Forecasting

Chapter Objectives Be able to: Discuss the importance of forecasting and identify the most appropriate type of forecasting approach, given different forecasting situations. Apply a variety of time series forecasting models, including moving average, exponential smoothing, and linear regression models. Develop causal forecasting models using linear regression and multiple regression. Calculate measures of forecasting accuracy and interpret the results.

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 (CPFR, discussed later)

Types of Forecasts Demand Supply Price Firm-level Market-level Materials Labor supply Price Cost of supplies and services Cost of money — interest rates, currency rates Market price for firm’s product or service

Forecast Laws Almost always wrong by some amount More accurate for shorter time periods More accurate for groups or families No substitute for calculated values.

Qualitative Forecasting Executive opinions Sales force composite Consumer surveys Outside opinions Delphi method Life cycle analogy* The various phases of the life cycle are discussed in detail in the presentation for Chapter 7. These can be used if needed to expand on this forecasting consideration. *See accompanying notes

Forecasting Approaches Qualitative Methods Used when situation is vague and little data exists New products New technology Involves intuition, experience ***************************** E.g., forecasting sales to a new market Quantitative Methods Used when situation is ‘stable’ and historical data exists Existing products Current technology Heavy use of mathematical techniques ******************************* E.g., forecasting sales of a mature product

Quantitative, then qualitative factors to “filter” the answer “Q2” Forecasting Quantitative, then qualitative factors to “filter” the answer

Demand Forecasting Uses historical data Basic time series models Linear regression For time series or causal modeling Measuring forecast accuracy

Time Series Models What assumptions must we make to use this data to Period Demand 1 12 2 15 3 11 4 9 5 10 6 8 7 14 8 12 What assumptions must we make to use this data to forecast?

Time Series Components of Demand . . . . . . randomness Time

Time Series with . . . Demand . . . randomness and trend Time

Time series with . . . . . . randomness, trend, and seasonality Demand Class discussion: what could account for this? Lawnmower sales? Camping trailer sales? Vacation package sales? May May May May

Idea Behind Time Series Models Distinguish between random fluctuations and true changes in underlying demand patterns.

 Moving Average Models Period Demand 1 12 2 15 3 11 4 9 5 10 6 8 7 14 1 12 2 15 3 11 4 9 5 10 6 8 7 14 8 12  3-period moving average forecast for Period 8: = (14 + 8 + 10) / 3 = 10.67

Weighted Moving Averages Forecast for Period 8 = [(0.5  14) + (0.3  8) + (0.2  10)] / (0.5 + 0.3 + 0.2) = 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. The heaviest weight is typically applied to the most recent data. If weights add up to 1.0, the denominator disappears as shown in the text. However, arbitrary weighting values like 4,3, and 1 can be used as long as the weighted demand sum is divided by the sum of the weights.

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 10.8 6 8 9.5 9.9 7 14 8.8 11.4 11.8

. . . and Resulting Graph Note how the forecasts smooth out demand variations

Exponential Smoothing I Sophisticated weight averaging model Needs only three numbers: Ft = Forecast for the current period t Dt = Actual demand for the current period t a = Weight between 0 and 1

Exponential Smoothing II Formula Ft+1 = Ft + a (Dt – Ft) = a × Dt + (1 – a) × Ft Where did the current forecast come from? What happens as a gets closer to 0 or 1? Where does the very first forecast come from? Very first forecast is often set equal to the actual demand to start the process. An alternate approach is to set the first forecast to the moving average of the previous two or three months. Alpha should be large if the demand data is relatively stable, small if the demand data varies quite a bit. Otherwise it takes a long time for the forecast to converge on relatively smooth demand (overdamped correction) and the forecast overshoots the variations for fluctuating demand (underdamped correction)

Exponential Smoothing Forecast with a = 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 11.15   11.41 F2 = 0.3×12 + 0.7×11 = 3.6 + 7.7 = 11.3 F3 = 0.3×15 + 0.7×11.3 = 12.41

Resulting Graph

Trends What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data?

Same Exponential Smoothing Model as Before: Period Actual Demand Exponential Smoothing Forecast 1 11 11.00 2 12 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   15.86 Since the model is based on historical demand, it always lags the obvious upward trend

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

Simple Linear Regression Time series OR causal model Assumes a linear relationship: y = a + b(x) y x

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?)

The Trick is Determining a and b:

Example: Regression Used for Time Series Period (X) Demand (Y) X2 XY 1 110 2 190 4 380 3 320 9 960 410 16 1640 5 490 25 2450 15 1520 55 5540 Column Sums

Resulting Regression Model: Forecast = 10 + 98×Period

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

Example: Simplified Regression II Period (X) Period (X)' Demand (Y) X2 XY 1 -2 110 4 -220 2 -1 190 -190 3 320 410 5 490 980 1520 10

Dealing with Seasonality Quarter Period Demand Winter 02 1 80 Spring 2 240 Summer 3 300 Fall 4 440 Winter 03 5 400 Spring 6 720 Summer 7 700 Fall 8 880

What Do You Notice? Forecasted Demand = –18.57 + 108.57 x 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 6 720 632.9 87.2 7 700 741.4 -41.4 8 880 850 30

Regression picks up trend, but not seasonality effect

Calculating Seasonal Index: Winter Quarter (Actual / Forecast) for Winter Quarters: Winter ‘02: (80 / 90) = 0.89 Winter ‘03: (400 / 524.3) = 0.76 Average of these two = 0.83 Interpret! The normal trend line prediction needs to be adjusted downward for Winter quarters.

Seasonally adjusted forecast model For Winter Quarter [ –18.57 + 108.57×Period ] × 0.83 Or more generally: [ –18.57 + 108.57 × Period ] × Seasonal Index

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 0.76 433.02 -33.02 6 720 632.9 1.14 742.42 -22.42 7 700 741.4 0.94 712.13 -12.13 8 880 850 1.04 889.84 -9.84

Would You Expect the Forecast Model to Perform This Well With Future Data?

More Regression Models I Non-linear models Example: y = a + b × ln(x)

More Regression Models II Multiple regression More than one independent variable y y = a + b1 × x + b2 × z x z

Causal Models Time series models 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.

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

Measures of Forecast Accuracy Error = Actual demand – Forecast or Et = Dt – Ft

Mean Forecast Error (MFE) For n time periods where we have actual demand and forecast values:

Mean Absolute Deviation (MAD) For n time periods where we have actual demand and forecast values: Comments about how negative errors cancel positive errors in MFE, showing bias. MAD, on the other hand shows the average offset of the error. What does this tell us that MFE doesn’t?

Example What is the MFE? The MAD? Interpret! MFE = – 2/6 = – 0.33

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

An Analogy (continued) Low MFE, but high MAD: On average, the darts hit the bulls eye (so much for averages!)

An Analogy (concluded) High MFE and MAD: The forecasts are inaccurate and biased

Collaborative Planning, Forecasting, and Replenishment (CPFR) Supply chain partners, supported by information technology, working together

CPFR Elements Mutual business objectives & measures Joint sales and operations plans Collaboration on sales forecasts & replenishment plans Electronic interchange of information

Case Study in Forecasting Top-Slice Drivers