Forecasting tools

Forecasting toolsRalins AIIM KHCCB Summer Internship

Forecasting & its ImportanceScientific prediction of futureForecast will not be 100% accurate but challenge lies in increasing forecast accuracyIntegral part of decision making and affects all the departmentsShould account for seasonality/ exceptions/ exclusions if requiredOBJECTIVE: Apply various forecasting techniques to historical data and find best fit method for each levels

Forecasting methods (quantitative) Time Series methods (Models that are most appropriate when future demand is expected to follow historical patterns)NaveMoving averageWeighted Moving AverageLinear RegressionExponential SmoothingHolts modelBasic model seasonalityWinters modelMedian method

Nave model(level, trend, seasonality)Simple and widely used.Does not need any complex calculationsFollows demand with a lagEg:

PeriodDemandForecast1252322532432428245262862726727

Moving AverageEliminates old data and concentrates on recent dataResponsiveness captured best when less data points consideredGives equal weightage to all the data consideredStability Vs ResponsivenessShould I use a 2-period moving average or a 3-period moving average? Larger the n, more stable the forecast2-period model will be more responsive to changeBalance stability with responsiveness

Weighted Moving AverageHistorical values of the time series are assigned different weights when performing forecast

= w1Ft + w2Ft-1 + w3Ft-2 + + wnFt-n+1Swi = 1

Linear Regression(level, trend, seasonality) If data follows a trend ( increasing/decreasing) we can try to fit with approximate linear equationUsing regression (or by simultaneous equation),a (intercept) and b(slope) can be found outForecast = a + btLine of best fitTimeDemandForecast12625.9523822827.638132929.3238143131.0095253232.6952463534.38095736.07

Exponential smoothingConsiders all the data pointsAcceptable weightIncreasing weight to more recent dataF(t+1) = Dt + (1-)FtFt+1 = Dt + (1 - ) Ft = Dt + (1 - ) ( Dt-1 + (1 - ) Ft-1) = Dt + (1 - )( )Dt-1 + (1 - )2 ( )Dt - 2 + . . .

Optimal value of has be found so as error is reducedPeriodDemandForecast1252723226.632427.6842826.94452627.155262726.92416726.93933

Holts modelIn Linear regression all data have equal weightagePerform exponential smoothing which captures trendRedefine slope at every pointInitialize , valuesFt+1 = at + btat = Dt + (1-)(at-1 + bt-1)bt = (at - at-1) + (1-)bt-1TimeDemandabForecast12626222827.841.8127.8032929.521.7729.6543131.241.7631.2953232.791.7032.9963534.591.7334.49736.317

Basic model Seasonality(level, trend, seasonality) Observe a increasing trend in the yearly dataFind out seasonality index (% demand in particular season)Using regression find out linear equation and find total demand for next yearMultiply the seasonality index for each(re-season)Demand dataFt = 141 + 16(t)Year 1Year 2Year 3Forecasted Data for year 4Quarter 153586268.39Quarter 222252729.21Quarter 337404447.81Quarter 445505659.58Sum157173189205seasonality indexYear 1Year 2Year 3averageQuarter 10.3380.3350.3280.334Quarter 20.1400.1450.1430.142Quarter 30.2360.2310.2330.233Quarter 40.2870.2890.2960.291

Basic model Seasonality(level, trend, seasonality)

Winters modelSame as basic model seasonality but incorporating exponential smoothingAlpha, beta and gamma are smoothing constantsP is the number of periods after a cycle repeats(here 4 quarters)Very good for seasonal demandat+1 = (Dt+1/Ct+1) + (1-)(at+bt) (level)

bt+1 = (at+1 - at) + (1-)bt (trend)

ct+p+1 = (Dt+1/at+1) + (1-)ct+1 (seasonality)

Ft+1 = (at + bt) * ct+1 (Forecast)

Demand dataYear 1Year 2Year 3ForecastQuarter 153586267.1982244Quarter 222252728.6918108Quarter 337404447.884197Quarter 445505659.7177333Sum157173189203.49Winters model

Dynamic smoothing factorsExponential smoothing, Holts and Winters model has constant smoothing factors It has been made dynamic with respect to the data for every set of 52 weeksAs smoothing factors optimized the forecast accuract has been improvedThank You!!!

Sales DataWallace Garden SupplyForecastingPeriodActual ValueThree-Month Moving AveragesJanuary10February12March16April1310+12+16/3=12.67May1712+16+13/3=13.67June1916+13+17/3=15.33July1513+17+19/3=16.33August2017+19+15/3=17.00September2219+15+20/3=18.00October1915+20+22/3=19.00November2120+22+19/3=20.33December1922+19+21/3=20.67

Storage Shed Sales

Wallace ForecastWallace Garden SupplyForecasting3 period moving averageInput DataForecast Error AnalysisPeriodActual ValueForecastErrorAbsolute errorSquared errorAbsolute % errorMonth 110Month 212Month 316Month 41312.6670.3330.3330.1112.56%Month 51713.6673.3333.33311.11119.61%Month 61915.3333.6673.66713.44419.30%Month 71516.333-1.3331.3331.7788.89%Month 82017.0003.0003.0009.00015.00%Month 92218.0004.0004.00016.00018.18%Month 101919.0000.0000.0000.0000.00%Month 112120.3330.6670.6670.4443.17%Month 121920.667-1.6671.6672.7788.77%Average2.0006.07410.61%Next period19.667MADMSEMAPE

Enter the data in the cells shaded YELLOW.Actual Value - Forecast

Graph1012161312.66666666671713.66666666671915.33333333331516.33333333332017221819192120.33333333331920.6666666667

Actual ValueForecastTimeValue3 period moving average

NaiveWallace Garden SupplyForecastingPeriodActual ValueNave ForecastErrorAbsolute ErrorPercent ErrorSquared ErrorJanuary10N/AFebruary12102216.67%4.0March16124425.00%16.0April1316-3323.08%9.0May17134423.53%16.0June19172210.53%4.0July1519-4426.67%16.0August20155525.00%25.0September2220229.09%4.0October1922-3315.79%9.0November2119229.52%4.0December1921-2210.53%4.00.818317.76%10.091BIASMADMAPEMSEStandard Error (Square Root of MSE) =3.176619129

Storage Shed Sales

Naive Graph12101612131617131917151920152220192221191921

Actual ValueNave ForecastPeriodShedsWallace Garden - Naive Forecast

Sales DataWallace Garden SupplyForecastingPeriodActual ValueThree-Month Moving AveragesJanuary10February12March16April1310+12+16/3=12.67May1712+16+13/3=13.67June1916+13+17/3=15.33July1513+17+19/3=16.33August2017+19+15/3=17.00September2219+15+20/3=18.00October1915+20+22/3=19.00November2120+22+19/3=20.33December1922+19+21/3=20.67

Storage Shed Sales

Moving AvgWallace Garden SupplyForecasting3 period moving averageInput DataForecast Error AnalysisPeriodActual ValueForecastErrorAbsolute errorSquared errorAbsolute % errorMonth 110Month 212Month 316Month 41312.6670.3330.3330.1112.56%Month 51713.6673.3333.33311.11119.61%Month 61915.3333.6673.66713.44419.30%Month 71516.333-1.3331.3331.7788.89%Month 82017.0003.0003.0009.00015.00%Month 92218.0004.0004.00016.00018.18%Month 101919.0000.0000.0000.0000.00%Month 112120.3330.6670.6670.4443.17%Month 121920.667-1.6671.6672.7788.77%Average12.0002.0006.07410.61%Next period19.667BIASMADMSEMAPE

Enter the data in the cells shaded YELLOW.Actual Value - Forecast

Moving Avg (4)Wallace Garden SupplyForecasting4 period moving averageInput DataForecast Error AnalysisPeriodActual ValueForecastErrorAbsolute errorSquared errorAbsolute % errorMonth 110Month 212Month 316Month 413Month 51712.7504.2504.25018.06325.00%Month 61914.5004.5004.50020.25023.68%Month 71516.250-1.2501.2501.5638.33%Month 82016.0004.0004.00016.00020.00%Month 92217.7504.2504.25018.06319.32%Month 101919.0000.0000.0000.0000.00%Month 112119.0002.0002.0004.0009.52%Month 121920.500-1.5001.5002.2507.89%Average16.2502.71910.02314.22%Next period20.250BIASMADMSEMAPE

Enter the data in the cells shaded YELLOW.Actual Value - ForecastInterpreting forecast errors:The 3 period is a better predictor because the MAPE is 10.61% compared to 14.22% in the 4 period model.

Graph1012161312.66666666671713.66666666671915.33333333331516.33333333332017221819192120.33333333331920.6666666667

Actual ValueForecastTimeValueThree Period Moving Average

Wt Mov Avg DataWallace Garden SupplyForecastingPeriodActual ValueWeightsThree-Month Weighted Moving AveragesJanuary100.222February120.593March160.185April132.2175708026+7.1129516993+2.9679511168/1=12.298May172.6610849631+9.483935599+2.4114602824/1=14.556June193.5481132842+7.7056976742+3.1534480616/1=14.407July152.8828420434+10.076681574+3.5244419512/1=16.484August203.7698703644+11.2621735239+2.782454172/1=17.814September224.213384525+8.8911896241+3.709938896/1=16.815October193.3263562039+11.8549194988+4.0809327856/1=19.262November214.4351416052+13.0404114487+3.5244419512/1=21.000December194.8786557657+11.2621735239+3.8954358408/1=20.036Next period20.185Sum of weights =1.000

Storage Shed Sales

Wt Move AvgWallace Garden SupplyForecasting3 period weighted moving averageInput DataForecast Error AnalysisPeriodActual valueWeightsForecastErrorAbsolute errorSquared errorAbsolute % errorMonth 1100.222Month 2120.593Month 3160.185Month 41312.2980.7020.7020.4925.40%Month 51714.5562.4442.4445.97114.37%Month 61914.4074.5934.59321.09324.17%Month 71516.484-1.4841.4842.2029.89%Month 82017.8142.1862.1864.77610.93%Month 92216.8155.1855.18526.88923.57%Month 101919.262-0.2620.2620.0691.38%Month 112121.0000.0000.0000.0000.00%Month 121920.036-1.0361.0361.0745.45%Average1.9886.9526.95210.57%Next period20.185BIASMADMSEMAPESum of weights =1.000