Production Planning and Control

1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression Time-Series Models Associative Model

 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

Demand for product or service |||| 1234 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 of PeriodLengthSeasons WeekDay7 MonthWeek4-4.5 MonthDay28-31 YearQuarter4 YearMonth12 YearWeek52

 Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships

 Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and nonrepeating MTWTFMTWTFMTWTFMTWTF

 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

 Recent periods are the best predictors of the future  Adjustments to naive models Trend Rate of Change

Use as initialization Use 1996 as the test data set Forecast the first period in 1996 Forecast error: Forecast for the remaining 1996 quarters and calculate the error - what do you see happening?

 Nonstationary - data values increase over time

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 = ∑ demand in previous n periods n This method is appropriate when there is no noticeable trend or seasonality.

January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / ( )/3 = 11 2 / 3

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.

||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales – – – – – – – – – – – Actual Sales Moving Average Forecast

 Used when trend is present  Older data usually less important  Weights based on experience and intuition Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3Last month 2Two months ago 1Three months ago 6Sum 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 – – – – – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average Figure 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 =Last period’s forecast +  (Last period’s actual demand – Last period’s forecast) F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0 ≤  ≤ 1)

Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0 ≤  ≤ 1)

Weight Assigned to Most2nd Most3rd Most4th Most5th Most RecentRecentRecentRecentRecent SmoothingPeriodPeriodPeriodPeriodPeriod Constant(  )  (1 -  )  (1 -  ) 2  (1 -  ) 3  (1 -  ) 4  =  =

Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142)

Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142) = = ≈ 144 cars

– – – – ||||||||| ||||||||| Quarter Demand  =.1 Actual demand  =.5

– – – – ||||||||| ||||||||| Quarter Demand  =.1 Actual demand  =.5  Chose high values of  when underlying average is likely to change  Choose low values of  when underlying average is stable

The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error= Actual demand - Forecast value = A t - F t

Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors) 2 n

Mean Absolute Percent Error (MAPE) MAPE = ∑ 100|Actual i - Forecast i |/Actual i n n i = 1

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = ∑ |deviations| n = 82.45/8 = For  =.10 = 98.62/8 = For  =.50

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = 1,526.54/8 = For  =.10 = 1,561.91/8 = For  =.50 MSE = ∑ (forecast errors) 2 n

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE = 44.75/8 = 5.59% For  =.10 = 54.05/8 = 6.76% For  =.50 MAPE = ∑ 100|deviation i |/actual i n i = 1

RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE MAPE5.59%6.76%