![Weighted moving average
2610/7/2018
January 10
February 12
March 13
April 16
May 19
June 23
July 26
Actual 3-Month Weighted
Month Shed Sales Moving Average
[(3 x 16) + (2 x 13) + (12)]/6 = 141/3
[(3 x 19) + (2 x 16) + (13)]/6 = 17
[(3 x 23) + (2 x 19) + (16)]/6 = 201/2
10
12
13
[(3 x 13) + (2 x 12) + (10)]/6 = 121/6](https://image.slidesharecdn.com/forcasting-181007052604/85/Forecasting-of-demand-management-26-320.jpg)
![Correlation Analysis
How strong is the linear relationship between the
variables?
- a measure of the strength of the relationship between
independent and dependent variables
Coefficient of correlation, r, measures degree of
association
Values range from -1 to +1
r =
nxy - xy
[nx2 - (x)2][ny2 - (y)2]](https://image.slidesharecdn.com/forcasting-181007052604/85/Forecasting-of-demand-management-40-320.jpg)
Forecasting of demand (management)
- 1. What We Can Forecast in our day to day life???
- 2. past ==> future I see that you will get an O this semester.
- 4. FORECAST: • A statement about the future value of a variable of interest such as demand. • Purpose of demand management is to coordinate and control all sources of demand so the productive system can be used efficiently and the product delivered on time • Forecasts affect decisions and activities throughout an organization – Marketing, sales – Operations – Accounting, finance – Human resources
- 5. Accounting Cost /profit estimates Finance Cash flow and funds Marketing Pricing, promotion, Sales Operations Inventory, Schedules, MRP, workloads Product/service design New products launch Human Resources Hiring/recruiting/training Uses of Forecasts
- 6. Elements of a Good Forecast Timely AccurateReliable Written / Data
- 7. Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Prepare the forecast Step 6 Monitor the forecast “The forecast”
- 8. Types of Forecasts • Quantitive :(Time series )– Uses historical data assuming the future will be like the past • Causal: Use the relationship between demand and some other factor to develop forecast e.g. Price, advertisement etc. • Qualitative: (Judgmental / Opinion )- Uses subjective inputs Rely on judgment and opinion (usually from experts, decision makers or customer) • Simulation – Imitate consumer choices that give rise to demand
- 9. Quantitative/Time Series Method • Moving average – Simple Moving average – Weighted moving average • Exponential smoothing – Simple exponential – Holt’s model (with trend) – Winter’s model (with trend and seasonality) • Regression analysis
- 10. Qualitative/Judgmental Method • Opinions – Sales force opinions – Executive – Outside • Surveys - Consumer - Competitor related • Delphi method – Opinions of managers and staff
- 11. Causal Method for forecasting • Regression analysis
- 12. Time Series Forecasting • Forecast based only on past values – Assumes that factors influencing past and present will continue influence in future 10/7/2018 12
- 13. Time Series Components 10/7/2018 13 Trend Seasonal Cyclical Random
- 14. Time Series Components 10/7/2018 14 Demandforproductorservice | | | | 1 2 3 4 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation
- 15. Trend Component 10/7/2018 15 Usual starting pointing developing a forecast. Adjusted for seasonal effects, cyclical elements and random effects. Changes due to population, technology, age, culture, etc. Typically several years duration
- 16. Seasonal Component 10/7/2018 16 Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year
- 17. Cyclical Component 10/7/2018 17 Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration 0 5 10 15 20
- 18. Random Component 10/7/2018 18 Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Short duration and no repeating M T W T F
- 19. Naive approach 10/7/2018 19 Assumes demand in next period is the same as demand in most recent period - e.g., If May sales were 48, then June sales will be 48 Sometimes cost effective and efficient
- 20. Moving Averages • Simple Moving average – A technique that averages a number of recent actual values, updated as new values become available. • Take the average demand for a defined number of past periods • Forecast will lag behind – Trends – Seasonality or other cyclicality MAn = n Di i = 1 n where n = number of periods in the moving average Di = demand in period i
- 21. 3-Month Moving Averages 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 MA3 = 3 i = 1 Di 3 = 90 + 110 + 130 3 = 110 orders for Nov – – – 103.3 88.3 95.0 78.3 78.3 85.0 105.0 110.0 MOVING AVERAGE
- 22. 5-Month Moving Averages 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 MA5 = 5 i = 1 Di 5 = 90 + 110 + 130+75+50 5 = 91 orders for Nov – – – – – 99.0 85.0 82.0 88.0 95.0 91.0 MOVING AVERAGE
- 23. Smoothing effect 10/7/2018 23 150 – 125 – 100 – 75 – 50 – 25 – 0 – | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Actual Orders Month 5-month 3-month
- 24. Weighted moving average 10/7/2018 24 Adjusts moving average method to more closely reflect data fluctuations Older data usually less important Weights based on experience and intuition WMAn = i = 1 Wi Di where Wi = the weight for period i, between 0 and 100 percent Di = demand in period i Wi = 1.00
- 25. Weighted moving average 10/7/2018 25 MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 WMA3 = 3 i = 1 Wi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders November Forecast
- 26. Weighted moving average 2610/7/2018 January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Weighted Month Shed Sales Moving Average [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2 10 12 13 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6
- 27. Weighted moving average 2710/7/2018 30 – 25 – 20 – 15 – 10 – 5 – Salesdemand | | | | | | | | | | | | J F M A M J J A S O N D Actual sales Moving average Weighted moving average
- 28. Exponential Smoothing 2810/7/2018 • Form of weighted moving average – Weights decline exponentially – Most recent data weighted most • Requires smoothing constant (α) – Ranges from 0 to 1 – Subjectively chosen • Involves little record keeping of past data
- 29. Exponential Smoothing 2910/7/2018 New forecast = last period’s forecast + a (last period’s actual demand – last period’s forecast) Ft = Ft – 1 + a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0 a 1)
- 30. Period Actual Alpha = 0.1 Error Alpha = 0.4 Error 1 42 2 40 42 -2.00 42 -2 3 43 41.8 1.20 41.2 1.8 4 40 41.92 -1.92 41.92 -1.92 5 41 41.73 -0.73 41.15 -0.15 6 39 41.66 -2.66 41.09 -2.09 7 46 41.39 4.61 40.25 5.75 8 44 41.85 2.15 42.55 1.45 9 45 42.07 2.93 43.13 1.87 10 38 42.36 -4.36 43.88 -5.88 11 40 41.92 -1.92 41.53 -1.53 12 41.73 40.92 Example - Exponential Smoothing
- 31. Impact of The Value of a
- 32. Choosing appropriate Value of ᾳ If real demand is stable: small ᾳ If real demand is rapidly increasing or decreasing: large ᾳ to try to keep up with the change. Two Approaches to control the value of ᾳ: Two or more predetermined values of ᾳ Computed values for ᾳ
- 33. Choosing appropriate Value of ᾳ Two or more predetermined values of ᾳ If error is large: ᾳ ≥ 0.8 If error is small: ᾳ ≤ 0.2 Computed values for ᾳ Tracking ᾳ = Exponentially smoothed actual error divided by exponentially smoothed absolute error.
- 34. Trend effects in exponential smoothing To correct the trend to smoothing constant are required: – Smoothing constant ᾳ and smoothing constant δ – δ reduces the impact of errors – For first time, trend value must be entered manually. – This trend value can be educated guess or a computation based on observed past data FITt-1 = Ft-1 + Tt-1 Ft = FITt-1 + ᾳ (At -1 - FITt-1 ) Tt = Tt-1 + δ (Ft - FITt-1 )
- 36. Linear Regression Analysis Useful for long term forecasting of major occurrences and aggregate planning. e.g. very useful for product families. Used for both time series forecasting and causal forecasting. Time series forecasting: If dependent variable changes as a result of time Casual forecasting: If one variable changes because of change in another variable.
- 37. Linear Regression Analysis • Ft = Forecast for period t (Dependent Variable) • t = Specified number of time periods • a = Y intercept • b = Slope of the line Ft = a + bt 0 1 2 3 4 5 t Ft b = n (xy) - y n x2 - ( x)2 x a = y - b x n
- 38. Example x y Week x2 Sales xy 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 x = 15 x2 = 55 y = 812 xy = 2499 (x)2 = 225
- 39. Calculation y = 143.5 + 6.3t a = 812 - 6.3(15) 5 = b = 5 (2499) - 15(812) 5(55) - 225 = 12495 -12180 275 -225 = 6.3 143.5
- 40. Correlation Analysis How strong is the linear relationship between the variables? - a measure of the strength of the relationship between independent and dependent variables Coefficient of correlation, r, measures degree of association Values range from -1 to +1 r = nxy - xy [nx2 - (x)2][ny2 - (y)2]
- 41. Correlation Analysis 10/7/2018 41 y x(a) Perfect positive correlation: r = +1 y x (c) No correlation: r = 0 y x(b) Positive correlation: 0 < r < 1 y x (d) Perfect negative correlation: r = -1
- 42. Correlation Analysis 10/7/2018 42 x y Week Sales 1 150 2 157 3 162 4 166 5 177
- 43. Forecast Accuracy Error - difference between actual value and predicted value Mean Absolute Deviation (MAD) - Average absolute error Mean Squared Error (MSE) - Average of squared error Mean Absolute Percent Error (MAPE) - Average absolute percent error
- 44. Forecast Accuracy MAD – Easy to compute – Weights errors linearly MSE – Squares error – More weight to large errors MAPE – Puts errors in percent
- 45. Forecast Accuracy 10/7/2018 45 MAD = Actual forecast n MSE = Actual forecast) -1 2 n ( MAPE = Actual forecast n / Actual*100)(
- 46. Example Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100 1 217 215 2 2 4 0.92 2 213 216 -3 3 9 1.41 3 216 215 1 1 1 0.46 4 210 214 -4 4 16 1.90 5 213 211 2 2 4 0.94 6 219 214 5 5 25 2.28 7 216 217 -1 1 1 0.46 8 212 216 -4 4 16 1.89 -2 22 76 10.26 MAD= 2.75 MSE= 10.86 MAPE= 1.28
- 47. Mean absolute deviation MAD = A - F n t t t=1 n 1 MAD 0.8 standard deviation 1 standard deviation 1.25 MAD • The ideal MAD is zero which would mean there is no forecasting error • The larger the MAD, the less the accurate the resulting model
- 48. Tracking Signal Tracking signal = (Actual-forecast) MAD •Tracking signal –Ratio of cumulative error to MAD
- 49. Choosing a Forecasting Technique • No single technique works in every situation • Two most important factors – Cost – Accuracy • Other factors include the availability of: – Historical data – Computers – Time needed to gather and analyze the data – Forecast horizon
- 50. Thank you!!