A Dynamic Pricing Method in E-Commerce Based on PSO-trained Neural Network

Transcription

1 A Dynamic Pricing Mehod in E-Commerce Based on PSO-rained Neural Nework Liang Peng and Haiyun Liu School of economics, Huazhong Universiy of Science and Technology, Wuhan Absrac. Recenly, dynamic pricing has been a common compeiive maneuver in e-commerce. In many indusries, firms adjus he produc price dynamically by he curren produc invenory and he fuure demand disribuion. In his paper, we used paricle swarm opimizaion (PSO) algorihm o rain neural neworks, hen inroduced he PSO-rained neural nework ino e-commerce and presened a new dynamic pricing mehod based on PSO-rained neural neworks. In he mehod, from producion funcion principles we obained he leas variable cos, and by making he error of mean square beween he acual oupus and expecaion oupus minimal we go he opimal dynamic price of producs. The PSO-rained neural nework can simplify he rapid change of prices and can successfully se he opimal dynamic prices in e-commerce. Inroducion The advancemen of inerne echnology has enabled he esablishmen of elecronic commerce which has made communicaion beween buyers and sellers easy. This has resuled in he esablishmen of elecronic price negoiaion. Thus in recen years, he problem of dynamic pricing has drawn much aenion. Dynamic pricing is a business sraegy ha adjuss he produc price in a imely fashion in order o allocae he righ service o he righ cusomer a he righ ime. The raionale of dynamic pricing can be undersood wih many examples in e-commerce, such as airline ickes, new designer suis, and oher markeing producs associaed wih paricular holidays ec. In all of hese cases, he firm can improve is revenues by dynamically adjusing he price of he produc raher han adoping a fixed price hroughou he produc's marke life []. Dynamic pricing akes advanages o boh buyers and sellers, some researchers have sudied dynamic pricing mehods [2-6]. Many ways o dynamic pricing are o change he price coninuously over ime by reacing o any shifs in demand

2 A Dynamic Pricing Mehod in E-Commerce Based on PSO-rained Neural Nework 325 characerisics. However, such a pracice is ofen eiher no feasible or oo cosly. This paper proposed a simple and feasible dynamic pricing mehod which can be used for on-line price seing. The mehod is based on he demand sensiive model where price changes depend on he quaniy demanded and he variable cos changes wih he quaniy of produc o be sold. In e-commerce, he informaion is incomplee. Considering neural neworks have he abiliy o work wih incomplee daa and can be applied successfully in learning, predicing, and opimizaion funcions [7-9], we inroduced neural neworks ino dynamic pricing in e-commerce. Because he paricle swarm opimizaion (PSO) has he abiliy of evoluionary learning [0], we used he PSO algorihm o rain neural neworks. In his mehod, he opimal dynamic price was se by he PSO-rained neural nework. The process of dynamic pricing is he process ha he PSO-rained neural nework makes he cos funcion minimal. The res of his paper is organized as follows. Firsly we inroduce he PSO algorihm and neural neworks simply, and hen build he PSO-rained neural nework in secion 2. In secion 3, we presened he dynamic pricing mehod by using he PSO-rained neural nework. The paper ends wih conclusions in secion 4. 2 The PSO-rained neural nework 2. Preliminaries of neural neworks Generally a neural nework ofen includes he following:. The number of layers in neural nework. 2. The number of neural unis in every layer. 3. The acivaion funcions beween layers. By Kosmogorov Theory, under he condiion of reasonable opology and righ weighs, a sandard 3-layer neural nework can approximae any coninuous funcions. Fig. is he general opology of a neural nework

3 326 Liang Peng and Haiyun Liu Figure.. The opology of a 3-layer neural nework. The normal hidden-unis were logisic unis wih oupus in he range beween 0 and. The inpu unis and conex unis did no do any processing-hey simply passed on heir inpu. The oupu uni was a linear uni. Generally, sigmoid acivaion funcion was adoped in hidden layer. The sigmoid acivaion funcion is he following: f ( x) x e Generally, he nework was rained using he error back-propagaion algorihm wih learning rae. The raining process is o updae he connecion weighs and makes he nework enhance learning. In his paper we used paricle swarm opimizaion algorihm o rain he neural nework. Afer raining has been compleed, he neural nework can record he corresponding oupu according o he inpus. 2.2 Paricle swarm opimizaion (PSO) The PSO echnique was inroduced by Kennedy and Eberhar. Inspired by he flocking behavior of birds, PSO has been applied successfully o funcion opimizaion, game learning, daa clusering, and image analysis. The PSO s operaion is as follows. Each paricle represens a possible soluion o he opimizaion ask. During each ieraion each paricle acceleraes in he direcion of is own personal bes soluion found so far, as well as in he direcion of he global bes posiion discovered so far by any of he paricles in he swarm. Le Pr esen denoe he curren posiion in he search space, V is he curren velociy. During each ieraion, each paricle in he swarm is updaed using () and (2). V ( ) V ( ) c rand ( pbes( ) Pr esen( )) () c2 rand ( gbes( ) Pr esen( )) Pr esen ( ) Pr esen( ) V ( ) (2) where, rand ~ U (0,) is he elemens from uniform random sequence in he range (0,), c and c 2 is he acceleraion coefficiens, usually c c2 2. is he weigh coefficien, and pbes, he personal bes posiion of each paricle, is updaed by

4 A Dynamic Pricing Mehod in E-Commerce Based on PSO-rained Neural Nework 327 pbes( ), if f (Pr esen( )) f ( pbes( )) pbes ( ) (3) Pr esen( ), if f (Pr esen( )) f ( pbes( )) and gbes, he global bes posiion, is he bes posiion among all paricles in he swarm during all previous seps. I means gbes( ) arg max f ( pbes ( )), for any paricle i (4) i i The value of V can be clamped o he range [ V, V max max ] o ensure paricles in he search space. In his paper, he variable is he ineria weigh, his means ha he value of is ypically seup o vary linearly from maximum o minimum during he course of ieraions, and is formulaed as follows. max min max ier (5) iermax where, ier max is he imes of maximum ieraion, ier is he imes of curren ieraion. 2.3 The process of raining Using PSO algorihm o rain neural neworks, each paricle corresponds o he complee augmened weigh vecor ha connecs he neural nework's inpu-ohidden and hidden-o-oupu layers. The error of mean square beween he acual oupus and expecaion oupus is looked as finess funcion, using PSO algorihm o seek he opimal posiion (or he opimal weigh value) and make he error of mean square minimal. The process of raining is as follows: Sep : Randomly choose a swarm of paricles, he maximal ieraion imes and he minimal error of mean square, for each paricle iniialize he posiion and velociy. Sep 2: Le pbes be curren bes posiion, le also gbes be curren bes posiion among all paricles. Sep 3: Judge wheher he convergence condiion is saisfied, if yes, go o sep 6. Oherwise, go o sep 4. Sep 4: For any paricles in he swarm: i. Updae posiion and velociy using () and (2). ii. Updae pbes using (3). iii. Updae gbes using (4). Sep 5: If he convergence condiion is saisfied, go o sep 6. Oherwise, urn o sep 4. Sep 6: Oupu gbes. 3 Dynamic pricing by he PSO-rained neural nework Suppose a firm has o sell more han one produc a a ime. All producs use he same facors of variable cos. The quaniy o sell according o demand and pricing

5 328 Liang Peng and Haiyun Liu decision is made simulaneously. A firm sells differen levels of quaniies by he demand. To faciliae maximizing profis he firm will ry o use a combinaion of inpus ha will minimize is oal cos of a given level of quaniy demanded. The firm is employing mehods dynamically, adjusing price over ime based on quaniy demanded. By applying principles of producion funcion, we can use he PSOrained neural nework o ge a selling price a he leas oal cos. From producion funcion principles: Q f (x) (6) where, Q is he vecor of producs q, q 2,, q n, X is he vecor of inpu variable facors x, x, 2, xm. All producs use he same ype of variable facors, and he oal number of variable facors is he same. The relaionship beween he quaniy demanded and he oupu quaniy of he nework is as follows: qn q n (7) where q n is a nework oupu quaniy a ime, while q n is a desired oupu quaniy (quaniy demanded). The variable cos funcion of oupu quaniy q n is: cv ) f ( wm, xm ) (8) where w m is a consan inpu uni price of x m and he oal cos C T ) is: CT ) cv ) cf (9) where c F is a fixed cos. The following is he process of dynamic pricing by PSO-rained neural nework. Sep : Inpu w m, q n as he unis of inpu layer in he neural nework. Sep 2: According o qn f ( x n ), compue q n by using he neural nework. Sep 3: If qn q n, go o sep 4, else urn o sep 2. Sep 4: Obain he oal cos C T ) by equaion CT ) cv ) cf. ' Sep 5: Oupu he selling price P from P C T ). A he beginning of his mehod he difference beween q n and q n is big and negaive, i measures he error ha he nework makes. The error used o aler he inpu variable facors x m in order ha he nework's response o he same inpu price w m is beer he nex ime around. A each aleraion he difference will coninue o decrease up o he poin when i finds he leas variable cos c v ) for he quaniy demanded q n. The variable cos c v ) is added o fixed cos c F o give he ' oal cos C T ). The marginal cos C T ) is he derivaive of oal producion cos funcion wih respec o he level of oupus. From Marginal Decision Rule he selling price is se a he poin of producion when marginal cos equals marginal revenue. A his poin he producion cos is he minimum. Seing ' selling price p equal o marginal cos C T ) means ha his is he minimum price he seller can sell he produc, selling below his price leads o loss, and selling above his price maximizes profis. Profis are he difference beween oal revenues and oal cos, where oal revenues are he produc of price and he quaniy demanded. The firm will maximize profis a he level of oupus where he slope of he profis curve is zero. Since profis are revenues less cos, he slope of he profis curve, marginal profis, is equal o marginal revenue less marginal cos. Therefore, when he firm maximizes profis where he slope of he profi curve is zero, marginal

6 A Dynamic Pricing Mehod in E-Commerce Based on PSO-rained Neural Nework 329 revenue will be equal o marginal cos. The profis maximizing firm is selling produc a is mos efficien (lowes uni cos) of quaniy demanded where marginal revenue equal o marginal cos. A ha level he firm will sell he produc a he price which is equal o he marginal cos, which will maximize he oal revenues, in oher words maximizing he oal profis funcion. For any demanded quaniy q n, c v ) mus be he leas variable cos funcion. The coninuous changes in demand quaniy permi he coninuous inpu subsiuion wihin he inpu bundle. The changes in demand quaniy qn change he inpu bundle and consequenly change he leas cos, and consequenly change he selling price p. 4 Conclusion and fuure work Dynamic pricing as a changing price in a markeplace is becoming characerisic of elecronic commerce. This paper presened a novel dynamic pricing mehod based on PSO-rained neural nework. According o producion funcion principles, he PSOrained neural nework can simplify he calculaions of he leas variable cos funcion ha is he main facor in dynamic pricing. The mehod can se he opimal dynamic price and can be used in e-commerce wih differen quaniies and differen levels of demand a one ime. In he fuure work, we will give numerical examples and simulaion experimens. Acknowledgemen We would like o hank he Chinese Naional 985 Research Projec Science & Technology Developmen and Human Culure Spri Innovaion. References. S. Jagannahan, J. Nayak, K. Almeroh e al, On Pricing Algorihms for Hached Conen Delivery Sysems, Elecronic Commerce Research and Applicaions,, (2002). 2. R. Chawin, Opimal Dynamic Pricing of Perishable Producs wih Sochasic Demand and a Finie Se of Prices, European Journal of Operaional Research, 25,49-74 (2000). 3. J. Kephar and J. Hanson, A. Greenwald. Dynamic Pricing by Sofware Agens, Compuer Neworks,32, (2000). 4. K. Lin, Dynamic Pricing wih Real-ime Demand Learning, European Journal of Operaional Research,74, (2006). 5. X. J. Wang, Y. L. Chen and W. Q. Zhu, The Pricing Sraegies for Agens in Real E-Commerce, WINE 2005, LNCS 3828, (2005). 6. S. Neessine, Dynamic Pricing of Invenory/Capaciy wih Infrequen Price Changes, European Journal of Operaional Research,74, (2006).

7 330 Liang Peng and Haiyun Liu 7. D. Ardii, F. E. Oksay and O. B. Tokdemir, Predicing he Oucome of Consrucion Liigaion Using Neural Nework, Compuer Aided Civil and Infrasrucure Engineering,3,75-8 (998). 8. L.C. Jiao, Neural Nework Sysem Theory,Xidian Universiy Press, Xi an(996). 9. S.A. Cong, Face he MATLAB oolbox nerve nework heory and he applicaion, Universiy of Science and Technology of China Press, Heifei(998). 0. J. Kennedy and R. C. Eberhar, Paricle Swarm Opimizaion, Proc IEEE inernaional conference on Neural Neworks,4, (995).