Chapter 7 Demand Forecasting in a Supply Chain

1. Forecasting -2 Exponential Smoothing ArdavanAsef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs, Chase, and Aquilano Supply Chain Management: Chopra and Meindl Chapter 7Demand Forecastingin a Supply Chain

2. Time Series Methods • Moving Average • Exponential Smoothing • More sophisticated techniques available

3. How did we use data • Moving average • Discard old records • Assign same weight for recent records • Advantage? Disadvantage? • Assign different weights • Weighted moving average • For example

4. Exponential Smoothing

5. Exponential Smoothing α=0.2 1 100 100 2 100 3 110 t At Ft 150 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 2. A1  F2 F3 =(1-α)F2 + α A2 F3 =0.8(100) + 0.2(150) F3 =80 + 30 = 110 F3 =(1-α)F2 + α A2 F2 & A2  F3 A1  F2 A1 & A2  F3

6. Exponential Smoothing α=0.2 3 110 1 100 100 2 150 100 4 112 t At Ft 120 F4 =(1-α)F3 + α A3 F4 =0.8(110) + 0.2(120) F4 =88 + 24 = 112 A3 & F3  F4 F4 =(1-α)F3 + α A3 A1 & A2  F3 A1& A2 & A3  F4

7. How do we pick ? • Large  • When does it work? • When does it not? • Small  • When does it work? • When does it not?

8. Given a = 0.1. What is the forecast for week 9?

9. Exponential Smoothing

10. Exponential Smoothing

11. Exponential Smoothing Similarly we get:

12. Two important questions • How to choosea? • What is better exponential smoothing • OR moving average?

13. Exponential Smoothing: a= 0.4

14. Comparison

15. Comparison • As a becomes larger, the predicted values exhibit more variation, because they are more responsive to the demand in the previous period. • A large a 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.

16. Comparison Choose the forecast with lower MAD.

17. Which a to choose? • In general want to calculate MAD for many different values of a 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.

18. Pieces of Data and Age of Data in Exponential Smoothing • Ft = a At–1 + (1 – a) Ft–1 • Ft–1 = a At–2 + (1 – a) Ft–2, etc • Ft = aAt–1+(1–a)aAt–2+(1–a)2Ft–2 • = aAt–1+(1–a)aAt–2+(1–a)2aAt–3 +(1–a)3aAt–4 • +(1–a)4aAt–5+(1–a)5aAt–6 +(1–a)6aAt–7+… • A large number of data are taken into account– All data are taken into account in ES. • “Age” of data is about 1/a periods.

19. What is better? Exponential Smoothing or Moving Average • If we set a = 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.

20. Compute MAD & TS

21. Data Table Excel Data, what if, Data table This is a one variable Data Table Min, conditional formatting

22. Office Buttton

23. Add-Inns

24. Not OK, but GO, then Check Mark Solver

25. Data Tab/ Solver

26. Target Cell/Changing Cells

27. Optimal a Minimal MAD

28. 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).

29. Regression Method Computedrelationship Least Squares Line minimizes sum of squared deviations around the line

30. Regression: Chart the Data

31. Regression: The Same as Solver but This Time Data Analysis

32. Data/Data Analysis/ Regression

33. Regression: Tools / Data Analysis / Regression

34. Regression Output Ft = 94.13 +30.71t Forecast for the next period. F11 = 94.13 +30.71(11) = 431.7

35. Assignment ….. Due at the beginning of the next class Based on the data below forecast the demand for September using the listed techniques: • 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?

36. Assignment ….. 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? (c) Tickets numbered from 100 to 200 have been sold. Using the random number rand() = 0.35 identify the winner.

37. 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?

38. Practice t 1 2 3 4 5 At 15000 16000 18000 20000 21000 17600 Ft 16000 Forecast for last year F5 = (1-α)F4+α(A4) F5 = .6(16000)+.4(20000)=17600 Forecast for this year F6 = (1-α)F5+α(A5) F6 = .6(17600)+.4(21000)=18960

39. 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?