ReviewESD.260 Fall 2003 1Demand Forecasting23& Logistics – Accuracy and Bias Measures 1. et = Dt -Ft iation: iation 1 n t t e MD n = = ∑ 1 n t t e MAD n = = ∑ 1 n t t t e DMPE n = = ∑ 2 1 n t t e n = = ∑ 1 n t t t e DMAPE n = = ∑ 2 1 n t t e RMSE n = = ∑ © Chris Caplice, MIT MIT Center for Transportation ESD.260 Forecast Error: 2. Mean Dev3. Mean Absolute Dev4. Mean Squared Error: 5. Root Mean Squared Error: 6. Mean Percent Error: 7. Mean Absolute Percent Error: MSE MD – cancels out the over and under – good measure of bias not accuracy MAD – fixes the cancelling out, but statistical properties are not suited to probability based dss MSE – fixes cancelling out, equivalent to variance of forecast errors, HEAVILY USED statistically appropriate measure of forecast errors RMSE – easier to interpret (proportionate in large data sets to MAD) MAD/RMSE = SQRT(2/pi) for e~N Relative metrics are weighted by the actual demand MPE – shows relative bias of forecasts MAPE – shows relative accuracy Optimal is when the MSE of forecasts -> Var(e) – thus the forecsts explain all but the noise. What is good in practice (hard to say) MAPE 10% to 15% is excellent, MAPE 20%-30% is average CLASS? 3© Chris Caplice, MIT4MIT Center for Transportation & Logistics – ESD.260 The Cumulative MeanThe Cumulative MeanGenerating Process: D t = L + n t where: n t ~ iid (µ = 0 , σ2 = V[n]) Forecasting Model: F t+1 = (D 1 +D 2 +D 3 +…. +Dt) / t Stationary model – mean does not change – pattern is a constant Not used in practice – is anything constant? Thought though is to use as large a sample siDe as possible to 4© Chris Caplice, MIT5MIT Center for Transportation & Logistics – ESD.260 The Naïve ForecastThe Naïve ForecastGenerating Process: D t = D t-1 + n t where: n t ~ iid (µ = 0 , σ2 = V[n]) Forecasting Model: F t+1 = D t 5© Chris Caplice, MIT6MIT Center for Transportation & Logistics – ESD.260 The Moving AverageThe Moving AverageGenerating Process: D t = L + n t ; t < t s D t = L + S + n t ; t ≥ t s where: n t ~ iid (µ = 0 , σ2 = V[n]) Forecasting Model: F t+1 = (D t + D t-1 + … +D t-M+1) / M where M is a parameter 6© Chris Caplice, MIT7MIT Center for Transportation & Logistics – ESD.260 Exponential SmoothingExponential SmoothingFt+1 = α Dt + (1-α) Ft Where: 0 < α < 1 An Equivalent Form: Ft+1 = Ft + αet 7© Chris Caplice, MIT8MIT Center for Transportation & Logistics – ESD.260 Holt's Model for Trended DataHolt's Model for Trended DataForecasting Model: Ft+1 = Lt+1 + Tt+1 Where: Lt+1 = αDt + (1-α)(Lt + Tt) and: Tt+1 = β(Lt+1 -Lt) + (1- β)Tt 8Winter's Model for Trended/Seasonal DataWinter's Model for Trended/Seasonal Data=Ft+1 (Lt+1 + Tt+1) St+1-m = α(Dt/St) + (1- α)(Lt + Tt)Lt+1 = β(Lt+1-Lt) + (1- β)TtTt+1 = γ(Dt+1/Lt+1) + (1- γ) St+1-mSt+1 MIT Center for Transportation & Logistics – ESD.260 © Chris Caplice, MIT9 910& Logistics – Notes from Homework 1 Problem 1 Did not used the model which yielded the lowest MSE Remove outliers Problem 2 initial values Penalty for waiting too long longer time to “adjust” itself Problem 3 Initializing seasonality indexes © Chris Caplice, MIT MIT Center for Transportation ESD.260 Setting initial values for level (L) and trend (T) The more data you use, the more accurate are these If initial values are off by a lot, the model will take a 10Inventory Management1112& Logistics – Bottomline Inventory is not bad. Inventory is good. Inventory is an important tool which, when correctly used, can reduce total cost and improve the level of service performance in a logistics system. © Chris Caplice, MIT MIT Center for Transportation ESD.260 12Fundamental Purpose of Inventory To Reduce Total System Cost To buffer uncertainties in: - supply, - demand, and/or - transportation the firm carries safety stocks. To capture scale economies in: -purchasing, - production, and/or - transportation the firm carries cycle stocks. MIT Center for Transportation & Logistics – ESD.260 © Chris Caplice, MIT 13 13li14i iDimensions of Inventory Modeling Known vs Random Instantaneous (deterministic/stochastic) Dependence of items ime Periodic None None All orders are backordered Substitution None Planning Horizon Single Period Finite Period ite © Chris Cap ce, MIT MIT Center for Transportat on & Logist cs – ESD.260 Demand Constant vs Variable Continuous vs Discrete Lead time Constant or Variable Independent Correlated Indentured Review TContinuous Discounts All Units or Incremental Excess Demand Lost orders Perishability Uniform with time Infin14Lot sizing15li16i iStock StockStock On Hand Cycle Stock & Safety Stock © Chris Cap ce, MIT MIT Center for Transportat on & Logist cs – ESD.260 Cycle Cycle Cycle Safety Stock Time 16li17i iI(t) Lot Sizing: Many Potential Policies T Q Objective: Pick the policy with the lowest total cost © Chris Cap ce, MIT MIT Center for Transportat on & Logist cs – ESD.260 Time Inventory On Hand 17li18i iWhat makes a cost relevant? Components Ordering Cost Holding Cost Shortage Cost Relevant Costs © Chris Cap ce, MIT MIT Center for Transportat on & Logist cs – ESD.260 Purchase Cost 1819& Logistics – Notation TC = Total Cost (dollar/time) D (units/time) Co Ch = Holding Cost Cp = Purchase Cost (dollars/unit) Q T (time/order) © Chris Caplice, MIT MIT Center for Transportation ESD.260 = Average Demand = Ordering Cost (dollar/order) (dollars/dollars held/time) = Order Quantity (units/order) = Order Cycle Time 19li20i i2][ Q pho += 2* o h p DCQ CC = * 2 o h pTC = Economic Order Quantity (EOQ) () 2o h p D QC Q ⎛⎞ ⎛⎞ = +⎜⎟ ⎜⎟⎝⎠⎝⎠ © Chris Cap ce, MIT MIT Center for Transportat on & Logist cs – ESD.260 Q C C D C Q TC DC C C TC Q C C From TC [Q] to Q* Take the derivate and set it to 0 20The Effect of Non-Optimal Q Q 2000 500 DCo/Q $500 $2,000 ChCpQ/2 $12,500 $3,125 TC $13,000 $5,125 200 400 $5,000 $2,500 $1,250 $2,500 $6,250 $5,000 20 $50,000 $125 $50,125 So, how sensitive is TC to Q? MIT Center for Transportation & Logistics – ESD.260 21 © Chris Caplice, MIT 21$-501502503504505506507508509501050115012501350145015501650175018501950 Total Cost versus Lot (Order) Size Annual Cost vs. Order Quantity $5,000 $10,000 $15,000 $20,000 $25,000 Lot Size Annual
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