Forecasting McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Forecast – a statement about the future value of a variable of interest We make forecasts about such things as weather, demand, and resource availability Forecasts are an important element in making informed decisions Instructor Slides 3-2

Expected level of demand The level of demand may be a function of some structural variation such as trend or seasonal variation Accuracy Related to the potential size of forecast error Instructor Slides 3-3

The forecast should be timely should be accurate should be reliable should be expressed in meaningful units should be in writing technique should be simple to understand and use should be cost effective

1. Determine the purpose of the forecast 2. Establish a time horizon 3. Select a forecasting technique 4. Obtain, clean, and analyze appropriate data 5. Make the forecast 6. Monitor the forecast

1. Techniques assume some underlying causal system that existed in the past will persist into the future 2. Forecasts are not perfect 3. Forecasts for groups of items are more accurate than those for individual items 4. Forecast accuracy decreases as the forecasting horizon increases Instructor Slides 3-6

Forecast errors should be monitored  Error = Actual – Forecast  If errors fall beyond acceptable bounds, corrective action may be necessary

MAD weights all errors evenly MSE weights errors according to their squared values MAPE weights errors according to relative error

Period Actual (A) Forecast (F) (A-F) Error |Error|Error AVG(A) Sum 1339 n = 5n-1 = 4 MADMSEMAPE=MAD / AVG(A) = 2.6= 9.75=2.6/114.6= 2.27%

Qualitative Forecasting Qualitative techniques permit the inclusion of soft information such as: Human factors Personal opinions Hunches These factors are difficult, or impossible, to quantify Quantitative Forecasting Quantitative techniques involve either the projection of historical data or the development of associative methods that attempt to use causal variables to make a forecast These techniques rely on hard data

Forecasts that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts Executive opinions Sales force opinions Consumer surveys Delphi method

Forecasts that project patterns identified in recent time-series observations Time-series - a time-ordered sequence of observations taken at regular time intervals Assume that future values of the time-series can be estimated from past values of the time-series

Trend Seasonality Cycles Irregular variations Random variation

Exhibit 9.4

Exhibit 9.5a

Exhibit 9.5b

Trend A long-term upward or downward movement in data Population shifts Changing income Seasonality Short-term, fairly regular variations related to the calendar or time of day Restaurants, service call centers, and theaters all experience seasonal demand

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Cycle Wavelike variations lasting more than one year These are often related to a variety of economic, political, or even agricultural conditions Random Variation Residual variation that remains after all other behaviors have been accounted for Irregular variation Due to unusual circumstances that do not reflect typical behavior Labor strike Weather event

Naïve Forecast Uses a single previous value of a time series as the basis for a forecast The forecast for a time period is equal to the previous time period’s value Can be used when The time series is stable There is a trend There is seasonality

These Techniques work best when a series tends to vary about an average Averaging techniques smooth variations in the data They can handle step changes or gradual changes in the level of a series Techniques Moving average Weighted moving average Exponential smoothing

Technique that averages a number of the most recent actual values in generating a forecast

WeekDemand Forecast (3-week)(5-week) ( )/3 = ( )/3 = ( )/3 = 1333 ( )/5 = ( )/3 = 1433 ( )/5 = ( )/3 = 1533 ( )/5 = ( )/5 = ( )/5 = ( )/5 =1560

As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the the average The number of data points included in the average determines the model’s sensitivity Fewer data points used-- more responsive More data points used-- less responsive

Exhibit 9.6

Exhibit 9.7

The most recent values in a time series are given more weight in computing a forecast The choice of weights, w, is somewhat arbitrary and involves some trial and error

A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error

Saturday Hotel Occupancy ( =0.5) Forecast Period Occupancy Forecast Error t A t F t |A t - F t | (84-79)=81.50 or ( )=82.25 or ( )=81.63 or ( )= or MAD =33/5= 6.6 Forecast Error (Mean Absolute Deviation) = ΣlA t – F t l / n The first actual value as the forecast for period

A simple data plot can reveal the existence and nature of a trend Linear trend equation

Slope and intercept can be estimated from historical data

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Week (t)Sales (y)t2t2 ty  t= 15  y= 812  t 2 =55  (ty)=2499

Substituting values of t into this equation, the forecast for next 2 periods are: F6= (6) = F7= (7) = 187.6

Seasonality – regularly repeating movements in series values that can be tied to recurring events Expressed in terms of the amount that actual values deviate from the average value of a series Models of seasonality Additive Seasonality is expressed as a quantity that gets added to or subtracted from the time-series average in order to incorporate seasonality Multiplicative Seasonality is expressed as a percentage of the average (or trend) amount which is then used to multiply the value of a series in order to incorporate seasonality Instructor Slides 3-36

Instructor Slides 3-37

Manager of a Call center recorded the volume of calls received between 9 and 10 a.m. for 21 days and wants to obtain a seasonal index for each day for that hour. VolumeSeason Overall DayWeek 1Week 2Week 3Average ÷ =SA Index Tues ÷ = Wed ÷ = Thurs ÷ = Fri ÷ = Sat ÷ = Sun ÷ = Mon ÷ = Overall Avg

Seasonal relatives The seasonal percentage used in the multiplicative seasonally adjusted forecasting model Using seasonal relatives To deseasonalize data Done in order to get a clearer picture of the nonseasonal components of the data series Divide each data point by its seasonal relative To incorporate seasonality in a forecast Obtain trend estimates for desired periods using a trend equation Add seasonality by multiplying these trend estimates by the corresponding seasonal relative

A coffee shop owner wants to predict quarterly demand for hot chocolate for periods 9 and 10, which happen to be the 1 st and 2 nd quarters of a particular year. The sales data consist of both trend and seasonality. The trend portion of demand is projected using the equation F t = t. Quarter relatives are Q 1 = 1.20, Q 2 = 1.10, Q 3 = 0.75, Q 4 = 0.95,

Use this information to deseasonalize sales for Q1 through Q8. PeriodQuarterSales ÷ Quarter Relative = Deseasonalized sales ÷ 1.20= ÷ 1.10= ÷ 0.75= ÷ 0.95= ÷ 1.20= ÷ 1.10= ÷ 0.75= ÷ 0.95=182.9

Use this information to predict for periods 9 and 10. F 9 = ( 9) = F 10 = (10) = Multiplying the trend value by the appropriate quarter relative yields a forecast that includes both trend and seasonality. Given that t =9 is a 1 st quarter and t = 10 is a 2 nd quarter. The forecast demand for period 9 = 191.5(1.20) = The forecast demand for period 10 = 199.0(1.10) = 218.9