Production Planning and Control. 1. Naive approach 2. Moving averages 3. Exponential smoothing 4....

Production Planning and Control

Production Planning and Control

1. Naive approach2. Moving averages3. Exponential

smoothing4. Trend projection

5. Linear regression

Time-Series Time-Series ModelsModels

Associative Associative ModelModel

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 influence in future

Trend

Seasonal

Cyclical

Random

Dem

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| | | |1 2 3 4

Year

Average demand over four years

Seasonal peaks

Trend component

Actual demand

Random variation

Persistent, overall upward or downward pattern

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

Typically several years duration

Regular pattern of up and down fluctuations

Due to weather, customs, etc. Occurs within a single year

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

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

and economic factors Multiple years duration Often causal or

associative relationships

00 55 1010 1515 2020

Erratic, unsystematic, ‘residual’ fluctuations

Due to random variation or unforeseen events

Short duration and nonrepeating

MM TT WW TT FF

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

February sales will be 68February sales will be 68

Sometimes cost effective and Sometimes cost effective and efficientefficient

Can be good starting pointCan be good starting point

Recent periods are the best predictors of the future

Adjustments to naive modelstt YY 1

ˆ

)(ˆ11 tttt YYYY

11

ˆ

t

ttt Y

YYY

Trend

Rate of Change

Period t Year Quarter Sales1 1990 1 5002 2 3503 3 2504 4 4005 1991 1 4506 2 3507 3 2008 4 3009 1992 1 35010 2 20011 3 15012 4 40013 1993 1 55014 2 35015 3 25016 4 55017 1994 1 55018 2 40019 3 35020 4 60021 1995 1 75022 2 50023 3 40024 4 65025 1996 1 85026 2 60027 3 45028 4 700

tt YY 1ˆ

65025 Y

Use 1990-95 as initializationUse 1996 as the test data set

Forecast the first period in 1996

Forecast error:

252525 YYe

65085025 e

Forecast for the remaining 1996 quarters and calculate the error - what do you see happening?

Nonstationary - data values increase over time

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Can also use Naïve models for seasonal forecasts - data indicates that Quarter 1 seems to be higher than 2,3,4.

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

Provides overall impression of data over time

Moving average =Moving average = ∑∑ demand in previous n periodsdemand in previous n periodsnn

This method is appropriate when there is no noticeable trend or seasonality.

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month3-MonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33

(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33

101012121313

((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33

Period t Year Quarter Sales1 1990 1 5002 2 3503 3 2504 4 4005 1991 1 4506 2 3507 3 2008 4 3009 1992 1 35010 2 20011 3 15012 4 40013 1993 1 55014 2 35015 3 25016 4 55017 1994 1 55018 2 40019 3 35020 4 60021 1995 1 75022 2 50023 3 40024 4 65025 1996 1 85026 2 60027 3 45028 4 700

If you suspect seasonality, with quarterly data, it makes sense to use a 4-period moving average (monthly data would use a 12 period moving average). The larger the number of periods, the smoother the fluctuations become.

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

Actual Actual SalesSales

Moving Moving Average Average ForecastForecast

Used when trend is present Older data usually less important

Weights based on experience and intuition

WeightedWeightedmoving averagemoving average ==

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

∑∑ weightsweights

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month Weighted3-Month WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33

[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22

101012121313

[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66

Weights Applied Period

3 Last month2 Two months ago1 Three months ago6 Sum of weights

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

Do not forecast trends well Require extensive historical data

To determine how many periods to use for a moving average, remember: The smaller the number, the more weight

given to recent periods. A smaller number is desirable when there

are sudden shifts in the level of the series. The greater the number, less weight is

given to more recent periods. A larger number is desirable when there

are wide or infrequent fluctuations in the data

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

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JJ FF MM AA MM JJ JJ AA SS OO NN DD

Actual Actual salessales

Moving Moving averageaverage

Weighted Weighted moving moving averageaverage

Figure 4.2Figure 4.2

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

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

– – Last period’s forecast)Last period’s forecast)

FFtt = F = Ft – 1t – 1 + + (A(At – 1t – 1 - F - Ft – 1t – 1))

wherewhere FFtt == new forecastnew forecast

FFt – 1t – 1 == previous forecastprevious forecast

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

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

FFtt = F = Ft – 1t – 1 + + (A(At – 1t – 1 - F - Ft – 1t – 1))wherewhere FFtt == new forecastnew forecast

FFt – 1t – 1 == previous forecastprevious forecast

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

Weight Assigned toWeight Assigned to

MostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th MostRecentRecent RecentRecent RecentRecent RecentRecent RecentRecent

SmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriodConstantConstant (()) (1 - (1 - )) (1 - (1 - ))22 (1 - (1 - ))33 (1 - (1 - ))44

= .1= .1 .1.1 .09.09 .081.081 .073.073 .066.066

= .5= .5 .5.5 .25.25 .125.125 .063.063 .031.031

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

New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

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

New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

= 142 + 2.2= 142 + 2.2

= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars

225 225 –

200 200 –

175 175 –

150 150 –| | | | | | | | |

11 22 33 44 55 66 77 88 99

QuarterQuarter

De

ma

nd

De

ma

nd

= .1= .1

Actual Actual demanddemand

= .5= .5

225 225 –

200 200 –

175 175 –

150 150 –| | | | | | | | |

11 22 33 44 55 66 77 88 99

QuarterQuarter

De

ma

nd

De

ma

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= .1= .1

Actual Actual demanddemand

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

Choose low values of Choose low values of when underlying average when underlying average is stableis stable

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

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

Forecast errorForecast error = Actual demand - Forecast value= Actual demand - Forecast value

= A= Att - F - Ftt

Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)

MAD =MAD =∑∑ |Actual - Forecast||Actual - Forecast|

nn

Mean Squared Error (MSE)Mean Squared Error (MSE)

MSE =MSE =∑∑ (Forecast Errors)(Forecast Errors)22

nn

Mean Absolute Percent Error (MAPE)Mean Absolute Percent Error (MAPE)

MAPE =MAPE =∑∑100|Actual100|Actualii - Forecast - Forecastii|/Actual|/Actualii

nn

nn

i = 1i = 1

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62

MAD =∑ |deviations|

n

= 82.45/8 = 10.31For = .10

= 98.62/8 = 12.33For = .50

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33

= 1,526.54/8 = 190.82For = .10

= 1,561.91/8 = 195.24For = .50

MSE =∑ (forecast errors)2

n

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24

= 44.75/8 = 5.59%For = .10

= 54.05/8 = 6.76%For = .50

MAPE =∑100|deviationi|/actuali

n

n

i = 1

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24MAPEMAPE 5.59%5.59% 6.76%6.76%