A Self-Adaptive Prediction Model for Dynamic Pricing and Inventory Control

Transcription

1 A Self-Adaptve Predcton Model for Dynamc Prcng and Inventory Control Hejun Lang* Shangha Unversty of Fnance and Economcs, School of Informaton Management and Engneerng, Shangha 00, Chna *E-mal: Abstract Based on the buldng of the consumer margnal utlty model and the consumer utlty model, and combnng the dynamc prcng and nventory control of products, the optmal sales prce of products and the optmal purchase amount of products n every perod can be analyzed from the qualtatve and quanttatve perspectve. The model s a relatvely deal system, because factors nfluencng the demands of products have been gven n every perod or factors, ncludng consumers, purchase prce and so on, n every perod have been clarfed. The analyss strategy of ths paper s to frst ntroduce the market predcton content and relevant predcton models, and then ntegrate the tradtonal predcton algorthm and the ntellgent algorthm nto the statc optmzaton system featurng the combnaton of the dynamc prcng and the nventory control. At last, through numercal analyss of the model, characterstcs of the optmzaton system featurng the combnaton of the dynamc prcng and the nventory control of varous predcton models are ponted out. The applcaton scope of relevant models s gven, thus layng a theoretcal bass for the commodty prce of enterprses and merchants. Keywords: dynamc prcn, nventory management, adaptve predcton model. Introducton Based on a full understandng of the qualtatve and quanttatve predcton model, ths paper analyzes the optmzaton results of the tradtonal predcton algorthm and the ntellgent predcton algorthm. Therefore, n order to analyze dfferences between the predcton algorthm and the practcal stuatons, t s necessary to unfy relevant model analyss parameters. Snce the gray system model s applcable to the stuaton when data shows the ndex varaton trend; the tme seres model s applcable to data wth certan varaton trend and perodcal changes; and the neural networks and the Support Vector Machne model has none requrements of the data, ths paper analyzes these models through the followng steps: Step : Accordng to characterstcs of varous models, relevant smulated parameters are unfed. The practcal data for the analyss of the gray predcton model are shown n Table ; whle the data for the analyss of the tme seres model, the neural networks model and the Support Vector Machne model are shown n Table. Besdes, the model adopts the specfc power demand functon. Step : Unfy the frst eght perods of data as the nput value and tranng value of varous predcton models, and the latter four perods of data as the predcton value. Step : Adopt the actual value of the perods of data as the nput data of the dynamc prcng and nventory control jont model, and obtan the optmzaton results of practcal data n every perod. Step : Adopt the latter four perods of varous market ndexes and data obtaned by varous predcton models and the former eght perods of actual 0 Metallurgcal and Mnng Industry No. 0

2 value as the nput data for the dynamc prcng and nventory control jont model. Work out the optmzaton results of varous predcton data n every perod. Step : Analyze and compare the optmzaton re- sults of varous predcton models and practcal data; evaluate the advantages and dsadvantages of varous predcton systems. Table. Smulated analyss of practcal data based on the gray predcton model Perod (t) 0 Consumers ncome (m),00,00 0,00 0,0 0,00 0,0 0,00 0,0 0,0 0,0 0,00 0,00 (r) Product orderng prce( p 0t ) Inventory cost (C) Table. Smulated analyss of practcal data based on the tme seres model, the neural networks model and the Support Vector Machne model Perod (t) 0 Consumers ncome (m),00,00,00,0,00,0,0,0,0,0,00,00 (r) Product orderng prce ( p 0t ) Inventory cost (C) Predcton of the market self-adaptve optmzaton based on the gray predcton model Under the condton when the hstorcal data are hard to collect, modelng based on few data can better reflect the role of the recent data [,]. Besdes, the market ndexes are subject to the nfluence of multple unpredctable factors, thus showng huge fluctuatons. It s hard to drectly employ the orgnal data for modelng. The gray system modelng uses the gray modules generated through accumulaton nstead of the orgnal data. Thus, t can weaken the randomness of data to a large extent, whle enhancng the data s regularty. At the same tme, the gray system theory combnes the qualtatve analyss wth the quanttatve analyss. In other words, durng the modelng process, the target system turns from a gray one nto a whte one through determnaton of the system scope to decomposton of the target system to confrmaton of system elements and behavors and relatonshp Durng the process, not only are mathematcal models of the modern control theory employed, but also knowledge of experence-based judgment. Qualtatve analyss and quanttatve analyss are combned to supplement each other, and to gradually obtan varous relatonshp between dfferent factors n the system and to form a modelng process from the qualtatve to the quanttatve, from the rough to the refned, from the gray to the whte. In other words, based on No. 0 Metallurgcal and Mnng Industry

3 the generated seres obtaned through the accumulated processng of a group of tme seres nformaton, fttng modelng s conducted of the generated seres whose randomness obtaned through the accumulatve processng s weakened whle regularty s enhanced. Ths paper adopts the gray predcton model to study the changng rend of the market demand ndexes based on the followng hypotheses: ) The data requred by the gray predcton model s few; ) The changng trend of most future ndex market data s progressve; ) The gray predcton model has an edge over other predcton models whle beng appled to short-term land demand predcton. GM (. ) for the gray predcton s based on the random orgnal tme seres. The regularty of the new tme seres formed by the tme accumulaton can use the soluton of the lnear frst-order dfferental equaton to draw near. The mmnent curve can be regarded as the model. At last, conduct an nverse accumulated generatng operaton of the model s predcted value, and predct the system. The establshment process of GM (. ) s shown below: () Data pre-treatment Assume the orgnal data seres to be: {,,, } ( 0) ( 0 ) x = x = n The seres generated after accumulaton: ( ) ( 0 ) x = x ( j) =,,, n j= () In order to revert the accumulated seres nto the orgnal seres, t s necessary to conduct the subtracton-based generaton, whch refers to the subtracton between the former seres and the latter seres. See Eq. () below: ( ) ( 0 ) 0 x = x x = x () Where, =,,, n, x 0 = 0. The generated seres weakens the randomness and nstablty of the orgnal seres and enhances the regularty. Conduct the ndex regularty test and the smoothness test of ( 0) x and ( ) x : ( x ) ( ) Step rato: σ ( ) = ( x ) ( ) ( 0 x ) ( ) Smoothness rato: ρ ( ) = ( x ) ( ) () () () When >, ρ ( ) < 0. and σ ( ) <, the data meet the smoothness condtons and the ndex rules. ( ) Conduct GM (,) modelng of x. () Modelng prncple Provde the observaton data seres: ( 0) ( 0 ) ( 0 ) ( 0 = {, (, ), ) } x x x x n () After one accumulaton, the followng equaton can be obtaned: ( ) ( { ) } x = x, x,, x n () ton Assume that x ( ) conforms to the frst order dfferental equaton: ( ) dx dt ( ) + ax = u In the equaton, a stands for the constant coeffcent, and the development gray number; u stands for the nternal control gray number, whch s a specfc nput of the system; the frst s the number of orders; the second stands for the number of varables. The equaton meets the ntal condtons. When t = t 0, the soluton of ( ) ( x ( t) = x ) ( t 0 ) s: ( ) ( ) u at ( t0 ) u x t = x ( t0 ) e + a () a The dscrete value ( t 0 = ) sampled at an equal nterval s: ( ) ( ( ) ) u ak u x k + = x ( ) e + a a (0) The gray modelng s to obtan an accumulated seres after one accumulaton. Use the least square method to calculate the constant a and u n Eq. (). ( Adopt x ) ( ) as the ntal value. Put ( ) ( ) ( x, x (, ), x ) ( n) nto Eq. () respectvely. Use the dfference to replace the dfferental. Based t = t+ t =, then: on equal-nterval samplng, ( ) ( ) x ( ) ( ) 0 = x = x x ( ) = x t Smlarly, ( ) x 0 x n 0 = x,, = x n t t Based on Eq. (-), then: + = 0 x ax u 0 x + ax = u 0 x n + ax n = u () () () () Move ax to the rght and wrte t nto the dot product form of the vector: Metallurgcal and Mnng Industry No. 0

4 x x 0 0 a = x ( ), u ( ) a = x ( ), u = 0 x n x n ( ) a, u x Snce t refers to the value accumulated to ( ) ( x ( ) on two moments, t s more feasble for x ) ( ) to use the average value of the two moments. Replace ( ) ( x ( ) wth ) ( x ( ) + x ) ( ), ( =,,, n). Rewrte Eq. () nto the matrx expresson: x x x ( 0 ) ( ) ( 0 ) ( ) ( 0 ) ( n) Make ( ) ( ) x + x ( ) ( ) ( ( ) ) x x ( ) a + = u ( ) ( x ( n) x ) + ( n ) () ( 0 ) ( ) ( (, 0 (, ), 0 ) ) y = x x x n ( ) ( x ( ) x ) ( ) + ( ) ( x ( ) + x ) ( ) B =, ( ) ( x ( n) x ) + ( n ) T a U = u Then, the expresson of Eq. () s shown below: y = BU () Therefore, the least square estmaton of Eq. () s: Put the estmated value, a and u, nto Eq. () to obtan the tme response equaton: ( ) ( ) u ak u x k + = x ( ) e a + a () When k =,,, n, ( x ) ( k+ ) obtaned through, () (), ( ) Eq. () s a ftted value. When k n x k+ s a predcted value. ( x ) ( k + ) s the ftted value of ( ) ( ) x. Subtract the former wth the latter to restore x. When k =,,, n, the ftted value, ( 0 x ) ( k + ), of ( 0) the orgnal seres, x, can be obtaned; when k n, the predcted value, ( 0 x ) ( k+ ), of the orgnal seres, ( 0) x, can be obtaned. Based on the above calculaton method, the predcted value at k + can be obtaned: ( 0 ) ( ) ( x k + = x k+ x ) ( k) The model s precson and relablty can be tested through resdual error, relatonal degree and posteror error. After the test, f the model s not precse enough, calbraton and optmzaton test can be conducted. () Precson test a. The major calculaton method of the resdual error test s shown below: Resdual error: ( 0 ) 0 0 ε = = k x k x k, k,,, n Relatve resdual error: ( 0 ) ( ) () Absolute error of the correspondng percentage: 0 0 e k = x k x k / x k, k =,,, n ε ( 0 ) ( k ) ( 0 ) n MAPE = n k = x k Generally speakng, f MAPE 0% and the error of the orgnal pont s less than %, t s apt to say that the model meets the precson requrement. b. The major calculaton method of the relatonal degree test s shown below: η ( ) ( 0 ) ( 0 { ε ( k) } + ξ max ε ) ( k) ( 0 ) ( 0 ( k) + max ) ( k) mn = ε ρ ε { } { } Where, ξ stands for the resoluton rato, whch s usually 0 and the relatonal degree s r n = η ( ). When ξ = 0., 0. r > meets the n = predcted precson. c. The major calculaton method of the posteror error test s shown below: Mean of ( 0) n n k = n n k = x : ( 0 X x ) ( k) = ( ( ) ) 0 S ( 0) = x k X Varance of x : Mean value of the resdual error: n ( 0 E = ε ) ( k) n k = () (0) () () () () () No. 0 Metallurgcal and Mnng Industry

5 Varance of the resdual error: n ( 0 S ) = ε ( k) E n k = S Specfc value of the posteror error: C = S Probablty of the small error: ( 0 { ε ) 0. } P = P k E < S Generally speakng, n order to dmnsh the error range of the predcted value, the value of C should be () () () small enough, even f the orgnal data have no rules to follow. The model predcton results can be judged accordng to the value of α, C and P. The hgher the value of α and C s, the smaller the value of P s. Generally speakng, the correspondng precson of the value of P and C s shown n Table. After the model s bult, t s tested. If the test results are unqualfed, the model can be mproved so as to effcently mprove the precson. Table. Precson test grade reference table Index Relatve error α Specfc value of the posteror error C Precson grade Grade Grade Grade Grade Based on the above dscusson, the major modelng steps of GM(,) can be boled down as below: Step : Assume the orgnal data seres to consttute x [See Eq. ()] and conduct an accumulaton ( 0) ( ) seres calculaton to obtan x [See Eq. ()]; Step : Buld the matrx form as lke Eq. () and obtan the correspondng B and y; T Step : Work out the nverse matrx, B B ; Step : Work out the estmated value, a and u, accordng to Eq. (); Table. Predcton results by the gray model Probablty of mnor error P Step : Work out ( x ) ( ) accordng to Eq. () and adopt the subtracton of the former wth the latter to acheve restoraton, namely: ( 0 ) ( x = x x ) ( ), =,,, n Step : Precson test and predcton: Put the data n Table nto GM (, ). Predct the future market ndexes. The predcton results, the predcton precson ndexes and the comparson results are shown n Table, Table and Fg. below: Perod (t) 0 Consumers ncome (m) 0,. 0,. 0,0. 0,. (r)..0.. Product orderng prce( p ) 0t Inventory cost (C) Table. Precson results of varous ndexes based on GM(,) Index Consumers ncome Product orderng prce Stock-holdng cost unt prce Development coeffcent (a) Gray actuatng quantty (u) Standard devaton error Mean relatve error (MAPE) Relatonal degree (r) Metallurgcal and Mnng Industry No. 0

6 Combne the orgnal data and the predcted data obtaned by the gray predcton model, namely the actual data n Table and the predcted data n Table. Put them nto the optmzed model of the specfc Fgure. Actual value and predcted value of GM(,) Table. Practcal optmzaton results of the specfc power demand functon model power demand functon respectvely to fnd a soluton. The optmzaton results of the actual data and the predcted data are shown n Table and Table below: T I t D t S t AI t p t Q t R t Table. Gray predcted optmzaton results of the specfc power demand functon model T I t D t S t AI t p t Q t R t No. 0 Metallurgcal and Mnng Industry

7 Based on soluton results of the above models, t can be seen that the overall predcton performance of GM (, ) s better. The precson ndexes of both models reach Grade, so the precson s relatvely hgh. Optmze the market ndexes obtaned through the predcted results and fnd a soluton. The results obtaned by the predcted model and the results obtaned by the practcal model dffer not greatly from each other. Except that n the 0 th perod the product sales prce s relatvely low and the product demand volume s relatvely large, the overall predcted value of the model s good. The fnal target benefts obtaned through the optmzaton show no sgnfcance dfference. Therefore, when the market demand varaton trend features an ndex varaton, the dynamc prcng based on the gray predcton model and the nventory control optmzaton model have no practcal gudng sgnfcance for the product sales plannng.. Self-adaptve market optmzaton and predcton based on the tme seres model When varous ndex data on the market cannot meet the exponental changes, the error of the gray predcton model s relatvely huge. Besdes, durng the varaton process of the practcal market ndexes, they usually fluctuated up and down. Therefore, t s necessary to predct the data wth perodcal fluctuatons. Ths problem can be well solved through the tme seres model. The tme seres s to arrange dfferent values of certan ndex on dfferent tme nodes n accordance wth the tme sequence [, ].Among the tme seres models, Auto Regressve Movng Average (ARMA) s one wth a full consderaton and a hgh feasblty. The model contans the characterstcs of the auto regresson model and the movng average model. However, snce the tme seres shows certan trend or characterstcs under most condtons, t cannot meet the stablty requrement of the model [, ]. Therefore, ARMA model cannot be drectly used. However, n the 0s, due to lmts of the ARMA model, Box and Jenkns put forward a new tme seres model, namely ARIMA, n 0 []. The model obtans a stable tme seres after d -order gradual dfferentaton of non-stable tme seres, y t. Based on the dfferentated tme seres, ARMA model can be bult. At last, the bult-up model obtans ts orgnal sequence through the nverse transformaton. The basc mathematc descrpton of ARIMA model s shown n Eq. 0: p q d d yt = θ0 + φ yt + εt + φε j t j = = d y t (0) Where, stands for the seres transformed by d -order dfferentaton of the seres, y t ; ε t stands for the mmedate error tem at the moment of t, whch s also the whte nose seres n lne wth the normal dstrbuton whose mean s 0 and whose varance s a constant; φ and φ j are the estmated parameters of the model; p and q are the number of order of the model. From Eq. 0, t can be seen that, f the seres d y t meets the modelng requrements of ARMA, then the seres, y t, meets the modelng requrements of ARIMA. Based on the analyss of the above ARIMA model, the calculaton steps of ARIMA are shown below: Step : Test the seres stablty and stablze t: Conduct the stablty test of the orgnal seres data; f the orgnal seres s stable, ARMA can be drectly used; f the orgnal seres s not a stable one, the orgnal seres should be dfferentated untl the stablty of the seres s met. Step : Confrm the number of orders of the model: The number of orders of the model, namely p and q, can be confrmed through the coeffcent of autocorrelaton and partal autocorrelaton coeffcent; Step : Estmate and test the model parameters: Judge whether the model s feasble through the estmaton of parameters and the test of sgnfcance and resdual error test of parameters; Step : Predct the orgnal seres based on the confrmed model and the model parameters. Put the data from Table nto the above ARIMA, Metallurgcal and Mnng Industry No. 0

8 and predct the future market ndexes. The predcton results, the predcton precson ndexes and the com- Table. Tme seres predcton results parson results of the model are shown n Table, Table and Fg. : Perod (t) 0 Consumers ncome (m),.,.,.,0.0 (r).0... Product orderng prce( p 0t ) Inventory cost (C) Table. Precson results of varous ndexes based on the tme seres model Indexes Consumers ncome Product orderng prce Stock-holdng cost unt prce Development coeffcent (a) Gray actuatng quantty (u) Standard devaton error Fgure. Results of the actual value and the predcted value of the tme seres model Put the actual data n Table and the predcted data n Table obtaned through the tme seres predcton model nto the optmzed model of the specfc power demand functon to fnd a soluton. The No. 0 Metallurgcal and Mnng Industry

9 optmzaton results of the actual data and the predc- ted data are shown n Table 0 and Table : Table 0. Practcal optmzaton results of the specfc power demand functon model T I t D t S t AI t p t Q t R t ,.,0.,.,.,.,.,0.,. 0,,,0,00 Table. Predcted optmzaton results of the specfc power demand model obtaned through the tme seres T I t D t S t AI t p t Q t R t ,0.,0.,,.,0,.,.,.,. 0,,, Based on the soluton results of the above models, t can be seen that the overall predcton performance of the tme seres model s good. The evaluaton of the precson ndexes of varous models accordng to the gray system also reached the Grade level. The market ndex value obtaned through the predcted results s optmzed to work out the soluton. The results obtaned by the predcton model and the practcal model dffer from each other slghtly. Ther dfference manly les n terms of sales prce of products. However, the product orderng amount and the model s accumulated profts obtaned by both models generally concde wth each other. Therefore, when the market demands fluctuate up and down, the dynamc prcng and nventory control optmzaton model based on the tme seres predcton model has no practcal gudng sgnfcance for the product sales plannng. Besdes, most practcal market ndexes are fluctuatng.. Dynamc prcng and nventory control model based on the ntellgent predcton algorthm Based on the optmzaton results through the above tradtonal predcton algorthms, t can be seen that the gray system predcton model has lots of prerequstes (for example, the gray system predcton requres the data to change n the exponental form); the predcted optmzaton results and the actual optmzaton results of the model dffer from each other slghtly. The cause of the dfference s that, when the seres s unstable, the error thus caused s relatvely huge. Through the nverse transformaton, the accumulated error wll be accumulated. Therefore, the fnal optmzaton results and the actual optmzaton results of the model show a larger error. Therefore, n order to overcome shortages of the above tradtonal predcton models, ths paper employs the BP neural networks model and the support vector bass model to predct varous market ndexes, compare ts optmzaton results wth those of the tmer seres model and the practcal model and show the characterstcs Metallurgcal and Mnng Industry No. 0

10 of the ntellgent optmzaton algorthm... BP neural networks mathematc model Accordng to the weght of the nput node and the output node, the weght between the nput node and the mplct node, and the weght between the mplct node and the output node, the relatonshp between varous layers of nodes can be expressed below: ()The forward transmsson process of sgnals: The nput of the node n the mplct layer, net : M net = w x + θ () j j j= The major dea of the BP neural networks s to rectfy the weght and the threshold to make the error functon to descend n the gradent drecton. After the step-by-step treatment of the nput nformaton n the mplct layer, the practcal output can be obtaned from the output layer. If the practcal output and the sample output dsagree wth each other, the error wll be sent back n a reverse drecton layer by layer. Modfy the weght of every layer n accordance wth the fttng rules requred by the algorthm. The mprovement s repeated untl reachng the convergence or stable state. In other words, the overall error of the practcal output and the target output should reach the requred mnmum error. Below are the specfc steps: The quadrc form error crteron functon of every sample, p, s E : p L E p = Tk ok () k = The overall error crteron functon of P tranng samples s: P L p p E = ( T ) k ok p= k= () Accordng to the error gradent descent method, the correcton of the weght of the correcton output layer s wk ; the correcton of the threshold of the output layer s ak ; the correcton of the weght of the mplct layer s wj ; and the correcton of the threshold of the mplct layer s θ. E wk = η E ; ak η E = ; wj = η ; w a w k E = k θ η θ The adjustment equaton of the weght of the output layer: Economy j () The output of the node n the mplct layer, y : M y = φ( net ) = φ wj x j + θ () j= The nput of the k node n the output layer, net k : q q M netk = wk y + ak = wkφ wj x j + θ + ak = = j= () The output of the k node n the output layer, o k : q q M ok = ψ ( netk ) = ψ wk y + ak = ψ wkφ wj x j + θ + a k () = = j= E E netk E ok netk wk = η = η = η w net w o net w () k k k k k k The adjustment equaton of the threshold of the output layer: E E netk E ok netk ak = η = η = η ak netk ak ok netk ak () The adjustment equaton of the weght of the mplct layer: E E net E y net wj = η = η = η wj net wj y net wj (0) The adjustment equaton of the threshold of the mplct layer: E E net E y net θ = η = η = η θ net θ y net θ () Besdes, P L E p p = ( Tk ok ) o k p= k= () netk netk = y, =, w a E y k net w j = x, net j = θ P L p p ψ = T o net w p= k= y net k k k k k = φ ( net ) ok = ψ ( netk ) net () k At last, the followng equaton can be obtaned: P L p p ψ w = η T o net y k k k k p= k= P L p p ak η ( Tk ok ) ψ ( netk) p= k= = () () () () () No. 0 Metallurgcal and Mnng Industry

11 P L p p w = η T o ψ net w φ net x j k k k k j p= k= () P L p p ( T o ) ( net ) w ( net ) θ = η ψ φ.. Establshment and optmzaton results of the BP neural networks modelng The network structure and relevant parameters establshed n ths paper are shown below: The neural networks have two layers. The number of neurons n the frst layer s and n the second layer. The transfer functon between the frst layer of neurons and the second layer of neurons s tansg (tangent transfer functon). The transfer functon between neurons of the second layer and neurons of the output layer s pureln (lnear transfer functon). Table. Predcton results of BP neural networks k k k k p= k= (0) Besdes, the tranng functon of the network s tranlm (Levenberg-Marquardt method). The maxmum teratons of the network are,000 tmes. The network fttng rate s 0. and the network s set error s 0. Put the data n Table nto the above BP neural networks model and predct the future market ndexes. The predcton results, predcton precson ndexes and comparson results of the models are shown n Table, Table and Fg. : Perod (t) 0 Consumers ncome (m),.,.,.,0. (r) Product orderng prce( p 0t ) Inventory cost (C) Table. Precson results of the BP neural networks model based on varous ndexes Index Consumers ncome Product orderng prce Stock-holdng cost unt prce Development coeffcent (a) Gray actuatng quantty (u) Standard devaton error Metallurgcal and Mnng Industry No. 0

12 Fgure. Predcted and evaluated results of the BP neural networks model Put the predcted data obtaned by the BP neural networks model, namely the predcted data n Table nto the optmzed model of the specfc power demand functon, to get the soluton. The optmzaton results of the predcted data are shown n Table. Table. Optmzed predcted results of the specfc power demand functon model T I t D t S t AI t p t Q t R t ,.,.,.,0,.,.,0.,,. 0,,,0 Based on the above soluton results obtaned through the above models, t can be seen that the overall predcton results of the BP neural networks model s better than those of the tme seres model. The value of varous precson ndexes of the model also reaches Grade level accordng to the gray system evaluaton. Through optmzaton soluton of the value of varous market ndexes obtaned through the predcton results, t can be found that the optmzaton results obtaned by the predcted model are n consstent wth those obtaned by the practcal model, whch s manly reflected n terms of product sales prce and product accumulated profts. Therefore, when market demands fluctuated up and down, the dynamc prcng and nventory control optmzaton model based on the BP neural networks predcton s closer to the practcal stuatons... Self-adaptve market optmzaton predcton based on the Support Vector Machne model Support Vector Machne (SVM) s a new-type machne fttng algorthm and an mprovement and optmzaton of the neural networks model. SVM s far more powerful n solvng over-fttng, under-fttng and local mnmum than that of the other machnes [, ].At present, SVM model has got extensve applcaton n the feld of securtes predcton, and can accurately predct the short-term market changes [0]. SVM bult n ths paper conducts parameter optmzaton through the genetc algorthm (GA). Relevant structural parameters of varous ndexes obtaned by the predcton model are shown n Table below: No. 0 Metallurgcal and Mnng Industry

13 Table. Parameter values of varous ndexes obtaned by SVM predcton model Index e C g Consumers ncome Product orderng prce Stock-holdng cost unt prce Put data n Table nto the SVM model already establshed above, and predct the future market ndexes. The predcton results, predcton precson ndexes and comparson results of the model are shown n Table -, Table and Fg. : Table. Predcton results of the SVM model Perod (t) 0 Consumers ncome (m),.,.,.,. (r) Product orderng prce( p 0t ) Inventory cost (C) Table. Precson results of varous ndexes obtaned by the SVM model Index Consumers ncome Product orderng prce Stock-holdng cost unt prce Development coeffcent (a) Gray actuatng quantty (u) Standard devaton error Metallurgcal and Mnng Industry No. 0

14 Fgure. Results of the actual value and the predcted value of the SVM model Put the predcted data obtaned by the SVM model, namely the predcted data nto Table, nto the optmzaton model of the specfc power demand functon to get a soluton. The optmzaton results of the predcton data are shown n Table : Table. Predcton optmzaton results of the SVM model of the specfc power demand functon T I t D t S t AI t p t Q t R Based on the soluton results obtaned through the above models, t can be seen that the overall predcton results of the SVM model are better than those of the tme seres model. Value of varous precson ndexes also reaches the Grade level accordng to the evaluaton of the gray system. At last, based on the market ndex value obtaned through the predcton results, the product s dynamc prcng and nventory control are optmzed together. The optmzaton results obtaned by the predcton model concde wth those obtaned by the practcal model, whch s manly reflected as the product s accumulated profts and product prcng. However, the product prce of 0 th and th perod obtaned by the BP neural networks and the SVM model s both slghtly hgher than the actual value. Ths s because, durng the model predcton process, tme s the only nput nformaton. In other words, t s caused by few ndex dmensons. However, generally speakng, t wll not nfluence the fnal predcton results. Based on the optmzaton results of the above tradtonal predcton models and the ntellgent predcton models, t can be seen that the fluctuaton of varous ndexes s not smply ndex changes, but perodcal random fluctuatons. Such fluctuatons have ther nternal varaton rules. Therefore, the combnaton of the ntellgent predcton model and the dynamc prcng and nventory control jont optmzaton model can better adapt to changes of varous market ndexes.. Conclusons Ths paper conducts optmzaton of the dynamc prcng and nventory control jont model, and focuses on the problem that the mode cannot be appled to No. 0 Metallurgcal and Mnng Industry

15 the predcton of the practcal market stuatons. Based on the smulaton of the tradtonal predcton algorthms and the ntellgent predcton model algorthms, ths paper comes to the followng conclusons: ) When market ndexes show exponental changes, the gray model can be easly combned wth the dynamc prcng and nventory control jont optmzaton model to predct and control the future market ndexes; ) When market ndexes fluctuate up and down rregularly, the tme seres model can be combned wth the optmzaton model to conduct predcton, but the predcton results devate greatly from the practcal results; ) BP neural networks model and the SVM model can be used to predct and optmze the future market stuatons. All these fndngs suggest that: the predcton results obtaned by the dynamc prcng and nventory control jont model based on the ntellgent predcton algorthm are closest to the practcal optmzaton results. Therefore, the ntellgent predcton algorthm can be used to predct varous future market ndexes, and can further obtan the optmal sales prce and optmal order quantty by combnng wth the dynamc prcng and nventory control jont model. References. Adda E, Peraks G. (00) A nonlnear contnuous tme optmal control model of dynamc prcng and nventory control wth no backorders. Naval Research Logstcs, (), p.p.-.. Jan WANG. Predcton of Changsha muncpal precptaton based on the GM (, ) Gray Model. (0) Fle, (0), p.p.-.. Le YANG & Maomao ZHANG. (0) Applcaton of tme seres model to the predcaton of logstcs demands. Commercal Economy Tmes, (), p.p.-.. Adda E, Peraks G. (00) A Robust Optmzaton Approach to Dynamc Prcng and Inventory Control wth no Backorders. Mathematcal Programmng, 0(-), p.p.-.. Adda E, Peraks G. (00) Dynamc prcng and nventory control: robust vs. stochastc uncertanty modelsa computatonal study. Annals of Operatons Research, (), p.p.-.. Qnhu LU. (0)Applcaton of BP neural networks to the prcng of commercal housng based on Hangzhou Cty. Journal of Zhejang Unversty of Technology (Socal Scences): (0), p.p. -.. Yuan WANG. (0)Applcaton of BP neural networks to the prcng of commercal housng. Journal of Shazhou Polytechncal Insttute of Technology, (0), p.p L S, Zhang J, Tang W. (0) Jont dynamc prcng and nventory control polcy for a stochastc nventory system wth pershable products. Internatonal Journal of Producton Research, (0), p.p.-0().. Xu Y, Chao X. (00) DYNAMIC PRIC- ING AND INVENTORY CONTROL FOR A PRODUCTION SYSTEM WITH AVERAGE PROFIT CRITERION. Probablty n the Engneerng & Informatonal Scences, (), p.p Gao W, Zhu J, Huang Z, et al. (0) Grey Self-adaptve Model of Dynamc Predcton of Surroundng Rock Deformaton of Tunnel and Intellgent Identfcaton of Parameters. Journal of Hghway & Transportaton Research & Development, (), p.p.-. Metallurgcal and Mnng Industry No. 0