can do to manage it? • Can take an active role to influence demand
• Can take a passive role and simply respond to demand
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Types of Forecasts • Qualitative (Judgmental)
• Quantitative – Time
Series Analysis
– Causal
Relationships
– Simulation
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Components of Demand
• Average demand for a period of time • Trend • Seasonal element • Cyclical elements • Random variation • Autocorrelation
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Finding Components of Demand Seasonal Seasonalvariation variation
x x x x x s e l a S
x
x x x
xx x x xx x x x x x x x xxx x x x x x x x xx
1
2
x x x x
x
3
Year
x
x
x
x x
4
Linear Linear Trend Trend
x x x
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Qualitative Methods
Executive Judgment
Historical analogy
Grass Roots
Qualitative
Market Research
Methods
Delphi Method
Panel Consensus
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Delphi Method l. Choose the experts to participate representing a variety of knowledgeable people in different areas 2. Through a questionnaire (or E-mail), obtain obt ain forecasts (and any premises or qualifications for the forecasts) from all participants 3. Summarize the results and redistribute them to the participants along with appropriate new questions 4. Summarize again, refining forecasts and conditions, and again develop new questions 5. Repeat Step 4 as necessary and distribute the final results to all participants
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Time Series Analysis • Time series forecasting models try to predict the future based on past data • You can pick models based on: 1. Time horizon to forecast 2. Data availability 3. Accuracy required 4. Size of forecasting budget 5. Availability of qualified personnel
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Simple Moving Average Formula • The simple moving average model assumes an average is a good estimator of future behavior • The formula for the simple moving average is:
Ft =
A t -1 + A t - 2 + A t - 3 +...+A t - n n
Ft = Forecast for the coming period N = Number of periods to be averaged A t-1 = Actual occurrence in the past period for up to “n” periods
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Simple Moving Average Problem (1) Ft = Week Week 1 2 3 4 5 6 7 8 9 10 11 12
Demand 650 678 720 785 859 920 850 758 892 920 789 844
A t -1 + A t - 2 + A t - 3 +...+A t - n n
Question: Question:What Whatare arethe the33week weekand and6-week 6-weekmoving moving average averageforecasts forecastsfor for demand? demand? Assume Assumeyou youonly onlyhave have33 weeks weeksand and66weeks weeksof of actual actualdemand demanddata datafor forthe the respective respectiveforecasts forecasts
Calculating the moving averages gives us: us:
Wee Week 1 2 3 4 5 6 7 8 9 10 11 12
Dem and 3-Wee Week 6-Wee Week 650 F4=(650+678+720)/3 678 =682.67 720 F7=(650+678+720 785 682. 67 +785+859+920)/6 859 727. 67 =768.67 920 788. 00 850 854. 67 768. 67 758 876. 33 802. 00 892 842. 67 815. 33 920 833. 33 844. 00 789 856. 67 866. 50 844 867. 00 854. 83
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Plotting Plottingthe themoving moving averages averagesand andcomparing comparing them themshows showshow howthe thelines linessmooth smoothout out to toreveal reveal the theoverall overallupward upwardtrend trendin inthis thisexample example 1000 900 Deman
d 8 0 0 n a m 7 0 0 e D
3-Wee 6-Wee
600 500 1
2
3
4
5
6
7
8
9 10 11 1 2
Wee
Note Notehow howthe the 3-Week 3-Weekisis smoother smootherthan than the theDemand, Demand, and and6-Week 6-Weekisis even evensmoother smoother
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Simple Moving Average Problem (2) Data
Wee Week
Demand
1
820
2
775
3
680
4
655
5
620
6
600
7
575
Question: Question:What Whatisisthe the33 week weekmoving movingaverage average forecast forecastfor forthis this data? data? Assume Assumeyou youonly onlyhave have33 weeks weeksand and55weeks weeksof of actual actualdemand demanddata datafor for the therespective respective forecasts forecasts
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Simple Moving Average Problem (2) Solution Wee Week 1 2 3 4 5 6 7
Demand 820 775 680 655 620 600 575
3-Wee Week
5-Wee Week
F4=(820+775+680)/3 =758.33
758.33 703.33 651.67 625.00
F6=(820+775+680 +655+620)/5 =710.00
710.00 666.00
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Weighted Moving Average Formula While Whilethe the moving movingaverage average formula formulaimplies impliesan anequal equal weight weightbeing beingplaced placedon oneach eachvalue value that thatis isbeing beingaveraged, averaged, the theweighted weightedmoving movingaverage average permits permitsan anunequal unequal weighting weighting on on prior prior time time periods periods The The formula formulafor for the themoving movingaverage averageis: is: Ft = w 1A t -1 + w 2 A t -2 + w 3A t -3 +. ..+w n A t - n n
w wt t==weight weightgiven givento totime timeperiod period“t” “t” occurrence occurrence(weights (weightsmust mustadd addto toone) one)
∑ wi = 1 i=1
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Weighted Moving Average Problem (1) Data Question: Question:Given Giventhe theweekly weeklydemand demandand andweights, weights,what whatisis thth the forecast for the 4 the forecast for the 4 period periodor orWeek Week4? 4? Week Week
Demand
1
650
2
678
3
720
4
Weights: t-1 .5 t-2 .3 t-3 .2
Note Notethat thatthe theweights weightsplace placemore moreemphasis emphasison onthe the most mostrecent recentdata, data,that thatisistime timeperiod period“t-1” “t-1”
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Weighted Moving Average Problem (1) Solution Wee Week
Demand
1
650
2
678
3
720
4
F4 = 0.5(720)+0.3(678)+0.2(650)=693.4
Foreca recas st
693.4
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Weighted Moving Average Problem (2) Data Question: Question:Given Giventhe theweekly weeklydemand demandinformation informationand and weights, weights,what whatisisthe theweighted weightedmoving movingaverage averageforecast forecast thth of the 5 of the 5 period periodor orweek? week?
Wee Week
Demand
1
820
2
775
3
680
4
655
Weights: t-1 .7 t-2 .2 t-3 .1
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Weighted Moving Average Problem (2) Solution W eek 1 2 3 4 5
Deman mand For Forecast cast 820 775 680 655 672
F5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672
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Exponential Smoothing Model
FFtt == FFt-t1-1 ++ α (At-t1-1 -- FFt-t1-1)) α (A
Where : Ft
Forcast va lue lue for the coming t time period
=
Ft - 1
=
At - 1 α
=
=
Forecast v alue in 1 past time period Actual occurance in the past t tim e period
Alpha smoothing constant
• Premise: The most recent observations might have the highest predictive value • Therefore, we should give more weight to the more recent time periods when forecasting
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Exponential Smoothing Problem (1) Data Wee Week
Demand
1
820
2
775
3
680
4
655
5
750
6
802
7
798
8
689
9
775
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Question: Question:Given Given the theweekly weekly demand demand data, data, what what are are the the exponential exponentialsmoothing smoothing forecasts forecastsfor forperiods periods2-10 2-10 using using =0.10 =0.10and and =0.60? =0.60? Assume AssumeFF1=D =D1 1
1
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Answer: Answer:The Therespective respectivealphas alphascolumns columnsdenote denotethe theforecast forecastvalues. values. Note Note that thatyou youcan canonly onlyforecast forecastone onetime timeperiod periodinto intothe thefuture. future.
Wee Week 1 2 3 4 5 6 7 8 9 10
Demand 820 775 680 655 750 802 798 689 775
0.1
820.00 820.00 815.50 801.95 787.26 783.53 785.38 786.64 776.88 776.69
0.6
820.00 820.00 820.00 817.30 808.09 795.59 788.35 786.57 786.61 780.77
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Exponential Smoothing Problem (1) Plotting Note sm resu lts in Notehow howthat thatthe thesmaller smaller smaller alleralpha alpharesults results results inaa smoother smootherline line in inthis thisexample example 900 800
De ma
d n 7 0 0 a m e D6 0 0
0 .1 0 .6
500 1
2
3
4
5
6
Wee
7
8
9
10
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Exponential Smoothing Problem (2) Data
Wee Week 1 2 3 4 5
Question: What are the Question: What are the Demand exponential exponential smoothing smoothing 820 forecasts forecasts for for periods periods 2-5 2-5 775 using using aa =0.5? =0.5? 680 655
Assume Assume FF11=D =D11
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Exponential Smoothing Problem (2) Solution F1=820+(0.5)(820-820)=820
Wee Week 1 2 3 4 5
Demand 820 775 680 655
F3=820+(0.5)(775-820)=797.75
0.5
820.00 820.00 797.50 738.75 696.88
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The MAD Statistic to Determine Forecasting Error n
∑ A t - Ft MAD =
t =1
1 MAD ≈ 0.8 standar dard deviatio tion 1 standard deviation ≈ 1.25 MAD
n
• The ideal MAD is zero which would mean there is no forecasting error • The larger the MAD, the less the accurate the resulting model
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MAD Problem Data Question: Question: What What is is the the MAD MAD value value given given the the forecast forecast values values in in the the table table below? below? Month 1 2 3 4 5
Sales Forecast 220 n/a 250 255 210 205 300 320 325 315
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MAD Problem Solution Month 1 2 3 4 5
Sales 220 250 210 300 325
Forecast Abs Error n/a 255 5 205 5 320 20 315 10
40 n
∑ A t - Ft MAD =
t=1
n
=
40 4
= 10
Note Notethat thatby byitself, itself,the theMAD MAD only onlylets letsus usknow knowthe themean mean error errorin inaaset setof offorecasts forecasts
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Tracking Signal Formula • The Tracking Signal or TS is a measure that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand. • Depending on the number of MAD’s selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts. • The TS formula is:
RSFE Runn Runnin ing g su m of fore forecc ast er erro rors rs TS = = MAD Mean absol bsol ute ute dev deviat iat ion ion
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Simple Linear Regression Model The Thesimple simplelinear linearregression regression model modelseeks seeksto tofit fitaaline line through throughvarious variousdata dataover over time time
Yt = a + bx
Y
a 0 1 2 3 4 5
x
(Time)
Is Isthe thelinear linearregression regressionmodel model
Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.
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Simple Linear Regression Formulas for Calculating “a” and “b”
a=y-bx
b =
(y)(x) (x) ∑ xy - n(y) 2
n( x) ∑ x - n(
2
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Simple Linear Regression Problem Data Question: Question:Given Giventhe thedata databelow, below,what whatisisthe thesimple simplelinear linear regression regressionmodel modelthat thatcan canbe beused usedto to predict predictsales salesin infuture future weeks? weeks?
W eek
Sales
1
150
2
157
3
162
4
166
5
177
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Answer: Answer:First, First,using usingthe thelinear linearregression regressionformulas, formulas,we we can cancompute compute“a” “a”and and“b” “b”
Wee Week Wee Week*Wee *Week 1 1 2 4 3 9 4 16 5 25 3
Average
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Sales Wee Week*S *Sa ales 150 150 157 314 162 486 166 664 177 885 162.4
Sum Average
2499
Sum
xy - n( y)(x) 2499 2499 - 5(16 5(162. 2.4) 4)(3) (3) 63 ∑ = b = = = 6.3 2 2 55 − 5(9 ) 10 n( x ) ∑ x - n( a = y - bx = 162.4 - (6.3)(3) = 143.5
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The resulting regression model is:
Yt = 143.5 + 6.3x
Now if we plot the regression generated forecasts against the actual sales we obtain the following chart:
s e l a S
180 175 170 165 160
Sales
155 150 145 140 135
Forecast
1
2
3
4
5
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Web-Based Forecasting: CPFR Defined • Collaborative Planning, Forecasting, and Replenishment (CPFR ) a Web-based tool used to coordinate demand forecasting, production and purchase planning, and inventory replenishment between supply chain trading t rading partners. • Used to integrate the multi-tier or n-Tier supply chain, including manufacturers, distributors and retailers. • CPFR’s objective is to exchange selected internal information to provide for a reliable, longer term future views of demand in the supply chain. • CPFR uses a cyclic and iterative approach to derive consensus forecasts.
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Web-Based Forecasting: Steps in CPFR • 1. Creation of a front-end partnership agreement • 2. Joint business planning • 3. Development of demand forecasts • 4. Sharing forecasts • 5. Inventory replenishment
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End of Chapter 12
