Container Loading Optimization in Rail–Truck Intermodal Terminals Considering Energy Consumption

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Article Container Loading Optimization in Rail–Truck Intermodal Terminals Considering Energy Consumption

Li Wang * and Xiaoning Zhu

School of Traﬃc and Transportation, Beijing Jiaotong University, Beijing 100044, China; [email protected] * Correspondence: [email protected]

Received: 28 February 2019; Accepted: 14 April 2019; Published: 22 April 2019

Abstract: Rail–truck intermodal terminals are an important type of dry port and play a vital role in inland freight transport. This paper addresses the container loading problem in rail–truck intermodal terminals considering energy consumption under the sustainability concept. We analyze the effect factors of energy efficiency for container loading operations and develop an optimization model to minimize the total handling time and container reshuffling. A genetic algorithm is designed to obtain the optimal container loading sequence. Computational experiments on a specific Chinese rail–truck intermodal terminal were conducted to evaluate the performance of our approach. Results show our approach has a good performance for different sizes, and the total handing time, reshuffling times and energy consumption of the handling task are prominently decreased.

Keywords: Sustainability; dry ports; intermodal freight transport; rail–truck intermodal terminal; energy consumption

1. Introduction Intermodal freight transport involves the transportation of freight in an intermodal container or vehicle using multiple modes of transportation (e.g., rail, ship, truck) without any handling of the freight itself when changing modes. The method reduces cargo handling, and so improves security, reduces damage and loss, and allows freight to be transported faster [1]. In intermodal freight transport systems, all containers are transshipped by rail, ship and truck in intermodal terminals. The handling efficiency of the terminal significantly impacts the performance and service quality of intermodal freight transport. Therefore, most terminals focus on optimizing loading, unloading and stockpiling operations to improve efficiency. With rapidly increasing concern about environment pollution, carbon dioxide emissions from transportation becomes a significant environmental threat. Sustainable transportation development is an important research field in sustainability, and green transportation is proposed by many countries to sustain the development of economic globalization. As key nodes of the freight transportation network, intermodal terminals have numerous heavy-duty pieces of equipment. These equipment operations can cause vast quantities of energy consumption and pollutant emission, so intermodal terminals play an important role in sustainable transportation development. Terminals have a responsibility for energy saving and emission reduction. Therefore, terminals need to consider not only handling efficiency but also energy consumption when they optimize loading, unloading and stockpiling operations. Recently, dry ports received more concern from researchers and practitioners around the world and have a vital role in inland freight transport. The rail–truck intermodal terminal is an important kind of dry port that is configured with advanced equipment. In rail–truck intermodal transportation systems, container trains are used to transport massive quantities of containers for long distances,

Sustainability 2019, 11, 2383; doi:10.3390/su11082383 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 2383 2 of 15 trucks are responsible for short distance pick-up and delivery activities, and containers are rapidly transshipped in terminals. With the rapid development of worldwide shipping and inland freight transportation corridors, inland container transportation volume has experienced a sharp increase, which generates a higher demand for handling efficiency of rail–truck intermodal terminals. However, the current handling strategy of terminal is inefficient, which means that the equipment efficiency cannot be fully developed. Therefore, rail–truck intermodal terminals must optimize equipment utilization to improve handling efficiency, as well as considering sustainable development to reduce energy consumption. For now, containers in rail–truck intermodal terminals are mainly outbound containers, and the main handling operation is container loading. Therefore, it is necessary for rail–truck intermodal terminals to optimize container loading. In this paper, the container loading optimization problem in rail–truck intermodal terminal is considered. We analyze the energy consumption in outbound container loading operations and determine the key factors for improving the energy efficiency. An outbound container loading optimization model is proposed by considering energy consumption and a genetic algorithm is developed to obtain an approximate optimal loading sequence. The rest of paper is organized as follows. The relevant literature is reviewed in next section. The container loading optimization problem is described in the third section and formulated in the fourth section. A genetic algorithm is developed in the fifth section. Computational results are reported in the sixth section and the final section covers the conclusion.

2. Literature Review Intermodal transportation has been largely studied in recent literature, mainly focusing on intermodal terminal operations, intermodal transportation network design, intermodal transportation routes optimization and synchronization of operations [2–4]. As the core node of the intermodal transportation system, intermodal terminals provide equipment and facilities for container transfer between ship, rail and truck. Most intermodal terminal operations research has specifically focused on container ports. Literature on container port operations is multi-faceted, having addressed issues such as berth scheduling [5–8], quay crane scheduling [9–12], stowage planning and sequencing [13,14], storage activities in the yard [15,16], and allocation and dispatching of yard cranes and transporters [17–19]. Many corresponding models and algorithms were developed for operational planning and scheduling in container ports. As the research further develops, problem formulation became more complex as more uncertain factors are considered, and the research focus develops from one operation optimization to integrated optimization of multiple operations [20–22]. In contrast with container ports, specific literature on operation optimization of rail–truck intermodal terminal is relatively scarce. Although rail–truck terminals and container ports have similar transfer equipment, the specific operation procedures and rules have significant differences between these two types of intermodal terminals. To compare operations in container ports and rail–truck intermodal terminals, the most significant distinction is that the ship handling area and container yard of the container port are compressed into one handling area in rail–truck intermodal terminals. The rail-mounted gantry crane of rail–truck intermodal terminals is simultaneously responsible for loading–unloading operations and storage activities, which are separately performed by quay cranes and yard cranes in container ports. Thus, the operations related to rail-mounted gantry cranes are more complex, especially the outbound container loading operations, which need to consider container reshuffling in the loading process. Relevant research achievements in container ports cannot be directly applied in rail–truck intermodal terminals. Recently, operation optimization of rail–truck intermodal terminals has gained more attention, and the existing literature mainly focuses on the storage space allocation problem (SSAP) and the rail-mounted gantry crane scheduling problem (RGCSP). The SSAP of inbound containers was formulated as a two-stage optimization model: first to balance the workload of inbound containers, then Sustainability 2019, 11, 2383 3 of 15 reducing the overlapping amounts [23]. The container assignment problem of rail–truck transshipment terminals was formulated as a two-stage optimization model for minimizing overlapping amounts and operation distance [24]. An exact solution procedure was developed to determine disjunct yard areas of varying size for multiple gantry cranes in polynomial runtime, and to ensure the workload for a given pulse of trains is equally distributed among cranes [25]. A dynamic programming approach was proposed to determine yard areas for gantry cranes to accelerate train processing speed [26]. The RGCSP was formulated as an optimization model whose objective is to determine an optimization handling sequence in order to minimize rail-mounted gantry crane idle load time in handling tasks [27]. An optimization model was proposed for the RMGC scheduling problem based on a dual cycle mode and a genetic algorithm was designed to obtain the optimization handling sequence [28]. For the study of sustainable intermodal transportation development. a multi-period mixed integer nonlinear single objective optimization problem was proposed to minimize transportation, hub location, rerouting, environmental and social costs with near optimal shipment quantities and hub allocations as the prime decisions [29]. An extensive survey for environmental sustainability in freight transportation is developed to help fill some of the gaps in the theory and to enhance practice [30]. A geospatial intermodal freight transport model was used to examine the environmental, economic, and time-of-delivery tradeoffs associated with freight transportation in the Great Lakes region and examine opportunities for marine vessels to replace a portion of heavy-duty trucks for containerized freight transport [31]. A mixed-integer mathematical programming model was presented for a multi-objective, multi-mode and multi-period sustainable load planning problem by considering import/export load flows to satisfy the transport demands of customers and many other related issues [32]. For the study on energy consumption in intermodal terminals, the yard crane (YC) scheduling problem was formulated as a mixed integer programming model whose two objectives minimize the total completion delay of all task groups and the total energy consumption of all YCs [17]. An optimal model was built with consideration of key factors such as the crane moving distance, turning distance and the practical operation rules, which are directly related to the total energy consumption [33]. The problem of integrated quay crane (QC) scheduling, internal truck (IT) scheduling and YC scheduling was formulated as a mixed integer programming model where the objective is to minimize the total departure delay of all vessels and the total transportation energy consumption of all tasks [21]. Based on the literature review above, we can draw three conclusions: (i) most existing studies focused on operations optimization in container ports, and scarce literature has focused on rail–truck intermodal terminals. Because of differences between two types of intermodal terminals in operation procedures and rules, the existing studies are hard directly apply to rail–truck intermodal terminals. (ii) The energy consumption of intermodal terminals has been the subject of much more attention in recent years, but current studies on energy consumption all focus on container ports; specific literature considering energy consumption in rail–truck intermodal terminal is scarce. (iii) In the scarce literature related to rail–truck intermodal terminals, studies only focused on improving handling efficiency and did not consider energy consumption while optimizing operations.

3. Problem Description All outbound containers are handled in the main operation area of rail–truck intermodal terminals, which is conﬁgured with arrival–departure lines, truck operation lanes, inbound container yard, outbound container yard and rail-mounted gantry cranes. Figure1 gives a schematic representation of the main operation area in a Chinese rail–truck intermodal terminal.

Sustainability 2019, 11, x FOR PEER REVIEW 4 of 16 Sustainability 2019, 11, x FOR PEER REVIEW 4 of 16 container yard, outbound container yard and rail-mounted gantry cranes. Figure 1 gives a schematic container yard, outbound container yard and rail-mounted gantry cranes. Figure 1 gives a schematic Sustainabilityrepresentation2019, 11of, the 2383 main operation area in a Chinese rail–truck intermodal terminal. 4 of 15 representation of the main operation area in a Chinese rail–truck intermodal terminal.

Figure 1. Schematic representation of the main operation area. FigureFigure 1. 1. SchematicSchematic representation representation of of the the main main operation operation area. area. According to the length of arrival–departure lines and the number of rail-mounted gantry AccordingAccording to thethe lengthlength of of arrival–departure arrival–departure lines lines and and the numberthe number of rail-mounted of rail-mounted gantry gantry cranes, cranes, the main operation area is equally divided, and each rail-mounted gantry crane is cranes,the main the operation main operation area is equally area divided,is equally and divi eachded, rail-mounted and each gantryrail-mounted crane is gantry responsible crane for is a responsible for a fixed area. Thus, the scope of our study is limited to one fixed handling area. responsiblefixed area. Thus,for a fixed the scope area. ofThus, our studythe scope is limited of our tostudy one is fixed limited handling to one area. fixed handling area. Outbound containers in rail–truck intermodal terminals can be classified into two types based OutboundOutbound containers containers in in rail–truck rail–truck intermodal intermodal terminals terminals can can be be classified classified into into two two types types based based on their status at different handling stages. The first type is the outbound containers brought into the onon their their status status at at different different handling handling stages. stages. The The firs firstt type type is the is theoutbound outbound containers containers brought brought into intothe theterminal terminal by bytrucks, trucks, abbreviated abbreviated as asOCT. OCT. OCT OCT1 areare allocated allocated in in the the container container yard yard and OCT2 are terminal by trucks, abbreviated as OCT. OCT1 are1 allocated in the container yard and OCT22 are directly loaded onto rail vehicles. The other is outbound containers that are already in the container directlydirectly loaded loaded onto onto rail rail vehicles. vehicles. The The other other is is outbound outbound containers containers that that are are already already in in the the container container yard waiting to being loaded onto rail vehicles, abbreviated as OCC. Because the loading operations yardyard waiting waiting to to being being loaded loaded onto onto rail rail vehicles, vehicles, abbreviated abbreviated as as OCC. OCC. Because Because the the loading loading operations operations are only for OCT 2 andand OCC, OCC, the the object object of of our our study is th theseese two types of outbound containers. are only for OCT22 and OCC, the object of our study is these two types of outbound containers. Outbound container loading operations can be described as moving from one initial loading OutboundOutbound container container loading loading operations operations can can be be described described as as moving moving from from one one initial initial loading loading position (container yard or truck) to a matching end position (rail vehicle), and an empty move back positionposition (container (container yard or truck) toto aa matchingmatching endend positionposition (rail (rail vehicle), vehicle), and and an an empty empty move move back back to to the next outbound container initial loading position. An outbound container handling task is tothe the next next outbound outbound container container initial initial loading loading position. position. An outbound An outbound container cont handlingainer handling task is finishedtask is finished when all outbound containers loaded onto rail vehicles. A sample of a container loading finishedwhen all when outbound all outbound containers contai loadedners onto loaded rail vehicles. onto rail A vehicles. sample of A a containersample of loading a container task isloading shown task is shown in Figure 2. taskin Figure is shown2. in Figure 2.

A container loading task A container loading task Empty Start End Empty Start End Start End Start End crane Start End …………… Start End position position crane position position …………… position position position position move position position position position move

Figure 2. A sample of a container loading task. Figure 2. A sample of a container loading task. Before the handling task begins, OCC have alreadyalready beenbeen allocatedallocated inin thethe container yard.yard. During Before the handling task begins, OCC have already been allocated in the container yard. During the handling task, OCT2 are brought into the terminal by trucks and park in the assigned space. All the handling task, OCT2 are brought into the terminal by trucks and park in the assigned space. All the handling task, OCT2 are brought into the terminal by trucks and park in the assigned space. All outbound containers have been assigned speciﬁcspecific initial and end loading positions before they are outbound containers have been assigned specific initial and end loading positions before they are loaded. A sample of the loading operation is shown in Figure3 3.. loaded. A sample of the loading operation is shown in Figure 3.

4 4

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Operation 1 Operation 2 Operation 3

OCC Outbound container yard OCC

Arrival-departure lines

OCT 2 Truck operation lane

Empty crane Initial loading Loading crane move End position move position FigureFigure 3. 3. AA sample sample of of loading loading operation. operation.

AccordingAccording toto thethe loading loading operations operations of outboundof outbound containers, containers, the energy the consumptionenergy consumption of container of containerloading in loading the terminal in the can terminal be divided can be into divide loadingd into crane loading energy crane consumption, energy consumption, empty crane empty energy craneconsumption energy andconsumption reshuﬄing craneand re energyshuffling consumption. crane energy The detailsconsumption. of energy The consumption details of are energy shown consumptionin Table1. are shown in Table 1.

Table 1. Details of energy consumption. Table 1. Details of energy consumption.

EnergyEnergy consumption Description Description consumption This aspect is generated by the loading crane moving from the This aspect is generatedcontainer by the yardloading or trucks crane to moving rail vehicles. from Because the container all outbound yard containers have specific handling positions, the loading crane Loading crane energy consumption Loading crane or trucks to rail vehicles.energy Because consumption all outbound is a fixed valuecontainers in one have handling specific task. In energy handling positions, thegeneral, loading this crane kind energy of energy consumption consumption is is a determined fixed value and in consumption one handling task. In general,never this changed kind of after energy the handling consumption task is generated.is determined and never changedThis aspect after is generated the handling by the task empty is generated. crane moving between This aspect is generatedtwo by outboundthe empty container crane moving loading between operations. two This outbound energy container loading operations.consumption This ener is determinedgy consumption by the is outbound determined container by the Empty crane handling sequence. Different handling sequences have a great Empty crane energyoutbound consumption container handling sequence. Different handling sequences have a energy influence on empty crane energy consumption, so optimizing great influence on empty crane energy consumption, so optimizing the consumption the handling sequence can directly reduce this kind of energy handling sequence can directlyconsumption reduce and this improve kind energyof energy efficiency consumption of outbound and improve energy efficiency of outboucontainernd container loading operations. loading operations. This aspect is generatedThis by aspect container is generated reshuffling by container operations reshuffl ining the operations loading in process. According to the loadingdifferent process. status Accordingof the upper to the container, different statusreshuffling of the upper container, reshuffling crane energy consumption can be crane energy consumption can be divided into two types. In the first type, the Reshuffling crane divided into two types. In the first type, the upper container upper container does notdoes belong not belong to th toe thesame same handling handling task, task, so so it it must must be Reshuenergyffling crane energy consumption reshuffled to ensure the reshuhandlingffled totask ensure can thego on handling smoothly. task canThis go type on smoothly. of energy consumption consumption is unavoidable.This type The of energyother ty consumptionpe is caused is by unavoidable. the overlapping The other of type is caused by the overlapping of containers in the same containers in the same handling task, and this type of energy consumption can handling task, and this type of energy consumption can be be reduced or avoidedreduced by or avoidedoptimizing by optimizing the handling the handling sequence. sequence.

As observed in Table 1, the key issue for improving the energy efficiency of outbound container As observed in Table1, the key issue for improving the energy e fficiency of outbound container loading in rail–truck intermodal terminals is to reduce the empty move distance of rail-mounted loading in rail–truck intermodal terminals is to reduce the empty move distance of rail-mounted gantry gantry cranes and container reshuffling operations in the handling task. Therefore, the optimization cranes and container reshuffling operations in the handling task. Therefore, the optimization objective objective of our study is to optimize the outbound container loading sequence to minimize the of our study is to optimize the outbound container loading sequence to minimize the handling move handling move distance and container reshuffling. Decreasing the energy consumption from empty distance and container reshuffling. Decreasing the energy consumption from empty crane movements

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crane movements and reshuffling crane move ments can be effective in improving the energy and reshuffling crane movements can be effective in improving the energy efficiency of outbound Sustainabilityefficiency 2019 of, 11 outbound, x FOR PEER containerREVIEW loading in rail–truck intermodal terminals. 6 of 16 container loading in rail–truck intermodal terminals. crane4. Problem movements Formulation and reshuffling crane movements can be effective in improving the energy efficiency4. Problem of outbound Formulation container loading in rail–truck intermodal terminals. 4.1. Coordinate Frame Transforming for Handling Area 4. Problem4.1. Coordinate Formulation Frame Transforming for Handling Area InIn order order to to expediently expediently formulate formulate the the problem, problem, th thee han handlingdling area area is is transformed transformed into into 4.1. Coordinate Frame Transforming for Handling Area threethree-dimensional-dimensional coordinate coordinates.s. In In the the XX directiondirection,, the the departure departure line, line, row rowss of of the the container container yard yard and and thetheIn t ruck truckorder operation operationto expediently lane lane are areformulate orderly orderly encodedthe encoded proble from fromm, the11 to to handling2+n2+n; n; n is is thearea the number numberis transformed of of row rowss ininto in the the container container three-dimensionalyard.yard. I Inn the the Y direction,coordinates.direction, thethe In bays thebay Xs of direction, of the the handling handling the departure area area are line,are orderly rowsorderly encoded of the encoded container from from1 yardto m 1 ;and mtois m the; m number is the the truck operation lane are orderly encoded from 1 to 2+n; n is the number of rows in the container numberof bays of in bay thes container in the contain yard.er Figure yard.4 Figure gives an4 gives encoding an enco exampleding example of the X of/Y thedirection. X/Y direction. yard. In the Y direction, the bays of the handling area are orderly encoded from 1 to m; m is the number of bays in the container yard. Figure 4 gives an encoding example of the X/Y direction. Y 1 2 3 ……… m-1 m Departure 1 line 2 X 3 Outbound container … yard

1+n Truck 2+n operation lane

Figure 4. An encoding example of the X/Y direction. Figure Figure4. An encoding 4. An encoding example of example the X/Y direction. of the X/Y direction.

In IntheIn the theZ direction,Z direction,direction the ,the layers the layers layers are areorderly are orderly orderly encoded encoded encoded from from low from low to high.to low high. Because to Because high. all Because allhandling handling all handling positions positionspositionsin the in departure thein thedeparture departure line and line truck andline truck operationand operationtruck lane operation lane have have only lane only one have one layer, onlylayer, the one z-valuethe layer,z-value of thethese of thesez- positionsvalue of these are all positionspositions1. A sample are areall 1. all of A coordinate 1.sample A sample of coordinate frame of coordinate transforming frame transformingframe is t shownransform is shown ining Figure iins shoFigure5. wn 5.in Figure 5.

Outbound container yard Truck operation lane Departure line 1 2 3 4 5 6 (3,4,2) (4,6,2) (2,1,2) (3,2,2) (2,3,2) Z 6 (2,5,2) 5 4 (2,1,1) (2,3,1) (2,6,1) X 3 (1,5,1) 2 1 (1,2,1) Y Figure 5. A sample of coordinate frame transforming.

After coordinateFigure frame 5. transforming,A sample of coordinate the handling frame transforming. positions in the handling task are transformed into coordinate points inFigure a three-dimensional 5. A sample of coo coordinaterdinate frame system, transform anding the. loading operations can be depictedAfter coordinate as movements frame among transforming, different the points. handling For describing positions thein sequentialthe handling relationship task are of operations transformed into coordinate points in a three-dimensional coordinate system, and the loading in the container loading task, we use moving time to replace moving distance, and the corresponding operationsAfter can cbeoordinate depicted fasrame movements transform amonging, differentthe handling points. For positions describing in thethe sequential handling task are objective is to minimize whole handling time and container reshuffling in the container loading task. relationshiptransformed of operations into coordinate in the container points inloading a three task,-dimensional we use moving coordinat time toe replace system moving, and the loading distance,operations and canthe corresponding be depicted asobjective movements is to minimize among different whole handling points. timeFor describand containering the sequential 4.2. A Mathematical Formulation reshufflingrelationship in the of container operations loading in thetask. container loading task, we use moving time to replace moving distance,4.2.1. Assumptions and the corresponding objective is to minimize whole handling time and container 4.2.Areshuffling Mathematic inal the Formulation container loading task. The following assumptions are introduced for the problem formulation: 4.2.1. Assumptions 4.2.A Mathematical Formulation (i) Each loading operation only involves one container once. (ii) Operation positions are assumed to be known and fixed after the loading task is generated. 4.2.1. Assumptions 6 (iii) All loading operations are non-preemptive; that is, once a loading operation starts, it must be completed without any pause or shift. 6

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(iv) The containers in the model are assumed to be of the same size.

4.2.2. Notations and Variables The parameters and variables used for the mathematical formulations are deﬁned in Table2.

Table 2. Notations and variables.

N Number of handling tasks L Maximum layer number of the container yard i, j Indices of the handling task Parameter a, b, c, d Row indices of operation positions e, f , g, h Bay indices of operation positions k, l Layer indices of operation positions (a, e, k) Indices of operation positions ϕ Time conversion coeﬃcient of container reshuﬄing

tij The empty move time from task i to task j M A sufficiently large constant eT The set of loading operations Set Pe The set of operation positions sti (a,e,k),(b, f ,l) Start time of task i from (a, e, k) to (b, f , l) cti ( ) ( ) Variables (a,e,k),(b, f ,l) Finish time of task i from a, e, k to b, f , l 1, if task j immediately begins after task i has finished; 0, otherwise. 1. Tasks S and T are considered to be the initial and Xij finish status, Thus, when task i is the first task, XSi = 1. When task i is the last task, XiT = 1 ri (a,e,k+m) Reshuffling times of task i caused by its m th upper container 0, if task i begins earlier than task j; 1, otherwise. (a, e, k) is the ij B starting position of task i, and (c, g, l) is the starting position of (a,e,k),(c,g,l) task j

4.2.3. Objective Function The objective function of the outbound container loading optimization model is written as follows:

N N N N L k X X X X X− (cti sti ) + X t + ϕ ri (1) (a,e,k),(b, f ,l) − (a,e,k),(b, f ,l) ij · ij (a,e,k+m) i=1 i=1 j=1 i=1 m=1

The objective function is to minimize total handling time and container reshuﬄing times in the container loading task.

4.2.4. Constraints The constraints of the outbound container loading optimization model are introduced as follows to ensure the practical feasibility of the solution:

XN X 1, i eT (2) ij ≤ ∀ ∈ j=1 Sustainability 2019, 11, 2383 8 of 15

XN X 1, j eT (3) ij ≤ ∀ ∈ i=1 j cti + t st M 1 X , i, j eT (4) (d,h,l),(c,g,k) ij − (a,e,k),(b, f ,l) ≤ − ij ∀ ∈ ij ri 1 B , i, j eT, (a, e, k), (a, e, k + m) Pe (5) (a,e,k+m) ≤ − (a,e,k),(a,e,k+m) ∀ ∈ ∀ ∈ ij B 1 X , i, j eT, (a, e, k), (a, e, k + m) Pe (6) (a,e,k),(a,e,k+m) ≤ − ij ∀ ∈ ∀ ∈ XN XSi = 1 (7) i=1 XN XiT = 1 (8) i=1 ri 0, i eT, (a, e, k), (a, e, k + m) Pe (9) (a,e,k+m) ≥ ∀ ∈ ∀ ∈ ij X , B = 0 or 1, i, j eT, (a, e, k), (c, g, l) Pe (10) ij (a,e,k),(c,g,l) ∀ ∈ ∀ ∈ Constraint (2) and Constraint (3) are preorder and subsequent operation constrains. Constraint (2) represents that there is at most one subsequent operation for each container loading operation. Constraint (3) represents that there is at most one preorder operation for each container loading operation. Constraint (4) indicates the continuous time relationship between two consecutive loading operations. Constraint (5) defines the reshuffling times of a task container caused by its upper container. Constraint (6) defines the relationship of two continuous handling tasks. Constraint (7) and Constraint (8) are the beginning and finishing operation constrains. They represent that the whole container loading task can only have one beginning operation and one finishing operation.

5. A Genetic Algorithm for the Problem The outbound container loading optimization ties into the crane scheduling problem, which has been proved to be non-deterministic polynomial [34], and the formulations presented above cannot be solved exactly in a reasonable time. Therefore, we developed a genetic algorithm (GA) to obtain the approximate optimal outbound container loading sequence. In genetic algorithm implementation, the chromosome representation and genetic operator design are two vital steps for quickly accessing the feasible space and an eﬀective movement toward the optimal solution. The proposed genetic algorithm is illustrated in Figure6 and the main implementation steps are elaborated as follows.

Sustainability 2019, 11, x FOR PEER REVIEW 9 of 16 beSustainability solved exactly 2019, 11 , inx FOR a reasonable PEER REVIEW time. Therefore, we developed a genetic algorithm (GA) to obtain9 of 16 the approximate optimal outbound container loading sequence. be solved exactly in a reasonable time. Therefore, we developed a genetic algorithm (GA) to obtain In genetic algorithm implementation, the chromosome representation and genetic operator the approximate optimal outbound container loading sequence. design are two vital steps for quickly accessing the feasible space and an effective movement toward In genetic algorithm implementation, the chromosome representation and genetic operator the optimal solution. The proposed genetic algorithm is illustrated in Figure 6 and the main design are two vital steps for quickly accessing the feasible space and an effective movement toward implementation steps are elaborated as follows. theSustainability optimal2019 solution., 11, 2383 The proposed genetic algorithm is illustrated in Figure 6 and the 9main of 15 implementation steps are elaborated as follows. Start Start

Generate initial population Generate initial population

Calculate the fitness value based Mutation on the Equation (11) Calculate the fitness value based Mutation on the Equation (11) Crossover Crossover N Stop criterion met? Selection N Stop criterion met? Selection Y Y End

End Figure 6. Flow digram of the genetic algorithm (GA).

5.1. Chromosome RepresentationFigure 6. Flow digram of the genetic algorithm (GA).

5.1. Chromosome ChromosomeThe chromosome Representation is designed by permutation encoding. Each chromosome represents a possible loading sequence for the outbound containers and consists of T number of genes. Each The chromosomechromosome is is designed designed by permutationby permutatio encoding.n encoding. Each chromosomeEach chromosome represents represents a possible a genepossibleloading represents sequenceloading a forsequence loading the outbound foroperation, the containers outbound and the and containers value consists of ofand the eT consistsnumbergene is ofthe genes.T indices number Each of geneof this genes. represents loading Each operation.a loading The operation, gene sequence and the is value the loading of the genesequence is the implemented indices of this from loading left to operation.right. The gene gene represents a loading operation, and the value of the gene is the indices of this loading sequenceThe operation is the loading indices sequence correlate implemented with operation from po leftsitions; to right. one operation index has a fixed start operation. The gene sequence is the loading sequence implemented from left to right. positionThe and operation finish position, indices correlate and the withtwo positi operationons cannot positions; be changed one operation in GA indeximplementation. has a fixed startThe The operation indices correlate with operation positions; one operation index has a fixed start geneticposition operators and finish are position, only used and for the the two operation positions index. cannot be changed in GA implementation. The position and finish position, and the two positions cannot be changed in GA implementation. The geneticFigure operators 7 shows are onlyan example used for of the chromosome operation index. representation. The chromosome represents a genetic operators are only used for the operation index. handlingFigure task7 shows with an examplefive loading of chromosome operatio representation.ns, which are The chromosomehandled in representsthe sequence a handling of Figure 7 shows an example of chromosome representation. The chromosome represents a 41325task→→→ with five loading → . operations, which are handled in the sequence of 4 1 3 2 5. handling task with five loading operations, which are handled→ in→ the→ sequence→ of →→→ → 41325. Operation 4 1 3 2 5 Indice Loading Operation 4 1 3 2 5 Operations Indice Operation Loading (2,1,2) to(1,3,1) (4,3,1) to (1,4,1) (6,2,1) to (1,2,1) (5,4,2) to (1,5,1) (4,2,1) to (1,1,1) Operations Positions Operation (2,1,2) to(1,3,1) (4,3,1) to (1,4,1) (6,2,1) to (1,2,1) (5,4,2) to (1,5,1) (4,2,1) to (1,1,1) Positions Chromosome 4 1 3 2 5

ChromosomeHandling 414 1323 52 5 Sequence Handling 4132 5 SequenceFigureFigure 7. 7. AA sample sample of of chromosome chromosome representation. representation. 5.2. Evaluation of Fitness ValueFigure 7. A sample of chromosome9 representation.

According to the objective function mentioned9 above, the fitness function can be designed as follows. The fitness value of the chromosome could be calculated based on the fitness function.   XN XN XN XN XL k   i i − i  Fitness = 1/ (ct st ) + Xij tij + ϕ r  (11)  (a,e,k),(b, f ,l) − (a,e,k),(b, f ,l) · (a,e,k+m) i=1 i=1 j=1 i=1 m=1

Sustainability 2019, 11, x FOR PEER REVIEW 10 of 16

5.2 Evaluation of Fitness Value According to the objective function mentioned above, the fitness function can be designed as follows. The fitness value of the chromosome could be calculated based on the fitness function. NNNNLk− = ii−+⋅+ϕ i SustainabilityFsirtne2019, st11, 23831( ct(,,),(,aek b f ,) l st (,,),(, aek b f ,) l ) X ij ij (,,+) aek m  (10)10 of 15 iijim=====11111

5.3. Genetic Operators Design 5.3. Genetic Operators Design For the selection operator, we chose roulette wheel selection, which selects potentially useful For the selection operator, we chose roulette wheel selection, which selects potentially useful chromosomes for recombination based on the selection probability of each individual chromosome. chromosomes for recombination based on the selection probability of each individual chromosome. 5.3.1.Crossover Crossover operator operator TheThe genes genes in in the the chromosome chromosome represent represent indices of all loadingloading operationsoperations inin thethe handling handling task, task, so sothe the gene gene values values cannot cannot bebe lostlost andand repeated in the offspring. offspring. To To avoid avoid infeasibility infeasibility of of the the offspring offspring generated,generated, an an order order crossover crossover operator operator is is adop adopted.ted. The The crossover crossover process process is is shown shown as as follows. follows. (i) (i)Firstly, Firstly, we we randomly randomly select select a a segment segment in in the the parents, parents, and and place place the the segment segment from from one one parent parent to tothe the frontfront of of the the other other parent. parent. (ii) In order to avoid duplication, we scan the offspring from left to right and delete the repeated (ii) In order to avoid duplication, we scan the offspring from left to right and delete the repeated gene values in the substring. gene values in the substring. (iii) The crossover operation is finished when the offspring generated by the order crossover (iii) The crossover operation is finished when the offspring generated by the order crossover operator operator are both feasible. are both feasible.

A sampleA sample of the of the crossover crossover operation operation is shown is shown in Figure in Figure8. 8.

Segment

Parent 1 13 9 10 14 6 3 12 7 11 5 1 8 4 2

Parent 2 6 3 13 5 12 4 9 14 2 8 11 7 1 10

Crossover

12 4 9 13 9 10 14 6 3 12 7 11 5 1 8 4 2

6 3 12 6 3 13 5 12 4 9 14 2 8 11 7 1 10 Repair

Offspring 1 12 4 9 13 10 14 6 3 7 11 5 1 8 2

Offspring 2 6 3 12 13 5 4 9 14 2 8 11 7 1 10

FigureFigure 8. 8.A Asample sample of ofthe the crossover crossover operation. operation.

5.3.2.Mutation Mutation operator operator AsAs mentioned mentioned above, above, for for ensuring ensuring the the integrity integrity of of the the handling handling tasks, tasks, missing missing and and duplicating duplicating genegene values values must must be be forbidden forbidden in in the the offspring. oﬀspring. Thus, Thus, an an inversion inversion mutation mutation operator operator is is used. used. The The operatoroperator randomly randomly picks picks two two mutation mutation points points in in the chromosome andand thenthen invertsinverts thethe genegene values values of ofthe the mutation mutation points. points. This This mutation mutation operator operator can guarantee can guarantee the generation the generation of a feasible ofchromosome. a feasible chromosome.ASustainability sample of 2019 thisA, sample11 mutation, x FOR of PEER this operation REVIEW mutation is shownoperation in Figure is shown9. in Figure 9. 11 of 16

Mutation Mutation point 1 point 2 10 13 9 10 14 6 3 12 7 11 5 1 8 4 2

Mutation

13 9 10 5 6 3 12 7 11 14 1 8 4 2

Figure 9. A sample of the mutation operation.

5.4. Stopping Criterion The algorithm iteration will stop when the iterative times meet the specified value. Then, the best individual from the current population will be reported as the final solution.

6. Computational Experiments To verify the proposed approach for container loading optimization, several experiments were performed. Computational experiments are applied to the data from a specific Chinese rail–truck intermodal terminal. For evaluating the performance of our approach, a comparison is made between our approach and the current approach applied in rail–truck intermodal terminals. The current approach is straightforward and does not involve any optimization techniques. The outbound containers are orderly loaded onto rail vehicles from left to right in the departure line. Furthermore, to further evaluate the performance of our approach, experiments on different sample sizes are conducted. The details of the specific rail–truck intermodal terminal are depicted as follows. One departure line can stop 120 rail vehicles for twenty-foot equivalent units. The outbound container yard has three rows and 120 bays, and the maximum layer number is two. There are four rail-mounted gantry cranes in the main operation area, and each crane is responsible for 30 bays. The maximum amount of loading operations in one handling task is 30. A handling task with a task size of 30 is shown in Table 3.

Table 3. Container loading task with a sample size of 30.

Operation Container Initial End Operation Container Initial End Index Type Position Position Index Type Position Position 1 OCC (3,2,1) (1,1,1) 16 OCT2 (5,13,1) (1,16,1) 2 OCC (4,1,1) (1,2,1) 17 OCC (3,17,1) (1,17,1) 3 OCC (2,5,2) (1,3,1) 18 OCC (4,14,2) (1,18,1) 4 OCC (3,8,1) (1,4,1) 19 OCC (3, 22,1) (1,19,1) 5 OCT2 (5,4,1) (1,5,1) 20 OCC (2,21,1) (1,20,1) 6 OCC (4,4,1) (1,6,1) 21 OCC (3,21,2) (1,21,1) 7 OCC (2,5,1) (1,7,1) 22 OCC (4,27,1) (1,22,1) 8 OCC (2,9,2) (1,8,1) 23 OCC (4,22,1) (1,23,1) 9 OCC (4,5,1) (1,9,1) 24 OCC (2,24,2) (1,24,1) 10 OCC (2,10,2) (1,10,1) 25 OCT2 (5,25,1) (1,25,1) 11 OCC (3,8,2) (1,11,1) 26 OCC (2,24,1) (1,26,1) 12 OCT2 (5,12,1) (1,12,1) 27 OCC (4,22,2) (1,27,1) 13 OCC (4,14,1) (1,13,1) 28 OCC (2,27,1) (1,28,1) 14 OCC (2,11,1) (1,14,1) 29 OCC (3,29,1) (1,29,1) 15 OCC (3,9,2) (1,15,1) 30 OCC (4,27,2) (1,30,1)

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5.4. Stopping Criterion The algorithm iteration will stop when the iterative times meet the speciﬁed value. Then, the best individual from the current population will be reported as the ﬁnal solution.

6. Computational Experiments To verify the proposed approach for container loading optimization, several experiments were performed. Computational experiments are applied to the data from a specific Chinese rail–truck intermodal terminal. For evaluating the performance of our approach, a comparison is made between our approach and the current approach applied in rail–truck intermodal terminals. The current approach is straightforward and does not involve any optimization techniques. The outbound containers are orderly loaded onto rail vehicles from left to right in the departure line. Furthermore, to further evaluate the performance of our approach, experiments on different sample sizes are conducted. The details of the specific rail–truck intermodal terminal are depicted as follows. One departure line can stop 120 rail vehicles for twenty-foot equivalent units. The outbound container yard has three rows and 120 bays, and the maximum layer number is two. There are four rail-mounted gantry cranes in the main operation area, and each crane is responsible for 30 bays. The maximum amount of loading operations in one handling task is 30. A handling task with a task size of 30 is shown in Table3.

Table 3. Container loading task with a sample size of 30.

Operation Container Initial End Operation Container Initial End Index Type Position Position Index Type Position Position

1 OCC (3,2,1) (1,1,1) 16 OCT2 (5,13,1) (1,16,1) 2 OCC (4,1,1) (1,2,1) 17 OCC (3,17,1) (1,17,1) 3 OCC (2,5,2) (1,3,1) 18 OCC (4,14,2) (1,18,1) 4 OCC (3,8,1) (1,4,1) 19 OCC (3, 22,1) (1,19,1)

5 OCT2 (5,4,1) (1,5,1) 20 OCC (2,21,1) (1,20,1) 6 OCC (4,4,1) (1,6,1) 21 OCC (3,21,2) (1,21,1) 7 OCC (2,5,1) (1,7,1) 22 OCC (4,27,1) (1,22,1) 8 OCC (2,9,2) (1,8,1) 23 OCC (4,22,1) (1,23,1) 9 OCC (4,5,1) (1,9,1) 24 OCC (2,24,2) (1,24,1)

10 OCC (2,10,2) (1,10,1) 25 OCT2 (5,25,1) (1,25,1) 11 OCC (3,8,2) (1,11,1) 26 OCC (2,24,1) (1,26,1)

12 OCT2 (5,12,1) (1,12,1) 27 OCC (4,22,2) (1,27,1) 13 OCC (4,14,1) (1,13,1) 28 OCC (2,27,1) (1,28,1) 14 OCC (2,11,1) (1,14,1) 29 OCC (3,29,1) (1,29,1) 15 OCC (3,9,2) (1,15,1) 30 OCC (4,27,2) (1,30,1)

For the computational sample above, experiments are conducted for 100 independent runs. Based on the preliminary tests, the algorithm parameters are set as follows: population size is 50, crossover rate is 0.95, mutation rate is 0.15, and the maximum number of generations is 200. Then, we chose empty move time and reshuﬄing times as evaluation indicators, and made a comparison between our approach and the current approach. The comparison results are shown in Table4. Sustainability 2019, 11, 2383 12 of 15

Table 4. Comparison results between our approach and the current approach.

a b c d e TW (min) Tr (times) Ee (kW) Er (kW) EW (kW) GAP GAP GAP GAP GAP Our Approach 68.3 2 153 30 371.5 (OA) Current 7.1% 60% 16.1% 41.2% 8.1% Approach 73.5 5 179 75 442.5 (CA)

Notes: TW is total handling time, Tr is reshuﬄing times, EW is total energy consumption, Ee is energy consumption of an empty move, Er is energy consumption of reshuﬄing. a, b, c, d, e are the indices of GAP.

There are five GAP shown in Table4. GAP a shows the optimization of the total handling time between our approach and the current approach. GAP b shows the optimization of the reshuffling times between our approach and the current approach. GAP c shows the optimization of the total energy consumption between our approach and the current approach. GAP d presents the percentage of empty move energy consumption in total energy consumption. GAP e presents the percentage of reshuffling energy consumption in total energy consumption. These GAP are calculated as follows.

a GAP = (TW obtained f rom CA TW obtained f rom OA)/TW obtained f rom CA (12) − b GAP = (Tr obtained f rom CA Tr obtained f rom OA)/Tr obtained f rom CA (13) − c GAP = (EW obtained f rom CA EW obtained f rom OA)/EW obtained f rom CA (14) − d GAP = Ee obtained f rom OA/EW obtained f rom OA (15) e GAP = Er obtained f rom OA/EW obtained f rom OA (16)

In Table4, the total energy consumption EW, energy consumption of an empty move Ee and energy consumption of reshuﬄing Er, are calculated as follows:

EW = TW Cp (17) ×

Ee = Te Cp (18) × Er = Tr Cr (19) × where Cp is the power consumption per hour of crane usage and Cr is the average power consumption per reshuffling. In this paper, Cp is set at 300 kW/h and Cr is set at 15 kW. As observed in Table4, the GAP of total handling time is 7.1% and the GAP of reshu ffling times is 60%. The reshuffling times obtained by our approach result from the overlapping of upper containers, which do not belong to the same handling task. The reshuffling operations caused by the overlapping between containers in the same handling task are optimized by our approach. Our approach observably reduces the total handling time and container reshuffling times in the outbound container loading process. There is a 22% decrease in total energy consumption after loading optimization by our approach. In order to further evaluate the performance of our approach, experiments on different sample sizes are conducted. In general, there are 2–4 rail-mounted gantry cranes in the main operation area of this Chinese rail–truck intermodal terminal. Therefore, the quantitative range of loading operations in one handling task is from 30 to 60. In this range, computational experiments are carried out to verify the effectiveness of our approach for different sample sizes. For each task size, experiments are implemented for 100 independent runs. The results are shown in Table5.

Sustainability 2019, 11, x FOR PEER REVIEW 13 of 16

=× EeepTC (18)

=× ETCrrr (19)

Where C p is the power consumption per hour of crane usage and Cr is the average power consumption per reshuffling. In this paper, C p is set at 300 kW/h and Cr is set at 15 kW. As observed in Table 4, the GAP of total handling time is 7.1% and the GAP of reshuffling times is 60%. The reshuffling times obtained by our approach result from the overlapping of upper containers, which do not belong to the same handling task. The reshuffling operations caused by the overlapping between containers in the same handling task are optimized by our approach. Our approach observably reduces the total handling time and container reshuffling times in the outbound container loading process. There is a 22% decrease in total energy consumption after Sustainability 2019, 11, 2383 13 of 15 loading optimization by our approach. In order to further evaluate the performance of our approach, experiments on different sample sizes are conducted. In general,Table there 5. Performance are 2–4 rail-m for diountedfferent gantry sample cranes sizes. in the main operation area of this Chinese rail–truck intermodal terminal. Therefore, the quantitative range of loading Our Approach Current Approach operations in one handling task is from 30 to 60. In this range, computational experiments are carried Total Total out Sampleto verify the effectiveness of ourAverage approach for different sample sizes.a For eachb task csize, Handling Reshuffling Handling Reshuffling GAP GAP GAP Size CPU experiments areTime implementedTimes for 100 independenTimet runs. The Timesresults are shown in Table 5. time (s) (min) (min) 40 102.4Table 2 5. Performance 15.9 for 109.6 different sample 6 sizes. 6.6% 66.7% 15.1% 50 124.7 3 24.7 135.5 10 8.0% 70.0% 19.3% Our Approach Current Approach Sample60 Total 154.3 3 37.4Average 164.2Total 12 6.1% 75.0% 18.5% Reshuffling Reshuffling GAPa GAPb GAPc Size Handling CPU Handling Times Times As observedTime (min) in Table 5, handling taskstime(s) with di ffTimeerent (min) sample sizes can be solved in a short time. The40 total computational102.4 time is 2 about 1–2 minutes 15.9 to generate109.6 a loading sequence 6 6.6% for a container66.7% 15.1% train combined50 with124.7 120 rail vehicles, 3 which can 24.7 meet the actual135.5 scheduling 10 requirements8.0% 70.0% in rail–truck 19.3% intermodal60 terminals.154,3 In Figure 3 10 , based on 37.4 optimizing 164.2 the outbound container 12 loading6.1% sequence,75.0% 18.5% the total handling time, reshuffling times and energy consumption of the handling task are decreased.

Figure 10. GAPGAP for different diﬀerent sample sizes.

AsBased observed on the in experimental Table 5, handling results tasks mentioned with differ above,ent sample our approach sizes can is be di solvedfferent in from a short previous time. Thestudies total from computational a sustainability time perspective, is about 1–2 as minutes we consider to generate not only a improving loading sequence handling for effi aciency, container but also reducing energy consumption in container13 loading operation optimization. The high energy efficiency of operations in rail–truck intermodal terminals is significant for sustainable development of freight transportation and contribute to energy conservation and emission reduction.

7. Conclusions The container loading optimization problem in rail–truck intermodal terminals was considered in this paper. By analyzing the energy consumption of loading operations in the terminal, the key issue to improve the energy efficiency of outbound container loading in rail–truck intermodal terminals was to optimize the loading sequence for reducing the energy consumption from empty crane movements and reshuffling crane movements. An optimization model was presented to minimize total handling time and container reshuffling times in container loading tasks. Based on a GA, computational experiments on data from a specific rail–truck intermodal terminal in China were implemented. The results showed that optimizing the loading sequence can significantly reduce the total handling time, reshuffling times and energy consumption, and had a good performance for different sizes. The proposed approach can be useful and practical to help the operators in rail–truck intermodal terminals make an outbound container loading plan. Sustainability 2019, 11, 2383 14 of 15

The limitations of our paper are as follows. First, we only consider direct energy consumption in container loading operations, and do not consider the influence from indirect energy consumption. Second, the current model is formulated under a specific environment, and do not consider the uncertain factors in container loading operations. In the future, the influence of indirect energy consumption needs to be analyzed in detail and container loading optimization should consider uncertain factors to make the study more realistic.

Author Contributions: Conceptualization, L.W. and X.Z.; Methodology, L.W.; Software, L.W.; Validation, L.W.; Formal Analysis, L.W.; Investigation, L.W.; Resources, L.W.; Data Curation, L.W.; Writing—Original Draft Preparation, L.W.; Writing—Review and Editing, L.W. and X.Z.; Visualization, L.W.; Supervision, L.W.; Project Administration, L.W. and X.Z.; Funding Acquisition, L.W. and X.Z. Funding: This work was supported by the National Key R&D Program of China (grant number 2018YFB1201403), the Fundamental Research Funds for the Central Universities (grant number 2018JBM028). Acknowledgments: The authors are grateful to the reviewers for their valuable and meaningful comments. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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