Manajemen Persediaan 3- Peramalan Dani Leonidas Sumarna ,ST.MT

Agenda Metode Peramalan Kuantitatif Kesalahan Peramalan Time Series Average Exponential Smoothing Causal Regresi Kesalahan Peramalan

Metode Time Series Digunakan untuk membuat analisis detail dari pola demand masa lalu dan memproyeksikan pola tersebut untuk masa yang akan datang

Average Simple Average 𝑆𝐴= 𝑖=1 𝑛 𝐷 𝑖 𝑛 n = Jumlah periode Metoda ini merupakan model yang menggunakan data historis untuk menghitung rata-rata demand yang masa lalu, dimana rata-rata ini digunakan sebagai peramalan. Merupakan rasio antara jumlah demand dari seluruh periode dengan jumlah periode 𝑆𝐴= 𝑖=1 𝑛 𝐷 𝑖 𝑛 n = Jumlah periode Di = Demand pada periode ke-i

Time Series: Moving average The moving average model uses the last t periods in order to predict demand in period t+1. There can be two types of moving average models: simple moving average and weighted moving average The moving average model assumption is that the most accurate prediction of future demand is a simple (linear) combination of past demand.

Time series: simple moving average In the simple moving average models the forecast value is At + At-1 + … + At-n Ft+1 = n t is the current period. Ft+1 is the forecast for next period n is the forecasting horizon (how far back we look), A is the actual sales figure from each period.

What will the sales be for July? Example: forecasting sales at Kroger Kroger sells (among other stuff) bottled spring water What will the sales be for July? Month Bottles Jan 1,325 Feb 1,353 Mar 1,305 Apr 1,275 May 1,210 Jun 1,195 Jul ?

What if we use a 3-month simple moving average? AJun + AMay + AApr FJul = = 1,227 3 What if we use a 5-month simple moving average? AJun + AMay + AApr + AMar + AFeb FJul = = 1,268 5

5-month average smoothes data more; 3-month average more responsive MA forecast 3-month MA forecast What do we observe? 5-month average smoothes data more; 3-month average more responsive

Stability versus responsiveness in moving averages

Time series: weighted moving average We may want to give more importance to some of the data… Ft+1 = wt At + wt-1 At-1 + … + wt-n At-n wt + wt-1 + … + wt-n = 1 t is the current period. Ft+1 is the forecast for next period n is the forecasting horizon (how far back we look), A is the actual sales figure from each period. w is the importance (weight) we give to each period

Demand for Mercedes E-class Why do we need the WMA models? Because of the ability to give more importance to what happened recently, without losing the impact of the past. Demand for Mercedes E-class Time Jan Feb Mar Apr May Jun Jul Aug Actual demand (past sales) Prediction when using 6-month SMA Prediction when using 6-months WMA For a 6-month SMA, attributing equal weights to all past data we miss the downward trend

What will be the sales for July? Example: Kroger sales of bottled water What will be the sales for July? Month Bottles Jan 1,325 Feb 1,353 Mar 1,305 Apr 1,275 May 1,210 Jun 1,195 Jul ?

6-month simple moving average… AJun + AMay + AApr + AMar + AFeb + AJan FJul = = 1,277 6 In other words, because we used equal weights, a slight downward trend that actually exists is not observed…

What if we use a weighted moving average? Make the weights for the last three months more than the first three months… 6-month SMA WMA 40% / 60% 30% / 70% 20% / 80% July Forecast 1,277 1,267 1,257 1,247 The higher the importance we give to recent data, the more we pick up the declining trend in our forecast.

Smoothing constant alpha α Time Series: Exponential Smoothing (ES) Main idea: The prediction of the future depends mostly on the most recent observation, and on the error for the latest forecast. Smoothing constant alpha α Denotes the importance of the past error

Why use exponential smoothing? Uses less storage space for data Extremely accurate Easy to understand Little calculation complexity There are simple accuracy tests

Exponential smoothing: the method Assume that we are currently in period t. We calculated the forecast for the last period (Ft-1) and we know the actual demand last period (At-1) … The smoothing constant α expresses how much our forecast will react to observed differences… If α is low: there is little reaction to differences. If α is high: there is a lot of reaction to differences.

Example: bottled water at Kroger Month Actual Forecasted Jan 1,325 1,370 Feb 1,353 1,361 Mar 1,305 1,359 Apr 1,275 1,349 May 1,210 1,334 Jun ? 1,309  = 0.2 =1,334+(0,2X(1,21-1,334))

Example: bottled water at Kroger Month Actual Forecasted Jan 1,325 1,370 Feb 1,353 1,334 Mar 1,305 1,349 Apr 1,275 1,314 May 1,210 1,283 Jun ? 1,225  = 0.8 =1,283+(0,8X(1,21-1,283))

Impact of the smoothing constant

Soal Latihan Lakukan peramalan menggunakan SMA 3 periode SMA 5 periode periode waktu Nilai Pengamatan   Aktual 1 200 2 135 3 195 4 197 5 310 6 175 7 155 8 130 9 220 10 277 11 235 12 - Lakukan peramalan menggunakan SMA 3 periode SMA 5 periode WMA 5 periode (30(2):70(3)) Eksponential smoothing alpha 0,1;0,5; dan 0,9

Jawaban

dependent variable = a + b  (independent variable) Linear regression in forecasting Linear regression is based on Fitting a straight line to data Explaining the change in one variable through changes in other variables. dependent variable = a + b  (independent variable) By using linear regression, we are trying to explore which independent variables affect the dependent variable

Example: do people drink more when it’s cold? Alcohol Sales Which line best fits the data? Average Monthly Temperature

The best line is the one that minimizes the error The predicted line is … So, the error is … Where: ε is the error y is the observed value Y is the predicted value

Least Squares Method of Linear Regression The goal of LSM is to minimize the sum of squared errors…

What does that mean? Alcohol Sales ε Alcohol Sales So LSM tries to minimize the distance between the line and the points! Average Monthly Temperature

Least Squares Method of Linear Regression Then the line is defined by

Contoh Soal Berikut ini data mengenai pengalaman kerja dan penjualan X=pengalaman kerja (tahun) Y=omzet penjualan (ribuan) Tentukan nilai a dan b!

Koefisien determinasi (R2)

Diperoleh nilai a = 3,25 dan nilai b = 1,25 Persamaan regresi linearnya adalah Y=3,25+1,25X

We need a metric that provides estimation of accuracy How can we compare across forecasting models? We need a metric that provides estimation of accuracy Forecast Error Errors can be: biased (consistent) random Forecast error = Difference between actual and forecasted value (also known as residual)

Kesalahan Peramalan Beberapa metode lebih ditentukan untuk meringkas kesalahan (error) yang dihasilkan oleh fakta (keterangan) pada teknik peramalan. Sebagian besar dari pengukuran ini melibatkan rata-rata beberapa fungsi dari perbedaan antara nilai aktual dan nilai peramalannya. Perbedaan antara nilai observasi dan nilai ramalan ini sering dimaksud sebagai residual.

Measuring Accuracy: MFE MFE = Mean Forecast Error (Bias) It is the average error in the observations 1. A more positive or negative MFE implies worse performance; the forecast is biased.

Measuring Accuracy: MAD MAD = Mean Absolute Deviation It is the average absolute error in the observations 1. Higher MAD implies worse performance. 2. If errors are normally distributed, then σε=1.25MAD

MFE & MAD: A Dartboard Analogy Low MFE & MAD: The forecast errors are small & unbiased

An Analogy (cont’d) Low MFE but high MAD: On average, the arrows hit the bullseye (so much for averages!)

MFE & MAD: An Analogy High MFE & MAD: The forecasts are inaccurate & biased

Forecast must be measured for accuracy! Key Point Forecast must be measured for accuracy! The most common means of doing so is by measuring the either the mean absolute deviation or the standard deviation of the forecast error

Measuring Accuracy: Tracking signal The tracking signal is a measure of how often our estimations have been above or below the actual value. It is used to decide when to re-evaluate using a model. Positive tracking signal: most of the time actual values are above our forecasted values Negative tracking signal: most of the time actual values are below our forecasted values If TS > 4 or < -4, investigate!

Question: Which one is better? Example: bottled water at Kroger Month Actual Forecast Jan 1,325 1,370 Feb 1,353 1,361 Mar 1,305 1,359 Apr 1,275 1,349 May 1,210 1,334 Jun 1,195 1,309 Month Actual Forecast Jan 1,325 1370 Feb 1,353 1306 Mar 1,305 1334 Apr 1,275 1290 May 1,210 1251 Jun 1,195 1175 Metoda A Metode B Question: Which one is better?

Bottled water at Kroger: compare MAD and TS Metode A 69,83 - 6 Metode B 32,83 - 1,92 We observe that B performs a lot better than A Conclusion: Probably there is trend in the data which A cannot capture

Which Forecasting Method Should You Use Gather the historical data of what you want to forecast Divide data into initiation set and evaluation set Use the first set to develop the models Use the second set to evaluate Compare the MADs and MFEs of each model

Eksponential Smoothing Jadi,,pilih metode yang mana?? (hitung MAD dan TS untuk masing-masing hasil peramalan) Periode waktu Nilai Pengamatan SMA (3 periode) SMA (5 periode) WMA (5 periode) Eksponential Smoothing   Aktual (30:70) α = 0,1 α = 0,5 α = 0,9 1 200 - 2 135 3 195 193,50 167,50 141,50 4 197 176,67 193,65 181,25 189,65 5 310 175,67 193,99 189,13 196,27 6 175 234,00 207,40 214,05 205,59 249,56 298,63 7 155 227,33 202,40 208,63 202,53 212,28 187,36 8 130 213,33 206,40 208,13 197,78 183,64 158,24 9 220 153,33 193,40 183,38 191,00 156,82 132,82 10 277 168,33 198,00 190,58 193,90 188,41 211,28 11 235 209,00 191,40 195,80 202,21 232,71 270,43 12 244,00 203,40 213,55 205,49 233,85 238,54

Eksponential Smoothing Nilai Pengamatan SMA (3 periode) SMA (5 periode) WMA (5 periode) Eksponential Smoothing Aktual   (30:70) α = 0,1 α = 0,5 α = 0,9 175,00 234,00 207,40 214,05 205,59 249,56 298,63 155,00 227,33 202,40 208,63 202,53 212,28 187,36 130,00 213,33 206,40 208,13 197,78 183,64 158,24 220,00 153,33 193,40 183,38 191,00 156,82 132,82 277,00 168,33 198,00 190,58 193,90 188,41 211,28 235,00 209,00 191,40 195,80 202,21 232,71 270,43 MAD 35,33 24,83 25,10 23,83 34,96 54,44 TS -4,40 -6,00 -4,96 -3,83