research article optimization of train trip package...

Research ArticleOptimization of Train Trip Package Operation Scheme

Lu Tong Lei Nie Zhenhuan He and Huiling Fu

School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China

Correspondence should be addressed to Lu Tong tonglu bjjt163com

Received 25 September 2014 Accepted 12 January 2015

Academic Editor Orwa J Houshia

Copyright copy 2015 Lu Tong 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

Train trip package transportation is an advanced form of railway freight transportation realized by a specialized train which hasfixed stations fixed time and fixed path Train trip package transportation has lots of advantages such as large volume longdistance high speed simple forms of organization and highmargin so it has become themainway of railway freight transportationThis paper firstly analyzes the related factors of train trip package transportation from its organizational forms and characteristicsThen an optimization model for train trip package transportation is established to provide optimum operation schemes Theproposed model is solved by the genetic algorithm At last the paper tests the model on the basis of the data of 8 regions Theresults show that the proposed method is feasible for solving operation scheme issues of train trip package

1 Introduction

Railway transportation is one of the main types of moderntransportation Railway transportation has the features of fastspeed low costs environmental friendship high reliabilityaccuracy and continuity Before the completion of high-speed railway network railway transportation in Chinaheavily focused on passenger transport For this reasonrailway freight transportation was always restricted by theproblem of insufficient capacity With the operation of motortrains and high-speed railway in recent years a large numberof railway capacities have been released and applied tofreight transportation As the main form of railway freighttransportation train trip package transportation is becomingincreasingly important Meanwhile it is also becoming morecomplex due to increased railway transport resources

Train trip package transportation provides luggage andparcel transportation fast freight and joint logistics servicesTrain trip package transportation is based on the existingrailway network and uses passenger baggage cars train trippackages and mail train lines as the carrier With the rapiddevelopment of social economy and the growing requirementof perfecting transportation service railway package trans-portation has been improving its level of service and hasbecome themain body of rapid railway freight transportation

There are two main types of railway freight transportationone is the packagemarshaled in the passenger train the otheris transport by a specialized train which consists of a certainnumber of baggage compartments and has fixed stationsfixed time and fixed pathThe second type is normally calledthe train trip package transportation In the near futuretrain trip package transportation will become the main formof package transportation Therefore a reasonable train trippackage operation scheme can help to improve the level oftrain trip package organization and the quality of service

Most of the current researches have focused on the pas-senger train operation scheme but few focused on train trippackage operation scheme [1ndash10] Crainic [11] summarizedthe transportation services network issues Barnhart et al [12]regarded railway marshaling issues as network design prob-lems where the network nodes represented marshaling yardand the arc segments represented marshaling train Changet al [13] used fuzzy mathematical programming to studyTaiwan high-speed railway train operation plan Crainicand Rousseau [14] used the heuristic algorithm based ondecomposition method and the column generation methodto solve railway freight service network design problem withno capacity limits Bussieck et al [15] discussed the oper-ation plan optimization problem with periodic timetableYu et al [16] proposed a transit operation for passengers

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 472591 8 pageshttpdxdoiorg1011552015472591

2 Mathematical Problems in Engineering

Railway packagestation



Package receptionPackage delivering

Road transportationLong-distance rail transportation

Figure 1 The whole process of package transportation

a

b

b c d

c d d

Originatingbase station

Final stationRejectionhanging station

Rejectionhanging station

c d

minusb+c+d

minusc+d minusd

Figure 2 The operation process of grouped trains

transportaion which considered passenger attraction fromcanidate nodes to destination nodes It is a novelty methodto the best of our knowledge Newton et al [17] establisheda path-based model without considering the associated fixedcosts of trains but adding capacity constraints to restrict thenumber of trains which could be marshaled and the freightamountwhich could be handledDue to some similar featuresof ldquopassenger trainrdquo and train trip package the train trippackage operation scheme optimization can refer to existingresearch of passenger train operation scheme

In this paper the existing research results and experiencesof passenger train operation scheme are studied Then therelated factors of train trip package operation scheme areanalyzed from its organizational characteristics Amathemat-ical model is developed to optimize the train trip packageoperation scheme for practical situation At the end theproposed model is verified through an example and someconclusions are obtained from the experiment

2 Problem Description

The whole process of package transportation can be dividedinto three operational phases reception and delivery in thestations of two ends and long-distance rail transportationbetween the stations The whole process of package trans-portation and the relationship among the operational phases

are shown in Figure 1 In this paper we only consider long-distance railway transport between stations and develop areasonable operation scheme

In train trip package transportation the train marshalingis composed of package trains with the same final station(single set of trains) or package trains whose final stationsare in the same running path (grouped trains)The operationprocess of grouped trains is shown in Figure 2 Groupedtrains start from the originating base station and will gradu-ally turn into a single set of trains after rejection and hangingfor once or several times along the way When groupedtrains reach the rejection and hanging stations before thefinal station they are required for rejection and hangingoperations

3 Model

31 Model Assumption Through the analysis of organiza-tional characteristics of train trip package transportation wefirst make the following assumptions before establishing theoptimization model of train trip package operation scheme

(1) The path of train trip package has been already pre-determined

(2) The transport capacity of train trip package is notrestricted and the ability to receive and send trains of

Mathematical Problems in Engineering 3


Change trainsstation

Finalstation

Departure time delay cost

Organizational cost

Running cost

Running time delay cost

Stop time delay cost Arrival time delay cost

Receive cost

Figure 3 Expenses in the service process of train trip package

each package station can satisfy any traffic intensityeach path can satisfy any traffic intensity

(3) Operation details and operation process inside sta-tions are not considered because the operation oftrain trip package only reflects the influence on theoperation scheme in some important links such asloading costs rejection and hanging operations costs

(4) The operation of train trip package depends on thetraffic situation and does not consider the constraintsof facing operation

32 Parameter Setting

119862 represents the cost per vehicle kilometer in traintrip package transportation1198620is the rejection and hanging costs for a train119875119894119895is the train flow leading from region 119894 to region 119895119860119903119904represents the collection of links that are passed

by train trip package between regions 119903 and 119904119871119903119904is the transport distance between regions 119903 and s119909119903119904

119894119895represents the train flow between regions 119903 and 119904

which are in the path from region 119894 to region 119895120572119903119904

119894119895is 0-1 variable if the railway freight flows between

regions 119903 and 119904 are carried by train trip packages fromregion 119894 to region 119895 120572119903119904

119894119895= 1 otherwise 120572119903119904

119894119895= 0

1205830represents the number of trains that can be mar-

shaled in a set of grouped trains119899119903119904is the number of train trip packages between re-

gions 119903 and 119904119872 represents infinity

33 Modeling All the expenses in the service process of traintrip package are shown in Figure 3

331 Loading Cost Train trip package transport is a kindof contractual transport and the contractors are obligated toorganize shipments In principle the contractors of train trippackage need to load and unload packages by themselvesTherefore the cost of train trip package in loading place isconsidered as a constant which is denoted by the averageloading cost

332 Rejection and Hanging Cost A single set of trains donot need rejection and hanging operations in the middlestation Grouped trains need rejection and hanging opera-tions in the operation stations along the way but do not needloading unloading and modifying marshaling operationsTherefore the rejection and hanging cost only existed in thegrouped trains and can be considered as a fixed value

In the model established in this paper the total cost oftrain trip package transportation consists of two parts one isin-transit cost such as locomotive traction cost and line usagecost which are decided by the cost per vehicle kilometer theother is the rejection and hanging cost which is decided by therejection and hanging costs for a train Because the loadingcost of train trip package can be considered as fixed loadingcost is not reflected in the model

The optimizationmodel of train trip package operation is

Min 119885 = sum119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895

+ 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(1)

st sum119894119895

119909119903119904

119894119895= 119875119903119904forall119903 119904 isin 119878 (2)

119909119903119904

119894119895minus 120572119903119904

119894119895sdot 119872 le 0 forall119903 119904 119894 119895 isin 119878 (3)

sum

119903119904

119909119903119904

119894119895le 1198991198941198951205830forall119894 119895 isin 119878 (4)

119909119903119904

119894119895ge 0 forall119903 119904 119894 119895 isin 119878 (5)

119899119903119904ge 0 119899

119903119904is integer (6)

The purpose of objective function (1) is to minimize the totaloperation cost of all train trip packages

Constraint (2) is the flow conservation constraint ensur-ing that train trip package operation scheme meets thetransport demand between each OD pair

Constraint (3) ensures that the railway freight flowscarried by train trip packages are assigned to feasible path

Constraint (4) ensures that the number of train flows ineach service interval does not exceed the carrying capacitythe train service can provide

Constraints (5) and (6) are nonnegative constraints of thedecision variables and constraint (6) requires the number oftrain trip packages to be integers


1 53 8Chromosome

Operation sequence 1 2 3 4

Figure 4 Representation of chromosome

34 Genetic Algorithm Because the formulation of train trippackage operation scheme is a linear discrete optimizationproblem the traditional method is difficult to get the optimalsolution to the problem Many literatures suggested thatheuristic algorithm was often the first choice to solve thiskind of complicated transportation optimization problems[18ndash21] Among heuristic algorithms genetic algorithm (GA)is a probabilistic search algorithm for global optimizationThe genetic algorithm is formed by simulating biologicalgenetic and evolutionary processes in the natural worldGenetic algorithm has good global search capability and fastcalculation speed It can quickly find an optimal solutionfrom the entire solution space and will seldom fall intothe local optimal solution Currently genetic algorithm hasachieved good application in the path optimization siteselection and other aspects which has been applied to solvelots of complicated problems [22ndash25] Therefore the geneticalgorithm is used in this paper to solve the problem

Step 1 (coding) The decimal coding is employed to generatean array of numbers namely a chromosome Each chromo-some represents an operation sequence of train trip package(Figure 4) A gene in a chromosome represents a station thattrain trip packages pass by for example 1ndash3ndash5ndash8 representsthat train trip packages start from station 1 and finally get tostation 8 passing by station 3 and station 5

Step 2 (generating initial populations) According to ODflows between package stations we successively select eachODpair and find a path between stations to produce a feasiblechromosome Repeat the process until feasible chromosomesbetween each OD pair have been produced

Step 3 (calculation of fitness value) Clearly some chromo-somes may not satisfy all of the constraints in the modelTherefore it is necessary to construct the fitness functionAdaptation function indicates the superiority of chromo-somes For the minimum value problem in this paper thefitness function is

119865 (1199091015840)

= 119873 minussum

119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895minus 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(7)

In the formula the value of 119873 will be determined accordingto the size of the problem to ensure 119865(1199091015840) ge 0

Step 4 (selection and crossover (Figure 5)) Roulette methodis used as a selection mechanism In the roulette method

1 52 8Parent individual 1

Parent individual 2 3 42 7

Offspring individual 1 2 4 7

Figure 5 Crossover operator of genetic algorithm

Chromosome A 1 52 8

1 42 8Chromosome A998400

Figure 6 Mutation operator of genetic algorithm

chromosomes will be selected for reproducing a new gen-eration with certain probability The selection probabilityof a chromosome is related to its fitness Generally thehigher the fitness value the bigger the selection probabilityMeanwhile the elite strategy is also implemented whichmeans the chromosome with the maximum fitness value ineach generation of populations will be copied to the nextgenerationThe optimal policymakes the next generation notworse than the parent generation

Crossover introduces random changes to the selectedchromosomes by crossing two parent individuals to produceoffspring individuals with a user-specified probability 119901

119888

called crossover rate In this paper the single-point crossoveris implemented

Step 5 (mutation) Mutation introduces random changes tothe chromosomes by altering the value of a gene with a user-specified probability 119901

119898called mutation rate (Figure 6)

Step 6 (stopping criterion) To compare the computation effi-ciency of different algorithms different stopping times are setas the stopping criteria When getting to the predeterminedstopping time the algorithm ends

4 Numerical Test

Based on ldquothree vertical and four horizontalrdquo train trans-portation physical network of China eight package stationsare chosen to build a spatial network graph of packagetransportation regions (as shown in Figure 7) then designa service network of train trip package The purpose is todetermine the organization form the running paths and theoperation number of trains


1

3

2

5

6

4

7

8

3768 1288

1463689

2042

1622998

1810

1605

25271100

1637

Urumchi

Harbin

Beijing

Zhengzhou

Shanghai

Guangzhou

Chengtu

Kunming

Figure 7 Spatial network graph of package transportation regions

Table 1 Space distance of package transportation regions (km)

Region 1 2 3 4 5 6 7 81 mdash 3768 mdash mdash mdash mdash mdash mdash2 mdash 1288 2042 689 1463 mdash mdash3 mdash mdash mdash mdash mdash mdash4 mdash 1622 mdash 1100 25275 mdash 998 mdash 16056 mdash mdash 18107 mdash 16378 mdash

41 Data Preparation

411 Data of Interregional Distance As the spatial networkgraph of package transportation regions shown in Figure 7the actual length of the links between each node pair canbe considered as the distance between center cities of eachregion Specific distance data are shown in Table 1

412 Data of OD Flows According to the statistics of Chinarailway transportation Table 2 shows OD flows by packagebetween 8 package regions in units of tons per year

In this paper assume that the length of the design cycle isone day and the OD flows for each period are constant It is

known that the OD flows in Table 2 are represented in unitsof tons per year so a conversion coefficient is introduced hereto obtain daily OD flows in units of trainsday

Since the volume of packages is difficult to accuratelygrasp in the actual operation the deadweight constraint ofpackage trains is considered as an alternativeThe deadweightcapacity of a package train is averagely 15 tons according toour survey and a year is calculated as 365 days The result ofthe conversion is shown in Table 3 Note that the numbers ofpackage trains have to be integer value so the final conversedvalues are rounded off

413 Cost Data The average operating cost is set to 90 pervehicle kilometer (119862 = 90) and the rejection and hangingoperating costs are set to 1000 per train (119862

0= 1000)

414 Other Data According to the regulation of the numberof marshaling train trip packages 120583

0= 20

42 The Results Based on the above model parameters thegenetic algorithm is used to calculate model through C++programming The crossover probability of GA is set as 08and the mutation probability is set as 005 The maximumevolution generation of GA is set as 100 The specific resultsare shown in Table 4


Table 2 OD flows by package among 8 package regions (tonsyear)

Region 1 2 3 4 5 6 7 81 mdash 139790 8284 34410 20431 80648 10753 440882 50294 mdash 62909 136105 57034 140123 67275 1088843 7710 96678 mdash mdash mdash 32028 mdash 154214 88962 172889 mdash mdash 120854 119176 186317 1007125 13255 46392 mdash 26510 mdash 64381 mdash 319546 44764 135649 42155 121667 104032 mdash 59998 1091457 20523 79930 mdash 106933 mdash 74529 mdash 734498 31014 180416 39662 96321 79025 188766 65606 mdash

Table 3 Daily OD train flows among 8 package regions (trainday)


7

75

8

85

9

95

10

0 20 40 60 80 100

Tota

l cos

t (m

illio

n yu

an)

Iteration

Figure 8 Result of each calculation

As shown in Table 4 parts of OD flows between stationsare transported directly from the start station to the finalstation without any transit operationsThe other parts of ODflows are required to stop at middle stations for rejection andhanging

43 Test Results Discussion Figure 8 depicts the convergenceof the calculation The results of computational tests showthat the algorithm of this paper can achieve convergencewithin 100 generations indicating a good convergence anda good adaptability to solve the proposed model

It is known that the initial operation scheme consistsof 48 single sets of trains All OD flows are transporteddirectly from the start station to the final station without anyoperation in transit Target cost of initial operation scheme is98574 million yuan

70

60

50

40

30

20

10

0 0

200

400

600

800

1000

120064

52

98574

72561

Operation Total cost

Initial operation scheme

Optimized scheme

Figure 9 Comparison of the results

After optimization the sample train transport servicenetwork consists of 26 kinds of train trip package transportservices In the optimized operation scheme there are 52operations within a day including 45 operations of single setof trains and 7 of grouped trains Compared with the initialscheme the optimized scheme reduces the operation numberof single set of trains in long distance and yet increases theoperation number of both single set of trains and group trainsin shortmiddle distance thus reducing the total cost of traintransportation The total cost of the optimized scheme is72561 million yuan reduced by 264 compared with theinitial one

To evaluate the performance of the proposed scheme theresults of initial operation scheme and optimized scheme canbe showed in Figure 9 It can be found that the optimizedscheme can greatly reduce the total cost Thus the proposedoptimized scheme is an effective method for train trippackage optimization

5 Conclusions

This paper focuses on how to arrange the train trip pack-age operation scheme to lower the transportation cost Anoptimization model is established based on the analysis of


Table 4 Calculation results train trip package operation scheme

Number Originating station Final station Running path The number of train flows Operation number Organizational form1 1 2 1 rarr 2 27 2 Single2 1 4 1 rarr 4 12 1 Single3 1 5 1 rarr 5 8 1 Single4 2 1 2 rarr 1 11 1 Single5 2 3 2 rarr 3 28 2 Single6 2 4 2 rarr 5 rarr 4 50 3 Single7 2 6 2 rarr 6 31 2 Single8 2 8 2 rarr 5 rarr 8 33 2 Grouped9 3 1 3 rarr 2 rarr 1 28 2 Single10 4 1 4 rarr 1 16 1 Single11 4 2 4 rarr 2 32 2 Grouped12 4 5 4 rarr 5 32 2 Single13 4 6 4 rarr 5 rarr 6 48 3 Grouped14 4 7 4 rarr 7 48 3 Single15 4 8 4 rarr 8 22 2 Single16 5 1 5 rarr 1 11 1 Single17 6 2 6 rarr 2 32 2 Single18 6 4 6 rarr 5 rarr 4 35 2 Single19 6 5 6 rarr 5 19 2 Single20 6 8 6 rarr 8 31 2 Single21 7 4 7 rarr 4 23 2 Single22 7 8 7 rarr 8 27 2 Single23 8 2 8 rarr 5 rarr 2 63 4 Single24 8 4 8 rarr 4 18 1 Single25 8 6 8 rarr 6 48 3 Single26 8 7 8 rarr 7 23 2 Single

the organizational forms and characteristics of the train trippackage transport as well as the existing research resultsand experiences of passenger train plan Computational testsshow that the proposed model can effectively reduce the costof transportationThemodel can also optimize the operationnumber of train trip packages in the experiment indicatingthat it has better applicability

An issue of future research is the consideration of moreconstraints such as the inconsistent loading cost betweensingle set of trains and group trains and the constraints offacing operation In further studies these constraints will beconsidered in order to get closer to the actual situation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by Railway Ministry Science andTechnology Management Project (2013X014-C) China Rail-way Corporation Project (2014X010-A) and FundamentalResearch Funds for the Central Universities (Beijing JiaotongUniversity) under Grant no 2014JBZ008

References

[1] A A Assad ldquoModels for rail transportationrdquo TransportationResearch Part A General vol 14 no 3 pp 205ndash220 1980

[2] A A Assad ldquoModelling of rail networks toward a routingmakeup modelrdquo Transportation Research Part B vol 14 no 1-2 pp 101ndash114 1980

[3] C Barnhart N Krishnan D Kim and K Ware ldquoNetworkdesign for express shipment deliveryrdquoComputational Optimiza-tion and Applications vol 21 no 3 pp 239ndash262 2002

[4] J M Farvolden andW B Powell ldquoSubgradient methods for theservice network design problemrdquo Transportation Science vol28 no 3 pp 256ndash272 1994

[5] Z Gao J Wu and H Sun ldquoSolution algorithm for the bi-leveldiscrete network design problemrdquo Transportation Research PartB Methodological vol 39 no 6 pp 479ndash495 2005

[6] H-Q Peng and Y-J Zhu ldquoIntercity train operation schemesbased on passenger flow dynamic assignmentrdquo Journal of Trans-portation Systems Engineering and Information Technology vol13 no 1 pp 111ndash117 2013

[7] M H Keaton ldquoDesigning railroad operating plans a dualadjustment method for implementing lagrangian relaxationrdquoTransportation Science vol 26 no 4 pp 263ndash279 1992

[8] M Yaghini M Momeni and M Sarmadi ldquoAn improved localbranching approach for train formation planningrdquo AppliedMathematical Modelling vol 37 no 4 pp 2300ndash2307 2013


[9] K R Smilowitz A Atamturk and C F Daganzo ldquoDeferreditem and vehicle routing within integrated networksrdquo Trans-portation Research Part E Logistics and Transportation Reviewvol 39 no 4 pp 305ndash323 2003

[10] Y Sun C Cao and C Wu ldquoMulti-objective optimization oftrain routing problem combined with train scheduling on ahigh-speed railway networkrdquo Transportation Research Part CEmerging Technologies vol 44 pp 1ndash20 2014

[11] T G Crainic ldquoService network design in freight transporta-tionrdquo European Journal of Operational Research vol 122 no 2pp 272ndash288 2000

[12] C Barnhart H Jin and P H Vance ldquoRailroad blocking anetwork design applicationrdquo Operations Research vol 48 no4 pp 603ndash614 2000

[13] Y-H Chang C-H Yeh and C-C Shen ldquoA multiobjectivemodel for passenger train services planning application toTaiwanrsquos high-speed rail linerdquo Transportation Research Part BMethodological vol 34 no 2 pp 91ndash106 2000

[14] T G Crainic and J-M Rousseau ldquoMulticommodity multi-mode freight transportation a general modeling and algo-rithmic framework for the service network design problemrdquoTransportation Research Part B vol 20 no 3 pp 225ndash242 1986

[15] M R Bussieck P Kreuzer and U T Zimmermann ldquoOptimallines for railway systemsrdquo European Journal of OperationalResearch vol 96 no 1 pp 54ndash63 1997

[16] B Yu H Zhu W Cai N Ma Q Kuang and B Yao ldquoTwo-phase optimization approach to transit hub locationmdashthe caseof Dalianrdquo Journal of Transport Geography vol 33 pp 62ndash712013

[17] H N Newton C Barnhart and P H Vance ldquoConstructing rail-road blocking plans tominimize handling costsrdquoTransportationScience vol 32 no 4 pp 330ndash345 1998

[18] B Z Yao B Yu P Hu J J Gao andM H Zhang ldquoAn improvedparticle swarm optimization for carton heterogeneous vehiclerouting problem with a collection depotrdquo Annals of OperationsResearch 2014

[19] B Z Yao P Hu X H Lu J J Gao and M H Zhang ldquoTransitnetwork design based on travel time reliabilityrdquo TransportationResearch Part C Emerging Technologies vol 43 pp 233ndash2482014

[20] B Z Yao P Hu M H Zhang and M Q Jin ldquoA support vectormachine with the tabu search algorithm for freeway incidentdetectionrdquo International Journal of Applied Mathematics andComputer Science vol 24 no 2 pp 397ndash404 2014

[21] B YuNMaW J Cai T Li X T Yuan andB Z Yao ldquoImprovedant colony optimisation for the dynamic multi-depot vehiclerouting problemrdquo International Journal of Logistics Research andApplications vol 16 no 2 pp 144ndash157 2013

[22] Y D Zhang S H Wang G L Ji and Z C Dong ldquoGeneticpattern search and its application to brain image classificationrdquoMathematical Problems in Engineering vol 2013 Article ID580876 8 pages 2013

[23] Y D Zhang S H Wang and G L Ji ldquoA rule-based modelfor bankruptcy prediction based on an improved genetic antcolony algorithmrdquo Mathematical Problems in Engineering vol2013 Article ID 753251 10 pages 2013

[24] B Yu Z Z Yang X S Sun B Yao Q Zeng and E JeppesenldquoParallel genetic algorithm in bus route headway optimizationrdquoApplied Soft Computing Journal vol 11 no 8 pp 5081ndash50912011

[25] H Derbel B Jarboui S Hanafi and H Chabchoub ldquoGeneticalgorithm with iterated local search for solving a location-routing problemrdquo Expert Systems with Applications vol 39 no3 pp 2865ndash2871 2012

Submit your manuscripts athttpwwwhindawicom

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

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Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of





Package receptionPackage delivering

Road transportationLong-distance rail transportation

Figure 1 The whole process of package transportation

a

b

b c d

c d d


Final stationRejectionhanging station

Rejectionhanging station

c d

minusb+c+d

minusc+d minusd

Figure 2 The operation process of grouped trains

transportaion which considered passenger attraction fromcanidate nodes to destination nodes It is a novelty methodto the best of our knowledge Newton et al [17] establisheda path-based model without considering the associated fixedcosts of trains but adding capacity constraints to restrict thenumber of trains which could be marshaled and the freightamountwhich could be handledDue to some similar featuresof ldquopassenger trainrdquo and train trip package the train trippackage operation scheme optimization can refer to existingresearch of passenger train operation scheme

In this paper the existing research results and experiencesof passenger train operation scheme are studied Then therelated factors of train trip package operation scheme areanalyzed from its organizational characteristics Amathemat-ical model is developed to optimize the train trip packageoperation scheme for practical situation At the end theproposed model is verified through an example and someconclusions are obtained from the experiment

2 Problem Description

The whole process of package transportation can be dividedinto three operational phases reception and delivery in thestations of two ends and long-distance rail transportationbetween the stations The whole process of package trans-portation and the relationship among the operational phases

are shown in Figure 1 In this paper we only consider long-distance railway transport between stations and develop areasonable operation scheme

In train trip package transportation the train marshalingis composed of package trains with the same final station(single set of trains) or package trains whose final stationsare in the same running path (grouped trains)The operationprocess of grouped trains is shown in Figure 2 Groupedtrains start from the originating base station and will gradu-ally turn into a single set of trains after rejection and hangingfor once or several times along the way When groupedtrains reach the rejection and hanging stations before thefinal station they are required for rejection and hangingoperations

3 Model

31 Model Assumption Through the analysis of organiza-tional characteristics of train trip package transportation wefirst make the following assumptions before establishing theoptimization model of train trip package operation scheme

(1) The path of train trip package has been already pre-determined

(2) The transport capacity of train trip package is notrestricted and the ability to receive and send trains of




Finalstation


Organizational cost

Running cost



Receive cost












119894119895= 1 otherwise 120572119903119904

119894119895= 0









Min 119885 = sum119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895

+ 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(1)

st sum119894119895

119909119903119904

119894119895= 119875119903119904forall119903 119904 isin 119878 (2)

119909119903119904

119894119895minus 120572119903119904


sum

119903119904

119909119903119904

119894119895le 1198991198941198951205830forall119894 119895 isin 119878 (4)

119909119903119904

119894119895ge 0 forall119903 119904 119894 119895 isin 119878 (5)

119899119903119904ge 0 119899

119903119904is integer (6)







1 53 8Chromosome







119865 (1199091015840)

= 119873 minussum

119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895minus 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(7)







Chromosome A 1 52 8





119888





4 Numerical Test



1

3

2

5

6

4

7

8

3768 1288

1463689

2042

1622998

1810

1605

25271100

1637

Urumchi

Harbin

Beijing

Zhengzhou

Shanghai

Guangzhou

Chengtu

Kunming




41 Data Preparation







0= 1000)


0= 20







7

75

8

85

9

95

10

0 20 40 60 80 100

Tota

l cos

t (m

illio

n yu

an)

Iteration





70

60

50

40

30

20

10

0 0

200

400

600

800

1000

120064

52

98574

72561



Optimized scheme




5 Conclusions









Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Finalstation


Organizational cost

Running cost



Receive cost












119894119895= 1 otherwise 120572119903119904

119894119895= 0









Min 119885 = sum119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895

+ 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(1)

st sum119894119895

119909119903119904

119894119895= 119875119903119904forall119903 119904 isin 119878 (2)

119909119903119904

119894119895minus 120572119903119904


sum

119903119904

119909119903119904

119894119895le 1198991198941198951205830forall119894 119895 isin 119878 (4)

119909119903119904

119894119895ge 0 forall119903 119904 119894 119895 isin 119878 (5)

119899119903119904ge 0 119899

119903119904is integer (6)







1 53 8Chromosome







119865 (1199091015840)

= 119873 minussum

119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895minus 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(7)







Chromosome A 1 52 8





119888





4 Numerical Test



1

3

2

5

6

4

7

8

3768 1288

1463689

2042

1622998

1810

1605

25271100

1637

Urumchi

Harbin

Beijing

Zhengzhou

Shanghai

Guangzhou

Chengtu

Kunming




41 Data Preparation







0= 1000)


0= 20







7

75

8

85

9

95

10

0 20 40 60 80 100

Tota

l cos

t (m

illio

n yu

an)

Iteration





70

60

50

40

30

20

10

0 0

200

400

600

800

1000

120064

52

98574

72561



Optimized scheme




5 Conclusions









Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1 53 8Chromosome







119865 (1199091015840)

= 119873 minussum

119894119895

sum

119903119904

sum

119896isin119860119903119904cap119860119894119895

119862119871119896119909119903119904

119894119895minus 1198620sum

119894119895

(sum

119903119904

119909119903119904

119894119895minus 119909119894119895

119894119895)

(7)







Chromosome A 1 52 8





119888





4 Numerical Test



1

3

2

5

6

4

7

8

3768 1288

1463689

2042

1622998

1810

1605

25271100

1637

Urumchi

Harbin

Beijing

Zhengzhou

Shanghai

Guangzhou

Chengtu

Kunming




41 Data Preparation







0= 1000)


0= 20







7

75

8

85

9

95

10

0 20 40 60 80 100

Tota

l cos

t (m

illio

n yu

an)

Iteration





70

60

50

40

30

20

10

0 0

200

400

600

800

1000

120064

52

98574

72561



Optimized scheme




5 Conclusions









Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1

3

2

5

6

4

7

8

3768 1288

1463689

2042

1622998

1810

1605

25271100

1637

Urumchi

Harbin

Beijing

Zhengzhou

Shanghai

Guangzhou

Chengtu

Kunming




41 Data Preparation







0= 1000)


0= 20







7

75

8

85

9

95

10

0 20 40 60 80 100

Tota

l cos

t (m

illio

n yu

an)

Iteration





70

60

50

40

30

20

10

0 0

200

400

600

800

1000

120064

52

98574

72561



Optimized scheme




5 Conclusions









Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














7

75

8

85

9

95

10

0 20 40 60 80 100

Tota

l cos

t (m

illio

n yu

an)

Iteration





70

60

50

40

30

20

10

0 0

200

400

600

800

1000

120064

52

98574

72561



Optimized scheme




5 Conclusions









Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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