1 Forecasting Demand in a Supply Chain4. Forecasting Demand in a Supply Chain
2 Learning Objectives Understand the role of forecasting for both an enterprise and a supply chain. Identify the components of a demand forecast. Forecast demand in a supply chain given historical demand data using time-series and regression methodologies. Analyze demand forecasts to estimate forecast error.
3 Overview of Forecasting Methods
4 Role of Forecasting in a Supply ChainThe basis for all planning decisions in a supply chain Used for both push and pull processes Production scheduling, inventory, aggregate planning Sales force allocation, promotions, new production introduction Plant/equipment investment, budgetary planning Workforce planning, hiring, layoffs All of these decisions are interrelated
5 Role of Forecasting in a Supply Chain – Some ExamplesInventory Management Accurate forecasting determines how much inventory a company must keep at various points along its supply chain Quality Management Accurately forecasting customer demand is a key to providing good quality service Strategic Planning Successful strategic planning requires accurate forecasts of future products and markets
6 Characteristics of ForecastsForecasts are always inaccurate and should thus include both the expected value of the forecast and a measure of forecast error Long-term forecasts are usually less accurate than short- term forecasts Aggregate forecasts are usually more accurate than disaggregate forecasts In general, the farther up the supply chain a company is, the greater is the distortion of information it receives
7 Types of Forecasting MethodsDepend on Time frame (how far into the future) Short- to mid-range forecast (immediate future - up to two years) Long-range forecast Demand behavior Causes of behavior
8 Types of Forecasting MethodsDemand Behavior Trend a gradual, long-term up or down movement of demand Random variations movements in demand that do not follow a pattern Cycle an up-and-down repetitive movement in demand Seasonal pattern an up-and-down repetitive movement in demand occurring periodically
9 Types of Forecasting MethodsTime (a) Trend (d) Trend with seasonal pattern (c) Seasonal pattern (b) Cycle Demand Random movement Forms of Forecast Movement
10 Components and MethodsCompanies must identify the factors that influence future demand and then ascertain the relationship between these factors and future demand, for example: Past demand Lead time of product replenishment Planned advertising or marketing efforts Planned price discounts State of the economy Actions that competitors have taken Notes:
11 Components and MethodsQualitative Primarily subjective Rely on judgment Time Series Use historical demand only Best with stable demand Causal – Regression Relationship between demand and some other factor Simulation Imitate consumer choices that give rise to demand Notes:
12 Components of an ObservationObserved demand (O) = systematic component (S) + random component (R) Systematic component – expected value of demand Level (current deseasonalized demand) Trend (growth or decline in demand) Seasonality (predictable seasonal fluctuation) Random component – part of forecast that deviates from systematic component (size and variability) Forecast error – difference between forecast and actual demand A good forecast has an error whose size is comparable to the random component
13 Time-Series Methods Use historical data onlyRelate the forecast to the time only Linear Trend Line method Static Methods Additive Methods
14 Time-Series TechniquesBest -> Forecast DES: MAPE 8.177
15 Time-Series Forecasting MethodsAssumption: what has occurred in the past will continue to occur in the future Relate the forecast to only one factor - time Linear trend line method Additive methods Static methods Three ways to calculate the systematic component: Multiplicative S = level x trend x seasonal factor Additive S = level + trend + seasonal factor Mixed S = (level + trend) x seasonal factor
16 Linear Trend Line Method= b a = y - b x where n = number of periods x = = mean of the x values y = = mean of the y values xy - nxy x2 - nx2 x n y S = level + trend y = a + bx where a = intercept coefficient b = slope of the line x = time period (variable coefficient) y = forecast for demand for period x
17 Linear Trend Line Methodx(PERIOD) y(DEMAND) xy x2 Least Squares Example
18 Linear Trend Line MethodLeast Squares Example (cont.) x = = 6.5 y = = 46.42 b = = =1.72 a = y - bx = (1.72)(6.5) = 35.2 (12)(6.5)(46.42) (6.5)2 xy - nxy x2 - nx2 78 12 557
19 Linear trend line y = 35.2 + 1.72x Forecast for period 13= units 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | | | | | | | Actual Demand Period
20 Adaptive Forecasting MethodsThe estimates of level, trend, and seasonality are adjusted after each demand observation Estimates incorporate all new data that are observed. Methods: Moving Averages + Weighted Moving Averages Simple Exponential Smoothing Trend-Corrected Exponential Smoothing (Holt’s model) Trend- and Seasonal-Corrected Exponential Smoothing (Winter’s model)
21 Adaptive Forecasting Methodswhere Lt = estimate of level at the end of Period t Tt = estimate of trend at the end of Period t St = estimate of seasonal factor for Period t Ft = forecast of demand for Period t (made Period t – 1 or earlier) Dt = actual demand observed in Period t Et = Ft – Dt = forecast error in Period t
22 Steps in Adaptive ForecastingInitialize Compute initial estimates of level (L0), trend (T0), and seasonal factors (S1,…,Sp) Forecast Forecast demand for period t + 1 Estimate error Compute error Et+1 = Ft+1 – Dt+1 Modify estimates Modify the estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Et+1
23 Moving Average Assumption: no observable trend or seasonalitySystematic component of demand = level The level in period t is the average demand over the last N periods Lt = (Dt + Dt-1 + … + Dt–N+1) / N Ft+1 = Lt and Ft+n = Lt After observing the demand for period t + 1, revise the estimates Lt+1 = (Dt+1 + Dt + … + Dt-N+2) / N, Ft+2 = Lt+1
24 Moving Average Example IA supermarket has experienced weekly demand of milk of D1 = 120, D2 = 127, D3 = 114, and D4 = 122 gallons over the past four weeks What is the forecast demand for Period 5 using a 4- period moving average? What is the forecast error if demand in Period 5 turns out to be 125 gallons?
25 Moving Average Example IL4 = (D4 + D3 + D2 + D1)/4 = ( )/4 = Forecast demand for Period 5: F5 = L4 = gallons Error if demand in Period 5 = 125 gallons E5 = F5 – D5 = 125 – = 4.25 Revised demand L5 = (D5 + D4 + D3 + D2)/4 = ( )/4 = 122
26 Moving Average Example II3-month Simple Moving Average Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - ORDERS MONTH PER MONTH – 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MOVING AVERAGE
27 Moving Average Example II5-month Simple Moving Average Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - ORDERS MONTH PER MONTH – 99.0 85.0 82.0 88.0 95.0 91.0 MOVING AVERAGE
28 Moving Average Example II150 – 125 – 100 – 75 – 50 – 25 – 0 – | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Actual Orders Month Smoothing Effects 5-month 3-month
29 Weighted Moving AverageEnhancement: Adjusts the moving average method to more closely reflect data fluctuations The level in period t is the weighted average demand over the last N periods Lt = Wt Dt + Wt-1 Dt-1 + … + Wt–N+1 Dt–N+1 Ft+1 = Lt and Ft+n = Lt Wt is the weight for period t, between 0 and 100 percent All weights must add up to 1.
30 Weighted Moving Average ExampleMONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 = (0.50)(90) + (0.33)(110) + (0.17)(130) = orders November Forecast
31 Simple Exponential SmoothingAssumption: No observable trend or seasonality Systematic component of demand = level Initial estimate of level L0 is assumed to be the average of all historical data (this is optional)
32 Simple Exponential SmoothingGiven data for Periods 1 to n (this step is optional) Current forecast Revised forecast using smoothing constant 0 < a < 1 Thus
33 Simple Exponential SmoothingUse supermarket data to forecast period 5 using a=0.1 E1 = F1 – D1 = –120 = 0.75
34 Simple Exponential SmoothingIf we continue the calculations for the next periods (2, 3 & 4), we obtain F5 = a 0.1 Period Dt Lt Ft Et 120.75 1 120 120.68 0.75 2 127 121.31 -6.33 3 114 120.58 7.31 4 122 120.72 -1.42 5
35 Simple Exponential SmoothingEffect of Smoothing Constant 0.0 1.0 If = 0.20, then Lt +1 = 0.20Dt Lt If = 0, then Lt +1 = 0Dt + 1 Lt = Lt Forecast does not reflect recent data If = 1, then Lt +1 = 1Dt + 0 Lt =Dt Forecast based only on most recent data
36 Simple Exponential SmoothingPeriod Month Dt Lt Ft Et 46.42 1 Jan 37 43.59 9.42 2 Feb 40 42.51 3.59 3 Mar 41 42.06 1.51 4 Apr 40.54 5.06 5 May 45 41.88 -4.46 6 Jun 50 44.32 -8.12 7 Jul 43 43.92 1.32 8 Aug 47 44.84 -3.08 9 Sep 56 48.19 -11.16 10 Oct 52 49.33 -3.81 11 Nov 55 51.03 -5.67 12 Dec 54 51.92 -2.97 13
37 Simple Exponential SmoothingPeriod Month Dt Lt Ft Et 46.42 1 Jan 37 41.71 9.42 2 Feb 40 40.85 1.71 3 Mar 41 40.93 -0.15 4 Apr 38.96 3.93 5 May 45 41.98 -6.04 6 Jun 50 45.99 -8.02 7 Jul 43 44.50 2.99 8 Aug 47 45.75 -2.50 9 Sep 56 50.87 -10.25 10 Oct 52 51.44 -1.13 11 Nov 55 53.22 -3.56 12 Dec 54 53.61 -0.78 13
38 Simple Exponential Smoothing
39 Trend-Corrected Exponential Smoothing (Holt’s Model)Appropriate when the demand is assumed to have a level and trend in the systematic component of demand but no seasonality Systematic component of demand = level + trend
40 Trend-Corrected Exponential Smoothing (Holt’s Model)Obtain initial estimate of level and trend by running a linear regression Dt = at + b T0 = a, L0 = b In Period t, the forecast for future periods is Ft+1 = Lt + Tt and Ft+n = Lt + nTt Revised estimates for Period t (β is a smoothing constant factor) Lt+1 = aDt+1 + (1 – a)(Lt + Tt) Tt+1 = b(Lt+1 – Lt) + (1 – b)Tt
41 Trend-Corrected Exponential Smoothing (Holt’s Model)MP3 player demand D1 = 8,415, D2 = 8,732, D3 = 9,014, D4 = 9,808, D5 = 10,413, D6 = 11,961 a = 0.1, b = 0.2 Using regression analysis (line trend method) L0 = 7,367 and T0 = 673 Forecast for Period 1 F1 = L0 + T0 = 7, = 8,040
42 Trend-Corrected Exponential Smoothing (Holt’s Model)Revised estimate L1 = aD1 + (1 – a)(L0 + T0) = 0.1 x 8, x 8,040 = 8,078 T1 = b(L1 – L0) + (1 – b)T0 = 0.2 x (8,078 – 7,367) x = 681 With new L1 F2 = L1 + T1 = 8, = 8,759 Continuing F7 = L6 + T6 = 11, = 12,072
43 Trend-Corrected Exponential Smoothing (Holt’s Model)Period Demand L T Forecast |Et| Et2 (|Et|/Dt)% 35.212 1.7238 January 1 37 36.97 1.73 36.94 0.06 0.00 0.17 February 2 40 39.35 1.93 38.70 1.30 1.69 3.25 March 3 41 41.14 1.89 41.28 0.28 0.08 0.68 April 4 40.01 0.98 43.03 6.03 36.31 16.29 May 5 45 43.00 1.58 41.00 4.00 16.04 8.90 June 6 50 47.29 2.40 44.58 5.42 29.37 10.84 July 7 43 46.34 1.39 49.69 6.69 44.71 15.55 August 8 47 47.37 1.28 47.74 0.74 0.54 1.57 September 9 56 52.33 2.39 48.65 7.35 54.01 13.12 October 10 52 53.36 1.98 54.71 2.71 5.21 November 11 55 55.17 55.33 0.33 0.11 0.61 December 12 54 55.55 1.46 57.10 3.10 9.58 5.73 57.01 b 0.300 MAD 3.167 a 0.500 MSE 16.649 MAPE 6.826
44 Trend-Corrected Exponential Smoothing (Holt’s Model)
45 Trend- and Seasonality-Corrected Exponential SmoothingAppropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factor Systematic component = (level + trend) x seasonal factor Ft+1 = (Lt + Tt)St+1 and Ft+l = (Lt + lTt)St+l
46 Trend- and Seasonality-Corrected Exponential SmoothingAfter observing demand for period t + 1, revise estimates for level, trend, and seasonal factors Lt+1 = a(Dt+1/St+1) + (1 – a)(Lt + Tt) Tt+1 = b(Lt+1 – Lt) + (1 – b)Tt St+p+1 = g(Dt+1/Lt+1) + (1 – g)St+1 a = smoothing constant for level b = smoothing constant for trend g = smoothing constant for seasonal factor
47 Winter’s Model Tahoe Salt Example L0 = 18,439 T0 = 524S1= 0.47, S2 = 0.68, S3 = 1.17, S4 = 1.67 F1 = (L0 + T0)S1 = (18, )(0.47) = 8,913 The observed demand for Period 1 = D1 = 8,000 Forecast error for Period 1 = E1 = F1 – D1 = 8,913 – 8,000 = 913 Year, Qtr Period t Demand Dt 1,2 1 8,000 1,3 2 13,000 1,4 3 23,000 2,1 4 34,000 2,2 5 10,000 2,3 6 18,000 2,4 7 3,1 8 38,000 3,2 9 12,000 3,3 10 3,4 11 32,000 4,1 12 41,000
48 Winter’s Model Assume a = 0.1, b = 0.2, g = 0.1; revise estimates for level and trend for period 1 and for seasonal factor for Period 5 L1 = a(D1/S1) + (1 – a)(L0 + T0) = 0.1 x (8,000/0.47) x (18, ) = 18,769 T1 = b(L1 – L0) + (1 – b)T0 = 0.2 x (18,769 – 18,439) x 524 = 485 S5 = g(D1/L1) + (1 – g)S1 = 0.1 x (8,000/18,769) x 0.47 = 0.47 F2 = (L1 + T1)S2 = (18, )0.68 = 13,093
49 Mean Squared Error MSEtWinter’s Model Period t Demand Dt Level Lt Trend Tt Seasonal Factor St Forecast Ft Error Et Absolute Error At Mean Squared Error MSEt MADt % Error MAPEt TSt 18,439 524 1 8,000 18,769 485 0.47 8,913 913 832,857 11 11.41 1.00 2 13,000 19,240 482 0.68 13,093 93 420,727 503 6.06 2.00 3 23,000 19,716 481 1.17 23,076 76 282,393 360 4.15 3.00 4 34,000 20,214 484 1.67 33,730 -270 270 230,049 338 3.31 2.40 5 10,000 20,776 500 9,637 -363 363 210,321 343 3.37 1.31 6 18,000 21,797 604 14,458 -3,542 3,542 2,265,821 876 20 6.09 -3.53 7 22,127 549 26,202 3,202 3,406,502 1,208 14 7.21 0.09 8 38,000 22,683 551 37,898 -102 102 2,981,997 1,070 6.34 0.01 9 12,000 23,479 600 10,855 -1,145 1,145 2,796,424 1,078 10 6.70 -1.06 23,543 493 0.69 16,715 3,715 3,896,961 1,342 29 8.89 1.92 32,000 24,399 565 1.16 27,801 -4,199 4,199 5,145,678 1,602 13 9.27 -1.01 12 41,000 24,921 557 41,731 731 4,761,357 1,529 8.65 -0.58 12,015 17,703 15 31,167 16 45,307 alpha 0.1 Beta 0.2 Gamma
50 Winter’s Model
51 Time Series Models Forecasting Method Applicability Moving averageNo trend or seasonality Simple exponential smoothing Holt’s model Trend but no seasonality Winter’s model Trend and seasonality
52 Static Forecasting MethodsStatic methods assumes that the estimates of level, trend, and seasonality within the systematic component do not vary as new demand is observed where L = estimate of level at t = 0 T = estimate of trend St = estimate of seasonal factor for Period t Dt = actual demand observed in Period t Ft = forecast of demand for Period t
53 Static Forecasting Methods - Tahoe Salt ExampleYear Quarter Period, t Demand, Dt 1 2 8,000 3 13,000 4 23,000 34,000 5 10,000 6 18,000 7 8 38,000 9 12,000 10 11 32,000 12 41,000
54 Static Forecasting Methods - Tahoe Salt ExampleObserve that the demand is seasonal, the lowest occurs every second quarter of each year, and the overall demand pattern repeats every year.
55 Static Forecasting Methods - Tahoe Salt ExampleHow to estimate level, trend, and seasonality factors? Basic Steps: Deseasonalize demand and run the linear trend line method to estimate level and trend To ensure that each season is given equal weight when deseasonalizing the demand, we must take the average of p consecutive periods of demand. Estimate seasonal factors The seasonal factor of a period t is the ratio between the actual demand and the deseasonalized demand
56 Static Forecasting Methods - Tahoe Salt ExampleEstimate Level and Trend Deseasonalized Demand formulas: Periodicity p = 4, t = 3
57 Static Forecasting Methods - Tahoe Salt ExampleEstimate Level and Trend
58 Static Forecasting Methods - Tahoe Salt ExampleEstimate Level and Trend A linear relationship exists between the deseasonalized demand and time based on the change in demand over time
59 Static Forecasting Methods - Tahoe Salt ExampleThe values of L and T for the deseasonalized demand can be estimated using the linear trend line method: See also later slides on Linear Regression Estimate Level and Trend
60 Static Forecasting Methods - Tahoe Salt ExampleEstimating Seasonal Factors
61 Static Forecasting Methods - Tahoe Salt ExampleEstimating Seasonal Factors Given r seasonal cycles in the data, for all periods of the form pt+1,1<=i<=p, we should obtain the seasonal factor for each period: For r = 3 (seasonal cycles) and p=4 (periods) we get:
62 Static Forecasting Methods - Tahoe Salt ExampleForecast for the next 4 periods Given the level, trend and all seasonal factors calculated earlier, using the following formula we obtain the forecast for the next 4 quarters:
63 Static Forecasting Methods - Tahoe Salt Example
64 Forecast Errors
65 Measures of Forecast ErrorDeclining alpha
66 Forecast Accuracy Forecast errordifference between forecast and actual demand MAD mean absolute deviation MAPD mean absolute percent deviation Cumulative error Average error or bias
67 Mean Absolute Deviation (MAD) Dt - Ft n MAD = where t = period number Dt = demand in period t Ft = forecast for period t n = total number of periods = absolute value
68 PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|MAD Example – – PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft| MAD = 53.39/11 = 4.85
69 Other Accuracy MeasuresMean absolute percent deviation (MAPD) MAPD = |Dt - Ft| Dt Cumulative error E = et Average error E = et n
70 Forecast Control Tracking signal (Dt - Ft) E MAD Tracking signal = =monitors the forecast to see if it is biased high or low 1 MAD ≈ 0.8 б Control limits of 2 to 5 MADs are used most frequently Tracking signal = = (Dt - Ft) MAD E
71 Tracking Signal Values– – – DEMAND FORECAST, ERROR E = PERIOD Dt Ft Dt - Ft (Dt - Ft) MAD – 1.00 2.00 1.62 3.00 4.25 5.01 6.00 7.19 8.18 9.20 10.17 TRACKING SIGNAL TS3 = = 2.00 6.10 3.05 Tracking signal for period 3
72 Statistical Control Charts = (Dt - Ft)2 n - 1 Using we can calculate statistical control limits for the forecast error Control limits are typically set at 3
73 Statistical Control ChartsErrors 18.39 – 12.24 – 6.12 – 0 – -6.12 – – – | | | | | | | | | | | | | Period UCL = +3 LCL = -3
74 Selecting the Best Smoothing Constants
75 Selecting the Best Smoothing Constant
76 Selecting the Best Smoothing Constant
77 Application at Tahoe Salt
78 Forecasting Demand at Tahoe SaltMoving average Simple exponential smoothing Trend-corrected exponential smoothing Trend- and seasonality-corrected exponential smoothing
79 Forecasting Demand at Tahoe Salt
80 Forecasting Demand at Tahoe SaltMoving average L12 = 24,500 F13 = F14 = F15 = F16 = L12 = 24,500 s = 1.25 x 9,719 = 12,148
81 Forecasting Demand at Tahoe Salt
82 Forecasting Demand at Tahoe SaltSingle exponential smoothing L0 = 22,083 L12 = 23,490 F13 = F14 = F15 = F16 = L12 = 23,490 s = 1.25 x 10,208 = 12,761
83 Forecasting Demand at Tahoe Salt
84 Forecasting Demand at Tahoe SaltTrend-Corrected Exponential Smoothing L0 = 12,015 and T0 = 1,549 L12 = 30,443 and T12 = 1,541 F13 = L12 + T12 = 30, ,541 = 31,984 F14 = L12 + 2T12 = 30, x 1,541 = 33,525 F15 = L12 + 3T12 = 30, x 1,541 = 35,066 F16 = L12 + 4T12 = 30, x 1,541 = 36,607 s = 1.25 x 8,836 = 11,045
85 Forecasting Demand at Tahoe Salt
86 Forecasting Demand at Tahoe SaltTrend- and Seasonality-Corrected L0 = 18,439 T0 =524 S1 = S2 = S3 = S4 = 1.67 L12 = 24,791 T12 = 532 F13 = (L12 + T12)S13 = (24, )0.47 = 11,940 F14 = (L12 + 2T12)S13 = (24, x 532)0.68 = 17,579 F15 = (L12 + 3T12)S13 = (24, x 532)1.17 = 30,930 F16 = (L12 + 4T12)S13 = (24, x 532)1.67 = 44,928 s = 1.25 x 1,469 = 1,836
87 Forecasting Demand at Tahoe Salt
88 Forecasting Demand at Tahoe SaltForecasting Method MAD MAPE (%) TS Range Four-period moving average 9,719 49 –1.52 to 2.21 Simple exponential smoothing 10,208 59 –1.38 to 2.15 Holt’s model 8,836 52 –2.15 to 2.00 Winter’s model 1,469 8 –2.74 to 4.00
89 Regression Methods
90 Regression Methods Linear regression Correlationa mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation Correlation a measure of the strength of the relationship between independent and dependent variables
91 Linear Regression Example(WINS) x (ATTENDANCE) y xy x2
92 Linear Regression Example (cont.)y = = b = = = 4.06 a = y - bx = (4.06)(6.125) = 49 8 346.9 xy - nxy2 x2 - nx2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125)2
93 Linear Regression Example (cont.)| | | | | | | | | | | 60,000 – 50,000 – 40,000 – 30,000 – 20,000 – 10,000 – Linear regression line, y = x Wins, x Attendance, y y = (7) = 46.88, or 46,880 Attendance forecast for 7 wins
94 Correlation and Coefficient of DeterminationCorrelation, r Measure of strength of relationship Varies between and +1.00 Coefficient of determination, r2 Percentage of variation in dependent variable resulting from changes in the independent variable
95 Computing Correlationn xy - x y [n x2 - ( x)2] [n y2 - ( y)2] r = Coefficient of determination r2 = (0.947)2 = 0.897 r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2] r = 0.947
96 Correlation Coefficienty x (a) Perfect negative correlation y x (e) Perfect positive correlation y x (b) Negative correlation y x (d) Positive correlation High Moderate Low Correlation coefficient values | | | | | | | | | –1.0 –0.8 –0.6 –0.4 – y x (c) No correlation
97 Standard Error of the EstimateA forecast is just a point estimate of a future value This point is actually the mean of a probability distribution 4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | Area payroll (in $ billions) Nodel’s sales (in$ millions) 3.25 Regression line,
98 Standard Error of the Estimatewhere y = y-value of each data point yc = computed value of the dependent variable, from the regression equation n = number of data points
99 Standard Error of the EstimateComputationally, this equation is considerably easier to use We use the standard error to set up prediction intervals around the point estimate
100 Standard Error of the Estimate4.0 – 3.0 – 2.0 – 1.0 – | | | | | | | Area payroll (in $ billions) Nodel’s sales (in$ millions) 3.25 The standard error of the estimate is $306,000 in sales
101 Regression Analysis with Excel
102 Regression Analysis with ExcelMaosplace.xls – Linear Regression
103 Study the relationship of demand to two or more independent variablesMultiple Regression Study the relationship of demand to two or more independent variables y = 0 + 1x1 + 2x2 … + kxk where 0 = the intercept 1, … , k = parameters for the independent variables x1, … , xk = independent variables
104 Multiple Regression with Excel
105 Example of Multi-Regression for Demand ForecastingDay Temperature Flyer Sales 1 63 ✓ 152 2 70 168 3 73 180 4 75 235 5 80 236 6 82 225 7 85 268 8 88 330 9 90 314 10 91 306 11 92 374 12 192 13 98 340 14 100 388 15 317 16 87 283 17 84 258 18 310 19 226 20 214 21 76 198 Can we predict customer reactions or the demand for a product (ice cream)? : Flyer was included in the local daily newspaper
106 Do you see any relationships in these data?Day Temperature Flyer Sales 1 63 152 2 70 168 3 73 180 4 75 235 5 80 236 6 82 225 7 85 268 8 88 330 9 90 314 10 91 306 11 92 374 12 192 13 98 340 14 100 388 15 317 16 87 283 17 84 258 18 310 19 226 20 214 21 76 198 Two parameters possibly affecting sales: temperature and flyer advertisement in the local daily newspaper Flyer = 0: No flyer included in the local daily newspaper Flyer = 1: Otherwise
107 Sales Forecast – Single RegressionUse as predictor variable the temperature, assuming a linear relationship between sales and temperature Can I use this model to forecast the demand for a day in 2 months from now? Can I make forecasts outside the above temperature range? Should I cleanup the historical data (e.g. days with sold outs)?
108 Sales Forecast - Multiple RegressionCan I increase predictability by considering flyer promotions on particular days? The relationship with TWO explanatory (predictor) variables can be formalized as follows: Sales(t) = B0 + B1*Temperature(t)+ B2*Flyer(t)
109 Sales Forecast - Multiple RegressionBetter predictability than the original regression (R Square was ) SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 21 ANOVA df SS MS F Significance F Regression 2 E-12 Residual 18 Total 20 Coefficients t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept E-07 Temperature E-12 Flyer Very small chance (<0.05) the independent values are not useful B0; B1; B2 Significance
110 Sales Forecast - Multiple Regression
111 Application in Practice
112 Demand Forecasting Extrapolate past demand data into the future using time-series forecasting methods: Select a preferred forecasting method from a set of techniques Quantify the forecasting errors to be experienced when forecasting the future Use regression analysis to build predictive models that will relate targeted customer segments with casual variable such as price, inventory, and so on.
113 The Role of IT in ForecastingForecasting module is core supply chain software Can be used to best determine forecasting methods for the firm and by product categories and markets Real time updates help firms respond quickly to changes in marketplace Facilitate demand planning
114 Risk Management Errors in forecasting can cause significant misallocation of resources in inventory, facilities, transportation, sourcing, pricing, and information management Common factors are long lead times, seasonality, short product life cycles, few customers and lumpy demand, and when orders placed by intermediaries in a supply chain Mitigation strategies – increasing the responsiveness of the supply chain and utilizing opportunities for pooling of demand
115 Forecasting In PracticeCollaborate in building forecasts Share only the data that truly provide value Be sure to distinguish between demand and sales
116 Basic Approach Understand the objective of forecasting.Integrate demand planning and forecasting throughout the supply chain. Identify the major factors that influence the demand forecast. Forecast at the appropriate level of aggregation. Establish performance and error measures for the forecast. Notes:
117 Forecasting In Practice1. Identify the purpose of forecast 2. Collect historical data 3. Plot data and identify patterns 6. Check forecast accuracy with one or more measures 5. Develop/compute forecast for period of historical data 4. Select a forecast model that seems appropriate for data 7. Is accuracy of forecast acceptable? No 8b. Select new forecast model or adjust parameters of existing model Yes 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8a. Forecast over planning horizon
118 Summary of Learning ObjectivesUnderstand the role of forecasting for both an enterprise and a supply chain Identify the components of a demand forecast Forecast demand in a supply chain given historical demand data using time-series methodologies Analyze demand forecasts to estimate forecast error