Forecasting Introduction An essential aspect of managing any organization is planning for the future. Organizations employ forecasting techniques to determine.

Forecasting Introduction

An essential aspect of managing any organization is planning for the future.

Organizations employ forecasting techniques to determine future inventory, costs, capacities, and interest rate changes.

There are two basic approaches to forecasting:

-Qualitative

-Quantitative

Time Span of Forecasts Long-range

time spans usually greater than one year necessary to support strategic decisions

about planning products, processes, and facilities

Short-range time spans ranging from a few days to a

few weeks cycles, seasonality, and trend may have

little effect random fluctuation is main data pattern

Qualitative Approaches to Forecasting

Delphi Approach A panel of experts, each of whom is physically

separated from the others and is anonymous, is asked to respond to a sequential series of questionnaires.

Scenario Writing Subjective or Interactive

Approaches

Quantitative Approaches to Forecasting

Quantitative methods are based on an analysis of historical data concerning one or more time series.

A time series is a set of observations measured at successive points in time or over successive periods of time.

If the historical data used are restricted to past values of the series that we are trying to forecast, the procedure is called a time series method.

If the historical data used involve other time series that are believed to be related to the time series that we are trying to forecast, the procedure is called a causal method.

Time series data-Data Patterns

Trends accounts for the gradual shifting of the time series over a long period of time.

Seasonality of the series accounts for regular patterns of variability within certain time periods, such as over a year.

Cycle Any regular pattern of sequences of values above and below the trend line is attributable

Random fluctuation series is caused by short-term, unanticipated and non-recurring factors that affect the values of the time series.

Smoothing Methods: Moving Average

Moving Average MethodThe moving average method

consists of computing an average of the most recent n data values for the series and using this average for forecasting the value of the time series for the next period.Error in Forecasting

Measures the average error that can be expected over time.

ttt YYe ˆ

n

en

tt

1

2 )(

MSE

Moving AveragesDiamond Garden SuppliesForecasting

PeriodActual Value Three-Month Moving Averages

January 10February 12March 16April 13 10 + 12 + 16 / 3 = 12.67May 17 12 + 16 + 13 / 3 = 13.67June 19 16 + 13 + 17 / 3 = 15.33July 15 13 + 17 + 19 / 3 = 16.33August 20 17 + 19 + 15 / 3 = 17.00September 22 19 + 15 + 20 / 3 = 18.00October 19 15 + 20 + 22 / 3 = 19.00November 21 20 + 22 + 19 / 3 = 20.33December 19 22 + 19 + 21 / 3 = 20.67

Storage Shed Sales

Moving Averages ForecastDiamond Garden SupplyForecasting 3 period moving average

Input Data Forecast Error Analysis

Period Actual Value Forecast ErrorAbsolute

errorSquared

errorMonth 1 10Month 2 12Month 3 16Month 4 13 12.667 0.333 0.333 0.111Month 5 17 13.667 3.333 3.333 11.111Month 6 19 15.333 3.667 3.667 13.444Month 7 15 16.333 -1.333 1.333 1.778Month 8 20 17.000 3.000 3.000 9.000Month 9 22 18.000 4.000 4.000 16.000Month 10 19 19.000 0.000 0.000 0.000Month 11 21 20.333 0.667 0.667 0.444Month 12 19 20.667 -1.667 1.667 2.778

Average 1.333 2.000 6.074Next period 19.667 BIAS MAD MSE

Actual Value - Forecast

Weighted Moving Average This is a variation on the simple moving average where

instead of the weights used to compute the average being equal, they are not equal

This allows more recent demand data to have a greater effect on the moving average, therefore the forecast

The weights must add to 1.0 and generally decrease in value with the age of the data

The distribution of the weights determine impulse response of the forecast

1tF = w1Yt + w2Yt-1 +w3Yt-2 + …+ wnYt-n+1

wi = 1

Weighted Moving AverageDiamond Garden SupplyForecasting

PeriodActual Value Weights Three-Month Weighted Moving Averages

January 10 0.222February 12 0.593March 16 0.185April 13 2.2 + 7.1 + 3 / 1 = 12.298May 17 2.7 + 9.5 + 2.4 / 1 = 14.556June 19 3.5 + 7.7 + 3.2 / 1 = 14.407July 15 2.9 + 10 + 3.5 / 1 = 16.484August 20 3.8 + 11 + 2.8 / 1 = 17.814September 22 4.2 + 8.9 + 3.7 / 1 = 16.815October 19 3.3 + 12 + 4.1 / 1 = 19.262November 21 4.4 + 13 + 3.5 / 1 = 21.000December 19 4.9 + 11 + 3.9 / 1 = 20.036

Next period 20.185

Sum of weights = 1.000

Storage Shed Sales

Weighted Moving Average

Diamond Garden Supply Forecasting 3 period weighted moving average

Input Data Forecast Error Analysis

Period Actual value Weights Forecast ErrorAbsolute

errorSquared

errorMonth 1 10 0.222Month 2 12 0.593Month 3 16 0.185Month 4 13 12.298 0.702 0.702 0.492Month 5 17 14.556 2.444 2.444 5.971Month 6 19 14.407 4.593 4.593 21.093Month 7 15 16.484 -1.484 1.484 2.202Month 8 20 17.814 2.186 2.186 4.776Month 9 22 16.815 5.185 5.185 26.889Month 10 19 19.262 -0.262 0.262 0.069Month 11 21 21.000 0.000 0.000 0.000Month 12 19 20.036 -1.036 1.036 1.074

Average 1.988 6.952 6.952Next period 20.185 BIAS MAD MSE

Sum of weights = 1.000

Following data is available about actual sales for the past 13 years.

YR 1 2 3 4 5 6 7 8 9 10 11 12 13Sales

2.3 2.2 2 2.25 2.6 3 4.1 3.8 4 4.3 4.2 4.8 5.2

Find the “Forecast” for the yr 14 using “Two Years” as well as “three years” moving averages. Which of the two forecasts is more reliable on

the basis of Mean Squared Error (MSE) criterion ?

Moving Average - Example

Weighted Moving Average Vacuum cleaner sales for 12 months is given below.

The owner of the supermarket decides to forecast sales by weighting the past 3 months as follows

Wt Applied Month

3 Last month

2 Two months ago

1 Three months ago

Months

1 2 3 4 5 6 7 8 9 10 11 12

Actual sales (units)

10 12 13 16 19 23 26 30 28 18 16 14

Exponential Smoothing The weights used to compute the forecast (moving

average) are exponentially distributed The forecast is the sum of the old forecast and a portion

of the forecast error

Ft = Ft-1 + (At-1-Ft-1) The smoothing constant, , must be between 0.0 and

1.0 A large provides a high impulse response forecast A small provides a low impulse response forecast

New Forecast = (Actual Demand) + (1-)(Old Forecast)

Exponential Smoothing Data

PeriodActual

Value(Yt) Ŷt-1 α Yt-1 Ŷt-1 Ŷt

January 10 = 10 0.1February 12 10 + 0.1 *( 10 - 10 ) = 10.000March 16 10 + 0.1 *( 12 - 10 ) = 10.200April 13 10.2 + 0.1 *( 16 - 10.2 ) = 10.780May 17 10.78 + 0.1 *( 13 - 10.78 ) = 11.002June 19 11.002 + 0.1 *( 17 - 11.002 ) = 11.602July 15 11.602 + 0.1 *( 19 - 11.602 ) = 12.342August 20 12.342 + 0.1 *( 15 - 12.342 ) = 12.607September 22 12.607 + 0.1 *( 20 - 12.607 ) = 13.347October 19 13.347 + 0.1 *( 22 - 13.347 ) = 14.212November 21 14.212 + 0.1 *( 19 - 14.212 ) = 14.691December 19 14.691 + 0.1 *( 21 - 14.691 ) = 15.322

Storage Shed Sales

Exponential Smoothing (Alpha = .42)

Input Data Forecast Error Analysis

Period Actual value Forecast ErrorAbsolute

errorSquared

errorMonth 1 10 10.000Month 2 12 10.000 2.000 2.000 4.000Month 3 16 10.838 5.162 5.162 26.649Month 4 13 13.000 0.000 0.000 0.000Month 5 17 13.000 4.000 4.000 16.000Month 6 19 14.675 4.325 4.325 18.702Month 7 15 16.487 -1.487 1.487 2.211Month 8 20 15.864 4.136 4.136 17.106Month 9 22 17.596 4.404 4.404 19.391Month 10 19 19.441 -0.441 0.441 0.194Month 11 21 19.256 1.744 1.744 3.041Month 12 19 19.987 -0.987 0.987 0.973

Average 2.608 9.842Alpha 0.419 MAD MSE

Next period 19.573

Exponential Smoothing - example

Estimate the trend values using the data given by taking a 4 yr moving average. In January a city hotel predicted a February demand for 142 room occupancy. Actual February demand was 153 rooms. Using

α= .20 forecast the march demand using exponential smoothing method