Exponential Smoothing 1 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Chapter 7 Demand Forecasting in a Supply Chain Forecasting -2 Exponential Smoothing Ardavan Asef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs, Chase, and Aquilano Supply Chain Management: Chopra and Meindl

Exponential Smoothing 2 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Time Series Methods  Moving Average  Discard old records  Assign same weight for recent records  Assign different weights  Weighted moving average  Exponential Smoothing

Exponential Smoothing 3 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing

Exponential Smoothing 4 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing α=0.2 t At Ft A1  F Since I have no information for F2, I just enter A1 which is 100. Alternatively we may assume the average of all available data as our forecast for period F3 =(1-α)F2 + α A2 F3 =0.8(100) + 0.2(150) F3 = = F2 & A2  F3 A1  F2A1 & A2  F3 F3 =(1-α)F2 + α A2

Exponential Smoothing 5 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing α=0.2 t At Ft F4 =(1-α)F3 + α A3 F4 =0.8(110) + 0.2(120) F4 = = 112 A3 & F3  F4 A1 & A2  F3A1& A2 & A3  F F4 =(1-α)F3 + α A3

Exponential Smoothing 6 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Example: Forecast for week 9 using  = 0.1 WeekDemand Forecast

Exponential Smoothing 7 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Week 4 WeekDemandForecast

Exponential Smoothing 8 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Exponential Smoothing WeekDemandForecast

Exponential Smoothing 9 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Two important questions  How to choose  ? Large  or Small  When does it work? When does it not?  What is better exponential smoothing OR moving average?

Exponential Smoothing 10 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 The Same Example:  = 0.4 WeekDemandForecast

Exponential Smoothing 11 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Comparison

Exponential Smoothing 12 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Comparison  As  becomes larger, the predicted values exhibit more variation, because they are more responsive to the demand in the previous period.  A large  seems to track the series better.  Value of stability  This parallels our observation regarding MA: there is a trade-off between responsiveness and smoothing out demand fluctuations.

Exponential Smoothing 13 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Comparison WeekDemand Forecast for 0.1 alpha AD Forecast for 0.4 alphaAD Choose the forecast with lower MAD.

Exponential Smoothing 14 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Which  to choose?  In general want to calculate MAD for many different values of  and choose the one with the lowest MAD.  Same idea to determine if Exponential Smoothing or Moving Average is preferred.  Note that one advantage of exponential smoothing requires less data storage to implement.

Exponential Smoothing 15 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Pieces of Data and Age of Data in Exponential Smoothing F t = a A t–1 + (1 – a) F t–1 F t–1 = a A t–2 + (1 – a) F t–2, etc F t = aA t–1 +(1–a)aA t–2 +(1–a) 2 F t–2 = aA t–1 +(1–a)aA t–2 +(1–a) 2 aA t–3 +(1–a) 3 aA t–4 +(1–a) 4 aA t–5 +(1–a) 5 aA t–6 +(1–a) 6 aA t–7 +…  A large number of data are taken into account– All data are taken into account in ES.  “Age” of data is about 1/  periods 

Exponential Smoothing 16 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 What is better? Exponential Smoothing or Moving Average  If we set  = 2/(N+1), then MA and ES are approximately equivalent.  What does it mean that the two systems are equivalent?  The variances of the errors are identical.  Does it mean that the two systems have the same forecasts?  Exponential smoothing requires less data storage to implement.

Exponential Smoothing 17 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Compute MAD & TS

Exponential Smoothing 18 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Data Table Excel Data, what if, Data table Min, conditional formatting This is a one variable Data Table

Exponential Smoothing 19 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Office Buttton

Exponential Smoothing 20 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Add-Inns

Exponential Smoothing 21 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Not OK, but GO, then Check Mark Solver

Exponential Smoothing 22 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Data Tab/ Solver

Exponential Smoothing 23 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Target Cell/Changing Cells

Exponential Smoothing 24 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Optimal  Minimal MAD

Exponential Smoothing 25 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Associative (Causal) Forecasting The primary method for associative forecasting is Regression Analysis. The relationship between a dependent variable and one or more independent variables. The independent variables are also referred to as predictor variables. We only discuss linear regression between two variables. We consider the relationship between the dependent variable (demand) and the independent variable (time).

Exponential Smoothing 26 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Regression Method Least Squares Line minimizes sum of squared deviations around the line Computed relationship

Exponential Smoothing 27 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Regression: Chart the Data

Exponential Smoothing 28 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Regression: The Same as Solver but This Time Data Analysis

Exponential Smoothing 29 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Data/Data Analysis/ Regression

Exponential Smoothing 30 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Regression: Tools / Data Analysis / Regression

Exponential Smoothing 31 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Regression Output F t = t Forecast for the next period. F11 = (11) = 431.7

Exponential Smoothing 32 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Assignment. Problem 1. Due at the beginning of the next class Linear regression 5 period moving average Exponential smoothing. α=.2 March forecast=19 Naive method Compute MAD for naive method and exponential smoothing. Which one is preferred? NM or ES? Based on the data below forecast the demand for September using the listed techniques:

Exponential Smoothing 33 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Assignment Problem 2 Due at the beginning of the next class (a) Exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be 5 units larger than actual demand. The next forecast is 65. Compute  ? (b) The 5-period moving average in month 6 was 150 units. Actual demand in month 7 is 180 units. What is the 6 period moving average in month 7?

Exponential Smoothing 34 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Practice The president of State University wants to forecast student enrollments for this academic year based on the following historical data: 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 Last year 21,000 What is the forecast for this year using exponential smoothing with α = 0.4, if the forecast for two years ago was 16,000?

Exponential Smoothing 35 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Practice t A t F t Forecast for last year F 5 = (1-α)F4+ α(A4) F 5 =.6(16000)+.4(20000)=17600 Forecast for this year F 6 = (1-α)F5+ α(A5) F 6 =.6(17600)+.4(21000)=

Exponential Smoothing 36 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Practice ……… For your own practice Based on the data below forecast the total number of new customers in year 9. Use the listed techniques: Linear regression (show equation) 4 period moving average Exponential Smoothing. α=.3 Year 3 forecast=43 Naive method Compute MAD for naive method and exponential smoothing. Which one is preferred? NM or ES? YearCustomers