The Research on the Inventory Prediction in Supply Chain based on BP-GA Chaos Prediction Algorithm

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1 Internatonal Journal of u- and e- Servce, Scence and Technology, pp The Research on the Inventory Predcton n Supply Chan based on BP-GA Chaos Predcton Algorth Wencheng u Zhjang College of Zhejang Unversty of technology Zhjang Road No. 182, Hangzhou Cty, Zhejang, Chna lwc198411@126.co Abstract In the odern supply chan anageent, optzng supply chan can reduce the cost of the enterprse. In the optzaton of supply chan, the nventory optzaton s a very portant part. Through forecastng the nventory aount, we can reduce the cost of the nventory. And we also can optze the supply chan. Because the supply chan networ s coplex, we use the chaos theory to study and predct the nventory. In ths paper, we put forward a chaotc forecastng ethod whch s based on the BP neural and genetc algorth. Ths new ethod s BP-GA chaos predcton algorth. We use the ethod to predct the nventory aount. The experent shows that the ethod has acheved good forecastng effect. Keywords: Supply chan networ; The nventory predcton; The chaos theory 1. Introducton Snce the dea of supply chan anageent s proposed, any enterprses have appled the dea of supply chan anageent to the daly anageent. Snce then, the anageent ode of the enterprse enters a new stage. The optzaton of the supply chan s an portant optzaton job for reducng the cost and provng the wor effcency. Aong the, the nventory optzaton s a very portant part n the optzaton of supply chan. Accordng to optzng the nventory of the enterprse, we can reduce the nventory cost. If we fnd out a good ethod to forecast the nventory, we can control the nventory aount better and optze the supply chan. Many scholars have studed the nventory predcton [1-2]. Agus Mansur and Tryoso Kuncoro used the aret baset analyss approach to predct the sall edu enterprse nventory [3]. They understood the behavor of consuers n purchasng the products so t can be used to predct the purchasng for the next perod. ater, the predcton was used as a decson support n deternng the approprate aount of nventory for each product. They use the Maret Baset Analyss (MBA) and Artfcal Neural Networ (ANN) Bac propagaton to study ths queston. Wang Xu and Wang Hong appled the artfcal ntellgence nto the nventory anageent and securty nventory forecast [4]. Ang to the securty nventory, Wang Dongxu and other people establshed B-P neural networ odel. Then they traned, studed and forecasted the actual proble. They acheved better results than the tradtonal ethod [5]. Xuan Chaotng and other people suarzed systeatcally the applcatons of the neural networ technology n the supply chan anageent. Then they ntroduced the fve applcatons about the neural networ technology n the supply chan anageent n detal. They were the optzaton, predcton, decson support, odelng and sulaton. Fnally, they appled BP neural networ to forecast the deand for Shangha bcycle aret and acheved good results [6]. u Yang and Zhen added the nfluence factor to the BP neural networ odel. And they used the ethod to forecast the nventory aount. Then they also used the tradtonal forecast ethod. Accordng to coparng the forecast results, t showed that ISSN: IJUNESST Copyrght c 2015 SERSC

2 Internatonal Journal of u- and e- Servce, Scence and Technology the BP networ odel had the hgher accuracy [7]. Jeong, Bongju and other people put forward a new supply chan optzaton odel and constructed a generalzed genetc algorth. Then they used the algorth to solve ths proble. Ths algorth ntegrated specal evoluton rules, overcoe the defect of the local convergence for the genetc algorth and proved the ablty of the global convergence. The experent results showed that the solvng of the supply chan optzaton proble was better than the tradtonal algorth [8]. u Qnghou put forward a nd of genetc algorth whch was based the nu gene fragent encodng and the two generaton copetton. They used the algorth to solve the best volue assgnent and the optal jont order pont. It acheved the ore scentfc anageent and control for the warehouse resources and the captal n order to use effectvely the nventory resources. Then t reduced the operatng cost and the nventory cost [9]. P.Radharshthnan establshed the hgher supply chan ateral deand forecast odel and used the genetc algorth to optze. Then he copared the optzed odel wth the tradtonal algorth and proved that the genetc algorth can acheve the good effect [10]. Snce the chaos produced, t nfltrated to any other nterdscplnary felds and got the wdely appled. The odelng of the chaotc te seres and predcton had the practcal sgnfcance. Ha Nafshan Ra,d Zaara Jalal and Hossen Jalalfar proposed a hybrd nonlnear Chaotc and Neuro-Fuzzy syste odelng for the basc RMR syste uncertanty based on contnuous functons. Ths odel also proved the theory of Benaws that s based on nonlnear systes by usng chaos theory and atheatcal relatons. The an advantage of proposed odel was to drectly predct output of RMR syste classfcaton syste wthout consderng the nput paraeters so that t leads to better results and a hgher level of predcton roc qualty [11]. Ehsan Maan Mandoab, Hossen Nejat Pshenarb, Aghl Yousef-Koa, Fard Tajaddodanfar proposed a new ethod that can avod the chaotc oton affect the resonator perforance n dfferent nonlneartes. The novel ethod was proposed for predcton of the chaos n the croand nano-electro-echancal resonators. Based on the proposed ethod, frst an accurate analytcal soluton for the dynacs behavor of the nano-resonators was derved usng the ultple scales ethod up to the second order [12]. Tang Yangshanetc used the chaotc ethod to study the traffc conflct flow. Usng the chaotc forecast ethod, the author studed the traffc conflct of the ntersecton. And he evaluated the forecast ethod and result accordng to the gray error test ethod. It showed that the chaotc forecast ethod was an effectve ethod for the traffc conflct flow [13]. Deng Zhongy studed the chaotc forecast ethod and the appled study [14]. The author analyzed n detal the current coonly used chaotc forecast ethods. It contaned the an thoughts of the chaotc te seres. Ths paper gave several representatve predcton exaples. And t ponted out the wde applcaton and the appled drecton of the chaotc predcton. Besdes, any other authors studed the chaos predcton and obtaned the draatcally acheveents [15-20]. Usng the chaotc theory to forecast the nventory of the supply chan can control the nventory cost and reduce the burden of the enterprses better. At the sae te, accordng to forecastng the nventory aount, t can better eet the deand of custoers. Therefore, ths paper put forward the chaotc forecast ethod whch s based on the BP neural and genetc algorth. The ethod s BP-GA chaos predcton algorth. We use ths ethod to forecast the nventory of the enterprses. The structure of ths paper s as follows. The frst part s the nstructon. In ths part, we ntroduce the research status of the nventory forecast and the chaotc theory. The second part s the chaotc predcton ethod. In ths part, we ntroduce the chaotc forecast ethods. The thrd part s the new chaotc forecast ethod-bp-ga chaos predcton algorth whch s based on the BP neural networ and the genetc algorth. In ths part, accordng to the defects of the tradtonal chaos predcton algorth, we cobned the chaotc forecast ethod, BP neural wth genetc algorth. And we put forward the proved BP-GA 296 Copyrght c 2015 SERSC

3 Internatonal Journal of u- and e- Servce, Scence and Technology chaos predcton algorth. The fourth part s the nuercal analyss. In the fourth part, we forecast the nventory aount. The ffth part s the concluson. 2. The Chaotc Predcton Method We assue that the chaotc te seres s x (1), x (2),, x ( t ), (1) The te seres reflects a state of one thng. It s not only a result of one thng, but also the nforaton of the future developent. Accordng to the research of the ancent scholars, constructng a state space can reveal the nforaton assocaton rules aong these oton states. M Y ( t ) ( x ( t ), x ( t ),, x ( t ( 1) )) R, ( t 1, 2,, N ) (2) Where, Y ( t ) s the state space vector. x ( t ), x ( t ),, are the coponents of the state space vector. s the sequence delayed te. s the denson of the state space. In general, the sequence delayed te s gven by the subjectve. s not too sall n order to prevent the lnear correlaton aong the coponents of the vector. s not too bg n order to prevent that the nonlnear correlaton range of the coponents of the vector s beyond the nforaton. The denson of the state space depends anly on the attractor fractal denson d of the sequence. Forecastng the future state of the te sequence s to deterne the functon relatonshp f () between the current state Y ( t ) and the future state Y ( t ). Y ( t ) f ( Y ( t )) (3) The ethod whch s accordng to the attractor ethod n the fttng phase space to fnd f () the nonlnear functon can be dvded nto the global chaotc predcton ethod and the local chaotc predcton ethod. The global chaotc predcton ethod s to ae the all ponts n the locus as the fttng object. Accordng to the polynoal and the ratonal type, t can fnd out the rules. That s f (). Then t can forecast the trend of the trac. Of course, t s possble for the lower ebeddng denson. However, f t eets the hgher ebeddng denson syste, t s not practcal to use the polynoal to do the syste sulaton. Ths ethod s feasble n theory. However, the actual data s lted and the phase space trajectory ay be coplcated, then t could not get the real appng relatonshp () accordng to the gven data to structure the appng: f : R R The functon aes f approxates to f n theory. That s, f. In general, (4) 2 [ Y ( t ) f ( Y ( t ))] (5) The local chaotc predcton ethod s to ae the last pont n the phase space trajectores as the center pont. And t aes the ponts whch are nearest to the center pont as the relevant ponts. Then s aes the fttng for ths ponts and estates the trend of these ponts. Fnally, t separates the deanded forecasted values fro the coordnates of the forecasted trajectory. 3. The Chaotc Forecastng Method BP-GA Chaos Predcton Algorth whch s based on the BP Neural Networ and the Genetc Algorth After we analyzed the global chaotc predcton and the local chaotc predcton, we found that the defect of the global predcton was that the coputaton was coplcated, especally when the ebeddng denson was hgh or very coplex. When applyng the local predcton ethod to forecast, frstly we found the center pont and ft a few ponts Copyrght c 2015 SERSC 297

4 Internatonal Journal of u- and e- Servce, Scence and Technology n the neghborhood. We dd not consder the nfluence of the space dstance on the predcton aong the center ponts. However, the space dstance aong the center ponts n the phase space was a very portant paraeter. The accuracy of the predcton depended on the several ponts that the space dstance was near to the center pont. In order to overcoe the above probles, we put forward a new hybrd chaotc predcton algorth. In ths paper, we establshed the BP-GA chaos predcton algorth whch was based on the neural networ and the genetc algorth. Frstly, we gave the chaotc te sequence and establshed the chaotc neural networ predcton odel. Then we used the genetc algorth to optze the weghts of the chaotc neural predcton odel. Fnally, we forecasted the chaotc te sequence. The output value s the predcton value. Aong the, the steps of hybrd predcton ethod between BP neural networ and genetc algorth are as follows. Frstly, we gve chaotc te sequence x ( t )( t 1, 2, ). Accordng to Taens theore, we select the proper delay te and ebeddng denson. Then, we reconstruct the phase space. Y ( t ) ( x ( t ), x ( t ),, x ( t ( 1) )) R, ( t 1, 2,, N ) Secondly, we use saple ponts n phase space as the nputs X [ ]( 1, 2,, ) for neural networ. We can establsh neural networ odel. In order to use genetc algorth and optze the connecton weghts of neural networ, we need to adjust the odel and structure of neural networ. The adjusted neural networ structure s as follows. xt () M xt ( ) 1 y x( t ( 1) ) x( t 1 ( 1) ) n Fgure 1. The Structure of the Adjusted Neural Networ In ths networ, there are nputs, n ddle layer nodes and one output node. There are n 1 nodes. For the n 1 nodes, ther nubers are1, 2,,, 1,, n, n 1. We use w (1, j n 1) to express the connected weght fro node to j node. Then, the chaotc te seres neural networ odel s as follows. j X [ ] x ( t ( 1) ), 1, 2,, (6) (7) j 1 y[ ] f ( w x[ ]), j 1, 2,, n j, n 1 (8) 1 z f ( w y[ j ]) z s the output of neural networ node. f () f s non-lnear Sgod functon. 298 Copyrght c 2015 SERSC

5 Internatonal Journal of u- and e- Servce, Scence and Technology The thrd step s to deterne the ntal populaton. In proved neural networ constructon, we assue w 0 f there s no connecton between node and j node. j Then we can gve the atrx that s foratted by the connecton weghts for each node. Aong the, w n W ( w ) j ( n 1 ) ( n 1 ) 0 w w n n n n n w w w w w w w w w 1, 1 1, 1 1, n 2, 1 2, 2 2, n, 1, 1, 1 w ( w, w,, w ) T n 1, n 1 2. n 1 n, n 1 And other odules are all zero atrxes. Then we assue threshold value for each node s They also forulate a atrx ( 1, 2,, n 1). ( ) 1 ( n 1 ) (,,, ) 1 2 n 1 The connecton weght atrx s a atrx that the lower trangular atrx s zero. Ths s because the neural networ s a non-feedbac networ. In networ, there are ( 1) n non-zero eleents. They express all connecton weghts n networ. Threshold atrx s a n 1 eleents atrx. Generally, there s on threshold value n nput layer. That s, 0. The atrx whch s constructed by non-zero threshold can be expressed as ( ) 1 ( n 1 ) (,,, ) 1 2 n 1 Therefore, we need to deterne n 1 non-zero thresholds. The connecton weght and threshold have ( 1) n ( n 1) non-zero values. We use the dgtal strngs whch are coposed by the bnary codes to express the ndvdual chroosoe n a populaton. ( 1) n non-zero connecton weght and n 1 non-zero threshold copose a group of data. That s ( w,, w,, w,, w, 1, 1 1, n, 1, n, w,, w,,, ) 1, n 1 n, n 1 1 n 1 In above functon, the data represents an ndvdual. A pluralty of such data sets can copose the ntal populaton. Such data n the group are real nuber. We need to convert the nto the bnary code dgt strng.., j, (9) (10) (11) A n ( w, ), B ax ( w, ), j, 1, 2,, n 1 (12) For all the weghts and threshold values, there are And A w, B j, j, 1, 2,, n 1, j, j j Copyrght c 2015 SERSC 299

6 Internatonal Journal of u- and e- Servce, Scence and Technology We use l bnary nuber to represent the weghts and thresholds n above range. Therefore, the values whch are expressed by the actual weghts or thresholds and the bnary dgtal strng have the followng relatonshp. or ( w ) A j l ( w ) ( 2 1) j b B A ( ) A l ( ) ( 2 1) b B A 1, 2,, n. j, 1, 2,, n 1 w or s the actual weght value. ( w ) or ( ) s the bnary nteger whch s j j b b expressed by l dgtal strngs. [ A, B] s the range of the weghts and thresholds. Accordng to the ult paraeter codng ethod, we cascade all weghts and threshold whch are correspondng to 0 1 codes. Then we can get an ndvdual of an ntal populaton. We express A, B as bnary ntegers and reeber the to ( A ) b and B b. That s, we substtute the weghts n forula [11] and thresholds for ( n (( A ), ( A ),, ( A ) ) b b b s the nu value n the group. Slarly, we substtute the weghts n forula [11]and thresholds for ( B ) b. That s, s the axu value n the group. Then, ax (( B ), ( B ),, ( B ) ) b b b H ax n s the populaton sze. That s, the group has H ndvduals. After deternng the populaton sze, we begn to select the ntal populaton. We convert all weghts n forula [11] and thresholds to bnary nubers and there are nuber. l ( n 2 n l ) We dvde nto H equal dvson. And we use the followng functon to calculate the nterval nuber I 2 1 H A.. Then we use bnary nuber I, 2 I,, h I to code and get the ntal populatons whch are coposed by h ndvduals equally. The fourth step s the ftness functon. The su of square error for output codes of neural networ s d and y functon s f n e ( d y ) are the desred output and actual output of output node. The ftness 1 e. Then we adjust the ftness functon f a f b. f s the adjusted selfftness functon. f s the orgnal ftness functon. And a and b are coeffcents. Aong the, a f ust be non-negatve. f a v g ( c 1) f a vg f ax f a vg, ax ) b ( f c f ) f ax a vg b f f s the average value of current group. f ax a vg a vg. (13) s the axu value n current group. The adjusted ftness degree axu value should be the average of specfed ultple for orgnal ftness degree. The rage of specfed ultple c s n [1,2]. Whether the ftness degree functon s sutable s related to the constant value. Accordng to the paper [20], we select c Copyrght c 2015 SERSC

7 Internatonal Journal of u- and e- Servce, Scence and Technology The ffth s the replcaton operaton. Frstly, we order all ndvduals n the group. Accordng to the level of the ftness degree for each ndvdual, we order the for descendng lst. Secondly, we dvde all ndvdual nto four equal parts fro the top to the botto. Fnally, we throw away 1/4 proporton ndvduals whch s ordered n the last. That s, they are elnated and could not nto the next generaton. We copy all ndvduals that the ftness degree are ordered n the ddle of 1/2 proporton. That s, they can be nto the next generaton. The rest ndvduals are coped two duplcates. That s, the two duplcates are selected nto the next generaton. The sxth s the crossover operaton. In the ntal stage of the evoluton, n order to enhance the dversfcaton degree of the populaton and ncrease the copetton aong ndvduals, t needs to expand the crossover operaton aong parents. Then t can produce any new ndvduals. However, n the later stage of evoluton, wth the ncrease of the evoluton tes, the soluton set group closes gradually to the optal soluton. At ths te, f we adopt the larger cross rato, t wll produce any new ndvduals whch dstrbute n the whole space. And t reduces the proporton that the food ftness ndvduals n groups. Therefore, larger cross rato wll lead to destruct the excellent ndvdual proporton and delay the convergence process. In ths paper, the forula for the cross rate s as follows. p p ( p ) * d D (14) c c 0 c n p s the ntal crass rato. d s the evoluton tes currently. And D s the total c 0 nuber of the evoluton. The seventh s the utaton operaton. In the basc genetc algorth, the utaton probablty s fxed and t s usually a very sall constant. In the later genetc evoluton, f the utaton probablty does not change, the average ftness of the populaton s close to the ost optal ndvdual. In addton, the ndvdual gene n the group s very slar. Therefore, t aes the genetc evoluton process have no copetton. It becoes le a rando selecton. It reduces the speed of the evoluton, even aes the evoluton stagnaton, reduces the dversty of the populaton and s easy to cause the local convergence. Then t produces the greatly nfluence on the effcency of the algorth. Therefore, we use the followng varant probablty forula. p p ( p p )( f f ) ( f f ) f p, f f _ ax a vg _ ax _ ax _ n a vg ax a vg a vg Aong the, p s the utaton probablty of the varaton ndvdual. p s the _ a x axu utaton probablty. Here, we tae p 0.2. p s the nu _ ax _ n utaton probablty. Here, we tae p f s the ftness degree of the varaton _ n ndvduals. f s the axu ftness degree n the populaton. And f s the average ax a v g value of the group ftness degree n each generaton. The eghth step s the populaton optzaton. At the te, drone-rearng colony and subgroup have h ndvduals respectvely. We put the drone-rearng colony and subgroup becoe one group. They copose 2 h ndvduals. And we nuber the accordng to ther szes of the ftness degree. Therefore, the copy probablty of n 2 h populaton s as follows. ( h 1), 0,1, 2,, h 1 h 1 p( ) h, h, h 1,, 2 h 1 h We select h ndvduals whch have the axu copy probablty to copose the new progeny populaton. The nnth s the teratve. For the new progeny populaton, we calculate, copy, exchange and operate the ftness degree for the teraton. The evaluaton rule of the (15) (16) Copyrght c 2015 SERSC 301

8 Internatonal Journal of u- and e- Servce, Scence and Technology teratve s to test the relatve error of the two adjacent teratons. We test whether they satsfy the accuracy. ( 1 ) ( ) ax ( f ) ax ( f ) ( 1 ) ( ) E ( f, f ) ( ) ax ( f ) 0,1,, 1, 2,, h (17) ( 1 ) ( ) ( ) In the forula, E ( f, f ) s the relatve error of two teratons. f a x ( ) ( 1 ) axu ftness degree of the chroosoe n the teraton. f a x ( ) s the s the axu ftness degree of the chroosoe n the 1 teraton. s the gven evaluaton standard. We tae If the relatve error s less than the gven standard, the genetc algorth ends and puts the optal soluton. Is the relatve error s ore than the gven standard, we contnue to copy, change and utate untl the optal soluton s obtaned. 4. The Nuercal Analyss We use the BP-GA chaos predcton algorth ethod to forecast the product nventory for one copany. We collect 100 sets of data. Aong the, the frst 90 sets are the tranng data. And the last 10 sets are the saple data. Frstly, we copute the axu yapunov ndex of the nventory te seres. The ndex s And t s greater than zero. Ths llustrates that the nventory te seres has the chaos. And we can use the chaotc ethod to forecast. The flow chart of BP-GA chaos predcton ethod s as follows. Deterne the delay te and ebeddng denson Reconstructed phase space Deterne the ntal populaton Calculate the ftness functon The replcaton operaton The crossover operaton The utaton operaton The populaton optzaton The teratve Fgure 2. The Flow Chart of BP-GA Chaos Predcton Method Then, we use the BP-GA chaos predcton to predct the nventory. The results are as follows. 302 Copyrght c 2015 SERSC

9 Internatonal Journal of u- and e- Servce, Scence and Technology Fgure 3. The Actual Value and the Predcton Value Fro the above fgure, we can see that the results of the chaotc predcton ethod are ore accurate and acheve good results. Ths ethod has ore accuracy for forecastng the nventory of supply chan. The error s saller. And the predcton result s ore deal. Then, we use the dfferent ethods to predct the nventory and copare wth BP-GA ethod. The results are as follows. Method The su of error Table 1. The Coparng of the Dfferent Methods near regresson analyss logarthc functon exponental soothng genetc algorth Chaos predcton ethod BP-GA 17.82% 15.21% 15.63% 9.58% 10.31% 4.57% Fro ths table, we can see that the su of the error of BP-GA s less than the other ethods. It follows that the predcton accuracy of BP-GA ethod s hgher. The fact proves that the ethod has good feasblty and applcablty. 5. Concluson For the daly busness, the nventory cost occupes a large proporton n the total cost of the enterprse. If the nventory of the enterprse s too low, the enterprse wll cause a lot of loss due to the out of stoc. If the nventory of the enterprse s too hgh, the enterprse wll tae a lot of nventory cost. Therefore, the enterprse s strct to the nventory level. Accordng to forecastng the nventory aount of the enterprse n supply chan, the enterprse can control better the nventory cost and ncreases the oney aount n crculaton. In ths paper, we dd the followng wor. Frstly, we suarzed the chaotc predcton ethods. Secondly, accordng to the suary of the results, we put forward a new chaotc predcton algorth whch was based on the BP neural networ and the genetc algorth. Thrdly, we used the algorth to forecast the nventory aount of the product. The results showed that the predcton results were ore accurate. And t had good feasblty and applcablty. Copyrght c 2015 SERSC 303

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