Application of Combination Forecasting Model in the Patrol Sales Forecast

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1 Joural of Applied Sciece ad Egieerig Iovatio, Vol.2 No.12, 2015, pp ISSN (Prit): ISSN (Olie): Applicatio of Combiatio Forecastig Model i the Patrol Sales Forecast Chogyu Jiag 1, Shuchag Zhag 2, Hogqig Sag 1 1 School of Iformatio, Beijig Wuzi Uiversity, Beijig, , Chia; chogyu_jiag@live.com 2 School of Logistics, Beijig Wuzi Uiversity, Beijig, , Chia Abstract: After aalyzig the ivetory ad coditio sales of patrol statio, combiatio forecastig model for the patrol sales is established by combiig the gray system model ad the BP-eural model based o time series. Durig the combiatio, oliear programmig problem is applied to miimize the sum of squares of the average predict error, whose variables are coefficiets of the combiatio forecastig model. The, a eample is give to compare the accuracy of the gray system model, the BP-eural model ad the combiatio forecastig model. It proves that he combiatio forecastig model is superior. Keywords: Gray System; BP-eural etwork; combiatio forecastig model; patrol sales INTRODUCTION As oe of the most importat strategic resources, oil resources affectig the coutry's security, social ad political stability. The supply of the oil is the basis for ecoomic ad social developmet of each coutry. At the same time, with the developmet of the automotive idustry, sales of patrol statio are icreasig. Meetig the market demad for patrol is the primary target of patrol statios. What has become a importat premise of patrol supplicatio is to forecast the sales due to the requiremet that out of stock is ot allowed. Therefore, accurately forecastig demad of petrol is of paramout importace as shortage will lead to highly udesirable cosequeces. Theories ad methods about sales forecastig has draw may eperts attetio. Some of the achievemets has bee applied to the predictio of the petrol demad. Huazhi Liu forecasted the demad of the petrol market i Sichua provice of Chia by usig the method of regressio aalysis. [Liu et al., 2004] I a similar edeavor, Ge Jig also forecasted it, with the cosumptio elasticity coefficiet method which he idicated is better for log horizo predictio. The gray system, however is more reliable for short term forecast [Jig et al., 2007]. Gray system was widely bee ad has bee applied by Guohua He to forecast regioal logistic demad [He et al., 2008]. Qigyua Li established a forecast model by combiig dyamic maagemet model with safety stock, demad forecastig model, vehicle loadig model ad vehicle routig model [Li et al., 2008] Jiaguo Zhag who combied the gray system ad BP-eural model[zhag et al., 2008]. Qiaoyu Wei forecasted the petrol demad by the epoetial smoothig method [Wei et al., 2008] while system dyamics method was used by Lei Yua [Lei et al., 2010]. Sihu Shi predicted the demad of automobile by buildig a liear combiatio forecastig model based o improved gray theory-bp eural etworksupport vector machie [Shi et al., 2012]. The improved grey markov chai model is established usig the lide trasitio probability matri by Lig Zhao to forecast the traffic accidet death rate [Zhao et al., 2013]. Zhepeg Jia proposed a kid of support vector machie method [Jia et al., 2014] ad Zhigag Sheg compared the sigle, secod, cubic of epoetial smoothig ad Holter-Witer s epoetial smoothig method for the demad predictio of diesel oil [Sheg et al., 2014]. I additio to historical data that ca be used as a referece for forecastig, the sales of patrol is additioally affected by weather, traffic coditios, day of the week, whether the limit lie ad equipmet maiteace. The factor impactig the sales of the patrol should be selected with prudece. Due to the difficulty to get the accurate iformatio of the weather ad traffic coditios, we take the time series method cosiderig the certai regularity i time of workig days, price chage ad limit lie. Time series method is a kid of traditioal way for sales predictio by aalyzig the basic rule of the developmet of the observed value i a time sequece withi the same period. Geerally, time series forecastig method commoly use the movig average, epoetial smoothig method, the grey system theory ad markov predictio, etc. It is cocluded that the predictio result, however, by the forecastig model above sigal used, is difficult to achieve required predictio accuracy. Therefore, it is effective to combie multiple forecastig models. I the process of establishig the model, we make a Correspodig Author: Chogyu Jiag, School of Iformatio, Beijig Wuzi Uiversity, Beijig, , Chia. 481

2 J. of Appl. Sci. ad Eg. Io., Vol.2 No , pp hypothesis that maiteace status of the petrol statio does ot happeed. The remaider of this paper is orgaized as follows. We established the combiatio forecastig model after buildig the gray system model ad the BPeural model based the time series i sectio 2. A eample is give i sectio 3.Summary of the research is i sectio 4. FORECASTING MODEL Gray system model The grey system theory is a method to establish the dyamic model of the differetial equatio by usig the discrete data colum after defiig the grey derivative ad grey differetial equatio based o the cocept of related space ad smooth discrete fuctio. [Shi et al., 2010] This kid of Model is called Grey Model (GM), for its attributes of approimate, ouique. Ad GM (1, 1) model is oe of the most commoly used models. If we build the model based o the data colum, the procedure is as follows: 1) After the origial data accumulated i order to weake the volatility ad radomess of radom sequece, the ew data sequece we get is like this: (, (2),, ( )) I the fuctio, () t represet the accumulatio of the data from 1 to t. or t ( t) ( k), t 1,2,, k1 t1 t 1,2,, ( t 1) ( k), k1 2) Build the first order liear differetial equatio. d a u dt I the fuctio, a ad u, which called developmet coefficiet ad grey actio, are the udetermied coefficiets. The matri a cosistig a ad u ca be writte as a.after u fidig out the value of a ad u, the predictive value of ca be kow from the value of () t. 3) Calculate the mea value of the accumulated data to geerate ad 0.5( (2)) B 0.5( ( 1) ( )) Y ( (2), (3),, ( )) T. 0.5( (2) (3)), 4) Solve the grey coefficiet a,ad a u 1 ( T T a B B) B Y 5) After puttig the grey coefficiet a ito ad solve the equatio fuctio: d dt a u, we get the u a at ( t 1) ( ) e u a Because a is the Approimate value through the ( t1) least square method, is a approimate epressio. 6) Discrete ad Strive for the differece betwee sequece ( t1) ad as follow: () t to reduce the origial ( t 1) ( t 1) ( t) BP-eural model Back Propagatio eural etwork (BP-eural etwork), putted forward by Rumelhart ad McCellad i 1986, is curretly oe of the most widely used eural etwork model. BP-eural etwork ca lear ad store umerous iput - output model mappig relatio, without itroduce the equatio which describe the relatioship. Its learig rule is to use the steepest descet method to miimize the squares of error sum of the etwork, by costatly adjustig the etwork weights ad threshold though back propagatio. [Shi et al., 2012] Topological structures of BP-eural etwork model iclude iput layer the hidde layer ad output layer, which are show i figure 1. Figure 1. Topological structures of BP-eural etwork BP-eural etwork, modeled based the iteral relatios betwee the data, has good self-orgaizig ad adaptability, strog learig ability ad ati- 482

3 J. of Appl. Sci. ad Eg. Io., Vol.2 No , pp iterferece ability. It automatically etracts kowledge from data, overcomes may limitatios of traditioal quatitative predictio method ad facig difficulties ad at the same time, avoids the ifluece of some huma factors. Betwee the iput layer ad output layer of the BP eural etwork, variables are determied by the weights betwee the differet layers. Regulatio of the weights is maily through the study of sigal. So, the more they lear, the more itelliget the etwork will be; i additio, the umber of hidde layers ad the accuracy of the etwork are positively related. To forecast sales by the BP eural etwork, the procedure should be divided ito several steps as follows: Step1: Select the appropriate traiig sample data. I the time series aalysis, the historical data has certai effect o the sales volume. Cosider sales of the petrol i a certai period, the same period of the previous year should be take ito accout. Step2: Pre-processig of sample data. Normalized the sales sample data to avoid ull result for output caused by too much sample data. I order to elimiate oise, result the ormalized data i [0, 1]. Step3: Costruct the traiig sample. We put two days data to be predicted ad the historical data of the same period the year before as traiig sample of the etwork model. Step4: Test the etwork model. Combiatio forecastig model Combiatio forecast model is built by combiig two or more sigle forecastig model based o the form of the appropriate weighted. Due to the defect of these sigle forecastig model, predictio results are ofte ieffective, while combiatio forecastig model performs better for its ability to cosider the iformatio sythetically[shi et al., 2010]. Based o the fuctioal relatioship betwee combiatio forecast model ad sigle forecastig model, combiatio forecast model ca be divided ito liear combiatio forecastig model ad oliear combiatio forecastig model. Here we use liear combiatio forecastig model. We assume that there are kid of forecast methods, t is the real value i the time uit t, ad e it is the forecastig value ad the error i the time uit t by the method i. Ad e, ( i 1,2,..., ; t 1,2,..., N),wher e it t it l i i1 represet the weighted of method i ad li 1, li 0, i 1,2,...,. Squares sum of error may reflect the size of the forecastig error. Based o this, the mathematical model established is as follows: it N mi f [ l ] t i it t1 i1 st.. l 0 Solvig the above oliear programmig, the combiatio forecastig model ca be obtaied as follows: t1 i it i1 i l, t 1,2,..., N Forecastig model build Table 1 shows the sales of oil tak 2 of a petrol statio i March 1, 2015 to 20.We forecast the sales volume of March 21, 2015 to 27 that the grey GM (1, 1) model ad the BP eural etwork based o time series are used respectively programmig by MATLAB2012b. The results are show i Table 2 Table 1. Sales of oil tak 2 of a petrol statio sales of oil tak sales of oil 2(L) tak 2(L) 2015/3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ Table 2. Results of GM (1, 1) model ad BP eural etwork results of GM (1, 1) results of BP eural etwork 2015/3/ /3/ /3/ /3/ /3/ /3/ /3/ Based o the method above, after solvig the mathematical programmig, the miimum value of the squares sum of error is e-12, weight coefficiets of GM (1, 1) model ad the BP eural etwork are ad The the combiatio forecastig model is established as follows: ( ) t1 1, t1 2, t1 t1 t 1, 1, t 1 ad 2, t1 is the forecastig value of the combiatio forecastig model, GM (1, 1) model ad the BP eural etwork. t 1 is 0-1 discrete variables. Whe ad oly whe the t+1 days petrol statio is out of Service for special reasos (equipmet maiteace, suspesio, etc.) t 1 0, otherwise, t

4 J. of Appl. Sci. ad Eg. Io., Vol.2 No , pp DISCUSSION Accordig to the historical sales data of oil tak 2 of the petrol statio i March 1st to 26 (Table 1 ad table 3), we forecast sales from March 27, 2015 to 29, respectively by GM (1, 1) model,the BP eural etwork ad the combiatio forecastig model. The results are show i Table 4 Table 3. Sales of oil tak 2 of a petrol statio sales of oil tak 2(L) sales of oil tak 2(L) 2015/3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ /3/ Table 4. Results of GM (1, 1) model, BP eural etwork ad combiatio forecastig model results of GM (1, 1) relative results of BP relative results of combiatio real value model error eural etwork error forecastig model 484 relative error 2015/3/ % % % 2015/3/ % % % 2015/3/ % % % Avg % % % The average relative error of the GM (1, 1) model, is 11.46%, the BP eural etwork is 2.77%, ad the combiatio forecastig model is 2.56%. Thus, compared with each sigle predictio methods, the combiatio forecast method has higher precisio. That meas the combiatio forecast model is a relatively effective forecastig model. At the same time, cosider that the predictio error ca be as low as 0.59%, also as high as 5.03%, the volatility of sales is ot fully reflected. The impact of eteral factors o the sales still eist. Meawhile, ruig the etire program requires early 3 miutes i forecastig sales of a sigle petrol statio, which ca be accepted. However, for a etwork cotaiig 100 petrol statios, the model ad the program will eed to be improved. CONCLUSION I this paper, the grey GM (1, 1) model ad BP eural etwork are combied to establish the combiatio forecast model. It has the advatages of requirig less iformatio, a simple method eed to build the GM (1, 1) model ad strog oliear mappig ability, good fault tolerace, selforgaizatio ad self-adaptatio of the BP eural etwork. The combiatio forecast model is applied i forecastig the sales of petrol ad the error aalysis is carried out with the results of each sigle demad forecastig model. The results show that the average error of the combied forecastig model is smaller tha that of ay sigle model, which idicates that the former forecastig model is effective. However, directly or idirectly, to build the model based o historical data, the iteral ad eteral coditios of a comple system caot be reflected well. Due to the isufficiet reflectio of the volatility of demad data, the reliability of the obtaied predictio results eeds to be improved. Therefore, factors, affectig the volatility of demad, which is combied with the time series forecastig model, will be the focus of future research. REFERENCES Chumei Li, 2009, The Research of Chiese Refied Oil Secodary Distributio Optimizatio, Master thesis, Chia Uiversity of Petroleum, Beijig, Chia. Geg Wag, Misheg Wag, 2008, Moder mathematical modelig method, Beijig: Sciece Press., Chia. Ge Jig., 2007, Oil demad forecast of Sichua provice AND Research o oil developmet strategy, Master thesis, Southwest Jiaotog Uiversity, Chegdu, Chia. HE Guo-hua, 2008, Forecast of Regioal Logistics Requiremets ad Applicatio of Grey Predictio Model, Joural of Beijig Jiaotog Uiversity(Social Scieces Editio), vol.7, No.1, pp Huazhi Liu., 2004, Market aalysis ad marketig coutermeasures of the product oil i Sichua, Master thesis, Southwest Petroleum Istitute, Chegdu, Chia. Jia Zhepeg, 2014, Study o Zhegzhou Airport Logistics Demad Forecastig Based o Support Vector Machie, Master thesis, Hea Uiversity of Techology, Zhegzhou, Chia. Jiwu Zhuo, 2011, The applicatio of MATLAB i mathematical modelig, Beijig: Beihag Uiversity Press., Chia. LI Qig-yua, LI Su-jia, 2008 A ovel logistic distributio model of refied oil based o vedor maaged ivetory, Joural of Chia Uiversity of Petroleum, vol.32, No.6, pp Sihu Shi, 2012, The Research of Demad Forecastig Model Based o Improved Gray System, BP eural etwork ad Support vector machie, Master thesis, Northeast Uiversity, Sheyag, Chia. WANG Zhuo, WANG Ya-hui, JIA L-i mi, LI Pig, 2005, The Applicatio of Improved BP Neural Network i the Predictio of Railway Passeger Volume Time

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