Proceedigs of the 011 Iteratioal Coferece o Idustrial Egieerig ad Operatios Maagemet Kuala Lumpur, Malaysia, Jauary 4, 011 Itermittet demad forecastig by usig Neural Network with simulated data Nguye Khoa Viet Truog, Shi Sagmu, Vo Thah Nha, Kwo Icho Departmet of Systems Maagemet & Egieerig, Ije Uiversity, Gimhae, 61-749, South Korea Abstract Recetly, with uusual chagig occurred occasioally i the global market, the maufactures are facig with oe of big issues is predictio of the itermittet demad of products. Utilizig available iformatio to estimate as well as possible the lumpy demad will be the key for success i supply chai maagemet. Eve though a umber of tools were developed for such situatios i literature, there are rooms for improvemet. I this paper, a comparative study is performed with simulated data to show that the eural etwork ca be a promisig tool to covetioal Crosto methods for predictig itermittet demad i term of two criteria mea squared error (MSE) ad mea absolute error (MAE). It is, to the best of our kowledge, usig simulated data for validatig the efficiecy of the proposed approach i the geeral cases is the first such attempt. Keywords Itermittet demad, eural etwork, Crosto methods, supply chai maagemet 1. Itroductio It is obvious that itermittet demad forecastig plays a crucial role i maufacturig ad ivetory maagemet. Itermittet demad or lumpy demad that happes at ifrequet, irregular ad ofte upredictable i both itervals ad quatities is characterized by itervals i which there is o demad. This kid of demad exists i both maufacturig ad service eviromets. The data of these irregular demads are appeared as time series of zerodemads ad ozero-demads that make them much more difficult to be predicted compare to covetioal time series data. There are umber of works have bee oted i literature that focused o the applicatio of eural etwork (NN) model i itermittet demad forecastig. I 004, Carmo ad Rodrigues have applied NN model o irregular spaced time series [1]. From aother aspect, usig ie large idustrial datasets of itermittet demads, Willemai T. R., et. al., 004 show that the bootstrappig method ca be produced more accurate forecasts of the distributio of demad over a fixed lead time tha do expoetial smoothig ad Crosto s method []. For itermittet demad forecastig, Gutierrez R. S. e.t utilized muti-layered perceptro (MLP) NN model ad compared its efficiecy with covetioal method s i 008 [3]. I the field of critical spare parts, which aturally have the characteristic of more expesive, larger demad variatio, loger purchasig lead time tha o-critical spare parts, Che et. al., 010 tried to apply movig back-propagatio eural etwork (MBPN) ad movig fuzzy-euro etwork (MFNN) to effectively predict their requiremet [4]. I aspect of NN, it is clear that the structure of euros ad their etwork cofiguratio are most importat factors that fudametally affect o the efficiecy of NNs as well as their predictable capabilities. As a cotiuous cotributio to this research brach, the aim of this paper is attempt to utilize the feed-forward back propagatio etwork as a alterative potetial tool to covetioal methods for predictig itermittet demad. To illustrate that proposed NN model ca perform better results of itermittet demad forecastig, radom itermittet time series data sets are geerated for both traiig ad validatig steps. Also, a compariso study betwee proposed method ad well-kow Crosto s method is coducted with two criteria such as mea squared error (MSE) ad mea absolutely error (MAE).. Forecastig methods ad data.1 Covetioal method 73
I this paper, the covetioal Crosto method with two values of alpha is used for compariso. There are two mai steps. First, the mea demad data per period are calculated by separately applyig expoetial smoothig. Secod, the mea itervals betwee demads are calculated. The, they are used i a form of the model to predict the future demads.. Neural etwork models Methodologically, modelig ca be classified ito two priciples: white box ad black box. While the white box priciple bases o the kowledge o the pheomeo ad the all perceived relatioship betwee iputs ad outputs ca be represeted by mathematical equatios, the black box priciple do ot required ay kowledge about the iput output relatioships, especially whe those relatioships are too complex or caot uderstadable. I time series data modelig, covetioal models ofte base o autocorrelatio aalysis. I the case of itermittet demad, it is seem that autocorrelatio aalysis based models do ot work well. It is difficult to fid the autocorrelative relatioship so that the forecastig is ot a easy issue. To fit such kid of problem, NN ca be a potetial cadidate tool. Pricipally, NN is a typical stochastic model based o black box approach. NN is a itercoected group of euros or a etwork of euros that uses a mathematical or computatioal model for iformatio processig. I NN, each euro is a uit of computatio i which a simple mathematical model is used. Hece, a NN based o a coective approach will possessed a powerful computatioal capability. A typical eural etwork is illustrated i followig Figure 1: Figure 1: A typical eural etwork (reprited from Wikipedia.org) I most cases, a NN is a adaptive system that ca chage its structure based o exteral or iteral iformatio flow through the etwork. I other word, based o the iput ad output data sets, the NN will repeatedly chage the weights ad biases i euro uits so that it ca represet a complex fuctio betwee output ad iput factors. This process is called traiig or learig i which NN ca lear or be traied to uderstad the complicated relatioships betwee iput ad output factors. The followig Figure shows the mathematical structure of a typical euro. 74
Figure : Mathematical structure of typical euro There are may kids of trasfer fuctio fuctios available for utilizig i NN, oe of most commo fuctio is logsig fuctio ca be showed i below figure: Figure 3: A typical trasfer fuctio: logsig fuctio.3 Data geeratio For comparative study, two data sets (traiig set ad validatig set) of itermittet demad demads are geerated radomly. Itermittet time ime series data ca be separated ito two parts: o-zero o zero demads (o-zero demad series) ad the iterval betwee two o-zero zero demads (zero iterval series). I each data set (traiig or validatig data set), these hese two subsets of data are geerated radomly first, the itegrated ito oe series. I traiig data set, for the o-zero zero demads series, 00 iteger data are geerated radomly radomly from 4 to 15. For zero iterval series, 00 data are geerated radomly based o geometric distributio. distributio As a result, about 1000 itermittet data i time series are used for traiig. Similarly, 60 iteger data ad 60 geometric distributed data are geerated geerated idepedetly i the same way for validatig set. Therefore herefore, about 300 itermittet data i time series ca be used for validatig step..4 Error estimatio For or evaluatig the efficiecy of proposed approach as well as comparig two predictig approaches, approach two criteria are used: mea squared error (MSE) ad mea absolute error (MAE). MSE ca be calculated by followig formula: MSE i 1 ei i 1 75 di pi (1)
i which e i is the deviatio betwee the observed demad d i ad the predicted demad p i at the time i, is the umber of data i series. Also, MAE ca be estimated by: e i di pi MAE () i 1 i 1 3. Results ad aalysis The followig table shows comparative results of two methods used for predictig the simulated itermittet data. There are 10 pairs of itermittet series data sets for traiig ad validatig are geerated ad ra with both Crosto ad proposed NN method. MSE ad MAE criteria are used for comparig their predictig capabilities. About 1000 itermittet data i time series date sets are used for traiig ad 300 for validatig. With Crosto method, two value of alpha 0.3 ad 0.5 are cosidered. Table 1: Comparative results N N Series Crosto alpha = 0.3 Crosto alpha = 0.5 Neural etwork MSE MAE MSE MAE MSE MAE traiig validatig 1 889 56 17.16518 3.13056 17.39775 3.94777 1.9856 0.414687 103 77 16.94134 3.113991 17.4845 3.179816 1.567149 0.440975 3 1053 317 18.019 3.1976 18.80318 3.37096 1.37688 0.36357 4 977 97 19.09358 3.37889 1.13574 3.68611 1.003908 0.319835 5 1047 310 15.7456.884753 17.05877 3.1333 1.15634 0.35136 6 956 67 18.0794 3.96088 18.0911 3.334309 1.580755 0.465035 7 1004 94 15.8756.966491 15.87653 3.08191 1.403137 0.3995 8 975 30 17.55667 3.096869 18.5341 3.34484 1.4466 0.348748 9 1006 304 16.46479.895371 17.106 3.03908 1.3647 0.36196 10 936 60 17.06976 3.73359 17.91836 3.37955 0.933998 0.333894 Arbitrary, the results of series 10 ca be selected to display i followig figures. I the Figure 4, the blue bars is the itermittet demad observatios from time =1 to time = 936. The red colored circles are the traied values with selected NN model. I the Figure 5, a set of 60 time series data for validatig is showed. Similar to figure 4, blue bars ad red colored circles represet observed demad ad predicted values respectively. Also, Crosto method with alpha = 0.3 ad alpha = 0.5 are displayed by cya color lie ad mageta color lie, respectively. 76
16 Traiig 14 1 10 Demad 8 6 4 0 0 100 00 300 400 500 600 700 800 900 Time Figure 4: Traiig data with NN 16 Validatig 14 1 10 Demad 8 6 4 0 0 50 100 150 00 50 Time Figure 5: Validatig data with NN, Crosto alpha = 0.3 (cya color) ad Crosto alpha = 0.5 (mageta color) 77
4. Coclusios This paper successfully showed that the feed-forward back propagatio etwork ca be cosidered as a better alterative tool to covetioal Crosto method for predictig itermittet demad. Not usig collected data sets, with radomly geerated data, a compariso study illustrates that i geeral, proposed NN model ca better perform i forecastig itermittet demad i term of two criteria MSE ad MAE. Ackowledgemets This research was supported by Basic Sciece Research Program through the Natioal Research Foudatio of Korea (NRF) fuded by the Miistry of Educatio, Sciece ad Techology (0100104). Refereces 1. Carmoa J. L. ad Rodrigues A. J. A. J., 004, Adaptive forecastig of irregular demad processes, Egieerig Applicatios of Artificial Itelligece 17(), 137-143.. Willemai T. R., Smart C. N., ad Schwarz H. F., 004, A ew approach to forecastig itermittet demad for service parts ivetories, Iteratioal Joural of Forecastig, 0, 375 387. 3. Gutierreza R. S., Solisb A. O., 008, Mukhopadhyay S. Lumpy demad forecastig usig eural etworks, It. J. Productio Ecoomics, 111, 409-40. 4. Che F. L., Che Y. C. ad Kuo J. Y., 010, Applyig movig back-propagatio eural etwork ad movig fuzzy euro etwork to predict the requiremet of critical spare parts, Expert Systems with Applicatios 37(9), 6695-6704. 78