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# Ch2hwsolutions - UTA Chapter 2 Forecasting 1 Printer...

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Unformatted text preview: UTA Chapter 2 Forecasting 1. Printer rentals a. The forecast for week 11 is 29 rentals. Forecast for Following Week Forecast Calculated 4 Week (EH) 5 23+24——32+26+31 227-2 or27 5 6 24+32——26+31+28 =28.2 or28 5 7 32+26——31+28+32 =29.8 (”30 5 8 26+31+28+32+35 230.4(“30 5 9 31+28+32+35+26 230.4(“30 5 10 W =29.0 or 29 5 b. The Mean Absolute Deviation is 4 rentals. Week Actual Forecast Absolute Error 6 28 27 1 7 32 28 4 8 35 30 5 9 26 30 4 10 24 30 Q TOTAL 20 MAD 205 = 4 2. Dalworth Company a. Three-month simple moving average Mouth Actual Sales Three—Mouth Simple Absolute Absolute Squared (Thousands) Moving Average Error % Error Error Forecast Jan. 20 Feb. 24 Mar. 27 Apr. 3] May 37 {24 27 31);“3 — 27.33 9.67 26.14 93.51 June 47 {27 31 37):“3 —31.67 15.33 32.62 235.01 July 53 {31 37 47):“3 — 38.33 14.67 27.68 215.21 Aug. 62 {37+47+53)x’3 = 45.67 16.33 26.34 266.67 Sept. 54 (47+53+62):’3 = 54.00 0.00 0.00 0.00 Oct. 36 {53 62 54):“3 = 56.33 20.33 56.47 413.31 Nov. 32 {62 54 36);“3 — 50.67 18.67 58.34 348.57 Dec. 29 (54 36 32);“3 — 40.67 E M 136.19 Total 106.67 267.83 1.708.47 Average 13.33 33.48 213.56 Such results also can be obtained from the Time Series Forecasting Solver of OM Explorer: Actual Data 3-Period Moving Average Forecast Error CFE 1117’2009 2117'2009 3f1f2009 4f1f2009 5.1179009 6117'2009 7"}17'2009 87'1f2009 97172009 101179009 114’17'2009 12l1f2009 Method 1 - Moving Average: Forecast for H1 1'10 32.33 CFE 5.33 MAD 13.33 MSE 213.513 MAPE 33.43% 3 -Period Moving Average b. Four-month simple moving average Month Actual Sales Four—Month Simple Absolute Absolute Squared (Thousands) Moving Average Error % Error Error Forecast Jan. 20 Feb. 24 Mar. 27 Apr. 31 May 37 (20 24 27 31).’4 = 25.5 11.50 31.08 132.25 June 47 {24 27 31 37):“4 —29.75 17.25 36.70 297.56 July 53 (27 31 37 47):“4 — 35.5 17.50 33.02 306.25 Aug. 62 (31+37+47+53):‘4 = 42.00 20.00 32.26 400.00 Sept. 54 {37 47 53 62):“4 — 49.75 4.25 7.87 18.06 Oct. 36 {47 53 62 54):“4 — 54.00 18.00 50.00 324.00 Nov. 32 (53 62 54 36):”4 — 51.25 19.25 60.16 370.56 Dec. 29 {62+54+36+32):‘4 = 46.00 w w 289.00 Total 124.75 309.71 2,137.68 Average 15.59 38.71 267.21 Similarly, using Time Series Forecasting Solver of OM Explorer, we get: 1:0 {2039 2:0 £039 3:0 :‘2l:09 4:032:09 57151039 5:001:09 70012039 Bf1:’20:|9 9:0 :‘21:09 10:0 3:09 11:0 :‘2009 12:0 {21:09 4—Period Moving Average Forecast Error CFE Method 1 - Moving Average: Forecast for 1:0:00 CFE MAD MSE MAPE 4 -F'erioc| Moving Average 297.21 39.71% 3?.7‘5 19.25 15.59 3. c.—e. Comparison of performance Question Measure 3—Montl1 4—Month Recommendation SMA SMA c. MAD 13.33 15.59 3-month SMA d. MAPE 33.48 38.71 3-month SMA e. MSE 213.56 267.21 3-month SMA Karl’s Copiers Week Forecast Calculation of Forecast for Next ‘Veek’s Demand Calculated iFiﬁZ'Q"E)—l_(1_a’r)I-:i EH 1 020(24) -- 080(24) = 24 2 020(32) -- 080(24) = 25.6 or 26 3 020(36) + 0.80(25.6) = 27.68 or 28 4 020(23) + 0.80(27.68) = 26.744 or 27 5 020(25) + 0.80(26.744) = 26.3952 or 26 Forecasts in each row are for the M week’s demand. For example, the calculations done in Week 1 (after the actual demand for Week 1 is known) of 24 units is actually the forecast for Week 2. It happens to be the same as the forecast made for Week l’s demand, because the default initial forecast is set equal to the ﬁrst week’s demand. The forecast for the week 6 is 26 sewice calls. Similarly, using Time Series Forecasting Solver of OM Explorer, we get: Actual Data Exponential Smoothing Forecast Error CFE 24.00 24.00 0.00 0.00 25.00 10.40 10.40 2?.00 -4.00 13.72 20.?4 -1.74 11.00 The forecasts are for the weeks listed in the row (not for the next week’s demand). Method 3 - Exponential Smoothing: o: 0.20 Initial Forecast 24.00 Forecast for Week 0 20.40 CFE 11.00 MAD 0.21 MSE 49.20 MAPE 20.30% 4. Dalwolth Company (continued) a. Three-month weighted moving average (weights of 376. 276, and 17’ 6) Month Actual Sales Three-Month \Veighted Absolute Absolute % Squared 0003 Movin Avera e Forecast Error Error Error Apr. 31 [(3 x 27) (2 x 24) (1 x 20)]76 = 24.33 6.17 19.90 33.07 May 37 [(3 x 31) (2 x 27) (1 x 24)]76 = 23.50 3.50 22.97 72.25 June 47 [(3 x 37) (2x 31) (1 x27)]76 = 33.33 13.67 29.09 136.37 July 53 [(3 x 47)+2 >< 37)+(1 >< 31)]76 = 41.00 12.00 22.64 144.00 Aug. 62 [(3 x 53) (2 x 47) (1 x 37)]76 = 43.33 13.67 22.05 136.37 Sept. 54 [(3 x 62)+(2 >< 53)+(1 >< 47)]76 = 56.50 2.50 4.63 6.25 Oct. 36 [(3 x 54) (2x 62) (1 x 53)]76 = 56.50 20.50 56.94 420.25 Nov. 32 [(3 x 36)+(2 >< 54)+(1>< 62)]76 = 46.33 14.33 44.73 205.35 Dec. 29 [(3 x 32) (2 x 36) (1 x 54)]76 = 37.00 m w M Total 99.34 250.59 1,323.91 Average 11.04 27.34 147.09 The results from Time Series F orecasring Solver of 0M Explorer give the same results: Actual Data 3-Perloo Weighted Hmong average Forecast Error CFE Method 2 - Weighted Moving Average: 3 -F'eri0d Weighted Moving Average Forecast for 1J11'1IJ 31.1?r CFE 3.6? MAD 11.04 MSE 14109 MAPE 2?.34 % b. Exponential smoothing (a. = 0.6) Month 1), F, 3+1 = F, + (1(1), — Ff) Absolute Absolute Squared millions Forecast for Next Month Error 0/0 Error Error Jan. 20 22.00 20.80 Feb. 24 20.80 22.72 Mar. 27 22.72 25.29 Apr. 31 25.29 28.72 5.71 18.41 32.60 May 37 28.72 33.69 8.28 22.38 68.56 June 47 33.69 41.67 13.31 28.32 177.16 July 53 41.67 48.47 11.33 21.38 128.37 Aug. 62 48.47 56.59 13.53 21.82 183.06 Sept. 54 56.59 55.04 2.59 4.80 6.71 Oct. 36 55.04 43.62 19.04 52.88 362.52 Nov. 32 43.62 36.64 11.61 36.28 134.79 Dec. 29 36.64 32.06 E 26.38 M Total 93.05 232.65 1,152.29 Average 10.34 25.85 128.03 c.—e. Comparison of performance Question Measure S—Month Exponential Recommendation WMA Smoothing c. MAD 11.04 10.34 Exponential smoothing d. MAPE 27.84 25.85 Exponential smoothing e. MSE 147.09 128.03 Exponential smoothing Convenience Store At = 0.27.)r + 0.8(21,_1 + TH) Tf = 0.1(Averoge ihis period — Average loaf period) + 0.9(Trertd East period) F 2 Ar + Tr r+l May AM” = 0.2(760)+ 0.8(700+ 50) = 752 rm,y = 0.1(752 — 750) +0.9(50) = 50.2 Forecast for .Tune 2 752 + 50.2 = 802.2 or 802 June Am = 0.2(800)+0.8(752+50.2) 2801.76 or 802 rm 2 0.1(801.76—752)+0.9(50.2) = 50.16 or 50 Forecast for July 2 801.76+ 50.16 = 851.92 or 852 July AJuly = 0.2(820)+0.8(801.76+50.16) 2845.54 or 846 TM], 2 0.1(845.54—801.76)+0.9(50.16)249.52 Forecast for August 2 845.54 +4952 2 895.06 or 895 ...
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