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2. Forecasting
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Forecasting Using past data to help us determine what we think will happen in the future Things typically forecasted Demand for products and services Raw material prices Human resources costs Economic forecasts: inflation rates, money supplies, housing starts
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Why do we forecast? We forecast as an input to production/services planning, so that we have some idea of demand/resources, etc. Forecasts drive a lot of decision-making We should never expect forecasts to be exactly correct, we only hope that they give us a reasonable idea as to what the future holds
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Laws of Forecasting Forecasts are always wrong Detailed forecasts are worse than aggregate forecasts The further into the future, the less reliable the forecast will be
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Ranges of Forecasts Short range less than three months Purchasing, job scheduling, workforce levels should be accurate Medium range Three months to three years Sales, production planning, budgeting should be good
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Ranges of Forecasts (Continued) Long range several years New products, capital expenditure, facility location and expansion hopefully good
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Types of Forecasting Qualitative Methods - Subjective estimates of future Time Series Analysis - using past data to predict future Causal Relationships - data pattern is explained by various factors
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Forecasting Sequence Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the forecast Select the forecasting models Gather the data Make the forecast Validate and implement results
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Qualitative Forecasting
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Quantitative Forecasting
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Components of Data Average value Trend - a slow direction/shift Seasonal influence - sensitivity to time of year Cyclical elements - high and low points Random variation (white noise) - unexplainable behavior
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Forecast Using Different Components Demand for product or service |||| 1234 Year Average demand over four years Seasonal peaks Trend component Actual demand Random variation
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Time Series Analysis - Notation D t is the actual demand for period t F t is the forecast for period t F t+k is the forecast made at period t for k periods ahead
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Moving Average F t+1 = (D t + D t-1 + …+ D t-N+1 ) / N F t+2 = (D t+1 + D t + …+ D t-N+2 ) / N = F t+1 + (D t+1 - D t-N+1 ) / N N is the number of averaging periods (typically, N is 5 to 7) Better for constant processes
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Effect of Number of Periods Smaller N is good for quick response, but larger N ignores random fluctuations
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Example January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average (12 + 13 + 16)/3 = 13 2 / 3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1 / 3 101213 (10 + 12 + 13)/3 = 11 2 / 3
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Example ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Shed Sales 30 30 – 28 28 – 26 26 – 24 24 – 22 22 – 20 20 – 18 18 – 16 16 – 14 14 – 12 12 – 10 10 – Actual Sales Moving Average Forecast
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Weighted Moving Average 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 / 2 101213 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights applied: 3, 2, 1
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Example 30 30 – 25 25 – 20 20 – 15 15 – 10 10 – 5 5 – Sales demand ||||||||||||JFMAMJJASONDJFMAMJJASOND||||||||||||JFMAMJJASONDJFMAMJJASOND Actual sales Moving average Weighted moving average
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Exponential Smoothing F t+1 = α D t + α (1- α )D t-1 + α (1- α ) 2 D t-2 + … F t+2 = α D t+1 + α (1- α )D t + α (1- α ) 2 D t-1 + … = α D t+1 + (1- α )F t+1 where 0 < α < 1. (typically, α is 0.1 to 0.3) Better for constant processes Weight Assigned to Most2nd Most3rd Most4th Most5th Most RecentRecentRecentRecentRecent SmoothingPeriodPeriodPeriodPeriodPeriod Constant( ) (1 - ) (1 - ) 2 (1 - ) 3 (1 - ) 4 =.1.1.09.081.073.066 =.5.5.25.125.063.031
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Effect of α Larger α gives greater weight to new data Use small values for if demand is stable, larger values for if demand is fluctuating
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Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant =.20 New forecast=.8 x 142 +.2 x 153 = 144.2 ≈ 144 cars
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Example 225 225 – 200 200 – 175 175 – 150 150 – |||||||||123456789123456789|||||||||123456789123456789 Quarter Demand =.1 Actual demand =.5
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Trend Process (Double Exponential Smoothing) Simple exponential smoothing tends to lag behind a trend. Correct this by estimating the slope and multiply this slope by the number of periods. A t = α D t + (1- α )(A t-1 +B t-1 ) B t = β (A t -A t-1 ) + (1- β )B t-1 F t+k = A t + kB t
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Example Period1234567 Demand74798090105142122
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Seasonal Process A t = α D t /C t-4 + (1- α )(A t-1 +B t-1 ) B t = β (A t -A t-1 ) + (1- β )B t-1 C t = γ D t /A t + (1- γ )C t-4 F t+k = (A t + kB t ) C t+k-4
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Example Q -- Y12 Sp6984 Su266310 F188212 W5964 Avg145.5167.5
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Causal Relationships – Linear (Multiple) Regression Model A forecasting technique that assumes that the relationship between the dependent and independent variables. Useful if there is a strong relationship and a time lag between variables. Y t = a + bX t where Y t is dependent variable to be solved for and X t is independent variable. a is intercept and b is slope of the line.
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Example Period1234567 Demand74798090105142122
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Forecast Error Projection of past trends into the future Bias errors Consistent mistakes causing a forecast to be too high or too low: wrong models, wrong trend line, errors in shifting seasonal demand, undetected trends Random errors Variations (noise) in a forecast that cannot be explained by the forecast model
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Forecast Error Measurements MAD (Mean absolute deviation) MSE (Mean squared error) MAPE (Mean absolute percent error)
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Example RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded =.10 =.10 =.50 =.50 11801755.001755.00 2168175.57.50177.509.50 3159174.7515.75172.7513.75 4175173.181.82165.889.12 5190173.3616.64170.4419.56 6205175.0229.98180.2224.78 7180178.021.98192.6112.61 8182178.223.78186.304.30 82.4598.62 MAD10.3112.33 MSE190.82195.24 MAPE5.59%6.76%
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Selection of Parameters
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Video Case Study Describe three different forecasting applications. Name three other areas in which you think Hard Rock could use forecasting models. Justify the use of the weighting system used for evaluating managers for annual bonuses. Name several variables besides those mentioned in the case that could be used as good predictors of daily sales.
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