# Introduction to Operations and Supply Chain Management Forecasting Why Forecast? Assess long-term capacity needs Develop budgets, hiring plans, etc. Plan production or order materials Get agreement within firm and across supply chain partners 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 2 Forecast Characteristics Almost always wrong by some amount More accurate for groups or families More accurate for shorter time periods No substitute for calculated demand. 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 3 Forecasting Approaches Qualitative Methods Quantitative Methods Used when situation is vague and little

data exists Used when situation is stable and historical data exists Involves intuition, experience Heavy use of mathematical techniques ******************************* E.g., forecasting sales of a mature product New products New technology ***************************** E.g., forecasting sales to a new market Existing products Current technology 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 4 Q2 Forecasting

Quantitative, then qualitative factors to filter the answer 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Man agement Bozarth & Handfield Chapter 10, Slide 5 Qualitative Forecasting Executive opinions Sales force composite Consumer surveys Outside opinions Delphi method 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 6 Demand Forecasting Basic time series models Linear regression For time series or causal modeling Measuring forecast accuracy Mini-case: Northcutt Bikes (A) 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 7

Time Series Models Period 1 2 3 4 5 6 7 8 Demand 12 15 11 9 10 8 14 12 What assumptions must we make to use this data to forecast? 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 8

Time Series Components of Demand . . . Demand . . . randomness Time 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 9 Time Series with . . . Demand . . . randomness and trend Time 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 10 Time series with . . . Demand . . . randomness, trend and seasonality May May

May 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield May Chapter 9, Slide 11 Idea Behind Time Series Models Distinguish between random fluctuations and true changes in underlying demand patterns. 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Man agement Bozarth & Handfield Chapter 10, Slide 12 Moving Average Models Period 1 2 3 4 5 6 7 8 Demand 12 15

11 9 10 8 14 12 n Ft 1 Dt 1 i i 1 n 3-period moving average forecast for Period 8: = = 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield (14 + 8 + 10) / 3 10.67 Chapter 9, Slide 13 Weighted Moving

Averages n Wt 1 i Dt 1 i Ft 1 i 1 n Wt 1 i i 1 Forecast for Period 8 = [(0.5 14) + (0.3 8) + (0.2 10)] / (0.5 + 0.3 + 0.1) = 11.4 What are the advantages? What do the weights add up to? Could we use different weights? Compare with a simple 3-period moving average. 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 14 Table of Forecasts and Demand Values . . . Period

Actual Demand Two-Period Moving Average Forecast Three-Period Weighted Moving Average Forecast Weights = 0.5, 0.3, 0.2 1 12 2 15 3 11 13.5 4 9 13

12.4 5 10 10 10.8 6 8 9.5 9.9 7 14 9 8.8 8 12 11

11.4 13 11.8 9 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 15 . . . and Resulting Graph 20 Volume 15 Demand 10 2-Period Avg 3-Period Wt. Avg. 5 0 1 2

3 4 5 6 7 8 9 Period Note how the forecasts smooth out variations 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 16 Exponential Smoothing I Sophisticated weight averaging model Needs only three numbers: Ft Dt = Forecast for the current period t = Actual demand for the current period t

= Weight between 0 and 1 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 17 Exponential Smoothing II Formula Ft+1 = Ft + (Dt Ft) = Dt + (1 Ft Where did the current forecast come from? What happens as gets closer to 0 or 1? Where does the very first forecast come from? 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 18 Exponential Smoothing Forecast with = 0.3 Period Actual Demand Exponential Smoothing Forecast

1 12 11.00 2 15 11.30 3 11 12.41 4 9 11.99 5 10 11.09 6

8 10.76 7 14 9.93 8 12 11.15 9 F2 = 0.312 + 0.711 = 3.6 + 7.7 = 11.3 F3 = 0.315 + 0.711.3 = 12.41 11.41 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 19

Resulting Graph 16 14 Demand 12 10 Demand 8 Forecast 6 4 2 0 1 2 3 4 5 6 7

8 9 Period 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 20 Trends What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data? 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Man agement Bozarth & Handfield Chapter 10, Slide 21 Same Exponential Smoothing Model as Before: Period Actual Demand Exponential Smoothing Forecast

1 11 11.00 2 12 11.00 3 13 11.30 4 14 11.81 5 15 12.47 6

16 13.23 7 17 14.06 8 18 14.94 9 Since the model is based on historical demand, it always lags the obvious upward trend 15.86 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 22

Adjusting Exponential Smoothing for Trend Add trend factor and adjust using exponential smoothing Needs only two more numbers: Tt = Trend factor for the current period t = Weight between 0 and 1 Then: Tt+1 = (Ft+1 Ft) + (1 ) Tt And the Ft+1 adjusted for trend is = Ft+1 + Tt+1 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 23 Simple Linear Regression Time series OR causal model Assumes a linear relationship: y y = a + b(x) x 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 24 Definitions Y = a + b(X) Y = predicted variable (i.e., demand)

X = predictor variable X can be the time period or some other type of variable (examples?) 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 25 The Trick is Determining a and b: n b xi y i xi i 1 2 n i 1 i 1 ( x i )( y i i 1 n

n n n 2 ( xi ) i 1 n a y bx 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 26 Example: Regression Used for Time Series Period (X) Demand (Y) X2 XY 1

110 1 110 2 190 4 380 3 320 9 960 4 410 16 1640 5

490 25 2450 15 1520 55 5540 15 1520 5540 5 b 98 2 15 55 5 1520 15 a 98 10 5 5 Column Sums 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain

Management Bozarth & Handfield Chapter 9, Slide 27 Resulting Regression Model: Forecast = 10 + 98Period 600 500 Y 400 Demand 300 Regression 200 100 0 1 2 3 4 5 X

2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 28 Example: Simplified Regression I If we redefine the X values so that their sum adds up to zero, regression becomes much simpler a now equals the average of the y values b simplifies to the sum of the xy products divided by the sum of the x2 values 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 29 Example: Simplified Regression II Period (X) Period (X)' Demand (Y) X2

XY 1 -2 110 4 -220 2 -1 190 1 -190 3 0 320 0 0

4 1 410 1 410 5 2 490 4 980 0 1520 10 980 0 1520 980 5

b 98 2 0 10 5 1520 0 a 98 304 5 5 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 30 Dealing with Seasonality Quarter Period Winter 02 Spring Summer Fall Winter 03 Spring Summer Fall

1 2 3 4 5 6 7 8 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Demand 80 240 300 440 400 720 700 880 Chapter 9, Slide 31 What Do You Notice? Forecasted Demand = 18.57 + 108.57 x Period Period Actual Demand Regression

Forecast Forecast Error Winter 02 1 80 90 -10 Spring 2 240 198.6 41.4 Summer 3 300 307.1

-7.1 Fall 4 440 415.7 24.3 Winter 03 5 400 524.3 -124.3 Spring 6 720 632.9 87.2

Summer 7 700 741.4 -41.4 Fall 8 880 850 30 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 32 Regression picks up trend, but not seasonality effect 1000 800 600

Demand 400 Forecast 200 0 1 2 3 4 5 6 7 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield 8 Chapter 9, Slide 33 Calculating Seasonal Index: Winter Quarter (Actual / Forecast) for Winter Quarters: Winter 02:

Winter 03: (80 / 90) = 0.89 (400 / 524.3) = 0.76 Average of these two = 0.83 Interpret! 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 34 Seasonally adjusted forecast model For Winter Quarter [ 18.57 + 108.57Period ] 0.83 Or more generally: [ 18.57 + 108.57 Period ] Seasonal Index 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 35 Seasonally adjusted forecasts Forecasted Demand = 18.57 + 108.57 x Period Period Actual

Demand Regression Forecast Demand/ Forecast Seasonal Index Seasonally Adjusted Forecast Forecast Error Winter 02 1 80 90 0.89 0.83 74.33

5.67 Spring 2 240 198.6 1.21 1.17 232.97 7.03 Summer 3 300 307.1 0.98 0.96 294.98

5.02 Fall 4 440 415.7 1.06 1.05 435.19 4.81 Winter 03 5 400 524.3 0.76 0.83 433.02

-33.02 Spring 6 720 632.9 1.14 1.17 742.42 -22.42 Summer 7 700 741.4 0.94 0.96 712.13

-12.13 Fall 8 880 850 1.04 1.05 889.84 -9.84 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 36 Would You Expect the Forecast Model to Perform This Well With Future Data? 1000 800 600 Demand

400 forecast 200 0 1 2 3 4 5 6 7 8 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 37 More Regression Models I Non-linear models Example: y = a + b ln(x)

2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 38 More Regression Models II Multiple regression More than one independent variable y y = a + b1 x + b2 z x z 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 39 Causal Models Time series assume that demand is a function of time. This is not always true. 1. Pounds of BBQ eaten at party. 2. Dollars spent on drought relief. 3. Lumber sales. Linear regression can be used in these situations as well. 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 40

Measuring Forecast Accuracy How do we know: If a forecast model is best? If a forecast model is still working? What types of errors a particular forecasting model is prone to make? Need measures of forecast accuracy 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 41 Measures of Forecast Accuracy Error = Actual demand Forecast or Et = Dt Ft 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 42 Mean Forecast Error (MFE) For n time periods where we have actual demand and forecast values: n

MFE Ei i 1 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield n Chapter 9, Slide 43 Mean Absolute Deviation (MAD) For n time periods where we have actual demand and forecast values: n MAD Ei i 1 n What does this tell us that MFE doesnt? 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield

Chapter 9, Slide 44 Example Period Demand Forecast 3 4 5 6 7 8 11 9 10 8 14 12 13.5 13 10 9.5 9 11 Error -2.5 -4.0 0 -1.5 5.0 1.0

Absolute Error 2.5 4.0 0.0 1.5 5.0 1.0 What is the MFE? The MAD? Interpret! 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 45 MFE and MAD: A Dartboard Analogy Low MFE and MAD: The forecast errors are small and unbiased 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 46 An Analogy (continued) Low MFE, but high MAD: On average, the

arrows hit the bulls eye (so much for averages!) 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 47 An Analogy (concluded) High MFE and MAD: The forecasts are inaccurate and biased 2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Management Bozarth & Handfield Chapter 9, Slide 48