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Population Growth and Harvesting Strategy

Explore a possible approach to managing population growth and harvesting in order to maintain a sustainable balance. Consider the implications of catching all but a certain number of fish after a certain time period.

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Population Growth and Harvesting Strategy

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  1. HW1 Q5: One Possible Approach • First, let the population grow • At some point, start harvesting the growth • Annual catch = annual growth • In year 30, catch all but 1,000 fish • Maybe not be a good idea in reality • Remaining question: how far should we let the population grow?

  2. MGTSC 352 Lecture 3: Forecasting “Simple” time series forecasting methodsIncluding SES = Simple Exponential Smoothing Performance measures “Tuning” a forecasting method to optimize a performance measure Components of a time series DES = Double Exponential Smoothing

  3. Today’s active learning • Groups of two again • Recorder: person who got up earlier this morning

  4. Ft+1 = LS Dt+ (1–LS)  Ft t = 6:F7 = LS D6+ (1–LS)  F6 t = 5: F6 = LS D5+ (1–LS)  F5 t = 4:F5 = LS D4+ (1–LS)  F4 t = 3:F4 = LS D3+ (1–LS)  F3 t = 2:F3 = LS D2+ (1–LS)  F2 t = 1:F2 = D1 Plug t = 5 equation into t = 6 equation: F7 = LS D6+ (1–LS)  (LS D5+ (1–LS)  F5) Active learning: Multiply out F7 = LS  D6+ LS  (1–LS)  D5 + (1–LS)2 F5 Repeat for t = 4, 3, 2, 1 SES is really a WMA (pg. 19) Final result: F7 = [LS D6] + [LS  (1–LS)  D5] + [LS  (1–LS)2  D4] + [LS  (1–LS)3  D3] + LS  (1–LS)4  D2] + (1–LS)5 D1

  5. The Weights LS = 0.5 LS = 0.3 LS = 0.1

  6. Weights get smaller and smaller for demand that is further and further in the past – except: • Oldest data point may have more weight than second oldest data point. • Only matters for small data sets and small LS

  7. Simple Models Recap • LP, AVG, SMA, WMA, SES • Three phases: • Initialization • Learning • Prediction • Prediction: so far, we’ve only done one-period-into-the-future • k periods-into-the-future: Ft+k = Ft+1, k = 2, 3, … • Active learning: translate formula into English

  8. Performance Measures • BIAS = Bias • MAD = Mean Absolute Deviation • SE = Standard Error • MSE = Mean Squared Error • MAPE = Mean Absolute Percent Error (formulas in course pack, p. 21) Excel

  9. Pg. 23 Components of a Time Series • level • trend • seasonality • cyclic (we will ignore this) • random (unpredictable by definition) • (Simple) Exponential Smoothing incorporates... • Level only • Will lag trend • Miss seasonality

  10. Level, Trend, Seasonality Level + random Level + trend + random Level + trend + seasonality + random

  11. Level, Trend, Seasonality • Additive trend, multiplicative seasonality • (Level + Trend)  seasonality index • Example: • Level: 1000 • Trend: 10 • Seasonality index: 1.1 • Forecast: (1000 + 10)  1.1 = 1111

  12. Models • Double Exponential Smoothing • Level, Trend • Today • Triple Exponential Smoothing • Next week • Simple Linear Regression with Seas. Indices • Next week

  13. Pg. 25 Double Exponential Smoothing • Initialization • Level, Trend • Learning • Prediction • Formulas in course pack • Work on an example Excel

  14. Learning In general: UPDATED =S NEW + (1 – S)  OLD

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