June july august actual demand 140 180 170 a using a

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June July August Actual demand 140 180 170 a) Using a simple three-month moving average, what is the forecast for September? X=3 F 9 = 140+180+170)/3=163.30 = 140/3+ 180/3+ 170/3
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b) Using a weighted moving average, what is the forecast for September with weights of 0.20, 0.30, and 0.50 for June, July and August, respectively? W 1 = 0.5; W 2 = 0.3; W 3 = 0.2 F 9 = 170(0.5) + 180(0.3) + 140(0.2) = 167
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c) Using simple exponential smoothing and assuming that the forecast for June had been 130, calculate the forecast for September with a smoothing constant alpha of 0.30. F 6 = 130, 2= 0.3 F 7 = F 6 + 2(A t –F 6 )= 130+0.3(140-130) =133 F 8 =133+0.3(180-133)=147.10 F 9 =149.1+0.3(170-147.10)=154
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Weighting of Past Data in Exponential Smoothing
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Exponential Smoothing Weights Demand Weight Numerical Weights for Α=0.1 Α=0.2 Α=0.8 D t α 0.1000 0.2000 0.8000 D t-1 α(1- α) 1 0.0900 0.1600 0.1600 D t-2 α(1- α) 2 0.0810 0.1280 0.0320 D t-3 α(1- α) 3 0.0729 0.1024 0.0064 D t-4 α(1- α) 4 0.0656 0.0819 0.0013 D t-5 α(1- α) 5 0.0590 0.0655 0.0003 D t-6 α(1- α) 6 0.0531 0.0524 0.0001 D t-7 α(1- α) 7 0.0478 0.0419 0.0000 D t-8 α(1- α) 8 0.0430 0.0336 0.0000 D t-9 α(1- α) 9 0.0387 0.0268 0.0000
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Time-Series Methods Time-Series Methods Simple Moving Averages Simple Moving Averages Week Week 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — | | | | | | 0 5 10 10 15 15 20 20 25 25 30 30 Patient arrivals Patient arrivals Actual patient Actual patient arrivals 3-week MA 3-week MA forecast forecast 6-week MA 6-week MA forecast forecast
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Time-Series Methods Time-Series Methods Exponential Smoothing Exponential Smoothing 450 450 — 430 430 — 410 410 — 390 390 — 370 370 — Patient arrivals Patient arrivals Week Week | | | | | | 0 5 10 10 15 15 20 20 25 25 30 30 A Larger forecast forecast A smaller A smaller forecast forecast Exponential Exponential smoothing smoothing = 0.10 = 0.10
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Forecasting Error Measurement 1. Forecasting error in period (t): E t = (A t - F t ) 2.Bias ( Mean Forecasting Error) Bias =∑E t )/n =∑(A t - F t )/n 3. MAD( Mean Absolute Deviation): MAD =∑(A t - F t )/n 4. Track signal: TS = Bias/MAD ( -1< TS < +1)
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Choosing a Method Choosing a Method Tracking Signals Tracking Signals Tracking signal = Tracking signal = CFE CFE MAD MAD +2.0 +2.0 — +1.5 +1.5 — +1.0 +1.0 — +0.5 +0.5 — 0 0 — 0.5 0.5 — 1.0 1.0 — 1.5 1.5 — | | | | | 0 5 10 10 15 15 20 20 25 25 Observation number Tracking signal Tracking signal Control limit Control limit Control limit Control limit Out of control
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Choosing a Method Choosing a Method Forecast Error Forecast Error Measures of Forecast Error Measures of Forecast Error E E t = = D D t F F t | | E E t | | n n E E t 2 n n CFE = CFE = E E t = = MSE = MSE = MAD = MAD = MAPE = MAPE = [ [ | | E E t t | (100) | (100) ] ] / / D D t n n ( ( E E t – E – E ) ) 2 n n – 1 – 1
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Exercise #2 Month 1 2 3 4 5 6 7 8 9 Actual Demand 26 32 39 40 38 47 50 59 56 a) What is the forecast for period 10 using the following models? i) Four period moving average ii) Four period weighted moving average with weights of 0.1, 0.15, 0.25 and 0.5 for month 6, 7, 8 and 9 respectively iii) Simple exponential smoothing with alpha =0.2, assuming that the forecast for month 9 is 60.
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