Demand Forecasting

- an estimate of an event which will happen in the future

S. Ajit

Need for forecasting

Basis for most planning decisions Scheduling Inventory Production Facility layout Work force Distribution Purchasing Sales

Sources of data for forecasting

Company Records Published records Journals Market Surveys News papers

Forecasting Model

Types of Forecasting Models

Types of Forecasts Qualitative --- based on experience, judgement, knowledge; Quantitative --- based on data, statistics;

Methods of Forecasting� time series models (e.g. exponential smoothing) – trend,

seasonal, cyclical patterns

� causal models (e.g. regression) – based on relationship between variable to be forecasted and an independent variable

Production Resource Forecasts

Long range Medium range Short range

Years Months Weeks

Factory Capacities

Capital funds

Plant location

Product Planning

Department capacities,

Purchased Material

Aggregate planning,

capacity planning,

sales forecasts,

Demand forecasting,

staffing levels (labor),

inventory levels,

Qualitative Quantitative, Quantitative

Forecasting Horizons

Forecasting Techniques

Correction needed

Forecasting Techniques

Quantitative Qualitative

•Delphi•Opinion Survey

•Regression•Time Series

Historical Time Series

Trend Pattern

Cyclical Pattern

Seasonal Pattern

Types of Forecasting Models

Types of Forecasts Qualitative --- based on experience, judgement, knowledge; Quantitative --- based on data, statistics;

Methods of Forecasting� time series models (e.g. exponential smoothing);

� causal models (e.g. regression) – based on relationship between variable to be forecasted and an independent variable

Assumptions of Time Series Models There is information about the past; This information can be quantified in the form of data; The pattern of the past will continue into the future.

Simple Moving Average Forecast Ft is average of n previous observations or

actuals Dt :

Note that the n past observations are equally weighted. Issues with moving average forecasts:

All n past observations treated equally; Observations older than n are not included at all; Requires that n past observations be retained; Problem when 1000's of items are being forecast.

Simple Moving Average

Include n most recent observations Weight equally Ignore older observations Applied to forecast for only one period into the future

weight

today123...n

Moving Average – Example 1

Determine the forecast for the 11th month, for n = 3.

Moving Average – Example 1 - Solution

Moving Average Forecasting for the 11th months is 96

Moving Average – Example 1 - Solution

Weighted Moving Average

Include n most recent observations More weight is assigned to the recent demand values Ignore older observations Applied to forecast for only one period into the future

weight

today123...n

∑ Wi Di

Weight = -------------- i = 1 to n ∑ Wi

Weighted Moving Average – Example 2

Determine the forecast for the 9th month, for n = 3.

Weighted Moving Average Example 2 - Solution

Weightd Moving Average Example 2 - Solution

Moving Average Forecasting for the 9th months is 81.5

Weighted Moving Average Example 2 - Solution

Exponential Smoothing I

Include all past observations Weight recent observations much more heavily than

very old observations Most popular

F t - Forecast for the time period ‘t’

F t-1 - Forecast for the time period ‘t-1’

D t-1 - Demand for the time period ‘t-1’

α - Smoothing constant (0 to 1)

Include all past observations Weight recent observations much more heavily

than very old observations:

weight

Decreasing weight given to older observations

weight

Exponential Smoothing: Math

F t = α * D t-1 + (1 – α) * F t-1

Exponential Smoothing: Math

Thus, new forecast is weighted sum of old forecast and actual demand

Notes: Only 2 values (Dt and Ft-1 ) are required, compared with n for

moving average Rule of thumb: < 0.5 Typically, = 0.2 or = 0.3 work well

)1()1(

DaaDaaaDF

Exponential Smoothing – Example 3

A firm uses simple exponential smoothing with α = 0.2 to forecast demand. The actual demand for January to July were 450, 460, 465, 434, 420, 498 and 462 Nos. The forecast for Jan was 400 nos. Forecast the demand for the period Feb to July

Month Actual Demand

Old Forecast

New Forecast

Forecast Error

Jan 450

Feb 460

Mar 465

Apr 434

May 420

Jun 498

Jul 462

Exponential Smoothing – Example 3Month Actual

DemandOld Forecast

New Forecast

Forecast Error

Jan 450 400

Feb 460

Mar 465

Apr 434

May 420

Jun 498

Jul 462

F t = α * D t-1 + (1 – α) * F t-1

α = 0.2

DemandOld Forecast

New Forecast

Forecast Error

Jan 450 400

Feb 460 410

Mar 465

Apr 434

May 420

Jun 498

Jul 462

F t = α * D t-1 + (1 – α) * F t-1

F Feb = 0.2 * 450 + (1 – 0.2) * 400 = 410

DemandOld Forecast

New Forecast

Forecast Error

Jan 450 400

Feb 460 410 410

Mar 465

Apr 434

May 420

Jun 498

Jul 462

F t = α * D t-1 + (1 – α) * F t-1

F Mar = 0.2 * 460 + (1 – 0.2) * 410 = 420

DemandOld Forecast

New Forecast

Forecast Error

Jan 450 400

Feb 460 410 410

Mar 465 420

Apr 434

May 420

Jun 498

Jul 462

F t = α * D t-1 + (1 – α) * F t-1

F Mar = 0.2 * 460 + (1 – 0.2) * 410 = 420

DemandOld Forecast

New Forecast

Forecast Error

Jan 450 400 - + 50

Feb 460 410 410 + 50

Mar 465 420 420 + 45

Apr 434 429 429 + 5

May 420 430 430 -10

Jun 498 428 428 + 70

Jul 462 442 442 + 20

F t = α * D t-1 + (1 – α) * F t-1

F Apr = 0.2 * 465 + (1 – 0.2) * 420 = 429

Holt’s Method:Double Exponential Smoothing

orExponential Smoothing with Trend

or Adjusted Exponential Smoothing

Holt’s Method:Double Exponential Smoothing

Ideas behind smoothing with trend: ``De-trend'' time-series by separating base from trend effects Smooth base in usual manner using Smooth trend forecasts in usual manner using

Smooth the base forecast Bt

Smooth the trend forecast Tt

Forecast k periods into future Ft+k with base and trend

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

Exponential Smoothing with Trend – Example 4

Compute the adjusted exponential forecast for the 1st week of March for a firm with the following data. Assume the forecast for the first week of January (F0) as 600 & corresponding initial trend (TO) as 0. Let = 0.1 and β = 0.2

Week Demand Week Demand

Jan 1 650 Feb 1 625

2 600 2 675

3 550 3 700

4 650 4 710

Let = 0.1 and β = 0.2 Week Demand Week Demand

Jan 1 650 Feb 1 625

2 600 2 675

3 550 3 700

4 650 4 710

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

F0 = 600

T0 = 0

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

= 0.1 * 650 + 0.9 (600 + 0) = 605

F0 = 600

T0 = 0

B t-1 D t-1 B t T t F t+1

Demand

Smooth

TrendNext

Projection

Jan 1 600 650 605

Feb 1 625

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

= 0.1 * 650 + 0.9 (600 + 0) = 605

F0 = 600

T0 = 0

= 0.2 * (605 – 600) + 0.8 * (0) = 1.00

Demand

Smooth

TrendNext

Projection

Jan 1 600 650 605 1.0

Feb 1 625

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

= 0.1 * 600 + 0.9 (605 + 1) = 605.4

F0 = 600

T0 = 0

= 0.2 * (605.4 – 605) + 0.8 * (1) = 0.88

= 605 + 1 = 606

Demand

Smooth

TrendNext

Projection

Jan 1 600 650 605 1.0 606

2 605 600

Feb 1 625

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

= 0.1 * 600 + 0.9 (605 + 1) = 605.4

F0 = 600

T0 = 0

Demand

Smooth

TrendNext

Projection

Jan 1 600 650 605 1.0 606

2 605 600 605.4

Feb 1 625

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

= 0.1 * 600 + 0.9 (605 + 1) = 605.4

F0 = 600

T0 = 0

= 0.2 * (605.4 – 605) + 0.8 * (1) = 0.88

Demand

Smooth

TrendNext

Projection

Jan 1 600 650 605 1.0 606

2 605 600 605.4 0.88

Feb 1 625

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

= 0.1 * 600 + 0.9 (605 + 1) = 605.4

F0 = 600

T0 = 0

= 0.2 * (605.4 – 605) + 0.8 * (1) = 0.88

= 605.4 + 0.88 = 606.38

Demand

Smooth

TrendNext

Projection

Jan 1 600 650 605 1.0 606

2 605 600 605.4 0.88 606.38

Feb 1 625

Let = 0.1 and β = 0.2

B t = α * D t-1 + (1 – α) *( B t-1 + T t-1)

T t = β * (B t – B t-1) + (1 – β) * T t-1

F t+1 = B t + T t

F0 = 600

T0 = 0

Demand

Smooth

TrendNext

Projec

Jan 1 600 650 605 1.0 606

2 605 600 605.4 0.88 606.38

3 605.4 550 600.65 -0.246 600.40

4 600.65 650 605.36 0.742 606.10

Feb 1 605.36 625 607.99 1.120 609.11

2 607.99 675 615.70 2.44 618.14

3 615.70 700 626.33 4.08 630.4

4 626.33 710 738.37 5.67 644.04

Forecasting Performance

Mean Forecast Error (MFE or Bias): Measures average deviation of forecast from actuals.

Mean Absolute Deviation (MAD): Measures average absolute deviation of forecast from actuals.

Mean Absolute Percentage Error (MAPE): Measures absolute error as a percentage of the forecast.

Standard Squared Error (MSE): Measures variance of forecast error

How good is the forecast?

Want MFE to be as close to zero as possible -- minimum bias

A large positive (negative) MFE means that the forecast is undershooting (overshooting) the actual observations

Note that zero MFE does not imply that forecasts are perfect (no error) -- only that mean is “on target”

Also called forecast BIAS

Mean Forecast Error (MFE or Bias)

Mean Absolute Deviation (MAD)

Measures absolute error Positive and negative errors thus do not cancel out (as with

MFE) Want MAD to be as small as possible No way to know if MAD error is large or small in relation

to the actual data

ttt FD

Mean Absolute Percentage Error (MAPE)

Same as MAD, except ... Measures deviation as a percentage of actual data

Mean Squared Error (MSE)

Measures squared forecast error -- error variance Recognizes that large errors are disproportionately more

“expensive” than small errors But is not as easily interpreted as MAD, MAPE -- not as

intuitive

Simple Regression / Linear Regression

Simple Linear Regression Equation

The following equation describes how the mean value of y is related to x.

Y = a + b X

a is the intersection with y axis, b is the slope.

Dependent Dependent (Response) (Response) VariableVariable(e.g., income)(e.g., income)

Independent Independent (Explanatory) (Explanatory) Variable Variable (e.g., education)(e.g., education)

Population Population Y-InterceptY-Intercept

Population Population SlopeSlope

Simple Linear Regression Equation

b > 0 b < 0 b = 0

Example

For example, advertising could be the independent variable and sales to be the dependent variable.

We first implement available data to develop a relationship between sales and advertising.

Sales = a + b (Advertising)

After estimating a and b , then we implement this relationship to forecast sales given a specific level of advertising.

How much sales we will have if we spent a specific amount on advertising.

To find the value of a, b use the formulae below

∑Y = n * a + b ∑X

∑XY = n ∑X + b ∑X2

∑ X2 * ∑Y - ∑X * ∑XY

a = -------------------------n * ∑ X2 – (∑X)2

∑XY - ∑X * ∑Y

b = --------------------n * ∑ X2 – (∑X)2

Find ∑X, ∑Y, ∑XY, ∑ X2

Reed Auto periodically has a special week-long sale. As part of the advertising campaign Reed runs one or more television commercials during the weekend preceding the sale. Data from a sample of 5 previous sales showing the number of TV ads run and the number of cars sold in each sale are shown below.

Number of TV Ads Number of Cars Sold

No. of TV ads – Independent Variable – X

No of cars sold – Dependent Variable - Y

Example : ABC Auto Sales

0 0.5 1 1.5 2 2.5 3 3.5

Y X14 124 318 217 127 3

Y X XY X214 1 14 124 3 72 918 2 36 417 1 17 127 3 81 9

Sum 100 10 220 24

Slope for the Estimated Regression Equation

y -Intercept for the Estimated Regression Equation

a = ? Estimated Regression Equation

Fortunately, there is software...

Demand Forecasting

y y y y

n past observations

observations older

recent observations

old observations

past y

n previous observations

exponential smoothing

Documents

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