Game-Theoretic Comparison Approach for Intercontinental...

Research ArticleGame-Theoretic Comparison Approach for IntercontinentalContainer Transportation A Case between China and Europewith the BampR Initiative

Xi Chen1 Xiaoning Zhu1 Qingji Zhou2 and Yiik Diew Wong2

1School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China2Centre for Infrastructure Systems School of Civil and Environmental Engineering Nanyang Technological UniversitySingapore 639798

Correspondence should be addressed to Xiaoning Zhu xnzhubjtueducn

Received 22 March 2017 Revised 20 August 2017 Accepted 4 October 2017 Published 9 November 2017

Academic Editor Jens Christian Claussen

Copyright copy 2017 Xi Chen et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper develops a game-theoretic model to analyze the competition between two container freight transportation modes(shipping and railway) using competitive game strategic interactions method namely deterrence by taking account of the mostcost-effective scale of the transportation capacity settingsThe competition was set against the background of Chinarsquos Belt and Road(BampR) Initiative as a new situation for intercontinental Sino-Europe container freight transportation The behavior of each mode(modeled as a carrier resp) is characterized by an optimization model with the objective of minimizing its cost by setting optimalbasic freight rate and transportation deployment A firm can use this method to compare the difference in the time value of thecargos and reduce the expense during the whole transportation process Finally the developed model is numerically evaluated bya case study of intercontinental transportation between Hefei (China) and Hamburg (Germany) The results show that deterrenceeffects largely depend on the deterrence objective and the differential in the cost of two transportationmodes tends to be stable withhigher values in the deterrence objective In the new intercontinental circumstance the mode of railway transportation provides anew way to transport the cargos between China and Europe

1 Introduction

In recent years shipperswith regular transport demands (egmanufacturing enterprise and sales companies) are alwayseager to minimize their transportation cost in the processThey always endeavor to select the optimal transport modeand perfect route to minimize the cost and time in thetransportation process

From another perspective global liner container ship-ping companies seek new emerging container shippingmarkets to maximize their profit margins while inter-continental trade and attendant transportation demandsamong China Central-Asia Russia and Europe continue togrow steadily For example several liner container shippingcompanies including APL (httpwwwaplcom) and PIL(httpswwwpilshipcom) have provided regular shippingservice between Shanghai Port (China) and Hamburg Port

(Germany) recently and they competed on basic freightrate and shipping deployment (a combination of frequencyand ship capacity setting) Furthermore several block trainsfrom China to Central-Asia Russia or Europe have addednew transportation mode that forged commercial containerfreight movements among the regions since the first Sino-Europe block train (officially named as ldquoCHINA RAILWAYExpressrdquo and abbreviated as ldquoCR expressrdquo) started its firsttrip at Chongqing (China) in 2011 However this newer traintransportation operates at higher basic freight rates and lowerfrequency than shipping and provides opportunity for serviceoptimization and improvement

In essence this study focuses on the competition ofcontainer freight movements mainly from the shippersrsquo per-spectives by setting the objective of how one can transport thecontainer cargo in a comparatively economic (both time andmoney) way In context the following questions are raised

HindawiJournal of Advanced TransportationVolume 2017 Article ID 3128372 15 pageshttpsdoiorg10115520173128372

2 Journal of Advanced Transportation

Proposed Silk Road routes

Railroad Entry Points

Proposed

Existing

Silk Road Economic

Belt the ldquoBeltrdquo21st-CenturyMaritime Silk Roadthe ldquoRoadrdquo

Figure 1 The Routes of ldquothe Silk Road Economic Belt and the 21st Century Maritime Silk Roadrdquo (source author adapted fromhttpwwwxinhuanetcom httpswwwwsjcom and httpwwwunorg)

(1) What are the aspects one should consider whenchoosing amode of transportation to transport containerizedcargo to another continent especially between China andEurope with the background of the Belt and Road (BampR)Initiative that offers a new mode of choice

(2) If the two modes of transportation (shipping andrailway) compete with each other using the deterrence gametheory which will win in the competition

The primary thrusts of the study are as follows (1) firstlythe BampR Initiative is introduced with both land andmaritimeroutes Meanwhile the main CR expresses and the tradingvolume from China to Hamburg (which is one of the mostimportant ports in Europe) are demonstrated (2) secondlythe two aspects that shippers (firms) care most namely timeand cost are illustrated in the study in which time valueconsideration in the cost function makes the overall costmore comparable and (3) finally the game-theoreticmodel isdeveloped from the perspectives of the shippers In additionthe application of the deterrence model (route from Hefei toHamburg) is proposed

The paper is organized as follows After this introductorysection the background and literature review are presentedThe following section proposes the methodology applied anddeveloped in this research including the problem descrip-tion the notations assumptions and formulas related to themodel the entry-deterrence gamemodels and the algorithmFurthermore a cased study is presented with the findingsThe final section gives the conclusions as well as furtherdiscussion of the study

2 Background and Literature Review

21 The Belt and Road Initiative The Chinese governmenthas in recent years embarked on a major plan in building

better linkages (especially transportation connection)between Europe and Asia by way of ldquothe Belt and Road(BampR) Initiativerdquo (also known as ldquoOne Belt One Roadrdquoor OBOR) OBOR is essentially a Chinese framework fororganizing multinational economic developments throughtwo component plans the land-based ldquoSilk Road EconomicBeltrdquo (SREB) and ocean-going ldquoMaritime Silk Roadrdquo (MSR)as is shown in Figure 1 The Belt and Road a reference to theSilk Road Economic Belt and the 21st Century Maritime SilkRoad was initialized by Chinese President Xi Jinping duringhis visit to Central-Asia and Southeast Asia in Septemberand October 2013 which also called for accelerating Beltand Road construction in the government work reportof China in March 2015 It offers a great opportunity forintercontinental logistics companies which shall engendersupport by the governments of many countries in AsiaAfrica and Europe

Several CR expresses have been set up to support theimplementation of the SREB and to meet the requirementsof the rapid growth of trade between China and Europe Asis shown in Table 1 there are basically two regions of transithubs which are located in Xinjiang and northeast part ofChina Until December 2016 there are more than fifteen CRexpresses from China to Europe originating within Chinathe majority are going out of China through Alashankou(Xinjiang) rather than through Manzhouli (Heilongjiang)andErenhot (InnerMongolia) As showed inTables 1ndash3 routedistances between the origins and destinations vary from8027 to 13052 km andmost journey durations are around 15days The earliest Sino-Europe block train ldquoYuxinourdquo (fromChongqing to Duisburg now all use CR express as a brand)has been in operation for more than 6 years and is animportant part of the cargo transportation network to Europe

Journal of Advanced Transportation 3

Table 1Major ldquoCR expressesrdquo (viaXinjiang (Alashankouhub)) (source author adapted from [1] and news from httpswwwyidaiyilugovcn)

Origin Destination Route distance (km) First start date Journey duration (days) DirectionChongqing Duisburg (Germany) 11179 Mar 19 2011 13 Two-wayChengdu Lodz (Poland) 9965 Apr 26 2013 14 Two-wayZhengzhou Hamburg (Germany) 10245 Jul 18 2013 15 Two-wayWuhan Pardubice (Czech ) 10863 Apr 24 2014 15 Two-wayYiwu Madrid (Spain) 13052 Nov 18 2014 21 Two-wayLanzhou Hamburg (Germany) 8027 Aug 21 2015 15 Two-wayHefei Hamburg (Germany) 11000 Jun 26 2015 15 One-wayWuhan Hamburg-Duisburg (Germany) Ca11000 Jan 1 2016 15 Two-way

Table 2 Major ldquoCR expressesrdquo (via Manzhouli hub) (source author adapted from [1] and news from httpswwwyidaiyilugovcn)

Origin Destination Route distance (km) First start date Journey duration (days) DirectionChongqing Cherkessk (Russia) 10000 Nov 11 2014 14 One-wayTomsk (Russia) Wuhan 9755 Nov 2014 13 One-waySuzhou Warszawa (Poland) 11200 Sep 29 2013 15 One-wayBrest (Belarus) Suzhou Ca 10000 Sep 29 2013 13 One-wayShenyang Hamburg (Germany) 11000 Nov 30 2015 12ndash14 Two-wayYingkou Zabaikalsky (Russia) 6500 Apr 9 2016 10 Two-way

Table 3 Major ldquoCR expressesrdquo (via Erenhot hub) (source author adapted from [1] and news from httpswwwyidaiyilugovcn)

Origin Destination Route distance (km) First start date Journey duration (days) DirectionZhengzhou Hamburg (Germany) 10399 Dec 3 2013 15 Two-way

0

5

10

15

20

25

30

TEU

20152016

China Russia Singapore USA Finland Malaysia SouthKorea

UnitedKingdom

Sweden India

times105

Figure 2 Top 10 trading partners in seaborne container traffic ofHamburg Port (source author adapted from httpswwwhafen-hamburgde)

in Southwest China Some CR expresses that are collectingcargos from almost the same regions compete with each otherwith shorter running time and lower freight rateThe numberof CR expresses (from China to Europe and to Central-Asia)has grown to twenty-one trains in total by December 2016and it is projected to soon expand further to twenty-six trainsin total

As illustrated in Figure 2 China commands the largestvolume in seaborne container traffic as a trading partner

with the Hamburg Port at above 2500000 TEUs in 2015and 2016 In this paper trading partner is one of the twoor more participants in an ongoing business relationshipWith the large trading volume and the huge potential marketthere is naturally huge transportation competition amongthe carriers and modes (shipping railway and airline) WithHamburg as a dominant European hub container throughputwith Chinese ports made good progress increasing by 16percent from 2015 to reach 26 million TEUs in 2016 Tobe more specific the volume in Figure 2 covers containersthat are transported from different origins to the HamburgPort as well as containers transported fromHamburg Port todifferent destinations

22 Literature Review With the background of BampR Initia-tive if a firm (shipper) wants to transport its cargos betweenChina and Europe usually there are three modes which areshipping railway and airline For container transportationairline is much more expensive than the other two modesand is also smaller in capacity hence airline mode is notconsidered in this study Therefore this research focuses oncomparing the transportation modes between shipping andrailway To study this issue it is essential to have knowledgeand findings of to-date research studies Hence existingliteratures are reviewed in the following parts about theinternational trade between China and Europe under BampRInitiative the competition in relative research ranges and theapplications of game theory in transportation

Although the world economy is experiencing a periodof slow-moving recovery global seaborne transport is still


an important way to move the world merchandise trade [2]In line with the increase in international business and tradethere has been growing interest in improving transportationconnection between Asia and Europe Fallon [3] studiedpolitical economic and ideological differences between SilkRoute Initiatives proposed by different countries and orga-nizations and believed that the BampR Initiative positivelyinfluences the world development and wealth Hilletofth etal [4] examined Eurasia as a land bridge for container trafficand applied the Finnish case to show the lead time advantageof the railway for amanufacturer but there are hindrances forrailway transport that need to be overcome Panova [5] con-sidered the BampR Initiative as a new modern transcontinentaltransportation system and stated that the corresponding levelof service is in high demand between China and Europe withthe growing market integration and globalization Hanaokaand Regmi [6] studied the status of intermodal freight trans-port in Asia from the environmental perspective In additionMo et al [7] discussed the economically suitable areas ofChinarsquos transnational container transport by land (rail orroad) in the BampR Initiative Wang [8] analyzed the situationon the development of Sino-Europe block trains (which arenow CR expresses) based on the aspects of market demandtransport organization and operation and proposed severalsuggestions on how to deal with the existing problems Wanget al [9] carried out a survey about the transport conditionurban transport development and the new mode of theinternational trade to analyze the industry structure statusand proposed suggestions on the economic development ofXirsquoan (a city in China) under the BampR Initiative

Freight transportation is usually carried out throughroad railway airline or shipping The research on theselection of the transport mode is always a key focus Differ-ent transport modes have different characteristics regardingthe time cost and capacity Peyrouse and Raballand [10]indicated that the selection of the transport modes is mainlydependent on time service andprice Rich et al [11] describedthe estimation of a weighted discrete choice model which isapplicable for selecting the proper transportmodeAccordingto Wang and Yeo [12] the transport modes differ in level ofreliability safety and capability Luo andChen [13] stated thata shipper makes decision on which transportation mode tochoose based on subjective reasons and experience Alvarez-SanJaime et al [14] compared the freight transport betweenthe road and maritime sectors

Competitions within one transport mode are also studiedby many researchers Lee et al [15] presented a novel multi-level hierarchical approach which modeled the oligopolisticand competitive behavior of carriers and their relationships inmaritime freight transportation networks Hao [16] proposeda framework in order to analyze the container port competi-tion and the feasibility of hub port implementation in ChinaWhat ismore in the process of the intermodal transportationWang and Zhu [17] focused on the optimization within therailway container terminal to shorten the transport timeMoreover some researchers studied entry-deterrence fora single transport mode Lin [18] investigated the role ofcode-sharing alliances on entry-deterrence with one majorcarrier that operated a network and one potential entrant

of the domestics spokes and demonstrated that the majorcarrierrsquos profits may vary according to the network size andits degree of product differentiation Aguirregabiria and Ho[19] presented an empirical dynamic game of airline net-work competition which incorporated this entry-deterrencemotive for using hub-and-spoke networks

The application of game theory in traffic and trans-portation analysis has attracted increasing attention by theresearchers Fisk [20] presented two game theory models(Nash noncooperative and Stackelberg games) applied intransportation system modeling Bell [21] envisaged a two-player noncooperative game to establish the performancereliability of a transport network as an important practicalproblem for engineers and planners involved in networkdesign Ishii et al [22] constructed a noncooperative game-theoretic model where each port selects port charges strategi-cally in the timing of port capacity investment and examinedthe effect of interport competition between two ports Thegame theorymodel also had been applied inmany other areaslike supply chain management traffic route choice behaviortraffic routing and so on (Leng and Parlar [23] Qi et al [24]Jiang et al [25])

The game-theoretic model is regarded as one of the mosteffective approaches to analyze the competitive behaviors forliner shipping [14] Song and Panayides [26] applied two-player cooperative game theory to analyze the interdynam-ics of liner shipping strategic alliances involving interor-ganizational relationships Min and Guo [27] developed acooperative game-theoretic model to determine the optimallocation of hub-seaports and then harmonize the port linksin a global supply chain network Imai et al [28] analyzedthe economic viability of deploying container megashipsbased on the game theory by applying a nonzero sumtwo-person game to obtain the optimal shipping servicestrategies in competitive shipping environments Liu et al[29] used cooperative game theory to analyze potentialimpacts of the Panama Canal expansion on the evolvingcompetitive-cooperative relationships and the distribution ofmarket power among the supply chain players in the UScontainer-importmarket Park andMin [30] analyzed fiercelycompetitive shippingmarkets in theAsia-Pacific region basedon the noncooperative game theory and revealed that thecontainer carrierrsquos optimal shipping strategy was insensitiveto changes in freight rates fuel prices and loadingunloadingfees at the destination ports Wang et al [31] developed threegame-theoretic models (Nash game Stackelberg game anddeterrence) to analyze shipping competition between twocarriers in a new emerging liner container shipping marketThe results showed that the deterrence effects largely dependon the deterrence objective an aggressive deterrence strategymay make potential monopolist suffer large benefit loss andan easing strategy has little deterrence effect

3 Methodology

31 Problem Description According to the starting time andthe capacity the shipping liners start (back to hundredyears ago or in 1975 when China reestablished diplomaticrelation with European Union) much earlier than the railway


Table 4 Advantages and disadvantages of different modes of transportation (source author)

Transport mode Advantage DisadvantageAirline Very fast safe Very expensiveShipping Cheap Slow humidTraditional railway Cheap Slow inconvenientCR express Fast convenient safe Expensive

transportation (started in 2011) and with larger capacitywhich means the shipping mode is more advanced andmature than the railway mode between China and Europe

In this paper we assume the scope of the entry-deterrencemodel can be enlarged into the container shipping servicescompetition between two different modes of transportationfrom port A to port B As a powerful economic tooldeterrence strategy has been introduced for quite a few ser-vice markets including the transportation freight industries(Wang et al [31]) By providing lower price to attract as manycustomers as possible the incumbents typically prevent newentrants (Shi and Voszlig [32]) However economists have somedoubts on the effect of lower price deterrence The entry-deterrence model has the advantage of using the competitionmethod other than the normal selection method thus onecan differentiate from the perspective of the problem as exist-ing studies The results can more readily indicate which car-rier or transport mode is competitive However by using theentry-deterrence model competitorsrsquo freight rate scope hasto be reasonable and comparative which may constrain thesetting of the capacity and basic freight rate in the research

This study aims to formulate an entry-deterrence modelon the premise that the scope of the model can be enlargedinto the container shipping services competition betweentwo different modes of transportation involving liner (CRexpresses and shipping liners) containermovement fromportA to port B It is also important to note that though shippingliners may differ from one another compared to railwayoperators shipping liners do possess many characteristics incommon among themselves Therefore with the upper andlower freight rate bounds the shipping liners can be treatedas one category of carrier in our study

In freight transportation the properties of the providedservices affect the choice of both the mode of transportationand the specific carrier Transport cost and transport time(including navigation time at sea andwaiting time at the port)are regarded as two most prominent properties that affectthe service choice decision-making which also constitutethe main considerations for the comparison analysis in thisstudy Without loss of generality we assume transportationmonetary cost and time cost as the two key costs

Generally each transportation mode has its own advan-tages and disadvantages For example the advantage of airlineis fast speed while its disadvantage is very expensive costIn Table 4 the airline ranks the first in time-saving howeverit is far more expensive than other modes Shipping andtraditional railway are quite cheap in price however thesafety of the cargos cannot be ensured the damage of cargos ismore than other modes and they have the longest transporttime The CR express is more expensive than shipping and

traditional railway however it is much cheaper than air (one-third of airline rate) and much faster (only half to one-thirdof shipping rate) than shipping mode

32 Notations Assumption and Modeling Process Considera shipper that is interested in delivering the cargos betweendifferent continents There are two alternative modes offreight transportation shipping and railway Each mode oftransportation has several carriers and several linesHoweverin order to make the problem easier to describe here wesuppose that each of the two modes has one carrier namelycarrier 1 and carrier 2 which represent the mode of shippingand railway respectively For the purpose of this study ldquocar-rierrdquo not only refers to the carrier in maritime transportationbut is also generalized as a carrier of the railway (which isnormally called ldquotrainrdquo in order to simplify the model) Atthe same time carrier 1 here stands for the shipping liners ofone category (since the shipping liners share many commoncharacteristics) within the upper and lower bounds so thatcarrier 1 is comparable with carrier 2 (railway operator)

In this paper we use FEU (Forty-foot Equivalent Unit)as the measurement unit of a container From the viewpointof the shippers if a shipper (usually a manufacturer or atrading company) wants the transport service between ports(or hubs) provided by carrier 119894 (119894 = 1 2) it can be indicated bythreemain variables in themodel namely freight rate servicefrequency and shipment capacity according to the maritimecontainer liners where the following is found119903119894 is the freight rate of transporting per FEU for carrier119894 (119894 = 1 2) which differs among the carriers119891119894 is the service frequency offered by carrier 119894 (119894 = 1 2)which presents the number of carriers calling from port (orhub) A to B in one week119888119894 indicates the shipment capacity setting for carrier 119894 (119894 =1 2) which is calculated in FEU in this paper as default

First we formulate the model of time It is assumedthat the container cargo delivery time follows a uniformdistribution during each periodic service time window (fromthe departure time in previous weekmonth to the departuretime in current weekmonth) Since the frequency of CRexpresses is sometimes measured with the unit of monthso we propose two ways to estimate the relation betweenfrequency and waiting time As a result the average waitingtime for a container to be delivered by carrier 119894 (119894 = 1 2) canbe estimated by

119879119882 (119891119894) = 12119891119894 (1)

in which 119879119882(119891119894) refers to the average time for a containerwaiting for the transport service offered by carrier 119894 (119894 = 1 2)


119879119882 (1198911015840119894 ) = 121198911015840119894 sdot

730 (2)

Equation (2) presents the situation where 1198911015840119894 refers toservice frequency per month besides it is same as (1) Inaddition to the above two elemental factors (ie basic freightrate and navigation time) some other important influentialfactors cannot be underemphasized including interport ter-minal handling charge (THC) and service-related attributesSo we consider the total time of the freight transportationgiven by

119879119894 = min 119879119878119894 + 119879119882 (119891119894) + 119879119867119894 (3)

where 119879119878119894 is travel time from A to B for carrier 119894 (119894 = 1 2)and 119879119867119894 is the container handling time at the port A or B forcarrier 119894 (119894 = 1 2)

According to Tavasszy et al [33] and Ravibabu [34] inthe service choice decision-making freight rate and transporttime are regarded as two properties of great importance inwhich the transport time includes navigation time and its hubwaiting time

Besides some other factors also occupy important posi-tions in freight transportation such as THC (interportterminal handling charge) and factors which are attributed tothe service indicatorsThese factors should not be overlookedsince the heterogeneity of THC affects the market share fortwo carriers in a market according to Anderson et al [35]even if it is of great difficulty to quantify the impactThen thegeneralized cost function of one FEU can be given as follows

119866 (119903119894 119891119894) = 120572 [119879119878119894 + 119879119882 (119891119894)] + 119903119894 + 120573 sdot 120582119894 + 119892 (]119894) (4)

in which 120572 is the value of time used as the additional amountof money that the shippers are willing to pay in order toshorten the transport time 120573 is the parameter used in thedisutility function for converting reputation intomoney cost120582119894 presents a score to reflect the reputation of carrier 119894 (119894 =1 2) measured from 0 to 10 119879119878119894 presents the transport timefrom port (or hub) A to port B for carrier 119894 (119894 = 1 2)

According to Oppenheim [36] and Wang et al [31] 120572and 120573 should be calculated using practical historical data Inaddition this function includes four parts cost measured bythe transport time transport (by rail or sea) cost in route costrepresenting the reputation and cost reflecting service levelrespectively

As part of the equation we consider the level of servicein terms of THC for each carrier The function of the level ofservice offered by carrier 119894 (119894 = 1 2) is

119892 (]119894) = 1198861 sdot ]119894 + 1198862 (5)

where 1198861 and 1198862 are two positive coefficients determined bythe real market To be noted we assume that the level serviceat the terminal is positively related to the unit containerhandling charge which means that the higher THC reflectsthe better service level As is shown in (5) it is a linearfunction to measure the level of service in terms of THC ]119894for each carrier 119894 (119894 = 1 2)The generalized cost equation (see

(6)) measures the utility with the length of time the freightrate and the service quality however pragmatically thereare also some factors for instance the congestions that existin the terminal or service tracking and other immeasurableor unheeded factors not defined However the utility theoryproposed by Ben-Akiva and Lerman [37] offers us a randomutility for decision-making which we take to reflect theattractiveness of transport service of a certain carrier Theequation is as follows

119880119894 = minus119866 (119903119894 119891119894) + 120576119894 119894 = 1 2 (6)

in which 120576119894 is assumed to follow Gumbel distributionWe usethis logit-based discrete choice model to evaluate the marketshare for each carrier since it is tractable and has a closed-form expression of the market share determination whichwill facilitate the property exploration and application of themodel

In addition an elastic demand function is introducedin terms of the expected maximum utility which is also avital issue in the market share determination Therefore theexpected value of themaximumof two utilities1198801 and1198802 canbe calculated by

119864 [max (1198801 1198802)]= minus1120579 ln [exp (minus120579 sdot 119866 (1199031 1198911)) + exp (minus120579 sdot 119866 (1199032 1198912))]

(7)

in which 120579 is the dispersion parameter used to measure thedegree of customersrsquo perception errors on the utility Whatis more since the freight rate (per FEU) from one continentto another is usually more than a thousand dollars whenthe expected maximum utility 119864[max(1198801 1198802)] is calculatedthe parameter 120579 should be comparatively small We take thefollowing container transport demand functions as

119889 = 119889119901 exp (minus120578 sdot 119864 [max (1198801 1198802)]) (8)

in which 119889 presents the actual weekly container shipmentdemand from port A to port B 119889119901 is the potential weeklycontainer demand from port A to B and 120578 is the elasticparameter predicting sensitivity of demand related to theutility In this section the demand function we chose is fromthe road freight transportation demand analysis and shippingliner competition and there are also some other demandfunctions not mentionedThe probability of choosing carrier119894 (119894 = 1 2) can be denoted as 119901119894 (119894 = 1 2) and it can also beconsidered as the container transportation market share forcarrier 119894 (119894 = 1 2) which is expressed as

119901119894 = exp (minus120579 sdot 119866 (119903119894 119891119894))sum2119894=1 exp (minus120579 sdot 119866 (119903119894 119891119894)) (9)

And 119889119894 presents the weekly number of the containerstransported by carrier 119894 (119894 = 1 2) and can be calculated by

119889119894 = 119889 sdot 119901119894 = 119889 sdot exp (minus120579 sdot 119866 (119903119894 119891119894))sum2119894=1 exp (minus120579 sdot 119866 (119903119894 119891119894)) (10)


In fact the market share is decided by the shippers (orsay as cargo owners) who are willing to spend less cost andexpecting to have shorter transportation time at the sametime No matter how much market share each carrier cantake the shippers always aim to minimize the net costs fortransporting containers from port A to port B

According to Notteboom and Vernimmen [38] thetransportation cost mainly includes total shipping cost totalcontainer cargo handling cost at the terminal and ship capitalcost Hence regardless of the sunk cost of the conveyance(which is also presented as ship or railway capital cost) weassume that the full freight rates (namely total transportationcost) paid by shippers are calculated from the basic rates plusthe surcharges added by the carrier (together with ports orhubs) to its customers including two main parts

(1) Basic Freight Cost 119865119861119862119894 The basic freight cost is thebasic cost of transporting containers from port A to port Bfor carrier 119894 (119894 = 1 2) which means only considering theprocess in transit from port to port while the surcharge feesand the relevant fees and charges within the ports or hubsare excluded And the basic freight cost 119865BC

119894 (119891119894 119888119894) can becalculated by

119865BC119894 (119891119894 119888119894) = min 119889119894 119862119894 sdot 119903119894 = min 119889119894 119891119894 times 119888119894 sdot 119903119894 (11)

in which119862119894 refers to the weekly transportation capacity of thecarrier 119894 (119894 = 1 2) and presented by 119862119894 = 119891119894 times 119888119894 (FEUsweek)Moreover min119889119894 119891119894 times 119888119894 indicates the actual quantity of theshipped containers

(2) Total Surcharges Cost 119865119878119862119894 The total surcharges cost ofthe transportation includes two parts which are the totalcontainer handling cost at the terminal (THC) (denotedas 119865HC119894 ) and the other surcharges excluding the THC (ie

bunker cost container usage cost and port or hub entrycharge denoted as 119865OC

119894 ) Therefore we assume that the totalsurcharge can be calculated by

119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)

in which the total surcharge cost is the result of total handlingcharge plus the other surcharges in light of its definition

A Total Handling Cost 119865119867119862119894 The reason for taking THC asan individual part in this session is that the THC has beenconsidered as the biggest and most mature parameter toevaluate the cost for shippers to pay To be more specifictwo sets of THC are charged and they are consideredunchangeable over time in the time cycle which are for portloading and port discharge according to Slack and Gouvernal[39] The total container handling cost can be calculated by

119865HC119894 (119891119894 119888119894) = min 119889119894 119862119894 sdot ]119894 = min 119889119894 119891119894 times 119888119894 sdot ]119894 (13)

in which min119889119894 119891119894 times 119888119894 indicates the actual quantity ofthe shipped containers as mentioned above (in (11)) and

the parameter ]119894 shows the unit container handling cost forcarrier 119894 (119894 = 1 2) which contains the THCs in the originand destination ports or hubs

B Other Surcharges 119865119874119862119894 119865OC119894 is the surcharge fees excluding

THC (eg bunker cost container usage cost and port or hubentry charge) for carrier 119894 which can be defined as

119865OC119894 (119891119894 119888119894) = 119877119894 sdot 119862119894 = 119877119894 sdot 119891119894 times 119888119894 (14)

and 119877119894 is surcharge fees excluding THC for carrier 119894 (119894 = 1 2)per container which is per FEU in this paper

Consequently the total transportation cost 119865119862119894 for carrier119894 (119894 = 1 2) can be written as follows

119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)

in which 119865119862119894 the total transportation cost for carrier 119894 (119894 =1 2) includes two parts which are the basic freight cost 119865BC

119894

and the total surcharges 119865SC119894

33 Model Description Based on the above process analysisof the deterrence game-theoretic competition between theshipping and railway we can obtain the total cost for a shipperto choose a specific shipping mode (considered as a carrier)The mathematical optimization model for the entrant is

119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)

= min 119889119894 119891119894 times 119888119894 sdot 119903119894 + 119877119894 sdot 119891119894 times 119888119894+min 119889119894 119891119894 times 119888119894 sdot ]119894

(16)

The above function mainly consists of two parts 119865BC119894 and

119865SC119894 119865BC119894 is the transportation (or presented as navigation

time in shipping) cost for carrier 119894 119865SC119894 is the surcharges cost

for carrier 119894 which includes119865OC119894 (the surcharge fees excluding

THC) and 119865HC119894 (the container handling cost for carrier 119894

resp)In this study we stand at the shipperrsquos point of view and

make a more superior choice in the two modes of transport(mainly railway and shipping) through a comparative analysisof both the advantages and disadvantages of each mode Thedeterrence game-theoretic strategy was used to measure thecosts of each mode of transport in which the changing scaleof transport demand for shippers service frequency of eachmode freight rate and transport capacity are fully taken intoconsideration

We define the incumbent carrier as carrier 119894 as well asthe entrant carrier as carrier 119894minus To be noted here we take thetransportation mode shipping as the incumbent carrier andrailway as the entrant carrier On this basis we can developa transportation mode choice model based on game theoryand it can be formulated as follows


min (119865119862119894 119865119862119894minus) = min( min 119889119894 119891119894 times 119888119894 sdot 119903119894 + 119877119894 sdot 119891119894 times 119888119894 +min 119889119894 119891119894 times 119888119894 sdot ]119894min 119889119894minus 119891119894minus times 119888119894minus sdot 119903119894minus + 119877119894minus sdot 119891119894minus times 119888119894minus +min 119889119894minus 119891119894minus times 119888119894minus sdot ]119894minus ) (17)

Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)

where 120590 is the given threshold of the entry-deterrenceobjective and the carriersrsquo costs under its best response canbe obtained by solving the optimization problem in (18)ndash(22)

In this model the above equations show the constraintsof the parameters where 120590 is the given threshold of the deter-rence objective and the carriersrsquo costs under its best responsecan be obtained by solving the optimization problem in(18)ndash(22) To bemore specific (18) shows the demand conser-vation constraint where the sum of the two modesrsquo transportdemands equals the total transport demand Meanwhile theside constraints for three decision variables are given by(19)ndash(22) Constraint (19) shows an integer weekly servicefrequency will be chosen and 119896 is the maximum servicefrequency in a week Constraint (20) means that there are 119899kinds of transport capacity setting plans (ship size or trainlength) for the shipperrsquos decision-making And (22) indicatesthe constraint of the range of freight rates Generally carrierschange their freight rate into a sequence with equal intervals(eg $5interval other differences are also applicable)WhereΩ119903 is the discrete feasible set of variable 119903119894 and based on theboundary constraint (21) we set 1199031 ge 119903min as well as 119903119898 le119903max

As a shipper we can use this deterrent game-theoreticmodel to compare the modes of shipping and railwaywhich compete mutually on different main variables suchas freight rate service frequency shipping capacity andother secondary parameters like reputation transportationtime and so on in order to choose the optimal mode oftransport

34 Algorithm In this section a numerical solution approachis developed to solve the deterrence game formulated bythe model In order to solve the practical problem we usesteps to make the solution more feasible Firstly set theparameter values for each carrier (according to the specificcircumstances of the line from Hefei to Hamburg in Step 1)Secondly obtain the matrices for two carriers and calculatethe market share and the transportation cost of each mode(Steps 2 and 3) Then we explain and analyze the results inorder to provide decision basis for the optimal selection oftwo transportation modes under certain conditions (Step 4)The details are shown in Figure 3

4 Application and Results

The following application analysis was carried out to assessthe effect of entry-deterrence strategy In this study anentry-deterrence game model was applied to develop thecompetition between two different modes of transportationnamely shipping and railway by setting a study case fromHefei in China to Hamburg in Germany The model wasdeveloped in MATLAB R2013b Intel I Core 2 Quad CPUQ9650 300GHz The model development is as follows

41 Preliminary Setting In this application we assume thatthe origin of the route is Hefei (China) where the route ofldquoHefei CR expressrdquo starts from Hefei as showed in Figure 4

In terms of starting time and the capacity the shippingliners between China and Europe start a lot earlier and entailmuch larger capacity than theCR express trains whichmakesthe former more developed Herein in order to simplifythe results we assume that the shipping carrier is set as anincumbent carrier (denoted by carrier 1) and the railwaycarrier as an entrant (denoted by carrier 2) The variousparameters are shown in Table 5

At present the basic freight rate for the CR expressesin BampR Initiative varies from 7500 to 12000 USD per FEUHowever some CR expresses (eg Chongqing-DuisburgZhengzhou-Hamburg) have government grants in order tolower the freight transportation cost by railway and toencourage shippers and manufacturing companies for long-term cooperation [8] The basic freight rate of CR expressesis often lower than its original cost because of the financialsubsidies from the government To be more specific theoriginal basic freight rate is from 7500 to 12000USD and thesubsidies from the government vary from 1000 to 7000 USD[8] Therefore the real basic freight rate for the CR expressesvaries from 3500 to 12000 USD per FEU As to shippingcompanies the freight rate varies from 1000 to 5000 USDper FEU which is normally much lower than the railwayfreight rate However when it comes to the problem we areinvestigating now the purpose of this study is to establishthose scenarios when it is meaningful to compare the twomodes of transportation In other words when a firm wantsto compare the two modes of transportation the rates scaleof the twomodes must be comparable So in this research we


Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo

fcustomersrsquoperceptio

nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi

cientindemandfunctio

n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies

andWang[8]Moetal[7]and

Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end

objective and select the optimal carrier

(b) change the calculating parameter recalculate

the transportation cost and make the optimal selection

Step 1 Input basic parameters

Step 2 Calculate intermediate variables

Step 4 Select the optimal carrier

Step 3 Calculate the transportation cost

(a) calculate the waiting time TW(fi)

(b) calculate the total time Ti

(d) calculate cost function G(ri fi)

(e) calculate the Ui E [ＧＲ (U1 U2)] and

(f) calculate the probability of choosing carrier pi(g) calculate the weekly number of the containers di

(a) calculate min(FCi FC

iminus) with the deterrence

for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i

(c) calculate the level of service g(]i)

the demand d

(a) calculate the basic freight cost Fi

(b) calculate the total handling cost F（i other

surcharges Fi and the total surcharges cost F３

i

(c) calculate the total transportation cost FCi

input the parameters ri fi ci

Figure 3 The algorithm of deterrence model

define the upper and lower bounds of the basic freight rateat 5000 and 3500 respectively In addition the frequency ofthe CR express is at least 1 or 2 per week while the shippingliner is at most once a week With similar method in orderto balance the frequency and the capacity we consider 2 CRblock trains in one week as 1 train in this study Accordinglywe set the potential weekly demand in the market as 300FEU (which is in the middle of average capacity of railwayas 50ndash60 FEU per train and shipping as 500ndash1000 FEU pership) to balance the difference of the two modes (these datacome from the interviews of three logistics companies and

references such as Wang [8] Mo et al [7] and Wang et al[9]) The navigation time (30 days) for carrier 1 (shipping) iscalculated as an average navigation time by different shippingcompanies and adds a dayrsquos delivery time from Hefei toShanghai Port 31 days in total For example in Asia-EuropeExpress route in PIL the navigation time from Shanghai Portto Hamburg Port is 37 days while others (APL COSCO etc)may have longer or shorter navigation time Moreover forcarrier 2 there is one CR express namely ldquoHefei CR expressrdquowhich runs direct to Hamburg in 15 days Additionally sincethe Chinese government makes unremitting effort to ensure


Table 6 Simulated market share of deterrence model

Deterrenceobjective (120590)

Servicefrequency(carrier 1)


Total cost (105)(carrier 1)


600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619

Figure 4 Route fromHefei to Hamburg based on ldquoAsia-Europe Expressrdquo in PIL (source author adapted from httpswwwpilshipcom andGoogle Map)

the smooth running of the Sino-Europe container trains(CR expresses) we propose that the reputation is higherthan the liner ships operated by the shipping companies at8 and 5 (from the interview of three logistics companies)respectively Additional data can be referred to in Wang [8]Wang et al [31] Google Map and other references

42 Numerical Results In this section the effect of deter-rence objective on these two transportation modes has beeninvestigated to obtain their optimal responses It is noted thatcarrier 1 (shipping) is assumed to be an incumbent in themarket and carrier 2 (railway) is an entrant which poses a

potential market threat to carrier 1 Consequently it results ina deterrence game between these two carriers the results ofwhich suggest an optimal choice of carrier for consignors thatfocus on the cost of transportation The deterrence objectiveis set to increase from 600000$ to 1000000$ with eachincrement of 20000$ Based on the deterrence competitionmodel and solution algorithm we give the deterrence effectsthat vary with increasing values in the deterrence objective(see Figures 5ndash8)

Firstly Table 6 gives the service frequency and total costfor the two carriers with different deterrence objectives Wecan see that both carriers mostly prefer to set their service


2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es

6 65 7 75 8 85 9 95 10Deterrence objective () times105

times105

Figure 5 Total transport cost for the two carriers varying with thedeterrence objective Black square for carrier 1 (shipping) red circlefor carrier 2 (railway)

29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105

Figure 6 Cost difference between two carriers varying with thesettled deterrence objective

frequency as one time except that frequency setting of carrier2 is 15 in the case of deterrence being 900000$ and 940000$whereby the required amount of service capacity can beworked out by changing the transportation capacity setting

It can be seen from Figure 5 that the level of the transportcost for both carriers 1 (black square) and 2 (red circle)increases with the increase in deterrence which is obtainedfrom Table 6 In fact for the shipping carrier the transportcost increases slowly at first and then increases faster withhigher value in the deterrence objective However for therailway carrier the cost always increases at a fast rate acrossthe range of the given deterrence objectiveWhat is more it isclear that the transport cost of railway is always higher thanthat of shipping which is as expected in the transportationmarket In additionwemade an analysis of the cost differencebetween these two carriers (Figure 5) We note that the cost

60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)


Figure 7 The transportation capacity for two carriers varying withthe deterrence objective Black square for carrier 1 (shipping) redcircle for carrier 2 (railway)

3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate

Figure 8 The basic freight rate for two carriers varying with thedeterrence objective Black square for carrier 1 (shipping) red circlefor carrier 2 (railway)

difference is increased as the deterrence objective increasesfrom 600000$ to 750000$ When the deterrence objectiveis beyond 750000$ the cost difference between two carrierstends to be a constant value of about 365000$ It followsfrom Figure 6 that when the deterrence objective is set withina small range and thus the total cost is relatively low it isbetter to choose the shipping transportation This is becausethe shipping cost is much lower than railway and has a slowincrement in the low deterrence objective region

Figure 7 shows the transportation capacity for the twocarriers (black square for carrier 1 (shipping) and red circlefor carrier 2 (railway)) varying with values in the deterrenceobjective It is found that railwayrsquos capacity experiencesfluctuations with increasing deterrence values while ship-pingrsquos capacity has a steady increment with higher valuein the deterrence objective above 750000$ Actually whenthe deterrence is below 750000$ carrier 1 always uses the


shipping with capacity of about 80 FEU while carrier 2 offersthe railway service with capacity slightly above 80 FEU As forthe scenario of 120590 gt 750000$ there is a big enhancement ofcapacity for carrier 1 changing from 80 FEU to 110 FEU thenits capacity linearly increases with increasing deterrenceThetransport capacity of carrier 2 generally speaking has a slowincrement with much fluctuation and is always below that ofcarrier 1

Variations of the basic freight rate for two carriers areplotted in Figure 8 Inspecting this figure we note thatthe basic freight rate for carrier 2 (railway red circle) isalso in fluctuation and generally increases with increase ofdeterrence objective Evidently for carrier 1 (shipping blacksquare) it provides the basic freight rate that increases at firstand then decreases to a stable value with higher deterrencefrom 750000$ onwards This stable basic freight rate islower than that for carrier 2 When the deterrence is below750000$ the basic freight rate for shipping is a little highercompared to that for railway It is shown in Figures 7 and 8that when the cost is high (beyond 750000$) the shippingcarrier will increase its ship capacity and decrease its basicfreight rate as the best response to the market demand Inpractical application the ship capacity is much larger thanrailway capacityTherefore the railway carrier has restrictionsin transportation capacity and its basic freight rate has to beenhanced

5 Conclusion and Further Discussion

The present study discussed a competition between twotransportation modes (shipping and railway) through devel-oping a game-theoretic model The deterrence strategy isutilized with consideration of economies of scale of thetransportation capacity settings Based on the deterrencemodel each transportation modersquos response to minimize itscost is evaluated by setting optimal service frequency basicfreight rate and carrier capacity The market share of eachmode is determined by the logit-based discrete choicemodelFurthermore with the reverse deduction of formula thestudy indicates the computing method to obtain the timevalue (120572) of the cargo that the carriers transport Whenmaking decisions about choosing the mode of transportationbetween continents a shipper can use thismethod to estimatethe different costs of the two modes and compare thedifference of the time value of the cargos to reduce theexpense during thewhole transportation process At the sametime a carrier can use this method to explore the directionto improve in order to be more competitive in the transportmarket

In the competition a carrier is an organization thattransports products or service using their own facilities anda shipper is a person or company that wants to send ortransport goods The competitions between the carriers areusually in the same transport mode However this does nothappen all the time Two transport modes can also be treatedas two carriers in the same mode of transport (shipping orairline etc) in some situation In this case the railway andshipping also have a lot in commonwhere they are exchange-able in many aspects In addition the entry-deterrence

is about the incumbent and entrant of the same market andthe CR express is newly started mode with the advantage intransport time which can be transferred into the inventorycost of the cargos and the reliability in transport with safetyinsurance while the disadvantage is its low capacity and highbasic freight rate It conforms to the features of an entrantAdditionally the shipping carrier with the advantage of lowbasic freight rate and high capacity already runs in decadesin the line between China and Europe It is typically anincumbent in the market

With the competitive relation between railway and ship-ping there are two perspectives we can take If we stand onthe perspective of the shippers the purpose of this study is tochoose the optimal mode of transport or the optimal carrierthrough two carriers in different modes of transport In thecase study in order to verify that this competition existswe set some boundaries in scope of the basic freight ratesdemand market capacity and time value Moreover we alsomake a simplification for the model so as to obtain moreintuitive results In a real market there is often more thanone carrier in one mode of transport (eg several carriersin a certain shipping line) but normally their basic freightrates are in the same range Therefore our bounds of thebasic freight rates are set in a certain scope However thereare not many choices for the shippers in one line Our studyendeavors to offer an option of methods to find the optimalcarrier from one city to another To sum up our method is tochoose the more competitive carrier or transport mode

On the other hand it is also reasonable if we stand onthe perspective of the carriers In general the competitionis believed to exist in carriers of the same transport modein a certain line However this study presents a new typeof competition between the carriers in different transportmodes As for the shipping carriers the demand market canbe extended to some smaller-scale ones and make profits onits containerized character of the container transportationAnd as for the demand market the shipping carriers haveadvantage in freight rate (lower price) but disadvantage inreliability of transport time Moreover if a shipping carrierwants to explore a better market it has to improve on theservice and time reliability to obtain more potential cus-tomers with high value cargos whereas the railway operatorsin order to place themselves in an advantageous positionhave to increase a number of the expresses according to themarker demand on one hand and keep on shortening thetransport time and transit time to expand its advantage intime reliability on the other hand

Finally the developed model is numerically evaluated bya case study of the intercontinental container freight trans-portation between Hefei (China) and Hamburg (Germany)The case study shows that deterrence effects largely dependon the deterrence objective and the differential cost of twomodes of transportation tends to be stable with higher valuesof the deterrence objectives In the new intercontinentalcircumstance the mode of railway transportation provides anew way to transport cargos between China and Europe

In a way the railway is relatively more expensive thanthe maritime transportation to some extent however it hasthe advantage of lesser time Railway is a new option for


long distance transportation from China to Europe and shallcontinue to evolve in the new circumstance of the BampRInitiative If the frequency is higher the waiting time andcost will be significantly reduced So both the two modes oftransportation have their own advantages and container CRexpress has much potential in the future especially for highvalue-added cargo

As for further discussion we set the time value of thetransportation fromHefei to Hamburg as 360USD per day inthis study However this figure may vary from cargo to cargo(less or more than 360 USD) where according to Wang [8]the high time-sensitive cargos may have the time value as 480USD whereas the low time-sensitive ones may have values at120 USD per day Moreover we can reverse the equations inthe model and treat the total cost model as a variable in suchcase we can then obtain the relation and expression of timevalue (120572) of the cargo and the total cost

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research is subsidized by the Specialized Research Fundfor the Doctoral Program of Higher Education of China (no20130009110001) and the National Natural Science Founda-tion of China (no 71390332-8) as well as the FundamentalResearch Funds for the Central Universities of China (noT14JB00230)

References

[1] Construction and development plan of CHINA RAILWAYExpress 2016-2020 2016 Beijing httpwwwndrcgovcn

[2] Q Zhou YDWongH Xu V VThaiH S Loh andK F YuenldquoAn enhanced CREAM with stakeholder-graded protocols fortanker shipping safety applicationrdquo Safety Science vol 95 pp140ndash147 2017

[3] T Fallon ldquoThe new silk road Xi Jinpingrsquos grand strategy forEurasiardquoAmerican Foreign Policy Interests vol 37 no 3 pp 140ndash147 2015

[4] P Hilletofth H Lorentz V-V Savolainen O-P Hilmola andO Ivanova ldquoUsing Eurasian landbridge in logistics operationsbuilding knowledge through case studiesrdquo World Review ofIntermodal Transportation Research vol 1 no 2 pp 183ndash2012007

[5] Y Panova and O P Hilmola ldquoJustification and evaluation ofdry port investments in Russiardquo Research in TransportationEconomics vol 51 pp 61ndash70 2015

[6] S Hanaoka and M B Regmi ldquoPromoting intermodal freighttransport through the development of dry ports in Asia Anenvironmental perspectiverdquo IATSS Research vol 35 no 1 pp16ndash23 2011

[7] H H Mo J E Wang and Z Y Song ldquoEconomically suitableareas of Chinarsquos transnational container transport by land in theSilk Road Economic Beltrdquo Progress in Geography vol 34 no 5pp 581ndash588 2015

[8] Y K Wang ldquoStatus problems and suggestions on developmentof Sino-Europe block trainsrdquo China Transportation Review vol37 pp 71ndash89 2015

[9] X M Wang L T Wang L L Liu and L Fan ldquoA comparativestudy on transport mode of China-EU international train onsilk road economic beltrdquo Value Engineering vol 36 no 2 pp9ndash11 2017

[10] S Peyrouse and G Raballand ldquoCentral Asia The New SilkRoad Initiativersquos questionable economic rationalityrdquo EurasianGeography and Economics vol 56 no 4 pp 405ndash420 2015

[11] J Rich P M Holmblad and C O Hansen ldquoA weighted logitfreight mode-choice modelrdquo Transportation Research Part ELogistics and Transportation Review vol 45 no 6 pp 1006ndash1019 2009

[12] Y Wang and G-T Yeo ldquoA study on international multimodaltransport networks from Korea to Central Asia focus onsecondhand vehiclesrdquo Asian Journal of Shipping and Logisticsvol 32 no 1 pp 41ndash47 2016

[13] J Luo and Y Chen ldquoResearch on mode selection of freighttransport based on risk preference theoryrdquo International Journalof Advancements in Computing Technology vol 4 no 16 pp138ndash146 2012

[14] O Alvarez-SanJaime P Cantos-Sanchez R Moner-Colonquesand J J Sempere-Monerris ldquoCompetition and horizontal inte-gration in maritime freight transportrdquo Transportation ResearchPart E Logistics and Transportation Review vol 51 no 1 pp67ndash81 2013

[15] H Lee M Boile S Theofanis and S Choo ldquoModeling theoligopolistic and competitive behavior of carriers in maritimefreight transportation networksrdquo Procedia - Social and Behav-ioral Sciences vol 54 pp 1080ndash1094 2012

[16] X Hao ldquoStated preference technique for analysis of containerport competitionrdquoTransportation Research Record no 2033 pp8ndash13 2007

[17] L Wang and X Zhu ldquoRail mounted gantry crane schedulingoptimization in railway container terminal based on hybridhandling moderdquo Computational Intelligence and Neurosciencevol 2014 Article ID 682486 2014

[18] M H Lin ldquoAirline alliances and entry deterrencerdquo Transporta-tion Research Part E Logistics and Transportation Review vol44 no 4 pp 637ndash652 2008

[19] V Aguirregabiria and C-Y Ho ldquoA dynamic game of air-line network competition Hub-and-spoke networks and entrydeterrencerdquo International Journal of Industrial Organizationvol 28 no 4 pp 377ndash382 2010

[20] C S Fisk ldquoGame theory and transportation systems mod-ellingrdquo Transportation Research Part B Methodological vol 18no 4-5 pp 301ndash313 1984

[21] M G H Bell ldquoA game theory approach to measuring theperformance reliability of transport networksrdquo TransportationResearch Part B Methodological vol 34 no 6 pp 533ndash5452000

[22] M Ishii P T-W Lee K Tezuka and Y-T Chang ldquoA game the-oretical analysis of port competitionrdquo Transportation ResearchPart E Logistics and Transportation Review vol 49 no 1 pp92ndash106 2013

[23] M Leng and M Parlar ldquoGame theoretic applications in supplychain management a reviewrdquo INFOR Information Systems andOperational Research vol 43 no 3 pp 187ndash220 2005

[24] WQi HWen C Fu andM Song ldquoGame theorymodel of traf-fic participants within amber time at signalized intersectionrdquo


Computational Intelligence and Neuroscience vol 2014 ArticleID 756235 7 pages 2014

[25] X Jiang Y Ji M Du and W Deng ldquoA study of driverrsquosroute choice behavior based on evolutionary game theoryrdquoComputational Intelligence and Neuroscience Article ID 1247162014

[26] D-W Song and P M Panayides ldquoA conceptual application ofcooperative game theory to liner shipping strategic alliancesrdquoMaritime PolicyampManagement vol 29 no 3 pp 285ndash301 2002

[27] H Min and Z Guo ldquoThe location of hub-seaports in the globalsupply chain network using a cooperative competition strategyrdquoInternational Journal of Integrated Supply Management vol 1no 1 pp 51ndash63 2004

[28] A Imai E Nishimura S Papadimitriou and M Liu ldquoTheeconomic viability of container mega-shipsrdquo TransportationResearch Part E Logistics and Transportation Review vol 42no 1 pp 21ndash41 2006

[29] Q LiuWWWilson andM Luo ldquoThe impact of PanamaCanalexpansion on the container-shipping market a cooperativegame theory approachrdquoMaritime PolicyampManagement vol 43no 2 pp 209ndash221 2016

[30] B I Park andHMin ldquoA game-theoretic approach to evaluatingthe competitiveness of container carriers in the NortheastAsian shipping marketrdquo Asia Pacific Journal of Marketing andLogistics vol 29 no 4 pp 854ndash869 2017

[31] H Wang Q Meng and X Zhang ldquoGame-theoretical modelsfor competition analysis in a new emerging liner container ship-ping marketrdquo Transportation Research Part B Methodologicalvol 70 pp 201ndash227 2014

[32] X Shi and S Voszlig ldquoGame theoretical aspects in modeling andanalyzing the shipping industryrdquo Computational Logistics vol6971 pp 302ndash320 2011

[33] L Tavasszy M Minderhoud J-F Perrin and T NotteboomldquoA strategic network choice model for global container flowsSpecification estimation and applicationrdquo Journal of TransportGeography vol 19 no 6 pp 1163ndash1172 2011

[34] M Ravibabu ldquoA nested logit model of mode choice for inlandmovement of export shipments A case study of containerisedexport cargo from IndiardquoResearch in Transportation Economicsvol 38 no 1 pp 91ndash100 2013

[35] C M Anderson Y-A Park Y-T Chang C-H Yang T-WLee and M Luo ldquoA game-theoretic analysis of competitionamong container port hubs the case of Busan and Shanghai 1rdquoMaritime Policy amp Management vol 35 no 1 pp 5ndash26 2008

[36] N Oppenheim Urban Travel Demand Modeling From Individ-ual Choices to General Equilibrium John Wiley and Sons Ltd1995

[37] M Ben-Akiva and S R Lerman S Discrete Choice AnalysisTheMIT Press Cambridge Massachusetts 1985

[38] T E Notteboom and B Vernimmen ldquoThe effect of high fuelcosts on liner service configuration in container shippingrdquoJournal of Transport Geography vol 17 no 5 pp 325ndash337 2009

[39] B Slack and E Gouvernal ldquoContainer freight rates and the roleof surchargesrdquo Journal of Transport Geography vol 19 no 6 pp1482ndash1489 2011

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Proposed Silk Road routes

Railroad Entry Points

Proposed

Existing

Silk Road Economic

Belt the ldquoBeltrdquo21st-CenturyMaritime Silk Roadthe ldquoRoadrdquo

Figure 1 The Routes of ldquothe Silk Road Economic Belt and the 21st Century Maritime Silk Roadrdquo (source author adapted fromhttpwwwxinhuanetcom httpswwwwsjcom and httpwwwunorg)

(1) What are the aspects one should consider whenchoosing amode of transportation to transport containerizedcargo to another continent especially between China andEurope with the background of the Belt and Road (BampR)Initiative that offers a new mode of choice

(2) If the two modes of transportation (shipping andrailway) compete with each other using the deterrence gametheory which will win in the competition

The primary thrusts of the study are as follows (1) firstlythe BampR Initiative is introduced with both land andmaritimeroutes Meanwhile the main CR expresses and the tradingvolume from China to Hamburg (which is one of the mostimportant ports in Europe) are demonstrated (2) secondlythe two aspects that shippers (firms) care most namely timeand cost are illustrated in the study in which time valueconsideration in the cost function makes the overall costmore comparable and (3) finally the game-theoreticmodel isdeveloped from the perspectives of the shippers In additionthe application of the deterrence model (route from Hefei toHamburg) is proposed

The paper is organized as follows After this introductorysection the background and literature review are presentedThe following section proposes the methodology applied anddeveloped in this research including the problem descrip-tion the notations assumptions and formulas related to themodel the entry-deterrence gamemodels and the algorithmFurthermore a cased study is presented with the findingsThe final section gives the conclusions as well as furtherdiscussion of the study

2 Background and Literature Review

21 The Belt and Road Initiative The Chinese governmenthas in recent years embarked on a major plan in building

better linkages (especially transportation connection)between Europe and Asia by way of ldquothe Belt and Road(BampR) Initiativerdquo (also known as ldquoOne Belt One Roadrdquoor OBOR) OBOR is essentially a Chinese framework fororganizing multinational economic developments throughtwo component plans the land-based ldquoSilk Road EconomicBeltrdquo (SREB) and ocean-going ldquoMaritime Silk Roadrdquo (MSR)as is shown in Figure 1 The Belt and Road a reference to theSilk Road Economic Belt and the 21st Century Maritime SilkRoad was initialized by Chinese President Xi Jinping duringhis visit to Central-Asia and Southeast Asia in Septemberand October 2013 which also called for accelerating Beltand Road construction in the government work reportof China in March 2015 It offers a great opportunity forintercontinental logistics companies which shall engendersupport by the governments of many countries in AsiaAfrica and Europe

Several CR expresses have been set up to support theimplementation of the SREB and to meet the requirementsof the rapid growth of trade between China and Europe Asis shown in Table 1 there are basically two regions of transithubs which are located in Xinjiang and northeast part ofChina Until December 2016 there are more than fifteen CRexpresses from China to Europe originating within Chinathe majority are going out of China through Alashankou(Xinjiang) rather than through Manzhouli (Heilongjiang)andErenhot (InnerMongolia) As showed inTables 1ndash3 routedistances between the origins and destinations vary from8027 to 13052 km andmost journey durations are around 15days The earliest Sino-Europe block train ldquoYuxinourdquo (fromChongqing to Duisburg now all use CR express as a brand)has been in operation for more than 6 years and is animportant part of the cargo transportation network to Europe








0

5

10

15

20

25

30

TEU

20152016


UnitedKingdom

Sweden India

times105














3 Methodology














119879119882 (119891119894) = 12119891119894 (1)



119879119882 (1198911015840119894 ) = 121198911015840119894 sdot

730 (2)


119879119894 = min 119879119878119894 + 119879119882 (119891119894) + 119879119867119894 (3)




119866 (119903119894 119891119894) = 120572 [119879119878119894 + 119879119882 (119891119894)] + 119903119894 + 120573 sdot 120582119894 + 119892 (]119894) (4)




119892 (]119894) = 1198861 sdot ]119894 + 1198862 (5)



119880119894 = minus119866 (119903119894 119891119894) + 120576119894 119894 = 1 2 (6)




(7)

















119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)











119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)


119894



119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)


(16)











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















0

5

10

15

20

25

30

TEU

20152016


UnitedKingdom

Sweden India

times105














3 Methodology














119879119882 (119891119894) = 12119891119894 (1)



119879119882 (1198911015840119894 ) = 121198911015840119894 sdot

730 (2)


119879119894 = min 119879119878119894 + 119879119882 (119891119894) + 119879119867119894 (3)




119866 (119903119894 119891119894) = 120572 [119879119878119894 + 119879119882 (119891119894)] + 119903119894 + 120573 sdot 120582119894 + 119892 (]119894) (4)




119892 (]119894) = 1198861 sdot ]119894 + 1198862 (5)



119880119894 = minus119866 (119903119894 119891119894) + 120576119894 119894 = 1 2 (6)




(7)

















119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)











119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)


119894



119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)


(16)











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















3 Methodology














119879119882 (119891119894) = 12119891119894 (1)



119879119882 (1198911015840119894 ) = 121198911015840119894 sdot

730 (2)


119879119894 = min 119879119878119894 + 119879119882 (119891119894) + 119879119867119894 (3)




119866 (119903119894 119891119894) = 120572 [119879119878119894 + 119879119882 (119891119894)] + 119903119894 + 120573 sdot 120582119894 + 119892 (]119894) (4)




119892 (]119894) = 1198861 sdot ]119894 + 1198862 (5)



119880119894 = minus119866 (119903119894 119891119894) + 120576119894 119894 = 1 2 (6)




(7)

















119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)











119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)


119894



119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)


(16)











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















119879119882 (119891119894) = 12119891119894 (1)



119879119882 (1198911015840119894 ) = 121198911015840119894 sdot

730 (2)


119879119894 = min 119879119878119894 + 119879119882 (119891119894) + 119879119867119894 (3)




119866 (119903119894 119891119894) = 120572 [119879119878119894 + 119879119882 (119891119894)] + 119903119894 + 120573 sdot 120582119894 + 119892 (]119894) (4)




119892 (]119894) = 1198861 sdot ]119894 + 1198862 (5)



119880119894 = minus119866 (119903119894 119891119894) + 120576119894 119894 = 1 2 (6)




(7)

















119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)











119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)


119894



119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)


(16)











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119879119882 (1198911015840119894 ) = 121198911015840119894 sdot

730 (2)


119879119894 = min 119879119878119894 + 119879119882 (119891119894) + 119879119867119894 (3)




119866 (119903119894 119891119894) = 120572 [119879119878119894 + 119879119882 (119891119894)] + 119903119894 + 120573 sdot 120582119894 + 119892 (]119894) (4)




119892 (]119894) = 1198861 sdot ]119894 + 1198862 (5)



119880119894 = minus119866 (119903119894 119891119894) + 120576119894 119894 = 1 2 (6)




(7)

















119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)











119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)


119894



119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)


(16)











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















119865SC119894 (119891119894 119888119894) = 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894) (12)











119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865SC

119894 (119891119894 119888119894) (15)


119894



119865119862119894 = 119865BC119894 (119891119894 119888119894) + 119865OC

119894 (119891119894 119888119894) + 119865HC119894 (119891119894 119888119894)


(16)











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Subject to 119889119894 + 119889119894minus = 119889 (18)

119891119894 119891119894minus isin 1 2 119896 (19)

119888119894 119888119894minus isin Ω119888 = 1198881 1198882 119888119899 (20)

119903119894 119903119894minus isin Ω119903 (21)

119865119862119894 119865119862119894minus le 120590 (22)











Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table5Parametersu

sedin

applicationtests

(sou

rceauthoradapted

from

references

andGoo

gleM

ap)

Parameters

Value

Unit

Sources

Valueo

ftim

e120572

360

$day

Wangetal[31]

Parameter

ingeneralized

costfunctio

n120573

minus36mdash

Wangetal[31]

Disp

ersio

nparameter

used

tomeasure

thed

egreeo


nerrorson

utility120579

125

times10minus3

Wangetal[31]

Elastic

coeffi


n120578

125

times10minus4

Wangetal[31]

Lower

boun

dof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903min 119894

3500

$Analysis

ofreferences

andinterview

Upp

erbo

undof

basic

freight

rateof

transportin

gperF

EUforc

arrie

r119894119903ma

x119894

500

0$

Analysis

ofreferences

andinterview

Potentialw

eeklycontainerd

emandin

them

arket119889 119901

300

FEU

Assumed

demandqu

antityby

authors

Transportin

gtim

efrom

Hefeito

Ham

burg

fortranspo

rtation

mod

e119894119879119878 119894

Carrier1

31day

Interviewof

threelogisticsc

ompanies

andTables

1ndash3

Carrier2

15

Ascoretoreflectther

eputation

Carrier1(120582 1

)5

mdashInterviewof

threelogisticsc

ompanies

Carrier2

(120582 2)

8mdash

Interviewof

threelogisticsc

ompanies

Term

inalhand

lingchargesfor

company119894] 119894

Carrier1

350

$FE

UInterviewof

logisticsc

ompanies


Wangetal[9]

Carrier2

200

0

Transportin

gdista

nce

Carrier1

11000

kmGoo

gleM

ap

Carrier2

12277

(asymp22737)

nm (km)

Goo

gleM

ap


end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










end

end

end















for i = 1 to n

for i = 1 to n

for i = 1 to n

TSi TH

i i ]i i


the demand d




i













600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















600000 1 1 293834401 599423874620000 1 1 3040454096 619922357640000 1 1 3138887676 639846894660000 1 1 3238445314 65973521680000 1 1 3339851551 679881542700000 1 1 3438504897 699845642720000 1 1 3540809401 719962378740000 1 1 3738800788 7399702546760000 1 1 3944699256 7599855057780000 1 1 4144096183 7798951093800000 1 1 4348494643 7999625798820000 1 1 4552293099 8199999897840000 1 1 4732502318 8399864545860000 1 1 4937300788 8599989839880000 1 1 5141499256 8799893663900000 1 15 5345097721 8999859671920000 1 1 5548096183 9199996018940000 1 15 5750494643 939992759960000 1 1 5952293099 9599747046980000 1 1 6135800788 97998746771000000 1 1 6338299256 9999935619







2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2

3

4

5

6

7

8

9

10

Cost

for t

wo

tran

spor

t mod

es


times105


29

3

31

32

33

34

35

36

37

38

Cost

die

renc

e bet

wee

n tw

o m

odes


times105




60

80

100

120

140

160

180

Tran

spor

tatio

n ca

paci

ty (F

EU)



3500

4000

4500

5000

5500

6000

6500

7000


Opt

imal

frei

ght r

ate




















Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























Acknowledgments


References










































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Game-Theoretic Comparison Approach for Intercontinental...

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Transcript of Game-Theoretic Comparison Approach for Intercontinental...