4 - 1 Course Title: Production and Operations Management Course Code: MGT 362 Course Book:...

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Course Title: Production and Operations Management

Course Code: MGT 362

Course Book: Operations Management 10th Edition. By Jay Heizer & Barry Render

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Chapter 4: Forecasting

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Summery of Previous Presentation (1/3)

Global Company Profile: Disney World What Is Forecasting?

Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts

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Summery of Previous Presentation (2/3)

The Strategic Importance of Forecasting Human Resources Capacity Supply Chain Management

Seven Steps in the Forecasting System

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Summery of Previous Presentation (3/3)

Forecasting Approaches Overview of Qualitative Methods Overview of Quantitative Methods

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Summary of Today's Presentation

Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections

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Overview of Quantitative Approaches

1. Naive approach2. Moving averages3. Exponential smoothing4. Trend projection5. Linear regression

time-series models

associative model

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Set of evenly spaced numerical data Obtained by observing response variable at

regular time periods Forecast based only on past values, no other

variables important Assumes that factors influencing past and

present will continue to influence in future

Time Series Forecasting

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Trend

Seasonal

Cyclical

Random

Time Series Components

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Components of DemandD

eman

d fo

r pro

duct

or s

ervi

ce

| | | |1 2 3 4

Time (years)

Average demand over 4 years

Trend component

Actual demand line

Random variation

Figure 4.1

Seasonal peaks

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Persistent, overall upward or downward pattern

Changes due to population, technology, age, culture, etc.

Typically several years duration

Trend Component

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Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year

Seasonal Component

Number ofPeriod Length SeasonsWeek Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

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Repeating up and down movements Affected by business cycle, political, and economic

factors Multiple years duration Often causal or associative relationships

Cyclical Component

0 5 10 15 20

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Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Short duration and no repeating

Random Component

M T W T F

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Naive Approach

Assumes demand in next period is the same as demand in most recent period e.g., If January sales were 68, then

February sales will be 68 Sometimes cost effective and efficient Can be good starting point

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MA is a series of arithmetic means Used if little or no trend

Used often for smoothing

Moving Average Method

Moving average =∑ demand in previous n periods

n

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January 10February 12March 13April 16May 19June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

Moving Average Example

101012121313

(1010 + 1212 + 1313)/3 = 11 2/3

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Graph of Moving Average

| | | | | | | | | | | |J F M A M J J A S O N D

Shed

Sal

es

30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –

Actual Sales

Moving Average Forecast

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Used when some trend might be present Older data usually less important

Weights based on experience and intuition

Weighted Moving Average

Weightedmoving average =

∑ (weight for period n) x (demand in period n)

∑ weights

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January 10February 12March 13April 16May 19June 23July 26

Actual 3-Month WeightedMonth Shed Sales Moving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141/3

[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2

Weighted Moving Average

101012121313

[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6

Weights Applied Period33 Last month22 Two months ago11 Three months ago6 Sum of weights

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Increasing n smooth the forecast but makes it less sensitive to changes

Do not forecast trends well Require extensive historical data

Potential Problems With Moving Average

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Moving Average And Weighted Moving Average

30 –

25 –

20 –

15 –

10 –

5 –

Sale

s de

man

d

| | | | | | | | | | | |J F M A M J J A S O N D

Actual sales

Moving average

Weighted moving average

Figure 4.2

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Form of weighted moving average Weights decline exponentially Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen

Involves little record keeping of past data

Exponential Smoothing

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Exponential Smoothing

New forecast = Last period’s forecast+ (Last period’s actual demand

– Last period’s forecast)

Ft = Ft – 1 + (At – 1 - Ft – 1)

where Ft = new forecast

Ft – 1 = previous forecast

= smoothing (or weighting) constant (0 ≤ ≤ 1)

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Exponential Smoothing Example

Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20

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Exponential Smoothing Example

Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20

New forecast = 142 + .2(153 – 142)

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Exponential Smoothing Example

Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20

New forecast = 142 + .2(153 – 142)= 142 + 2.2= 144.2 ≈ 144 cars

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Impact of Different

225 –

200 –

175 –

150 –| | | | | | | | |1 2 3 4 5 6 7 8 9

Quarter

Dem

and

= .1

Actual demand

= .5

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Impact of Different

225 –

200 –

175 –

150 –| | | | | | | | |1 2 3 4 5 6 7 8 9

Quarter

Dem

and

= .1

Actual demand

= .5 Chose high values of when underlying average is likely to change

Choose low values of when underlying average is stable

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Choosing

The objective is to obtain the most accurate forecast no matter the technique

We generally do this by selecting the model that We generally do this by selecting the model that gives us the lowest forecast errorgives us the lowest forecast error

Forecast error = Actual demand - Forecast value

= At - Ft

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Common Measures of Error

Mean Absolute Deviation (MAD)

MAD =∑ |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE =∑ (Forecast Errors)2

n

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Common Measures of Error

Mean Absolute Percent Error (MAPE)

MAPE =∑100|Actuali - Forecasti|/Actuali

n

n

i = 1

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Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

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Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD =∑ |deviations|

n

= 82.45/8 = 10.31For = .10

= 98.62/8 = 12.33For = .50

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Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24

For = .50

MSE = ∑ (forecast errors)2

n

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Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24

= 44.75/8 = 5.59%For = .10

= 54.05/8 = 6.76%For = .50

MAPE =∑100|deviationi|/actuali

n

n

i = 1

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Comparison of Forecast Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%

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Summary of Today's Presentation

Time-Series Forecasting Decomposition of a Time Series Naive Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections