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# INVENTRYSUPPLY CHAIN EIN 4343

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This 46 page Class Notes was uploaded by Tod Murray on Friday September 18, 2015. The Class Notes belongs to EIN 4343 at University of Florida taught by Staff in Fall. Since its upload, it has received 15 views. For similar materials see /class/206888/ein-4343-university-of-florida in Industrial Engineering at University of Florida.

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Date Created: 09/18/15

Demand Forecasting Siqian Shen1 1Dept of Industrial and Systems Engineering University of Florida Fall 2009 146 Outline 0 Introduction 9 Extrapolation Forecasting 0 MovingAverage Forecast Methods a quotRandomquot 0 Simple Exponential Smoothing a quotRandomquot 0 Holt39s Method Exponential Smoothing a Linear Trendquot 0 Winter39s Method Exponential Smoothing a Seasonality 0 Forecasting Accuracy 9 Causal Forecasting O Simple Linear Regression O The Real World Can Be Much More Complicated a Reference 246 Case Study 1 WaIMart o WaIMart Supply chain management practices Ref Wordpresscom 346 Why Uncertain Demands are inevitable 0 Natural variation 0 Competitor 0 Customer preference 0 Changes in related goods 445 Why does it matter o It takes time to source o It takes time to produce a It takes time to deliver 546 Introduction Exn apolauon For Causal Forecasting mg ooooooooooeooooooooo 00000000000000 Analyze Your Demands Characteristics 0 Random A time series that fluctuates based on a base level 4500 Mac os x Vursian Trends avg weakly unit sales 7102 jaguar 1o3 panther 3000 1500 n x A B Q 6quot 8 m 646 Introduction ooooooo Analyze Your Demands Characteristics 0 Trend A time series that follows a particular pattern of function lPhone Traffic per Month mama SUJJDCWDD 40000000 SEEDODDD zomionn l 7 7 7 7 7 7 is is is is is is is is is is v was f 69 4 his M as39 339 as 0039 a i i 59 06 day as a Q adm l 39 Figure Trend Forecasting Chart Ref techcrunchcom 746 Analyze Your Demands Characteristics 0 Seasonality The peaks and valleys repeat at regular time intervals Seasonal Patterns in US Oil Demand May Jun Jul Aug Sap Famnnl Ahoy1 a Balnw Annual Mange 19912002 Figure Seasonality Forecasting Chart Ref eiadoegov in 846 Forecasting Techniques 0 Extrapolation Methods Use historical data to predict future event ie the past is a good predictor of the future 6 Causal Forecasting Methods Using regression techniques to estimate the relationship between the future values of a variable and one or more independent variables 946 Outline 9 Extrapolation Forecasting 0 MovingAverage Forecast Methods a Random 1046 Methods Details 0 Xti observed data at time period t t 1 2 o ftk forecast for time period 1 k after observations of X1 Xt In this course we only consider fm ie we use observations from time 1 to tto predict period 1 1 outcome fut 2tiNJr1XIN7 VT 3 N where N is a given parameter ie how many periods a decision maker thinks are enough to be looked back to predict the value of next period 1146 Choice of N Use Mean Absolute Deviation MAD Table Example 1 MovingAverage W39th N 3 Rm 1 o MAD the average of the absolute values of Month Sales Forecast Error a e XI 7 71 1393 the 1 30 f t 2 32 orecas error 3 30 4 39 30 2 0 3067 333 0 Criteria Choose an 5 33 324330439 3357 057 appropriate N that 6 34 W 34 0 minimize MAD MAD i833iig67ii0i 3 1246 Outline 9 Extrapolation Forecasting 0 Simple Exponential Smoothing a Random 1346 Methods Details 0 Generally performs better than the Movingaverage when forecasting random data 0 Let A forecast at the end of time period 1 Le At ftk for some value setting of k we assume k 1 in this class 0 Given a as a smoothing constant A 0th 1 7 00AM 0 Recall that et Xtft11 Xt 7 At1 0 At At71 aXt 7 At71 At71 aet we see et as an adjustment which modifies our previous forecast AM 1446 Example 2 Regarding the example 2 in next slide we show how to compute one entry using the equation from last slide 0 Look at the row of t 1 we are given X1 30 and AH A0 32 0 We want to predict at the end of the first period ie Ar A1 7 0 We have A aX117 aAg 0130 0932 318 0 Now we know that we can fill in both A entry in row 1 and AH entry in row 2 as 318 colored in blue 0 In practice it means we predict there will be 318 sales in period 2 However X2 32 and the prediction error is 92 X2 7 A1 32 7 318 02 colored in red 1546 Choice of a Table Example 2 Exponential Smoothing with a 01 Ref 1 Month Sales AM A et 1 30 32 31 8 200 32 318 3182 020 30 3182 3164 182 3164 3237 736 33 3237 3244 063 34 3244 3260 156 GUIACON Co 0 l72ll02ll7182ll736ll063ll156l o MAD f 7 226 0 We can change the value of a and compare the resulting corresponding MADs The best value of 0 appears between 02 and 03 1646 Outline 9 Extrapolation Forecasting 0 Holt s Method Exponential Smoothing a Linear Trend 1746 Case Study 2 Heinz o Heinz Heinz gets to one number forecasting Ref SupplyChainDigest 1846 Methods Details 0 Let L and Tr represent estimates of base level and increasedecrease perperiod at the end of time period 1 respectively 0 Given smoothing constants a and B 6 01 Lt 04Xt1 04Lt71 Ttet 1 Tr 5Lt Lt711 BTtil 2 0 To obtain an estimation for time period 1 k at the end of period I simply use fak Lt th o What is the intuition behind equations 1 and 2 1946 Example 3 Regarding the example 3 in next slide assume that we are given all X and L1 T1 0 First given L1 3771 F 283 we know that our prediction at the end of the first period will be fm 3771 283 4054 colored in red 0 Since the actual sale in period t 2 is X 47 the resulting error is 92 X2 7 fm 47 7 4054 646 colored in orange Now in the end of period t 2 what should be our predictions of L2 and T27 Recall holt s method L2 Cith 1 7 aL1 T1 03047 O703771 283 4248 colored in blue 0 T2 6L2 7 L1176T1 O1O424873771090283 302 colored in blue 2046 Choice of Oz 3 Compute the MAD Table Example 3 Holt s Method with a 030 B 010 Ref 1 Month Sales Lt Tt ft et 1 40 3771 283 3673 327 2 47 4248 302 4054 646 3 50 4685 316 4550 450 4 49 4970 313 5010 101 5 56 5378 322 5283 317 6 53 5580 310 5700 400 o MAD 132711e4e114512110111317114oo1 285 2146 Outline 9 Extrapolation Forecasting 0 Winter s Method Exponential Smoothing a Seasonality 2246 Methods Details 0 Recall L and Tr represent estimates of base level and increasedecrease perperiod at the end of time period t respectively Let s be an estimate of a seasonal multiplier for period t Let c be the number of periods in a cycle of a seasonal pattern Given smoothing constants a B and 7 6 01 Lt aXtstic l 1 04Lti1 Th1 Tr U t Lt711 371 5t 39YXtLt 1 05H 0 To obtain an estimation for time period t k at the end of period t simply use frk Lt th5tkic 2346 Further explanation and insights of c O c is a parameter that we choose to present the seasonality behavior For instance if we use monthly data then c 12 since it says the multipliers in the same month each year have strong relationsquot if we use seasonal data then c 4 and it says the multipliers from the same quarter are strongly relating to each other For instance if we assume we use monthly data then in order to predict s1 s12 we need 3112 s1212 311so pregiven And in the third equation in winter39s method for instance if we need to compute 31 we would need 311 ie we are using the multiplier from last january to make forecast for this january 2446 Example 4 Regarding the example 4 in next slide assume that we are given all X and L1 T1 0 First we compute our prediction M in the end of period t 1 as f1y1L117 T1s1112 5317 387016 913 colored in red 0 Since our prediction for month 2 is 913 and the actual sale is X2 7 the error is then e2 X2 7 11 7 7 913 7213 colored in orange 0 Now how do we decide the values of L2 T2 and 52 in the end of time period t 2 0 Following winter s method we have colored in blue L2 GHQ52712 1 04L271 T271 7 0507016 0505317387 75039 T2 7 ag 7 L2117 19m1 7 0405039 7 5317 7 060387121 52 7 7X2L2 17 7mm 7 06005039 7 040016 7 015 2546 Choice of a 5 7 Given 511 022 519 016 59 050 58 072 57 7 128 55 133 55 197 54 205 54 141 52 082 50 065 088 51 Table Example 4 Winter s Method with a 050 5 040 y 060 Month Sa es 13 7 888288 gag s U accmmcammNm gsasagjggsg 007 2646 Outline 9 Extrapolation Forecasting 0 Forecasting Accuracy 2746 Estimate the standard deviation of forecast errors 0 Assumptions Forecast errors follow normal distribution 0 Let 36 be the standard deviation of errors 36 125MAD o How can this help us to evaluate our forecast 0 Recall that for normal distribution 68 of all predictions should be within 36 of the actual value and 95 are within 239 2846 Estimate the standard deviation of forecast errors 0 Now assuming that MAD 10 a se 125MAD 125 o if we forecast demands for 24 months then for 68 x 24 16 months our predictions will not be off by more than 125 and for 95 x 24 23 months our predictions will not be off by more than 125 x 2 25 2946 Outline 9 Causal Forecasting 0 Simple Linear Regression 3046 Dependent Variables Vs Independent Variables 0 Examples Dependent Variables Independent Variables Total production cost Units produced Automobile sales Interest rate o If dependent variable and one independent variable are related in a linear fashion simple linear regression can work 0 Note that we have learnt Holt s method can be used to predict a lineartrend time series data Here we are talking about linear relationship between two variables usually one is the cause of the other They are two different concepts 3146 Methods Details 0 Let y and X be the ith dependent and independent observations respectively 5 is an error term 30 and B1 are the intercept and the slope respectively We have Yi o 1XEi 0 Goal We want to estimate 30 denoted as 30 and B1 31 such that we minimize the least squares estimates given as Fi o i 2in e m2 2 y e 30 e 31x02 I i 3246 Goal Minimize the least squares estimates Regession Line Y 8o 81X d 3346 Method Details 0 Recall that F is a quadratic function in terms of 30 and 31 convex function the minimum of F quothappensquot when 8F 7 8F 7 0 5 30 5 31 o Qomputing 3 we obtain the optimal settings of 30 and 31 as Z XI 7 My 7 7 2007302 3 31 73073177 where fr 7 are the averages of given X and y respectively a The resulting least squares regression line y3031X 3446 Example Linear regression for trains production Given trains production amount and cost in the following table Week Trains Produced Xi Costs of producing trains yr 1 2 20 60160 3 30 78200 4 40 76540 5 45 89550 6 50 113300 7 60 115280 8 55 113270 9 70 145920 10 40 97010 First the averages are ZXr10 42 7 Zyr10 91497 3546 Example Linear regression fortrains production It The following table gives all values that we need to compute B1 and Bo Recall that r 42 and J7 91497 X Ji X17 Ji J7 XI750007 M7302 10 2574 32 65757 2104224 1024 20 6016 22 31337 689414 484 30 7820 12 13297 159564 144 40 7654 2 14957 29914 4 45 8955 3 1947 5841 9 50 11330 8 21803 174424 64 60 11528 18 23783 428094 324 55 11327 13 21773 283049 169 70 14592 28 54423 1523844 784 40 9701 2 5513 11026 4 And we should be ready to calculate 31 and 30 now 3646 Example Linear regression fortrains production I o The parameters39 estimates of the linear relationship between y and X are A 2XiyJ7 3 2 x e n2 5375663010 1786 30 J7 i 31 91497 7 178642 16488 0 Our least squares line is y 31x r90 16488 1786X It means each extra train incurs a variable cost of 51 1786 in 3746 Outline 9 Causal Forecasting 0 The Real World Can Be Much More Complicated M 3846 Multiple Regression and Nonlinear Relationship 0 Does single linear regression ever happen in reality a For instance in order to make plans for purchasing office supplies we usually evaluate it in terms of number of employees 0 But usually y is a function of more than one variable ie y 50 B1X1 3an for multiple independent variables X1 Xn 0 Similarly write the least squares estimates as F30731773n XXV 30 31W1quotquot nxin2 i o and compute the optimal settings by using i 7 8F 7 7 8F 7 7 A 70 5 50 5 31 a n 3946 Multiple Regression and Nonlinear Relationship 0 What if y and X are nonlinear relationship 6 One way is to use regression softwares Excel Minitab SPSS Matlab 4046 Other questions that I get from the Class Q Recalling holds and winter39s methods in which we predict a series of data with trends T and seasonality factor 3 taken into account there should exist other factors that effect our predictions for instance economy situation interest rate etc So the prediction model is not accurate enough 4146 My answers 0 No model can EXACTLY describe the real problem To extract the things that we care about to understand what we can model and what we cannot to know what we want to take into account and what we do not is the art of modeling 4246 My answers 0 No model can EXACTLY describe the real problem To extract the things that we care about to understand what we can model and what we cannot to know what we want to take into account and what we do not is the art of modeling I said this 4346 My answers 0 0 No model can EXACTLY describe the real problem To extract the things that we care about to understand what we can model and what we cannot to know what we want to take into account and what we do not is the art of modeling I said this As you can see the evolution of exponential smoothing holt s method and winter s method one can expend the model and make things more complicated by introducing more and more estimators likethe trend T or the seasonality factor s There is no rule saying that which variables should be included and which ones should not For example if you want to predict things happening during say economy crisis you should definitely introduce another estimator to represent the effects of economy Conclusion An ancient Chinese adage Textbooks are static humans are dynamicquot 4445 Corresponding book Chapters for reviewing o Winston39s book 241 242 243 244 246 4546 Reference W L Winston Operations Research Applications and Algorithms Chapter 24 Duxbury Press 2003 S Nahmias Production and Operations Analysis 6th Edition Chapter 2 McGrawhill 2008 4646

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