Handling Equipment Allocation Optimization of Railroad-Highway Combined Transportation: Bi-Objective Model and MEACO Algorithm

DOI 10.7603/s40707-013-0007-6

GSTF Journal of Engineering Technology (JET), Vol. 2 No. 3, Dec 2013

Handling Equipment Allocation Optimization of Railroad-highway Combined Transportation: Bi-Objective Model and MEACO Algorithm

Qi Zhang, Yuan Ye, Li Zhang, and Hao Yang

equipments are the machine both for such work and the crucial Abstract—Coordinating connection between railroad and conjunction t o c onnect t he r ailroad a nd hi ghway. Thus, one highway in multimodal transportation is very complex and important problem needs to be settled is to select properly and important. It is concerned with the time and cost consuming of allocate reasonably the equipments. There are at least two major containers, the operation efficiency, and resources allocation of railroad and highway. This paper studies the equipment allocation aspects need to be considered in the equipment selection and optimization in railway container center station. It establishes a allocation problem, ESAP. One is the machine type. It must be bi-objective optimization model to solve the problem. The two high e fficient a nd be suitable for what t o do. Another i s t he objectives of the model are getting the minimum daily machine a mount. It m ust b e en ough an d r easonable, either comprehensive costs of equipments, and getting the minimum meeting the business demand or without much idleness. dwelling time of railway container flatcars on loading and unloading line. Allocating more equipment will reduce the dwelling time obviously. But there are some risks of idle II. LITERATURE REVIEW equipment and high costs, too. These are two irreconcilable In recent years, many researchers are focusing on the objectives. The MEACO algorithm is used to solve this problem equipment selection and allocation problem. Some researchers making Chongqing container center station as an example. The are concerned with the most s uitable equipment selection in model is verified by actual data. The results suggest the optimal allocation of the handling equipments and are in accordance with railway stations, such as Song et al. (2005), Bai et al. (2002), Ma the fact of the station. (2005), Li et al. (2005). Some researchers are concerned with the tusk allocation basing on the equipment selection, such as Index Terms—Bi-objective optimization model, handling Murty K G (2000), Linn R (2003). Some r esearchers ar e equipment allocation, MEACO algorithm, railroad-highway concerned with the a mount d ecision problem of r ailway combined transportation container station, for example Liang et al. (2009), Huo et al. (2006), W ong ( 2008), L i e t al. (2009). Comparatively, m ost advanced r esearches ar e concerned with th e e quipments I. INTRODUCTION allocation problem of harbor and dock, such as Yang (1995), CF MOOTH connection co uld r educe t he t ime and co st Daganzo (1989), R. I. Peterkofsky & CF Daganzo (1990), J. B. S consuming in the transportation process. The advantage and Tabernacle (1995), J. Bose et al. (2000), Lai K.K & Lam K efficiency of railroad-highway combined transportation require (1994), Kozan E & Preston P (1999), CF Daganzo (1989), much f or co nnecting ef fectively o f these two different Pyung Hoi Koo (2004), Hao (2003), Ji et al. (2010), Yong et al. transportation m odes. Reducing t he l oading a nd unl oading (2008). business work and dwelling time seems to be a good measure. Researchers applied different m ethods and de veloped Railway c ontainer c enter s tation is th e j oint h ub in the different m odels, f rom v arious r esearch p oints, to solve the railroad-highway combined t ransportation. There are a lot of equipment selection and allocation problem. The r esearch results ar e ab undant, es pecially i n t he as pects o f harbor and loading a nd unl oading businesses in th e s tation. Handling dock. Bai et a l. ( 2002) s tudied th e alternative ty pes o f h andling Manuscript submitted on October 31, 2013. This work was supported in equipments which were lik ely to b e s uitable f or th e r ailway part by China Railway Corporation (2012X012-H), and Fundamental Research Funds for the Central Universities (2011JBM061). container station. The authors studied the yard utilization rate of Qi Zhang. An a ssociate p rofessor of School of Traffic & Transportation, each kind of equipments adopting the unit-acreage. Basing on Beijing J iaotong U niversity, B eijing, 100044, China (1-662-518-1762 o r the operation costs by the whole life cycle input-output method +86-18600231123; e-mail: [email protected]). (WLCIO), the authors gave the optimal selection of equipment Yuan Ye. Xiamen airport logistics management Co. Ltd, No.95 Xiangyun Rd, Huli District, Xiamen, 361000, China (email: [email protected]). type as Rail Mounted Gantry Crane (RMGC). Li Zhang. An associate professor of Civil and Environmental Department, Liang et al. (2009) combined the discrete event simulation Mississippi State University, S tarkville, MS 39759, U SA (e-mail: principle (DESP) with event graph method (EG/ED) to develop [email protected]). the simulation model. The authors divided the trailers into two Hao Yang. P rofessor o f S chool o f T raffic & T ransportation, Beijing Jiaotong University, Beijing, 100044, China (e-mail: [email protected]). types, the inner trailer operated by railroad yard and the outer

©The Author(s) 2013. This article is published with open access by the GSTF DOI: 10.5176/2251-3701_2.3.89 GSTF Journal of Engineering Technology (JET), Vol. 2 No. 3, Dec 2013 trailer operated by t he hi ghway t ransportation c orporations. III. Bi-objective Optimal Model of Handling Equipment With the simulation of outer trailer randomly arrival, the authors ALLOCATION obtained th e o ptimal allocation o f t ransferring resources, The handling equipment a llocation in r ailway c ontainer including t he i nner t railers a nd t he loading and unloading center s tations s hould meet the d emand o f timeliness o f equipments. container t ransportation an d t he r equirement o f o peration Basing on the research results of equipment type selection, benefits o f s tation a t th e s ame tim e. This paper d eveloped a Linn R (2003) solved the tusk allocation problem by proposing bi-objective o ptimal m odel with the bou nds f rom both daily mixed integer programming (MIP). The authors got the working comprehensive costs and dwelling time, making the equipment sequence and t ime s cheduling o f RMGC between d ifferent amount as its decision variable. container yards. R. I. Peterkofsky and CF Daganzo (1990) combined a A. Daily comprehensive costs of handling equipments Cg mathematical programming model with an allocation strategy to Basing on the relevant research results, this paper considered solve the static Quayside Container Crane Allocation Problem the main equipment of loading and unloading in railway (QCCAP). The authors calculated the maximum throughput of container center station is Rail Mounted Gantry Crane (RMGC). one b erth i n r ush ho ur a iming to reduce the waiting f ee an d Daily comprehensive costs of this machine should include some dwelling time of container ship. While J. B. Tabernacle (1995) kinds of costs, shown as table I. considered t he Q uayside C ontainer C rane (QCC) as parallel business a nd t ransferred t he Q CCAP i nto O pen Shop TABLE I Scheduling Problem (OSSP). The authors developed an integer COST CATEGORIES OF RMGC programming model and applied the branch and bound method Fixed Costs Variable Costs to solve the problem. depreciation funds daily maintenance cost Cost categories major repair funds fuel and electric power cost CF Daganzo (1989) formed an integer programming model acquisition cost cost of labor and designed an optimal inventory strategy to obtain an optimal

RMGC business plan. The programming model aimed for the There ar e s ome m atching f acilities f or the operation of highest e fficiency of loading and unl oading b usiness o f a ll RMGC, such as the loading and unloading lines, hard-surface RMGCs allocated to work for the specific container ship. pavement of yards, and the running lines of RMGC. Then, there Ji e t a l. ( 2010) developed a S hortest P ath P roblem ( SPP) are the corresponding costs arising. optimal model from the point of view of simultaneous business f jth between in-port and ex-port container s hips. The authors Daily fixed costs j of the RMGC is shown as (1). applied th e P OEM o ptimal platform and used the s imulative 1i− c data to get results. According to the results, with the constraints () M fcjf=⋅+ of m inimum w aiting tim e o f Q uayside C ontainer Crane, the Nd× d (1) authors estimated the optimal amount of trailers matching the working plan of QCC. In equation (1), cf is the acquisition cost of each RMGC. cM is This paper focused its studies on the loading and unloading the average annual maintenance cost of each RMGC. N is the equipment amount decision in railway container center station. depreciation period and i is the residual value of the machine. Based on the problem description and literature review above, The last d is the working day of the railway container center the main contributions of this paper are described as follows. stations. • The paper considers the core of the seamless connection in th Daily operation costs cvj of the j RMGC is defined in (2). railroad-highway combined transportation is the coordination between different businesses, including railway c=+ cQc ×+× cT container flatcars, handling equipments and highway trailers vj l j m p j (2) or chassis. The paper makes the coordinative connection between those businesses as objective to study the Handling In equation (2), cl is the daily cost of labor of each RMGC. Qj th Equipment Allocation Problem (HEAP). is the total number of containers loaded or unloaded by the j • A bi-objective model stresses the coordination between machine in one day. The average maintenance cost of each TEU different businesses by daily comprehensive costs of is cm. The electric power cost of RMGC per hour is cp. Tj is the th equipments and dwelling time of rail flatcars. Business average daily working time of the j RMGC. efficiency and operation costs are the constraints of the Construction costs of matching facilities Cb is shown as (3). model. MEACO algorithm is represented to search for the optimal results. ()1i− C= cc ++× c × r Basing on the factual of Chongqing railway container center b() r cr s Nd× (3) station, the model is verified to b e u seful. A nd th e optimal equipment allocation is given by the results of the model. There ar e t hree k inds o f costs in ( 3). Infrastructural construction costs of each railway loading and unloading line is cr. Construction cost of running line is crs. Hard-pavement cost

©The Author(s) 2013. This article is published with open access by the GSTF GSTF Journal of Engineering Technology (JET), Vol. 2 No. 3, Dec 2013 of working areas and yards is cs. N is the depreciation periods of Definition2. It is a P areto o ptimal s olution o r a these infrastructures and i is the residual value. The number of non-dominance s olution. When a nd o nly w hen t he s olution loading a nd unl oading l ines m atching with the amount x ∈Ωdoes not exist and there is xx ∗ , the solution x∗ ∈Ωis allocation of RMGC is defined as r. called as the Pareto optimal solution. Then, the average daily costs of handling equipment Cg can Definition3. It is a Pareto optimal set. The set of the Pareto be defined as (4). optimal solutions for the bi-objective optimal problem is called as the P areto o ptimal s et. It is d efined ∗∗ ∗ mm12as P= x ∈Ω ¬∃ x ∈Ω :x x . C=⋅ξξ∑∑ fc + + C  +−⋅ 1 f′′ + c + C ′  { } g ()j vj b () ( j vj) b j1= j1=  Definition4. It i s t he r eal P areto f ront s urface. Given a n    (4) optimal solution set of a bi-objective optimal problem P*. The

curved surface reflected by all the Pareto optimal solutions in As illustrated in equation (4), m1 and m2 are the numbers of the objective space is called as the real Pareto front surface. It is RMGC and Front Crane respectively. The ξ is a coefficient. If ∗ ∗ ∗ ∗∗ ∗ defined as PF= Fx()()() = fx,fxx12 ∈ P . ξ=1, the equipment selection decision will be the RMGC. Then, { ( )} (2) B i-objective o ptimal m odel o f h andling e quipment it will be the Front Crane. If the equipment selection decision is ’ ’ allocation the Front Crane in railway container center station, the fj , cvj ’ According to t he pr oblem description above, t he t wo and Cb will be the daily fixed costs, daily operation costs and minimum objectives of the bi-objective optimal model are the construction costs of matching facilities o f th e F ront C rane ’ ’ daily comprehensive costs of handling equipments Cg and the respectively. And fj and cvj have the same expressions as (1) ’ dwelling time of r ailway c ontainer f latcars o n lo ading a nd and (2), but Cb is shorten because of without the infrastructural unloading lines T . The bi-objective optimal modal of handling construction costs of running line, crs. equipment allocation is expressed as (7). B. Average dwelling time on loading and unloading lines of T railroad flatcars min F() x= min() Cg ,T (7) Dwelling time of railroad flatcars on loading and unloading lines is consisted of two parts, the loading and unloading time T and the waiting time W. The average dwelling time on loading IV. ALGORITHM FOR THE BI-OBJECTIVE OPTIMAL MODEL OF T and unloading lines of railroad flatcars is expressed as (5). HANDLING EQUIPMENT ALLOCATION

m3 A. MEACO algorithm for bi-objective optimal model T=∑ T + W /m ()jj 3 j1= (5) This paper studied t he c ontainer ha ndling e quipment allocation problem based o n t he r ailroad-highway s eamless In t he e quation ( 5), loading and unl oading time o f t he jth conjunction. The timeliness is the key for this problem. Then, in railroad flatcars is Tj, and their waiting time is Wj. And m3 is the the objective function, T is more important than Cg. In applying number o f r ailroad f latcars entering t he lines d uring t he the MEACO to solve the problem, the paper transferred the Cg operation period of the railway container center station. into the constraint of min T , the objective function. Then the Getting the dwelling time of railroad flatcars under different bi-objective optimal problem, as (7), is transferred into a single equipment selection decision will be helpful for analyzing the objective problem with optimal constraints, shown as (8). efficiency change caused by the technology characteristics of loading and unloading equipments. Thus, the paper makes the minT dwelling time as one of its objective function. s.t.Cm()()()≤≤ Cm Cm gimin gi gimax C. Bi-objective optimal model mD∈ i (8) (1) Definitions of the bi-objective optimal problem When the two o bjectives in th e o ptimal m odel a re a ll the As in equation (8), D is the domain of decision variables. It is minimum objectives, the problem could be expressed as (6). defined as m≥∈ 0,m Z n , Zn means n-dimensional integer set. ii B. Decision variables notations and values range min F()()() x= min( f12 x , f x ) (6) Daily comprehensive costs are determined by the acquisition

costs of the equipments, the infrastructure construction costs of According to the multi-objective theory, the paper proposed the matching facilities and the daily operation costs. Then, one some definitions about the bi-objectives. important variable is the amount of RMGC, m1. Definition1. It is a kind of Pareto dominance relationship. The va lue r ange o f m1 is co ncerned with th e c ontainer For th e s olution x ,x ∈Ω, x1 dominates x2. W hen a nd only 12 throughput of the railway container center station, the number when e xists ∀∈i{} 1,2 , it g ets fx()()≤ fx . And it i1 i2 and the valid length of loading and unloading lines of the station. exists ∃∈i{} 1,2 , it g ets fxi1()()< fx i2. Then, t he e quation In general speaking, m1 is concerned with the daily total volume xx is defined as x1 dominates x2. 12 of loading and unloading business Q from the point of view of

©The Author(s) 2013. This article is published with open access by the GSTF GSTF Journal of Engineering Technology (JET), Vol. 2 No. 3, Dec 2013 throughput. The va lue o f m1 is no l ess t han t he demand of In e quation ( 10), N is the maximum number o f r ailway 24-hour continuously business. In C hina, t he s tandard va lid flatcars waiting o n t he l oading a nd unl oading l ines, r is th e lengths of loading and unloading lines are 850m and 1050m in number of loading and unloading lines in the station, Lr is the railway container center station. The running distance of RMGC valid length of loading and unloading line, and Lts is the average is about 250m to 350m (Yu, et al., 2005). Then the amount of length of each flatcars. RMGC allocated will be up to 4 in 850-meter line and up to 5 in While the number of railway flatcars waiting on the lines is 1050-meter line. It is supposed that the number of loading and up to N, the next group will be rejected into the lines. While the unloading lines in the railway container center station is r. The groups entering on the lines need to wait, and this waiting makes amount range of RMGC allocated could be expressed as (9). the P0N > , PN is the p ossibility o f th e n umber o f w aiting flatcars up to N. It means that the amount of RMGC allocated Q /() 24⋅≤≤ v m 4r L = 850m cannot meet the demand o f l oading a nd unl oading b usiness

work. PN could be obtained by applying the Queuing Theory Q /() 24⋅≤≤ v m 5r L = 1050m (9) based on the following assumptions. • Assumption1. Considering each loading and unloading line In equation (9), v is the average rate of loading and unloading as a service desk, then the number of service desks c is the of RMGC. The value of v is 30TEU/h, and mZ∈ . same as the number of the lines r. It is necessary to say that under some conditions, m is not • Assumption2. The interval time of each flatcar’s arrival determined by r thoroughly. The amount of RMGC allocated is yields to the Poisson distribution. m. This allocation plan could meet the demand of loading and • Assumption3. The loading and unloading businesses on unloading business. While the number of loading and unloading different lines are mutual independent. Each line is allocated the same number of RMGCs. lines is added up to r′ , rr′ > . According to (9), m needs to be Then, it can be considered as a service system with limited m′ mm′ > mm′ − added up to , . Then the number of () RMGC capacity M /M/c/N/ (AG Hernández-Díaz, e t a l., 2 007), a s will be in idle state. In order to get the minimum operation costs (11). of equipments, the amount of RMGC allocated will be kept at ∞ k −1 the level of m. c cN c ()cρ c ρρ()− ρ p0 =∑ +⋅ ,1ρ ≠ C. Notations and values of time parameters in objective k0= k! c! 1− ρ function   cρ ρ The loading and unloading time Tj and the waiting time on ()  p0 ,0≤≤ n c line Wj are concerned with some factors, including the interval  n! pn =  time o f r ailway f latcars ar rival, t he n umber of loading and cc  ρ n p ,c≤≤ n N unloading lines of the station, as well as the amount of RMGC  c! 0 allocated for each line. Those RMGCs on the same loading and ρλ= / cu unloading line are working together or cooperatively. They are (11) interdependent. At the same time, different RMGCs on different lines work respectively. They are mutual independent. Thus we (2) Tj and Wj. considered all RMGCs allocated to a single line as one service If the station has only one line, the loading and unloading desk while applying the Queuing Theory to simulate the loading business time Tj and waiting time for loading and unloading on and unloading business process i n r ailway co ntainer cen ter line Wj are calculated by (12). station. But the amount of RMGC allocated for different lines maybe  ()[]δδ/mi+⋅ 1 60/v, ii[] /m∉ Z different. It causes the different business time in different line. It Tj =   [][]δδ/mi⋅∈ 60/v, ii /m Z means that the service time s ervicing o ne cu stomer o f each  service desk maybe different. This is not accordance with the Wjj= max() T − λ ,0 Queuing Theory. Then we developed the theory to calculate the (12) Tj and Wj by using the ratio between the number of loading and unloading lines r and the amount of the RMGCs m. As illustrated in equation (12), is the number of containers (1) Judgment of r and m. loaded by each railway container flatcars, vi is the average rate In order to coordinate the connection between railroad and of l oading a nd unl oading b usinessδ of each RMGC, mi is th e highway in container transportation, the waiting time Wj should amount of RMGCs allocated to a single loading and unloading be cut down to zero as far as possible. WhenW0j > , there will line, a nd λ is th e in terval tim e of railway co ntainer f latcars be a q ueue. The length of the loading a nd unl oading l ine i s arrival. limited. And the length of the waiting queue is limited, as (10). V. OPTIMAL MODEL VERIFICATION AND EXAMPLE N≤⋅ r L /L r ts (10) This paper used the data from Chongqing railway container center station to testify the bi-objective model.

©The Author(s) 2013. This article is published with open access by the GSTF GSTF Journal of Engineering Technology (JET), Vol. 2 No. 3, Dec 2013

Chongqing r ailway c ontainer c enter station was p ut in to The m ain ha ndling equipment of C hongqing r ailway operation in D ecember 2 009. It to ok th e c ontainer container center station is Railway Mounted Gantry Crane. The transportation a round C hongqing hub , a s w ell a s relevant amount of the equipment allocated i s n ot eq ual t o zer o. The logistics b usinesses r adiating a ll o ver C hina. The f irst te rm valid length of loading and unloading line is 780m. According construction finished one loading and unloading line with valid to (9), the value range of m is 2<< m 4r . length of 780m. The station was allocated 3 RMGCs i n (2) Calculation of objective function Cg. container yard. The running line of RMGC is 790m. In the long The constraints of single objective function are in (13). term, the station will have 8 loading and unloading lines. It can hold 4 trains to be loaded or unloaded simultaneously in its yard. r1≥ 2≤≤ m 4r A. The values of parameters in objective function n r,m∈ Z (13) There are many parameters involved in calculating the daily comprehensive co sts Cg. This p aper s elected s ome i mportant ones and listed them in tableⅡ. According to the (1), (2), (3) and (4), we can calculate the C value of g. Because the handling equipment is RMGC, the ξ=1. Ⅲ TABLEⅡ The calculation results of Cg are shown as table . THE VALUES OF PARAMETERS IN OBJECTIVE FUNCTION Parameters Unit RMGC TABLE Ⅲ TIME AND COSTS PARAMETERS OF DIFFERENT ALLOCATION PLANS OF RMGC Acquisition costs cfi ten-thousand 1000 1 2 3 4 5 6 7 8 9 10 Yuan/each line RMGC TEU hour hour Yuan Yuan Yuan Yuan Annual major repair funds cMi ten-thousand Yuan 37.5 1 3 -- 445 14.87 18.58 7083.3 4560.2 18255.3 29898.9 Daily costs of labor cli Yuan/day 450 Infrastructural construction costs of ten-thousand 879.27 4 3:1 445 14.87 18.58 9444.4 9120.5 19795.9 38360.9 running line ccr Yuan/per line 2 5 3:2 445 14.87 18.58 11805.6 9120.5 18705.3 39631.4

Hard-surface pavement costs of yard csi ten - thousand 1185 6 3:3 445 14.87 18.58 14166.7 9120.5 19155.3 42442.5 Yuan/per line … … … … … … … … … … Depreciation period of running line N year 30

Depreciation period of hard-surface year 30 ’ As illu strated in ta ble Ⅲ, p arameter1 i s t he n umber of yard N loading a nd unl oading l ines i n C hongqing r ailway container i Residual value - 5% center s tation. Parameter2 i s t he t otal am ount o f RMGCs. Depreciation period of handling year 20 Parameter3 is the ratio between the number of the lines and the N equipments i amount o f t he eq uipments al located. Parameter4 i s t he d aily Construction costs of loading and ten-thousand 3120 volume of container to be loaded or unloaded by each RMGC in c unloading line r Yuan/per line line1. Parameter5 is t he av erage d aily t ime o f l oading an d Annual working day of equipments d day 360 unloading business of each RMGC in the line*. Parameter6 is Power and electricity costs of Yuan/hour 73.36 the average daily operation time of power and electricity of each equipments cpi RMGC in line*. Parameter7 is the average daily fixed costs of Maintenance costs of equipments cmi Yuan/TEU 10.07 RMGCs. Parameter8 is the average daily construction costs of Daily container volume of loading and TEU 1334 matching f acilities. Parameter9 i s t he av erage daily business unloading Q costs of loading and unloading of RMGCs. Parameter10 is the average daily comprehensive costs of RMGCs. Line* is the line According to a great deal of observation, the arrival process which has the loading or unloading business. of container flatcars is a random dynamic process. It yields to According to the results of table4, we can get the allocation Markov ch ain an d f ollows s ome r ules in arrival interval and and the costs shown as (14). amount. The a mount of flatcars is a bout 6 T EU e ntering t he 29898.9≤≤ C 38360.9 loading and unloading lines every 5 minutes. To simplify the g model, the paper assumed that the process yields to a normal 3m4≤≤ distribution with =6TEU. Then, the interval time of flatcars 1r2≤≤ arrival is λ1=5min. S hown a s in ta ble3, th e daily container r,m∈ Z (14) δ volume of loading and unloading in Chongqing container center station is 1334TEU/day. Then, the average flatcars arriving at As shown in table Ⅲ and (14), we can see some allocation the loading and unloading lines per day are 223 groups plans of RMGC. While r=1 and m=3, the flatcars entering the according to the assumption above. line could be loaded or unloaded directly without waiting. The B. The amount of RMGC allocated total business time for finishing the loading and unloading is less than 24 hours. It means that the amount of RMGC allocated (1) Value range of objective function m.

©The Author(s) 2013. This article is published with open access by the GSTF GSTF Journal of Engineering Technology (JET), Vol. 2 No. 3, Dec 2013 to this line could meet the demand of loading and unloading 29898.90Yuan. A nd t he opt imal a verage dw elling time on business. loading and unloading lines of railroad flatcars T ∗ is 4 minutes While r=2 and m=4, the new added RMGC will be in idle state. That means if the amount of RMGCs is increasing, all new VI. CONCLUSION added equipments w ill b e in id le s tate, too. Meanwhile, the The o ptimal a llocation o f h andling e quipments is in power and electricity utilization rate is 0.8 under the allocation accordance with the equipment allocation facts of Chongqing plan of r=1 an d m=3. I t is efficiency. And t his m aybe the railway container center station. The bi-objective optimal model optimal allocation plan. is valid and can be used in equipment allocation in other railway (3) Calculation of objective functionT . According t o e quation ( 5) and e quation ( 12), w ith th e container center stations. constraints of equation (14), the objective function T could be calculated. The results of T are shown as table Ⅳ. ACKNOWLEDGMENT Besides the sponsor and financial support acknowledgments TABLE Ⅳ above, t he authors g ratefully ack nowledge C hinese R ailway VALUES OF OBJECTIVE FUNCTION T UNDER DIFFERENT ALLOCATION PLANS Container Transportation Co. Ltd f or p roviding th e d ata th at 1 2 3 4 5 6 7 form the basis for this paper. line RMGC min min min min REFERENCES 1 3 -- 4.00 -- 0.00 4.00 [1] Beijing J iaotong U niversity, Research on the key technology of 2 4 3:1 4.00 0.00 0.00 4.00 multi-modal container express transit system, Beijing J iaotong University, 2012. Ⅳ [2] Yuan Ye, Research on Handling Equipment Allocation and Rail-Truck As illustrated in table , the parameter1 is the number of the Connection Organization Based on Rail-Road Combined loading and unl oading l ines o f C hongqing r ailway c ontainer Transportation, Beijing Jiaotong University, 2012. center s tation. Parameter2 is the t otal am ount o f R MGCs [3] Xin Song, Yinghong Li, and Ruoyu Wu, “Handling equipment selection allocated to th e s tation. Parameter3 i s t he r atio b etween t he and al location i n K unming r ailway co ntainer center s tation”, Railway transportation and economy, pp. 76–77, Aug. 2005. number of lines and the amount of the equipments allocated. [4] Ruihai Bai, Jun Yang, “Research on the handling equipment selection of Parameter4 i s t he a verage t ime o f l oading a nd unl oading railway co ntainer h ub-station”, Journal of railway engineering, p p. business for each flatcar in line1. And parameter5 has the same 77–82, Mar. 2002. meaning as parameter4 but in line2. Parameter6 is the average [5] Yuzhen Ma, “Selection of handling equipment of railway container center station”, Railway transportation and economy, pp. 51–52, Oct. 2005. waiting tim e o f flatcars on l oading a nd unl oading l ines. [6] Jianyong Huo, Hui Xie, and Bo Hu, “Handling equipment selection in Parameter7 is the average dwelling time of them. railway container hub and center station”, Railway transportation and According to th e r esults o f ta bleⅤ, w e can f ind that the economy, pp. 68–69, June. 2006. average business time of loading and unloading of every flatcar [7] Zongze Li, Wenming Cheng, Xiao Wu, and Zeqiang Zhang, “Research on equipment t echnology a nd layout i n r ailway c ontainer c enter s tation”, is le ss th an th e in terval tim e o f flatcars arrival under t he Journal of transportation engineering and information, p p. 1 01–105, allocation plan of r=1 and m=3. That means the waiting time of Feb. 2005. flatcar for loading a nd unl oading b usiness o n lines e quals t o [8] Jian Liang, Wenming Cheng, and Min Zhang, “Simulation research for m3≥ the loading and unloading business of train in railway container center zero. When adding t he a mount o f R MGCs up t o , t he station”, Journal of system simulation, pp. 6290–6294, Oct. 2009. average rate of loading and unloading business for every flatcar [9] Linn R, Zhang C Q, “A heuristic for dynamic yard crane deployment in a is keeping at the level of 4 minutes. That is to say, adding more container terminal”, IEE transactions, pp. 161–174, Vol35, Feb. 2003. RMGCs co uld n ot r educe t he av erage t ime o f l oading and [10] Peng G uo, “Modeling a nd s imulation a nalysis o f r ailway c ontainer logistics center”, “Computer engineering and application”, pp. 235–238, unloading business for each flatcar. We obtained the o ptimal Vol.17, 2011. * objective function T= 4.00 minutes. [11] Zhong W ei, Research on schedule optimization of container yard Combined with Cg in e quation ( 14), w e g ot th e o ptimal logistics system, Beijing Jiaotong University, pp. 16–17, 2002 allocation p lan o f R MGC i n C hongqing r ailway c ontainer [12] Xingyan Yang, “Optimal investment scale of equipment in container yard based on the comprehensive cost model”, Technology of ports, pp. 17–21, center station, shown as equation (15). Feb. 1995. [13] CF Daganzo, “The crane scheduling problem”, Transportation Research, T* = 4.00 minutes Part B, pp. 159–175, Vol.23, 1989. [14] R.I.peterkofsky, CF Daganzo, “A branch and bound solution method for C* = 29898.90Yuan g the c rane s cheduling p roblem”, Transportation Research, Part B, p p. ∗ 159–172, Vol. 24, 1990. m3= [15] J.B.Tabernacle, “A s tudy o f t he c hanges in performance o f q uayside ∗ r1= (15) container cr anes”, Maritime Policy and Management, pp. 1 15–124, Vol.22, 1995. [16] J.Bose, Torsten R eines, Dirk S teenken, an d Stefan V ob, “Vehicle Under the first term construction condition of the station, the dispatching at seaport container terminals using evolutionary algorithms”, optimal allocation of handling equipments is 3 with only one Proceedings of the Annual Hawaii International Conference on System Sciences, IEEE, Piscataway, 2000, pp.1–10. loading a nd unl oading l ine. The o ptimal to tal d aily [17] Lai,K.K, Lam,K, “A study o f c ontainer y ard e quipment a llocation ∗ International Journal of Modeling and comprehensive c osts o f ha ndling e quipments Cg are strategy in H ong K ong”, simulation, pp. 134–138, Vol. 14, 1994.

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[18] Kozan,E, Preston,P, “Genetie algorithm to schedule container transfers at multimodal te rminals”, International Transactions in Operational Research, pp. 311–329. June, 1999. [19] CF Daganzo, “The crane scheduling problem”, Transportation Research, Part B, pp. 159–175, Vol.23, 1989. [20] Huijun Yang, “Research on handling equipment allocation optimization in container ports”, Crane and transportation equipment, pp. 93–96, Dec. 2008. [21] Pyung Hoi Koo, “Fleet sizing and routing for container transportation in a static environment”, OR Spectrum, pp. 193–209, Vol.26, 2004. [22] Mingjun Ji, “Allocation optimization of trailer in container yard based on simultaneous business”, Journal of Dalian Marine University, pp. 47–49, Feb. 2010. [23] Shuyan Zhang, Multi-objective optimization algorithm based on optimal constraints, Dalian Institute of Technology, 2010. [24] Laumanns M , Thiele L , an d Deb K , “Combining c onvergence a nd diversity in e volutionary m ulti- objective o ptimization”, Evolutionary Computation, pp. 263–282, Oct. 2002. [25] AG Hernández-Díaz, LV Santana-Quintero, an d CA Coello Coello, “Pareto-adaptive ε-dominance”, Evolutionary Computation, pp. 493–517, Vol.15, 2007.

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Qi Zhang (Female), born in Lanzhou, Gansu Province, China, Sep. 1973. Dr. Zhang got h er B achelor d egree of Transportation E ngineering f rom B eijing Jiaotong University in 1992, Master degree in 1999 and Doctoral degree in 2012 o f T ransportation E ngineering in B eijing J iaotong U niversity. The author ’s major fields of study are traffic a nd t ransportation p lanning a nd management, freight transportation, multi-modal transportation, and logistics. Her w ork ex perience include: f rom 2006 to n ow, associate professor in School of Traffic & Transportation, Beijing Jiaotong University; from 2001 to 2006, lecturer; from 1999 to 2001, teaching assistant. Her research interests are freight transportation, intermodal transportation, and logistics.