Dynamic Pricing Model of Container Sea-Rail Intermodal Transport on Single OD Line

Transcription

1 JOURNAL OF RANSPORAION SYSEMS ENGINEERING AND INFORMAION ECHNOLOGY Volume 12, Issue 4, Augus 2012 Online English ediion of he Chinese language journal Cie his aricle as: J ranspn Sys Eng & I, 2012, 12(4), RESEARCH PAPER Dynamic Pricing Model of Conainer Sea-Rail Inermodal ranspor on Single OD Line LIU Di 1,2, YANG Hualong 1, * 1 ransporaion Managemen College, Dalian Mariime Universiy, Dalian , Liaoning, China; 2 School of raffic and ransporaion Engineering, Dalian Jiaoong Universiy, Dalian , Liaoning, China Absrac: In he managemen of conainer sea-rail inermodal ransporaion, dynamic pricing problem wih uncerain condiions has significan impacs on he benefi and compeiiveness of a mulimodal ranspor operaor. Based on he revenue managemen heory and he feaures of conainer sea-rail inermodal ranspor, his paper develops a wo sages opimal model which inegraes dynamic pricing and slo allocaion on single origin-desinaion line. he firs sage is proposed by considering long-erm slo allocaion in conrac marke, and he second sage is se up in consideraion of he dynamic pricing in free marke. Because of he demand uncerainy and he saisic error characerisics, he mehod of chance consrained programming and a robus opimizaion model are used o solve he models, respecively. he simulaion shows he feasibiliy and efficiency of he proposed models and algorihms. Key Words: inegraed ransporaion; dynamic pricing; revenue managemen; conainer; sea-rail inermodal ranspor; opimal model 1 Inroducion Due o is high efficiency, fas speed, large capaciy, low cos, less polluion, and oher ousanding advanages, conainer sea-rail inermodal ranspor becomes he focus model promoed by he inegraed ranspor sysem in he 12h Five-Year Naional Plan. he relevan deparmens, such as governmen, railways, pors, and shipping companies, are acively making improvemens and co-ordinaions o conainer sea-rail inermodal ranspor from he aspecs of managemen sysem, infrasrucure, and operaional organizaion. hus, he developmen of he environmenal and echnical condiion for conainer sea-rail inermodal ranspor will be gradually improved, and he marke demand will grow wih diverse characerisics, which will resul in an enormous challenge o MOs. Conainer sea-rail inermodal ranspor has he ypical characerisics of applying he revenue managemen heory, such as he ranspor capaciy in a cerain period of ime is fixed; ranspor services canno be sored wih perishabiliy, bu can be pre-sold; fixed cos is high, and marginal cos is low; marke demand can be segmened, bu is volaile. herefore, employing revenue managemen ideas in he conainer sea-rail inermodal ranspor sysem is feasible. How o use he revenue managemen heory o respond o inermodal marke demand changes flexibly and o increase ranspor efficiency and effeciveness are imporan decisions relaed o he fuure survival and developmen of MOs. Domesic as well as foreign scholars have conduced a lo of researches on conainer ranspor revenue managemen. Ha [1] has sudied he slo conrol sraegies of a conainer shipping company using he expeced marginal revenue (EMR) and hreshold curve (hreshold calve) model; Feng e al. [2] have sudied he opimal slo allocaion problem of a conainer liner on specific roues by aking he cos of an empy conainer allocaion ino accoun, and esablished a mahemaical programming model wih he objecive of maximizing liner companies operaing profis, and he consrains on shipping capaciy, conainer demand, and he supply of empy conainers; Sebasian [3] has sudied he discree simulaion of liner slo booking, and esablished liner slo allocaion quaniaive models wih aking he ransfer possibiliies among muli secions and muli roues ino accoun, which were simulaed in differen siuaions, Received dae: Mar 13, 2012; Revised dae: May 9, 2012; Acceped dae: May 15, 2012 *Corresponding auhor. hlyang@dlmu.edu.cn Copyrigh 2012, China Associaion for Science and echnology. Elecronic version published by Elsevier Limied. All righs reserved. DOI: /S (11)60216-X

2 LIU Di e al. / J ranspn Sys Eng & I, 2012, 12(4), neworks, and inpu seings o deermine he opimal slo-booking sraegy for shipping companies; Pu [4] has esablished a series of mahemaical models based on he conainer liner slo allocaion problem wih sochasic programming and dynamic programming mehods in his Ph.D. hesis, and solved he models wih chance-consrained programming and robus opimizaion mehods; Yang e al. [5] conduced quaniaive research on he pricing of conainer liner slos, and esablished a slo pricing model wih he objecive of maximizing he expeced reurn and he consrains ha demands obey Poisson disribuion and shippers' reservaion prices obey exponenially disribuion, hen go he opimal slo pricing equaion and analyzed he naure of he opimal price; Ren [6] has sudied he pricing problem of China Railway Conainer ranspor in his maser s degree hesis, and esablished a railway conainer ranspor pricing model wihou considering empy conainer allocaion, hen simulaed, and analyzed he impacs of ranspor coss, differences of shippers subjecive value, shippers arrival rae, and iniial slo changes on he opimal pricing and he maximum expeced reurn. As menioned above, exising lieraures only focus on conainer ranspor revenue managemen of a single mode of ranspor (by sea or rail ranspor) from he perspecive of a paricular decision-making behavior (eg, capaciy or slo allocaion decisions, dynamic pricing decisions); however, he research on conainer sea-rail inermodal ranspor revenue managemen and he comprehensive decision making of slo allocaion and dynamic pricing is sill rare. Based on he business and organizaional characerisics of conainer sea-rail inermodal ranspor, his aricle inegraes he pricing sraegy wih slo allocaion by considering he pricing differences beween conrac sale and free sale as well as he dynamic pricing during he free sale period from he MOs poin of view, and esablishes he dynamic pricing model of conainer sea-rail inermodal ranspor based on revenue managemen in order o enrich he heory and pracice of conainer sea-rail inermodal ranspor revenue managemen and o provide a scienific decision-making ool for he operaional managemen of MOs. 2 Modeling 2.1 Problem descripion I is assumed ha an MO enerprise in an imperfecly compeiive marke has a monopoly pricing power. Based on he conainer sea-rail inermodal ranspor demand beween A and B, he MO decides o operae a conainer sea-rail inermodal ranspor line beween A and B as he Origin-Desinaion poin (O-D). he MO selecs por P as he seamless ransferring por of rail and sea hrough a pah selecion decision; deermines a railway company and a liner company as he acual carriers of railway and mariime secions hrough a sub-carrier selecion decision; hen signs a long-erm agreemen wih he acual carriers; and, finally, ges he operaional righ of he same amoun of slos in boh railway conainer rains beween A and P and shipping conainer liners beween P and B, so as o ensure a sable capaciy as well as he reducion of operaing coss. In he agreemen period, he MO will sign sea-rail inermodal ranspor conracs wih shippers as a conrac carrier and charge for oal freigh a a single rae o organize he conainer sea-rail inermodal ranspor. In order o adap o marke compeiion and increase efficiency and effeciveness, he MO needs o formulae a reasonable pricing sraegy and a slo allocaion sraegy for differen ranspor demands. Since he demands of conainer sea-rail inermodal marke beween A and B is in a one-way direcion, he MO conrols slos sale a he originaing poin, ha is o say, he MO sells slos a A and B separaely. he selling process can be divided ino wo sages: In he firs sage, he MO sells a par of he slos in advance according o he requess of large cusomers, which are manifesed as a series of sale conracs; in he second sage, he MO sells he remaining bi of slos freely a public price according o demand forecasing, and acceps he booking from a variey of scaered cusomers. In he firs sage, he inermodal price for conrac cusomers who have a srong bargaining power is cerain; hus, he MO needs o decide how many slos a mos can be allocaed o hese conrac cusomers a a negoiaed price o make maximum revenue. In he second sage, since scaered cusomers who do no have bargaining power have o book slos a he public price announced by he MO, he MO may divide freigh soliciaion ime ino periods and deermine he inermodal price and slo allocaion in each period, respecively, according o he forecas of demands o make maximum revenue. he revenue managemen problem of he MO is depiced in Fig Model he objecive in he firs sage is o deermine he appropriae slo number for conac sale o maximize he revenue of he MO, as he model (M1) Objecive: max z p x x D s.. x C x N 0 where x is a decision variable ha represens he slo number allocaed o conrac cusomers for conac sale; D represens he random demands of conrac cusomers; p indicaes he negoiaed price for conrac cusomers; C represens he oal slo capaciy of he inermodal line. Consrain shows ha he slo number for conac sale canno be greaer han he random demands of conrac cusomers; consrain expresses ha he slo number for

3 YANG Xiaoguang e al. / J ranspn Sys Eng & I, 2010, 10(4), 1121 Fig. 1 Dynamic pricing problem of he MO based on revenue managemen conac sale canno exceed he oal slo capaciy of he inermodal line; and consrain is an ineger consrain of he decision variable, ha is o say, his model is a random ineger programming model. he objecive in he second sage is o deermine he inermodal price and slo number in each period of freigh soliciaion ime for free sale. In he freigh soliciaion ime for free sale, he demands of scaered cusomers change wih he price changes. I is assumed ha he freigh soliciaion ime of he MO for free sale is, which can be divided ino periods according o weeks (or days). p is he inermodal price a he h period of free sale, and p is a decision variable; x is he slo demands in he h period of free sale, and x is a linear funcion of p, ha is, x p, 1,2,, (1) where he coefficiens, need o be esimaed using saisical mehods. he mahemaical model in he second sage (M2) is as follows: max z p x p ( p ) 1 1 x x p x C 1 1 p p P, Objecive: s.. Consrain indicaes ha he slo number for conac sale and free sale in he sum canno exceed he oal slo capaciy of he inermodal line; consrain represens ha he price for free sale a any period canno be less han he price for conac sale, and canno be more han a price upper limi P as well. 3 Model soluion 3.1 Model soluion in he firs sage Model (M1) is a random ineger programming model because of he exisence of he random demand variable D ; hus, he chance-consrained programming mehod is used in his aricle [4]. Considering he decision made in he adverse siuaion may no saisfy he consrain, i is allowed ha he decision does no saisfy he consrain o a cerain exen, bu he decision should make he probabiliy of saisfying he consrain o be no less han a cerain confidence level ; hus, he consrain in model (M1) can be ransformed ino a chance consrain, ha is, Prx D (2) Le o be he disribuion funcion of D ; hus, he cerainy equivalence consrain of chance consrain (2) is Model (M1) is convered ino an equivalen deerminisic model (M3): Objecive: max z p x x K 1 K supk K 1 s.. x C x N 0 Solving model (M3) wih Lingo sofware packages can resul in an opimal slo allocaion sraegy in he firs sage. 3.2 Model soluion in he second sage In he free sale model (M2), he acual demands flucuae randomly; hus, he opimal soluion depends very much on he coefficiens of x. If he esimaion of coefficiens and in Eq. (1) is no accurae, he opimal soluion may no saisfy he consrain of he slo capaciy limi; herefore, he goal of obaining he maximum revenue will no be me. As a resul, his aricle employs he robus dynamic pricing model [7] o fi he uncerainy of demands. Le ˆ, ˆ, ˆ, ˆ where, represen he acual value of he demand funcion coefficiens,, and ˆ 0, ˆ 0 indicae he variaion in he coefficiens,. Supposing and are decision variables whose values are in a closed inerval [ 1,1], is he deviaion degree beween he acual value and he esimaion, is he deviaion degree beween he

4 LIU Di e al. / J ranspn Sys Eng & I, 2012, 12(4), acual value and he esimaion, ha is, ˆ, ˆ. hus, he absolue value of he differences beween acual demands and nominal demands in he h period is ˆ ˆ p. he parameer, which is a given non-negaive real number, is inroduced o consrain he deviaion beween oal acual demands and oal nominal demands in each period, ˆ ˆ p ˆ ˆ p, can be ha is, 1 1 0, ˆ ˆ P 1 ; he larger value of, he less demand funcion informaion is masered by he MO; on he conrary, he smaller value of, he more demand funcion informaion is masered by he MO. Model (M2) can be ransformed ino a dynamic pricing robus model (M4), as follows: valued on Objecive: max z p ( p ) min p p ˆ ˆ 1 1 p p Cx 1 1 s.. ˆ ˆ p 1 1, 1, p p P, Merge consrain and in model (M4) ino a new consrain: ˆ ˆ p Cx 1 (4) hus model (M4) can be slacked ino he following robus model (M5): Objecive: max z p ( p ) min p p ˆ ˆ 1 1 p Cx 1 s.. ˆ ˆ p 1 1, 1, p p P, Model (M5) is a bi-level programming problem, and is inner minimizaion problem can be seen as a linear programming based on he decision variables, ; using he srong dualiy heorem, model (M5) is equivalen o he following convex programming problem model (M6): Objecive: max ˆ ˆ z p p y p p y s.. p p P, y 0 p Cx where y is he decision variable in he dual programming of he inner programming of model (M5). Solving model (M6) wih Lingo sofware packages can resul in an opimal pricing sraegy in he second sage. 4 Simulaion example analysis I is assumed ha an MO operaes a domesic conainer sea-rail inermodal ranspor on a single OD line wih he oal slo capaciy of C=100 EU. In he firs sage, he price for conrac sale is known as p I =3871 yuan/eu, he slo demand of conrac cusomers has been obained hrough hisorical daa, which is a random 2 variable following a normal disribuion of D N(54,2 ). Wih given confidence level of 95%, model (M3) is solved wih he Lingo sofware package o obain he resul of slo allocaion in he firs sage. he resul is ha he slo number allocaed o conrac cusomers is x I =57 EU. In he second sage, i is assumed ha he freigh soliciaion ime for free sale is divided ino hree periods on an average. he greaer of, he closer o he canvassing deadline, and he less sensiive of shippers demands o price changes. hrough a saisical analysis of relevan daa, he esimaion and variaion of demand funcion coefficiens in differen periods are shown in able 1. If he price cap limi P 4324 yuan, hen Providing he MO can grasp more informaion on he demand funcion hrough an exensive demand survey of he new pricing sysem, i is assigned 2 in his example. Model (M6) is solved wih he Lingo sofware package o obain he pricing sraegy in he second sage, as shown in able 2. he sraegy in he second sage is inegraed wih he sraegy in he firs sage o obain he slo allocaion sraegy and pricing sraegy of he inermodal line in able 3. able 1 Esimaion and variaion of demand disribuion in differen periods Freigh soliciaion periods of free sale Esimaion of demand funcion coefficiens, Variaion of demand funcion coefficiens ˆ, ˆ , , , , , , able 2 Pricing sraegy in he second sage Freigh soliciaion periods of free sale Pricing of free sale (yuan/eu)

5 LIU Di e al. / J ranspn Sys Eng & I, 2012, 12(4), able 3 Pricing sraegy and slo allocaion of he inermodal line wo-sage sraegy inegraing slo allocaion wih dynamic Slo allocaion sraegy pricing General Sraegy he firs-sage he second-sage free sale he firs-sage he second-sage sraegy conrac sale conrac sale unified sale Pricing (yuan/eu) Slo (EU) Revenue (yuan) oal revenue(yuan) From able 3, i can be observed ha if he MO adops a wo-sage sraegy ha inegraes slo allocaion wih dynamic pricing, he oal revenue is 396,901 yuan. If he MO adops he slo allocaion sraegy only, ha is o say, he MO adops slo allocaion in he firs sage while i sells he remaining slos a a unified price in he second sage, he oal revenue is 391,873 yuan. If he MO adops he general sraegy, ha is o say, he MO sells all slos a he same negoiaed price o all shippers wihou dividing he sages, he oal revenue is only 387,100 yuan. hus, he wo-sage sraegy ha inegraes slo allocaion wih dynamic pricing can increase he revenue as well as saisfy he shippers demands for he MO. 5 Conclusions Based on he revenue managemen heory, his aricle esablishes a wo-sage opimal model ha inegraes dynamic pricing and slo allocaion on a single O-D line from he viewpoin of he differen pricing sraegy of MOs, and solves he models wih mehods of chance-consrained programming and robus opimizaion. In he firs sage, he model solves he problem of slo allocaion for conrac cusomers a a negoiaed price. In he second sage, he model considers price as a decision variable, and solves he problem of dynamic pricing and slo allocaion in free sale according o he rules of scaered shippers demands changing wih price. he prices during differen booking periods are differen, which makes he conainer sea-rail inermodal pricing more flexible, hereby increasing he revenue of MOs. he simulaion verifies boh he feasibiliy and effeciveness of he models and algorihms. Only one single O-D inermodal line is considered in his model, and also only one value of confidence level and demand variance is used o calculae he slo allocaion and pricing resuls in he simulaion example. I should be noed ha, in he firs-sage model soluion, if he confidence level values are larger, he acual demand of conac sale deviaes larger from he mean, and he calculaed slo number allocaed o conac cusomers in he firs sage is more; hus, he remaining slo number for free sale in he second sage becomes less, bu here is no effec on he negoiaed price. Conversely, if he confidence level values are smaller, he calculaed slo number allocaed o conac cusomers in he firs sage is less; hus, he remaining slo number for free sale in he second sage becomes more, bu here is no effec on he negoiaed price. he research on conainer sea-railway inermodal ranspor revenue managemen will be furher compleed wih considering he acual siuiaion, such as he muli O-D inermodal line wih several railway and shipping poins, differen ypes of conainers, unsubscribing and overbooking, he impacs of differen values of demand variance and he parameer on he resuls of slo allocaion, and pricing. Acknowledgmens his research was funded by he Naional Naural Science Foundaion of China (No ), he excellen science and echnology innovaion eam incubaion program funding projec of he Dalian Mariime Universiy (No. 2011ZD027). References [1] Ha D. Capaciy managemen in he conainer shipping indusry: he applicaion of yield managemen echniques. Universiy of ennessee, [2] Feng Cheng-Min, Chang Chia-Hui. Opimal slo allocaion wih empy conainer reposiion problem for Asia ocean carriers. Inernaional Journal of Shipping and ranspor Logisics, 2010, 2(2): [3] Sebasian Zurheide, Kahrin Fischer. A simulaion sudy for evaluaing a slo allocaion model for a liner shipping nework. Proceedings of he Second inernaional conference on Compuaional logisics, Springer-Verlag, Berlin, Heidelberg, 2011, [4] Pu X Z. Slo allocaion sochasic models for conainer liner shipping wih revenue managemen. Souhwes Jiaoong Universiy, [5] Yang C H, Wang C H, Du W. A pricing model of conainer liner shipping. Journal of sysems engineering, 2007, 25(4): [6] Ren J W. Sudy on pricing of railway conainer based on revenue managemen. Souhwes Jiaoong Universiy, [7] Ran L, Li J L, Xu L P. Sudy on he robus model in single-uni produc dynamic pricing in revenue managemen. Journal of applicaion of saisics and managemen, 2009, 28(5):