Lecture 3 Forecasting CT – Chapter 3

Forecast A statement about the future value of a variable of interest such as demand. Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing Operations Product / service design

Uses of Forecasts Accounting Cost/profit estimates Finance Cash flow and funding Human Resources Hiring/recruiting/training Marketing Pricing, promotion, strategy Operations Schedules, MRP, workloads Product/service design New products and services

Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Prepare the forecast Step 6 Monitor the forecast “The forecast”

Types of Forecasts Judgmental - uses subjective inputs Time series - uses historical data assuming the future will be like the past Associative models - uses explanatory variables to predict the future

Judgmental Forecasts Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method Opinions of managers and staff Achieves a consensus forecast

Time Series Forecasts Trend - long-term movement in data Seasonality - short-term regular variations in data Cycle – wavelike variations of more than one year’s duration Irregular variations - caused by unusual circumstances

Forecast Variations Figure 3.1 Trend Cycles Irregular variation 90 89 88 Seasonal variations

Smoothing/Averaging Methods Used in cases in which the time series is fairly stable and has no significant trend, seasonal, or cyclical effects Purpose of averaging - to smooth out the irregular components of the time series. Four common smoothing/averaging methods are: Moving averages Weighted moving averages Exponential smoothing

Example of Moving Average Sales of gasoline for the past 12 weeks at your local Chevron (in ‘000 gallons). If the dealer uses a 3-period moving average to forecast sales, what is the forecast for Week 13? Past Sales Week Sales Week Sales 1 17 7 20 2 21 8 18 3 19 9 22 4 23 10 20 5 18 11 15 6 16 12 22

Management Scientist Solutions MA(3) for period 4 = (17+21+19)/3 = 19 Forecast error for period 3 = Actual – Forecast = 23 – 19 = 4

MA(5) versus MA(3)

Review of last class Forecasting Smoothing/averaging method What is a forecast? Organizational functions that use forecasts Desirable characteristics of a forecast Types of forecasts Types of time series Smoothing/averaging method Moving averages Weighted moving averages Advantage

Exponential Smoothing Premise - The most recent observations might have the highest predictive value. Therefore, we should give more weight to the more recent time periods when forecasting.

Exponential Smoothing Ft+1 = Ft + (At - Ft) Weighted averaging method based on previous forecast plus a percentage of the forecast error A-F is the error term,  is the % feedback

Picking a Smoothing Constant  .1 .4 Actual

Suitable for time series data that exhibit a long term linear trend Linear Trend Equation Suitable for time series data that exhibit a long term linear trend Ft Ft = a + bt a Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line 0 1 2 3 4 5 t

Sale increases every time period @ 1.1 units Linear Trend Example Linear trend equation F11 = 20.4 + 1.1(11) = 32.5 Sale increases every time period @ 1.1 units

Actual/Forecasted sales Actual vs Forecast Linear Trend Example 35 30 25 Actual/Forecasted sales 20 Actual 15 Forecast 10 5 1 2 3 4 5 6 7 8 9 10 Week F(t) = 20.4 + 1.1t

Forecasting with Trends and Seasonal Components – An Example Business at Terry's Tie Shop can be viewed as falling into three distinct seasons: (1) Christmas (November-December); (2) Father's Day (late May - mid-June); and (3) all other times. Average weekly sales ($) during each of the three seasons during the past four years are known and given below. Determine a forecast for the average weekly sales in year 5 for each of the three seasons. Year Season 1 2 3 4 1 1856 1995 2241 2280 2 2012 2168 2306 2408 3 985 1072 1105 1120

Management Scientist Solutions

Interpretation of Seasonal Indices Seasonal index for season 2 (Father’s Day) = 1.236 Means that the sale value of ties during season 2 is 23.6% higher than the average sale value over the year Seasonal index for season 3 (all other times) = 0.586 Means that the sale value of ties during season 3 is 41.4% lower than the average sale value over the year

Forecast Accuracy Error - difference between actual value and predicted value Mean Absolute Deviation (MAD) Average absolute error Mean Squared Error (MSE) Average of squared error

MAD and MSE  Actual  forecast MAD = n MSE = Actual forecast)   n ( 2   n (

Measure of Forecast Accuracy MSE = Mean Squared Error

Forecasting Accuracy Estimates Example 10 of textbook

Sources of Forecast errors Model may be inadequate Irregular variations Incorrect use of forecasting technique

Characteristics of Forecasts They are usually wrong A good forecast is more than a single number Aggregate forecasts are more accurate The longer the forecast horizon, the less accurate the forecast will be Forecasts should not be used to the exclusion of known information

Choosing a Forecasting Technique No single technique works in every situation Two most important factors Cost Accuracy Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon