1. Chapter 7 of Chopra Forecasting of Demand 1 Read: Chap. 7.1-7.4; p207; p212-214 (upto/exclude “Trend-corrected …”); 7.6; 7.7-upto p220 (exclude “Trend-corrected …”); 7.10.

2. components take different lead times before reaching the destinations Global Sourcing wooden casing: sea, Sweden Cheap peripheral : van, HK LCD: truck, China screws: train, China (Sichuan) microphone: air, Japan microprocessors: air, Malaysia destination: USA Resistors, capacitors, controllers, etc. 2

3. DVD Players A CM/OED 3

4. About 10 pages Murphy’s Law: If anything can go wrong, it will. 4

5. When and In What Quantity to “Buy/Make” of Each Parts/Finished Goods? Push/Pull Processes (Chapter 1) With pull processes, execution is initiated in response to a customer order -- reactive With push processes, execution is initiated in anticipation of customer orders -- speculative Clock’s assembly factory Suppliers: Parts, … Procurement process Manufacturing/ Fulfillment Processes Orders Make-to-order, assemble-to-order Make-to-stock 5

6. Learning Objectives Describe types of forecasts Describe time series Use time series forecasting methods Explain how to monitor & control forecasts 6

7. What Is Forecasting? Process of predicting a future event “Forecasting is difficult especially when it has to deal with future” -- Mark Twin Underlying basis of all business decisions –Production –Inventory –Facilities, …... Sales will be $200 Million! 7

8. Why forecast demand? We need to know how much to make ahead of time, i.e. our production schedule –How much raw material –How many workers –How much to ship to the warehouse in XXX We need to know how much production capacity to build 8

9. Why Forecasting ? You’re managing merchandises for Park’n Shop. Fruits take 3 wks to arrive from Australia. You need to commit to a number of containers NOW for the month of March in order for a better price Coca-Cola Bottling: next quarter’s demand + promotions -> production plan/ orders of concentrates 9

10. Forecasting is Always Wrong “I think there is a world mkt for maybe 5 computers” - Thomas Watson, Chairman of IBM, 1955 “There is no reason anyone would want a computer in their home.” - Ken Olson, CEO and Founder of Digital Equipment Corp., 1977 “640K should be enough for anybody.” -- Bill Gates, 1981 “Economists are good at explaining why their forecasts always went wrong” -- Economist, xx, 1998 “Fore. represents a constant pain for human being” -- some one 10

11. Coping with Forecast Errors Better forecasting methods (e.g., new SCM concepts) Buffer mechanism (e.g., safety stock) Shorter lead time (i.e., reducing f horizon) Flexible ops (mass customisation approach) 11

12. Forecasting v.s. Planning Forecast: –About what will happen in future Plan: – About what should happen in future – Forecasts as input All plans are based upon some fore. explicitly or implicitly 12

13. Forecasting v.s. Planning When sales dept. shows sales forecasts, be cautious. They may be goals Both forecasting and planning are art and science –Quant f methods - educated guessing must be tempered by judgement bec’s quant f assumes future is a continuation of the past 13

14. Types of Forecasts by Time Horizon Short-range forecast –Up to 1 year; usually < 3 months –Procurement, worker assignments Medium-range forecast –3 months to 3 years –Sales & production planning, budgeting Long-range forecast –3 + years –Capacity planning, facility location 14

15. 15

16. Types of Forecasts by Item Forecast Key forecasts in business: Future demand for products, Sales Demand (sales = demand - lost sales) Future price of various commodities Lead times Processing times (learning curves) … 16

17. Forecasting Steps Define objectives Select items to be forecasted Determine time horizon Select forecasting model(s) Gather data Validate forecasting model Make forecast Implement results Monitor forecast performance 17

18. Used when situation is ‘stable’ & historical data exist –Existing products –Current technology Involves mathematical techniques e.g., forecasting sales of milk, tissue papers, … Quantitative Methods Forecasting Approaches Used when situation is vague & little data exist –New products –New technology Involves intuition, experience e.g., forecasting sales on Internet Qualitative Methods 3G 18

19. Causal Models Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Regression Exponential Smoothing Trend & Season Moving Average A future is continuation of the past (short run) Simulation Qualitative 時間序列 因果關係 19

20. ERP: Enterprise Resource Planning Black Box 20

21. What’s a Time Series? Set of evenly spaced numerical data –Obtained by observing response variable at regular time periods Forecast based only on past values –Assumes that factors influencing past, present, & future will continue 21

22. 1 st & 2 nd Law of Forecasting 1.In forecasting, we assume the future will behave like the past –If behavior changes, our forecasts can be terrible 2.Even given 1, t here is a limit to how accurate forecasts can be (or nothing can be predicted with complete accuracy) –The achievable accuracy depends on the magnitude of the noise component 22

23. Monthly Demand for Sport-3506 23

24. TS of a Raw Material’s Price 24

25. Monthly Australian Red Wine Sales 25

26. Monthly new polio cases in the U.S.A., 1970-1983 26

27. Monthly Traffic Injuries (G.B) beginning in January 1975 27

28. U.S. Pop., 10-year Intervals, 1790-- 1980 28

29. Annual Canadian Lynx Trappings 29

30. Daily Dow Jones & HSI 30

31. Time Series Components Original T.S. Time Sales 31

32. Time Series Components Trend Seasonal Cyclical Random 32

33. Trend Component Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Mo., Qtr., Yr. Response 33

34. HK Regional Headquarters 34

35. Cyclical Component Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle  35

36. 19821985 1990 1995 2000 03 36

37. Port Unloading (Annual, 1993-2005) 37

38. Seasonal Component Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within 1 year Mo., Qtr. Response Spring Festives 38

39. Quarterly 39

40. 40

41. Random Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events –Union strike –Tornado Short duration & nonrepeating 41

42. General Time Series Models Any observed value in a time series is the product (or sum) of time series components Multiplicative model Y i = T i · S i · C i · R i (if quarterly or mo. data) Additive model Y i = T i + S i + C i + R i (if quarterly or mo. data) Hybrids 42

43. Time Series Components Original T.S. Time Sales 43

44. Time Series Components Original T.S. Cycle Seasonal Trend Random 44

45. Sub-summary Common Time Series Patterns Time Demand Time Demand Purely Random Error - No Recognizable Pattern Increasing Linear Trend Seasonal Pattern Seasonal Pattern plus Linear Growth 45

46. Underlying model and definitions -- Static Method Systematic component = (level + trend) x seasonal factor L = estimate of level for period 0 (de-seasonalised demand) T= estimate of trend (increase/decrease in demand per period) S t = Estimate of seasonal factor for period t D t = Actual demand observed for period t F t = Forecast of demand for period t F t+k = [ L+ (t+k)T ]S t+k Note: pp 207-211 on Static Forecast. – skip 46 It assumes the estimates of level, trend, and seasonality do not vary as new demand is observed, at least for a fairly large number of periods.

47. HK Regional Headquarters 47 You may use 1991-2002 to estimate the “trend line”; after 2003/05, you still use this line to project the future – not update it with 2003/05 new observation! Static

48. Monthly Demand for Sport-3506 48

49. Adaptive forecasting The estimates of level, trend and seasonality are updated after each demand observations 49

50. Moving Average Assumes no trend and no seasonality =>=> Level estimate is the average demand over most recent N periods Update: add latest demand observation and and drop oldest Forecast for all future periods is the same Each period’s demand equally weighted in the forecast How to choose the value of N? –N large => –N small => 50

51. You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 1998 using a 3- period moving average. 19944 1995 6 19965 19973 19987 Moving Average Example 51

52. Time Demand D i Moving Total (N = 3) Moving Avg. ( N = 3) 19944NANA 19956NANA 19965NANA 19973 4 + 6 + 5 = 15 15/3 = 5.0 19987 6 + 5 + 3 = 14 14/3 = 4.7 1999NA Moving Average Solution 1999NA 5 + 3 + 7 = 15 15/3 = 5.0 Forecast for 1999 All of what we need to know is this number: 5, which is the forecast for all future periods! Why do we need to calculate the forecasts for the past periods? 52 Forecasts

53. Moving Average Graph Year Sales 0 2 4 6 8 949596 97 9899 Actual Forecast 53

54. Milk– weekly data / Pet products – monthly data A pet supply product ( 6 varieties) 54

55. Moving Average Method Used if little or no trend Used often for smoothing –Provides overall impression of data over time Why “moving” not just overall mean? 55

56. Cereal Sales in HK Year Quantity (kg) 56

57. Month Monthly Sales Within a year 57

58. Disadvantages of Moving Averages Increasing N makes forecast less sensitive to changes Do not forecast trend well Require much historical data – N, while exponential only last forecast! 58

59. Simple Exponential Smoothing (No trend, no seasonality) Rationale: recent past more indicative of future demand Update: level estimate is weighted average of latest demand observation and previous estimate  is called the smoothing constant (0 <  < 1) Forecast for all future periods is the same Assume systematic component of demand is the same for all periods (L) L t is the best guess at period t of what the systematic demand level is After observing D t+1 for period t+1, we revise the estimate of the level (as defined in the textbook) Or After observing D t for period t, L t =  D t + (1-  ) L t-1  For all n  1, F t+n = L t 59

60. Simple Exponential Smoothing – Example 7-2 Data: 120, 127, 114, 122. L 0 = 120.75  = 0.1 F 1 = L 0 =120.75 D 1 = 120 E 1 = F 1 – D 1 = 120.75 – 120 = 0.75 L 1 =  D 1 + (1 -  L 0 = (0.1)(120) + (0.9)(120.75) =  F 2 = L 1 = 120.68, F 3 = L 2 = 121.31, … F 5 = L 4 = 120.72 => the forecast for period 5 Alternatively, if you are only interested in F 5, then L 3 = (120+127+114)/3 =120.33 L 4 = 0.1 D4+0.9 L3 = 12.2+108.2 =120.4 => F 5 = 120.4 Note: L 0 can be estimated in a subjective way! Here L 0 =(120+127+114+122)/4 Especially when there is insufficient data. 60

61. Simple Exponential Smoothing – Example: Tables 7-1 & 7-5 L 0 = 22083  = 0.1 F 1 = L 0 D 1 =8000 E 1 = F 1 – D 1 = 22083 – 8000 = 14083 L 1 =  D 1 + (1 -  L 0 = (0.1)(8000) + (0.9)(22083) =  F 2 = L 1 = 20675, F 10 = L 1 = 20675 Note: this example appears in pp 208-219 61

62. Simple Exponential Smoothing Update: new level estimate is previous estimate adjusted by weighted forecast error How to choose the value of the smoothing constant  ? –Large  responsive to change, forecast subject to random fluctuations –Small  may lag behind demand if trend develops Incorporates more information but keeps less data than moving averages –Average age of data in exponential smoothing is 1/  –Average age of data in moving average is (N+1)/2 If  is 0 then … If  is 1 then... 62

63. Understanding the exponential smoothing formula Demand of k-th previous period carry a weight of hence the name exponential smoothing Demand of more recent periods carry more weight 63

64. Forecast Effect of Smoothing Constant (  ) The alpha parameter for exponential smoothing... Period.10.30.50.70 1.10.30.50.70 2.09.21.25.21 3.08.15.13.06 4.07.10.06.02 5.07.07.03.01 6.06.05.02.00 7.05.04.01 8.05.02.00 The alpha parameter for exponential smoothing... Period.10.30.50.70 1.10.30.50.70 2.09.21.25.21 3.08.15.13.06 4.07.10.06.02 5.07.07.03.01 6.06.05.02.00 7.05.04.01 8.05.02.00 F t =  ·D t - 1 +  ·(1-  )·D t - +  ·(1-  ) 2 ·D t - 3 +  ·(1-  ) 3 ·D t - 4 +... 64

65. You’re organising a international meeting. You want to forecast attendance for 2000 using exponential smoothing (  =.10). The 1994 forecast was 175. 1994180 1995 168 1996159 1997175 1998190 Exponential Smoothing Example 65

66. Exponential Smoothing Solution L t = L t-1 +  ·  (D t - L t-1 ) TimeActual Forecast,F t (  =.10) 1994180 175.00 (Given) 1995168 175.00 +.10(180 - 175.00) = 175.50 1996159 175.50 +.10(168 - 175.50) = 174.75 1997175 174.75 +.10(159 - 174.75) = 173.18 1998190 173.18 +.10(175 - 173.18) = 173.36 1999NA 173.36 +.10(190 - 173.36) = 175.02 66

67. Trend corrected exponential smoothing (Holt’s model)  is the smoothing constant for trend updating If  is large, there is a tendency for the trend term to “flip-flop” in sign Typical  is   67 Skipped

68. Holt’s model - Example L 0 = 12015T 0 =1549  = 0.1  0.2 F 1 = L 0 + T 0 = 12015 + 1549 = 13564, D 1 =8000 E 1 = F 1 – D 1 = 13564 – 8000 = 5564 L 1 =  D 1 + (1 -  L 0 + T 0 ) = (0.1)(8000) + (0.9)(13564) =  T 1 =  L 1   L 0 ) + (1 -  T 0 = (0.2)(13008  12015) + (0.8)(1549) =  F 2 = L 1 +T 1 = 13008+1438 = 14446, F 10 = L 1 + 9 T 1 = 13008 + 9(1438) = 25950 68 Skipped

69. Trend and seasonality corrected exponential smoothing (Winter’s model) 69 Skipped

70. Trend- & Seasonality-corrected Exp Smooth. (level +trend ) x seasonal factor (Winter’s Method/Model) Need 3 revision eqns (1)L t+1 =  (D t+1 / S t+1 )+ (1-  ) (L t + T t ) (2)T t+1 =  ( L t+1 – L t ) + (1-  ) T t (3)S t+p+1 =  (D t+1 / L t+1 ) + (1-  ) S t+1 Forecast of t+n: F t+n = (L t + nT t ) S t+n, n >1 , ,  = smooth. para. Smoothed value for t+1 D t+1 = Actual S t+1 = Seasonal factor, p? T t+1 = Trend forecast T t = Forecast for t+n 70 Skipped

71. Winter’s model - Example L 0 = 18439T 0 =524 S 1 = 0.47, S 2 =0.68, S 3 =1.17, S 4 =1.67,  = 0.1,  0.2,  = 0.1, F 1 = (L 0 + T 0 ) S 1 = (18439 + 524)(0.47) = 8913 D 1 =8000,E 1 = F 1 – D 1 = 8913 – 8000 = 913 L 1 =  D 1 /S 1 ) + (1 -  L 0 + T 0 ) = T 1 =  L 1   L 0 ) + (1 -  T 0 = (0.2)(18769  ) + (0.8)(524) =  S 5 =  D 1 /L 1 ) + (1 -  S 1 = (0.1)(8000/18769) + (0.9)(0.47) =  F 2 = (L 1 +T 1 )S 2 = F 11 = (L 1 + 10 T 1 )S 11 = 71 Skipped

72. Winter’s ES Why D t+1 /S t+1 ? How to initialize the forecast? How to choose alpha, beta and gamma values? Winter’s method is an extension of Holt’s 72 Skipped

73. Exponential Smoothing with Seasonality (no trend) De-seasonalise demand data Apply exponential smoothing update Seasonalise forecast See Excel file 73 Skipped

74. De-seasonalising Demand De-seaonalised demand is the demand that would have been observed in the absence of seasonal fluctuations The periodicity p is the number of periods after which the seasonal cycle repeats itself (e.g. if period length = 3 months, p = 4) 74 Skipped

75. Estimating Model Parameters Seasonal factors: Seasonal factor for a given period (in the future) can be estimated by averaging seasonal factors of periods of corresponding seasons 75 Skipped

76. Example: Natural Gas Figure 7.5 76 Skipped

77. Winter’s model - Example L 0 = 18439T 0 =524 S 1 = 0.47, S 2 =0.68, S 3 =1.17, S 4 =1.67,  = 0.1,  0.2,  = 0.1, F 1 = (L 0 + T 0 ) S 1 = (18439 + 524)(0.47) = 8913 D 1 =8000,E 1 = F 1 – D 1 = 8913 – 8000 = 913 L 1 =  D 1 /S 1 ) + (1 -  L 0 + T 0 ) = (0.1)(8000/0.47) + (0.9)(18439+524) =  T 1 =  L 1   L 0 ) + (1 -  T 0 = (0.2)(18769  ) + (0.8)(524) =  S 5 =  D 1 /L 1 ) + (1 -  S 1 = (0.1)(8000/18769) + (0.9)(0.47) =  F 2 = (L 1 +T 1 )S 2 = (18769+485)(0.68) = 13093, F 11 = (L 1 + 10 T 1 )S 11 = (18769 + 10(485))(1.17) = 27634 77 Skipped

78. Special Forecasting Difficulties for Supply Chains New products and service introductions –No past history –Use qualitative methods until sufficient data collected –Examine correlation with similar products –Use a large exponential smoothing constant Lumpy derived demand –Large but infrequent orders –Random variations “swamps” trend and seasonality –Identify reason for lumpiness and modify forecasts Spatial variations in demand –Separate forecast vs. allocation of total forecasts Not required 78

79. A Lumpy Demand Example 79 Skipped

80. Analysing Forecast Errors Choose a forecast model Monitor if current forecasting method/model accurate –Consistently under-predicting? Over-predicting? –When should we adjust forecasting procedures? Understand magnitude of forecast error –In order to make appropriate contingency plans Assume we have data for n historical periods 80

81. Measures of Forecast Error Mean Square Error (MSE) –Estimate of variance (    of random component Mean Absolute Deviation (MAD) –If random component normally distributed,  25 MAD Mean Absolute Percent Error (MAPE) 81

82. Further Error Equations What does it mean when MFE  0 ? What does it mean when MFE = MAD? What does it mean when MSE < MAD? Why do we need MAPE? 82

83. Guidelines for Selecting Forecasting Model No pattern or direction in forecast error –Error = (Fore. -Actual ) –Seen in plots of errors over time Smallest forecast error –Mean square error (MSE) –Mean absolute deviation (MAD) 83

84. Pattern of Forecast Error Trend Not Fully Accounted for Desired Pattern Time (Years) ErrorError 00 Error 0 Examples? 84

85. Forecasting Steps Define objectives Select items to be forecasted Determine time horizon Select forecasting model(s) Gather data Validate forecasting model Make forecast Implement results Monitor forecast performance 85

86. Tracking Errors Errors due to: –Random component –Bias (wrong trend, shifting seasonality, etc.) Monitor quality of forecast with a tracking signal Alert if signal value exceeds threshold –Indicates underlying environment changed and model becomes inappropriate You have been using one! 86

87. Monitoring: Tracking Signal Tracking signal -- Checks for consistent bias over many periods Measures how well forecast is predicting actual values Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) –Good tracking signal has low values 87

88. TS = RSFE / MAD RSFE(t)=RSFE(t-1)+E(t) = Bias MAD = sum of | forecast errors| over time/ n If TS is greater than some maximum value then report a problem. TS = RSFE / MAD RSFE(t)=RSFE(t-1)+E(t) = Bias MAD = sum of | forecast errors| over time/ n If TS is greater than some maximum value then report a problem. 88

89. Tracking Signal Equation 89

90. Tracking Signal Computation* 90

91. Tracking Signal Plot 91

92. Tracking Signal Limits used for tracking signal ratio usually between (-3/6, 3/6) Used for monitoring Time Re-evaluate the model 6 -6 0 92

93. Tracking Signal Cautious! – Is it always good to have TS=0? –TS: the smaller the better? –Can TS be used for comparing models? 93

94. Summary so far Importance of forecasting in a supply chain Forecasting models and methods Exponential smoothing –Stationary model –Trend –Seasonality Measures of forecast errors Tracking signals 94

95. A Remark Adaptive method Observed D t-1 : F t = f(D t-1, …), observed D t : F t+1 = f(D t, …), … Static method (Section 7.5) – it assumes the estimates of level,. trend, and seasonality do not vary as new demand is observed: Observed D t-1 : F t = f(D t-1, …), observed D t : F t+1 = f(D t-1, …), … 95

96. Forget all beyond this slide 96

97. Part 1 of As# 1 Chapter 7 in 3 rd edition Discussion questions –Q4, Q9 Exercises –Q1, Q 2 & Q3. The deadline: hand in the class before ?. Part 2 will be released later. All are posted as downloadable 97

98. Reading List (Chap. 7) Adaptive Forecasting, up to “Trend- and Seasonality- … Winter’s Model)”. Section 7.6. Measures of Forecast Errors. Section 7.7, up-to “Trend- and Seasonality- … Winter’s Model)”. 98

99. Moving Average Method MA is a series of arithmetic means Used if little or no trend Used often for smoothing –Provides overall impression of data over time Equation LtLtLtLt N N   Demand in Previous Periods Periods 99

100. Moving Average Method Systematic component of demand = Level Chopra: p. 82 Adaptive Forecasting 100

101. Trend-corrected Exp Smooth.  Systematic component = level +trend D t = a t + b + Random (Holt’s Model) Need two revision eqns (1)Level component New forecast = Old forecast+ correction = L t-1 + T t-1 + correction Error = D t – (L t-1 + T t-1 ) L t = L t-1 + T t-1 +  (D t – (L t-1 + T t-1 ) ) =  D t + (1-  ) (L t-1 + T t-1 ) 101

102. Trend-corrected Exp Smooth. (2) Trend component T t =  ( L t -L t-1 ) + (1-  ) T t (3) Forecasting F t+1 = L t + T t, F t+n = L t + n T t Correction: Chopra, p84 under eqn 4.14: Should be “After observing demand for period t+1”. 102

103. Trend- & Seasonality-corrected Exp Smooth. Systematic component = (level +trend ) x seasonal factor, with periodicity p. D t = (a t + b) s + Random (Winter’s Model) Need 3 revision eqns (1)L t =  ( D t / S t )+ (1-  ) (L t-1 + T t-1 ) (2)T t =  ( L t -L t-1 ) + (1-  ) T t-1 (3)S t+p =  (D t / L t ) + (1-  ) S t, t+p and t are the same “season”, and S t is the latest estimate of seasonal factor which was made t-p periods ago (for period t). Forecast: T t+n = (L t + nT t ) S t+n Ignore the formulas 4.18-4.20. 103

104. Static Methods It assumes that the estimates of level, trend and seasonality do not vary as new demand is observed – no need to update Systematic component = (Level+ trend)x seasonal factor F t+n = [L+ (t+n ) T] S t+n 104

105. Visual Inspection or Systematic Diagnosing 105

106. Equations fh 106

107. Forecast Error Equations Mean Square Error (MSE) Mean Absolute Deviation (MAD) 107

108. Selecting Forecasting Model Example You’re an analyst for Hasbro Toys. You’ve forecast sales with Holt’s model & expo. smoothing. Which model do you use? ActualHolt’s ModelExpo Smooth YearSalesForecastForecast 199210.61.0 199311.31.0 199422.01.9 199522.72.0 199643.43.8 108

109. Year D i F i 199210.6 0.4 0.40.160.4 199311.3-0.30.090.3 199422.0 0.0 0.00.000.0 199522.7-0.70.490.7 199643.4 0.6 0.60.360.6 Total0.01.102.0 Holt’s Model Evaluation MSE =  Error 2 / n = 1.10 / 5 =.220 MAD =  |Error| / n = 2.0 / 5 =.400 Error Error 2 |Error| 109

110. Exponential Smoothing Model Evaluation Year D i F i 199211.00.00.000.0 199311.00.00.000.0 199421.90.10.010.1 199522.00.00.000.0 199643.80.20.040.2 Total0.30.050.3 MSE =  Error 2 / n = 0.05 / 5 = 0.01 MAD =  |Error| / n = 0.3 / 5 = 0.06 Error Error 2 |Error| 110

111. Further Error Equations Mean absolute percentage error MAPE =  i=1 | E i / D i | x100/n Bias (Mean forecast error = MFE) Bias =  i=1 E i 111

112. Further Error Equations What does it mean when MFE  0 ? What does it mean when MFE = MAD? What does it mean when MSE < MAD? Why do we need MAPE? 112

113. Tracking Signal Plot 113

114. Tracking Signal Limits used for tracking signal ratio usually between (-6, 6) Used for monitoring Time Re-evaluate the model 6 -6 0 114

115. Tracking Signal Cautious! – Is it always good to have TS=0? –TS: the smaller the better? –Can TS be used for comparing models? 115

116. An Example CLP Power has been collecting data on demand for electric power in a recently developed residential area for only the past 2 years. 1.What are weaknesses of the standard fore. methods as applied to this set of data? 2.Propose your own approach to forecasting. 3.Forecast demand for each month of next year using your model. 116