Research Article Storage Space Allocation of Inbound Container in Railway Container Terminal

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1 Mathematical Problems i Egieerig, Article ID , 1 pages Research Article Storage Space Allocatio of Iboud Cotaier i Railway Cotaier Termial Li Wag, Xiaoig Zhu, ad Zhegyu Xie School of Traffic ad Trasportatio, Beijig Jiaotog Uiversity, Beijig 144, Chia Correspodece should be addressed to Xiaoig Zhu; xzhu@bjtu.edu.c Received 21 February 214; Revised 14 Jue 214; Accepted 29 Jue 214; Published 22 July 214 Academic Editor: Hu Shao Copyright 214 Li Wag et al. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Efficiet storage strategy of railway cotaier termials is importat i balacig resource utilizatio, reducig waitig time, ad improvig hadlig efficiecy. I this paper, we cosider the formulatio ad solutio algorithm for storage space allocatio problem of iboud cotaiers i railway cotaier termial. The problem is formulated as two-stage optimizatio models, whose objectives are balacig the workload of iboud cotaiers ad reducig the overlappig amouts. A algorithm implemet process based o rollig horizo approach is desiged to solve the proposed models. Computatioal experimets o a actual railway cotaier termial show that the proposed approach is effective to solve space allocatio problem of iboud cotaier ad is sigificat for the operatio ad orgaizatio of railway cotaier termials. 1. Itroductio With rapid developmet of passeger-dedicated railway i Chia, more trasportatio capacities of railway freight corridor are released, which puts forward huge opportuities ad challeges for railway cotaier trasportatio. At preset, operatio ad orgaizatio of railway cotaier termials caot meet developig demads of cotaier trasportatio. To eable cotaier to rapidly trasfer betwee rail ad truck, moder trasshipmet techologies are required to improve the resource utilizatio i railway cotaier termials. As key resources of railway cotaier termials, storage spaces are resposible for temporarily storig cotaiers which are moved over log distaces by cotaier trais ad short distaces by trucks. Storage space allocatio is importat i balacig space utilizatio, improvig the efficiecy of cotaier hadlig, ad reducig the turaroud time of cotaiers. The storage space allocatio is a vital basis ad costrait for other resources utilizatio i railway cotaier termial. Iboud ad outboud cotaier operatios i railway cotaier termial are differet. Iboud cotaiers arrive predictably i large quatities, are temporarily stored i cotaier, ad depart oe by oe i a upredictable sequece. O the cotrary, outboud cotaiers arrive i a radom sequece ad depart predictably. This paper focuses o the iboud cotaiers i railway cotaier termials. The rest of this paper is orgaized as follows: the relevat literature is reviewed i the ext sectio. The storage space allocatio problem of iboud cotaiers i railway cotaier termials is described i Sectio 3 ad formulated i Sectio 4.Aalgorithmimplemetprocessbasedorollig horizo approach is developed i Sectio 5. Computatioal results are reported i Sectio 6 ad fially Sectio 7 covers the coclusio. 2. Literature Review The storage space allocatio problem of iboud cotaiers i railway cotaier termial belogs to the storage space allocatio problem (SSAP) which is defied as the temporary allocatio of the iboud/outboud cotaiers to the storage blocks at each time period with aim of balacig the workload betwee blocks i order to miimize the storage/retrieval times of cotaiers [1]. The SSAP was firstly formulated for a cotaier termial i Hog Kog [2]. The problem was solved by a rollig horizo approach. I each plaig horizo, the problem

2 2 Mathematical Problems i Egieerig is decomposed ito two levels ad formulated each level as a mathematical programmig model. I order to determie the storage locatio of arrivig export cotaiers by cosiderig its weight, a dyamic programmig model is formulated to miimize the umber of relocatio movemets expected for the loadig operatio [3]. The process of determiig the storage locatios for outboud cotaiers was divided ito two stages: space allocatio stage ad stage of locatig idividual cotaiers [4]. A storage locatio assigmet problem for outboud cotaiers of maritime termial was decomposed ito two stages. The problem i the first stage is solved by a mixed iteger programmig model, while a hybrid sequece stackig algorithm is applied to solve the problemithesecodstage[5]. A approach for allocatig storage space to groups of outboud cotaiers i port cotaier termials was proposed with cosiderig the impacts of various space-reservatio strategies o the productivity of the loadig operatio [6]. For fidig the best allocatio of cotaiers i a bay i order to miimize the umber of reshuffles, a domaidepedet heuristically guided plaer for obtaiig the optimized reshufflig pla was proposed with a stackig state ad a cotaier demad kow [7]. I order to improve the operatios efficiecy of retrievig iboud cotaiers i a moder automatic cotaier termial, iboud cotaier space allocatio models were proposed to optimally allocate the arrival iboud cotaiers so as to miimize the expected cotaier retrieval time [8]. A ovel approach usig atbased cotrol was proposed for allocatig cotaiers to storageblocksiamariecotaiertermialwiththecompetig objectives of balacig the workload amog blocks ad miimizigthedistacetraveledoftrucksbetwee blocks ad berths [9]. I order to solve the storage space problem of outboud cotaiers for utilizig space efficietly ad make loadig operatios more efficiet, two heuristic algorithms are suggested based o the duratio-of-stay of cotaiers ad the subgradiet optimizatio techique, respectively [4]. A exteded versio of SSAP was proposed ad a efficiet geetic algorithm was developed to solve the exteded problem i a cotaier termial [1]. Costructioalgorithms ad a tabu search heuristic are preseted for dyamic space allocatio problem to optimize the space/resource assigmets durig the implemetatio of project activities [1]. Three tabu search heuristics are preseted for dyamic space allocatio problem. The first heuristic is a simple basic tabu search heuristic. The secod heuristic adds diversificatio ad itesificatio strategies to the first ad the third heuristic is a probabilistic tabu search heuristic [11]. A hybrid isertio algorithm is desiged for solvig the problem which itegrates the truck schedulig ad the storage allocatio to miimize the weighted sum of total delay of requests ad the total travel time of trucks [12]. For the problem of determiig the stackig positios for icomig cotaiers i automated cotaier termials, a olie search algorithm was proposed to dyamically adjust ad optimize a stackig policy by cotiuously geeratig ad evaluatig variats of stackig policies [13]. A decisio support system was preset to maage cotaier stackig problem, berth allocatio problem, ad the quay crae assigmet problem i a coordiated way. A domaiorieted heuristic plaer for calculatig the umber of reshuffles eeded to allocate the cotaiers i the appropriate place [14]. A costructio ad a hybrid algorithm (HGT) based o the GRASP ad tabu search metaheuristics were proposed to solve the dyamic space allocatio problem, where project duratio is divided ito a umber of cosecutive periods, each of them associated with a umber of activities []. Accordig to the literature review above, most studies focusedothestoragespaceallocatioproblemimaritime cotaier termials. Specific literature o railway cotaier termial is scarce. Because storage strategy of iboud ad outboud cotaiers i railway cotaier termials is obviously differet from maritime cotaier termials, existig studies are hardly applied i railway cotaier termials. I this paper, we cosider the storage space allocatio problem of iboud cotaier i railway cotaier termials. Give that cotaier arrival-departure time ad operatio sequeces are kow, two-stage storage space allocatio modelsareproposed,whoseobjectivesaretobalaceworkloads amog cotaier blocks ad assig cotaiers to the optimum positios. 3. Problem Descriptio The Chiese railway cotaier termials have advaced arrival-departure lies, storage spaces, ad hadlig equipmet. Figure 1 gives a schematic represetatio of a typical railway cotaier termial i Chia. Our study is based o the cofiguratio ad layout of the represetatio i Figure 1. As observed i Figure 1, cotaier of railway cotaier termial is composed by iboud cotaier, outboud cotaier, ad auxiliary cotaier. Sice most of iboud cotaier allocatio operatios occur i iboud cotaier, we set iboud cotaier as the study scope of this paper. Accordig to the iboud cotaier status i differet hadlig stages, cotaiers to be hadled i iboud cotaier ca be classified ito the followig three types. (i) Iboud cotaiers o cotaier trai wait for uloadig ad allocatig to the iboud cotaier, abbreviated as ICT. (ii) ICT cotaiers temporarily stored i iboud cotaier wait for loadig to trucks for customers, abbreviated as ICTY. (iii) ICT cotaiers are uloaded ad directly loaded to trucks for customers, abbreviated as ICTT. Accordig to optimizatio objectives of SSAP, most literatures decomposed the storage space allocatio problem ito two stages. The first stage is to balace cotaiers workloads amog blocks ad evely allocate cotaiers to each block. The secod stage is the slot allocatio for cotaiers which areallocatedtoblocksbasedothefirststageoptimizatio results. I this paper, our study decomposed the storage space allocatio problem of iboud cotaier i railway cotaier

3 Mathematical Problems i Egieerig 3 Iboud cotaier Rail hadlig track Outboud cotaier Truck operatio lae Special cotaier Refrigerated cotaier Empty cotaier Auxiliary cotaier Security ispectio area Gatry crae Cotaier trai Cotaier service area Parkig area Cotaier truck Reach stacker Cotrol area Itelliget gate Figure 1: Schematic represetatio of a railway cotaier termial. termial ito two stages based o the optimizatio objectives of SSAP. (i) The first stage is workload balace similar to the excitig study, whose objective is to balace workloads of iboud cotaiers amog blocks ad evely allocate iboud cotaiers to each block. (ii) The secod stage is cotaier slot allocatio based o the first stage optimizatio results, whose objective is to miimize overlappig amouts of ICT. 4. Problem Formulatio I this sectio, accordig to the problem descriptio above, the storage space allocatio problem of iboud cotaier i railway cotaier termial is formulated as two-stage optimizatio models based o rollig horizo approach. At each plaig epoch, we pla for a fixed horizo i immediate future ad execute the pla accordigly up to the ext plaig epoch; the we formulate a ew pla based o the latest iformatio; this patter goes o cotiually [2]. The rollig of plaig horizo is show i Figure 2. The workload balace is implemeted i each plaig epoch, ad the cotaier slot allocatio is implemeted i each period of plaig epoch. Cotaier slot allocatio model Plaig horizo o day Day 1. Day 2 Day 3 Day 4 Day 5 Day 6. Day 7 Workload balace model Plaig horizo o day 2 Figure 2: Rollig of plaig horizo Assumptios. The followig four assumptios are itroduced for the formulatio of the problem. (1) There is eough resource, that is, gatry crae ad cotaier space, to hadle the allocatio workload at the cosidered block. (2) The arrivig ad departure time of cotaiers are kow i advace ad there is o time delay i schedulig period. (3) Hadlig sequece of cotaiers is assumed to be kow. (4)Thecotaiersithemodelareassumedtobeofoe size.

4 4 Mathematical Problems i Egieerig 4.2. Workload Balace Model Notatios ad ariables. The otatios ad variables of workload balace model are defied as follows: IB: total umber of blocks i iboud cotaier ; T: total umber of plaig periods i a plaig epoch; C i :storagecapacityofblocki, 1 i IB; i :iitialivetoryofblocki, 1 i IB; it : total umber of cotaiers i block i at begiig of period t, 1 i IB, 1 t T; ICTY it :umberofictyiblockithatarepickedup at begiig of period t, 1 i IB, 1 t T; ICT tk :umberofictthatareuloadedfromtraisi period t adtobepickedupiperiodt+k, 1 t T, k T t; ICT it :umberofictiblocki that are uloaded from trais i period t, 1 i IB, 1 t T; ICT itk :umberofictiblocki that are uloaded from trais i period t adtobepickedupiperiod t+k, 1 i IB, 1 t T, k T t; ICTY it :umberofictyiblockithatarepickedup i period t, 1 i IB, 1 t T; ICTT t : umber of ICTT that are uloaded ad directly loaded to trucks i period t, 1 t T Objective Fuctio. By attetio to the problem descriptio i Sectio 3, the objective fuctio of workload balacemodeliswritteasfollows: Mi T t=1 [max {i} (ICT it + ICTY it ) mi (ICT it + ICTY it )]. {i} (1) Objective fuctio is to balace workloads of iboud cotaiers amog blocks ad evely allocate ICT to blocks i each plaig epoch Costraits. The costraits of workload balace model are itroduced as follows to esure the practical feasibility of the solutio. (1) Costraits o ICT: ICT tk = ICT it = IB i=1 ICT itk, t=1,2,...,t; k=,1,...,t t, (2) T t k= ICT itk, i=1,2,...,ib; t=1,2,...,t. (3) Costrait (2) esures that the total umber of ICT thatareuloadedfromtrucksiperiodt ad to be loaded oto rail vehicles i period t+kis the sum of these cotaiers assiged to all the blocks. Costrait (3) esures that the total umber of ICT i block i thatareuloadedfromtrucksiperiodt is the sum of these cotaiers loaded oto rail vehicles i period t+ki this block. (2) Costraits o ICTY: ICTY it = ICTY t 1 it + ICT i(t k)k, i=1,2,...,ib; k= t=1,2,...,t. (4) Costrait (4) idicates that the umber of ICTY i block i durig period t is the sum of iitial umber of ICTY i block i ad the umber of ICTY trasferred from the ICT that uloaded i the block i plaig epoch. (3) Costraits o ICTT: ICTT t = t=1,2,...,t, IB i=1 (ICT it ICT itk ), k=t,t+1,...,t. Costrait (5) idicates that the umber of ICTY i block i durig period t is the sum of iitial umber of ICTY i block i ad the umber of ICTY trasferred from the ICT that uloaded i the block i plaig epoch. (4) Capacity costraits: it = i(t 1) +(ICT it OICT it ), i=1,2,...,ib; t=1,2,...t (5) (6) it C i, i=1,2,...ib; t=1,2,...t. (7) Costrait (6) idicates the ivetory of cotaiers i block i at begiig of period t. Costrait (7) idicates the storage capacity of block i. (5) Iteger costrait: All variables take up oegative iteger values. (8) 4.3. Cotaier Slot Allocatio Model Notatios ad ariables. The otatios ad variables of cotaier slot allocatio model are defied as follows: N: total umber of ICT which are allocated i cosidered block at the same plaig period; : the sequece umber of allocated cotaier; B: total umber of bays i the cosidered block; R: total umber of rows i cosidered block; L: maximum layer umber of stack; b: bay idetifier of cotaier slot, 1 b B; r: row idetifier of cotaier slot, 1 r R;

5 Mathematical Problems i Egieerig 5 l: layer idetifier of cotaier slot, 1 l L; s(r, b, l): cotaier slot of r row, b bay, ad l layer; t rbl : departure time of cotaier i cotaier slot of r row, b bay, ad l layer; : overlappig amouts of the ICT; M: a ifiitesimal umber; S rbl :ifs(r, b, l) has cotaier, S rbl = 1.Otherwise, S rbl =; S rbl :ifthecotaier is allocated to s(r, b, l), S rbl =1. Otherwise, S rbl =; rbl,rb(l e) : overlappig of s(r, b, l e) after ICT was allocated to s(r, b, l). Ift rbl <t rb(l e), rbl,rb(l e) =1. Otherwise, rbl,rb(l e) =; H : if there are o empty bays while the ICT is allocated, H =1.Otherwise,H = Objective Fuctios. By attetio to the problem descriptio i Sectio 3, the objective fuctios of cotaier slot allocatio model are writte as follows: Mi D =1. (9) The secod stage objective fuctio (9) miimizes overlappig amout which is caused by ICT allocated i cosidered block at same plaig period Costraits. The costraits of cotaier slot allocatio model are itroduced as follows to esure the practical feasibility of the solutio. (1) Overlappig amouts costrais of ICT: l 1 =(1 H )M+H mi =1,2,...,N, b=1,2,...,b, rbl,rb(l e), e=1 r=1,2,...,r, l=2,3,...,l. (1) Costrait (1) represets the calculatio of overlappigamoutwhichiscausedbyictallocatedi cosidered block. (2) Allocatio costrai: S rbl S rb(l 1), r=1,2,...r, (11) b=1,2,...,b, l=2,3,...,l, =1,2,...,N. Costrait (11) esures that each cotaier caot be allocated upo the empty cotaier slot. (3) Allocatio prefereces costraits: N m S rbl =1r=1 N R (m 1) =1 r=r S rbl, b=1,2,...,b, l=1,2,...,l, m= R 2 1. (12) Costrait (12) idicates the allocatio prefereces costrait of ICT. It esures that the allocatio positios of ICT are close to the truck operatio lae i order to reduce loadig time of ICTY. 5. Solutio Algorithm I order to solve the two-stage models preseted above, a algorithm implemet process based o rollig horizo approach is proposed i this sectio. The workload balace model is coverted to a liear iteger programmig model ad a heuristic algorithm is desiged to solve the cotaier slot allocatio model. The implemet process is show i Figure Workload Balace Model Coversio. The workload balace model proposed i Sectio4 is a oliear model, because of the objective fuctio of model. I order to obtai asolutio,acoversiomethodshouldbeusedtocovert the model to a liear model. Accordig to the coversio metioed i [2], we defie A t = max (ICT {i} it + ICTY it ) ad B t = mi (ICT {i} it + ICTY it ).Thetheworkloadbalace model ca be coverted as the liear iteger programmig model as follows: T Mi (A t B t ). (13) t=1 The costraits iclude (2) to(8) ad the costraits o A t ad B t : ICT it + ICTY it A t, i=1,2,...,ib; t=1,2,...,t (14) ICT it + ICTY it B t, i=1,2,...,ib; t=1,2,...,t. After the coversio of workload balace model, it ca be solved by Ligo HA Implemetatio for Cotaier Slot Allocatio Model. The otatios of HA are show i Table 1 ad the procedure of HA is show as follows. Step 1. Accordig to the iitial block iformatio at the begiig of period, get a feasible allocated set of cotaier slots F by removig ifeasible cotaier slots. Parameter iitializatio: let = 1, r = R, b = 1,K = {φ}, S = {φ}, =I,ad go to Step 2. Step 2. Allocate the ICT. Search empty cotaier slots i block row from R to R (m 1). If empty cotaier slot exists, go to Step 3.Ifemptycotaierslotdoesotexist,go to Step 4. Step 3. Let S=S {S rbl } ad = +1;theif N,goto Step 2. Otherwise, let =ad go to Step 8. Step 4. If s(r, b, l) F, gotostep 6. Otherwise allocate cotaier to s(r, b, l) ad judge the feasibility of solutio. If the solutio is ot feasible, go to Step 8.Ifthesolutioisfeasible, go to Step 5.

6 6 Mathematical Problems i Egieerig Iput parameters: Iitial iformatio of cotaier Cotaiers arrival-departure time Plaig horizo divisio, etc. Cotaiers arrival-departure iformatio i the plaig epoch i Iitial iformatio of the cotaier i epoch i Update the cotaier iformatio Workload balace model coversio ICT allocatio iformatio for each block i plaig period j of plaig epoch i Block 1 Block 2 Block HA for cotaier slot allocatio model Iitial iformatio of the block i period j Update the block iformatio Set i=i+1 Rollig to the ext epoch i+1i plaig horizo ICT allocatios lot iformatio i plaig period j of plaig epoch i Update the blocks iformatio i period j N Ed of periodj? Y Update the iformatio i epoch i Set j=j+1 Rollig to the ext period j+1i plaig epoch i N Ed of epoch i? Y Output Iboud cotaier allocatio iformatio i plaig horizo. Workload balace iformatio i each epoch. Overlappig amout i each period Figure 3: Algorithm implemet process. Table 1: Notatios. Notatio Declaratio K The set of overlappig amouts S The optimal set of slots allocatio with miimum overlappig amout S rbl The cotaier allocated to s(r, b, l) the overlappig amout icreased by the feasible solutioofict d mi The miimum crae operatio distaces of the rbl cotaier allocated to s(r, b, l) A The alterative set of the allocated slot with miimum overlappig amout F The feasible allocated set of cotaier slots The umber of feasible solutios d rbl The operatio distace of crae for the allocated cotaier I A arbitrary positive big umber Step 5. Let the solutio be If > ad compare,gotostep 6. Otherwise,if ad.,let = A=A {S rbl } ad go to Step 6; otherwise,letkict A={φ}, A=A {S rbl },adgotostep 6. =, Step 6. Let b=b+1.ifb B,gotoStep 4. Otherwise,let r=r 1.Ifr 1,gotoStep 4.Ifr<1,calculatethed rbl i set A ad select d mi,setk=k {KICT rbl }, S=S {S rbl },ad go to Step 7. Step 7. Allocatio of the ICT has fiished. Let r=r, b=1, ad = +1;theif N,gotoStep 2; otherwisegoto Step 8. Step 8. Calculate the overlappig amouts based o K ad output the set of cotaier slot allocatio S. Procedure termiates. 6. Computatioal Experimet Toillustratetheproposedmodeladalgorithmforspace allocatio problem of iboud cotaier i railway cotaier termial, computatioal experimets are performed by usig the actual data from a specific railway cotaier termial

7 Mathematical Problems i Egieerig Imbalace amout (TEU) Overlappig amout (a) Imbalace amouts (b) Overlappig amouts Figure 4: Computatioal results of 1 day. 3 3 Imbalace amout (TEU) Overlappig amout (a) Imbalace amouts (b) Overlappig amouts Figure 5: Computatioal results of 7 days. i Chia [16]. I order to evaluate the improvemet of our approach, a compariso is made betwee our approach ad radom allocatio algorithm which is curretly used i railway cotaier termials. Furthermore, to evaluate the effectiveess ad practicability of our approach, umerical experimets of 7 days ad 3 days are carried out. To implemet the proposed algorithm, the parameters related to the specific railway cotaier termial are eeded. There are four blocks i the iboud cotaier. Each block is composed by 3 bays, 6 rows, ad 2 layers. The umerical experimets are performed based o a persoal computer with Itel Core 2.5 GHz processors ad 4 GB RAM. Because most of ICTY are picked up o more tha two days after they allocated to blocks, we choose 3 days as a plaig horizo, 1 day as a plaig epoch, ad 6 Table 2: Iboud cotaier iformatio of 4 plaig periods i 1 day (TEU). Cotaier type t=1 t=2 t=3 t=4 ICT ICTY ICTT hours as a plaig period. There are 4 plaig periods i oe plaig epoch ad 12 plaig periods i oe plaig horizo. A small size sample of 1 day is carried out firstly. The iboud cotaier iformatio of 4 plaig periods i 1 day is show i Table 2.The ICTY loadig pla of each block i plaig period is show i Table 3.

8 8 Mathematical Problems i Egieerig Imbalace amout (TEU) Overlappig amout (a) Imbalace amouts (b) Overlappig amouts Figure 6: Computatioal results of 3 days. Table 3: ICTY loadig pla of each block i plaig period (TEU). Cotaier i=1 i=2 i=3 i=4 type t=1 t=2 t=3 t=4 t=1 t=2 t=3 t=4 t=1 t=2 t=3 t=4 t=1 t=2 t=3 t=4 ICTY Plaig period Our approach () Table 4: Compariso betwee ad RAA i 1 day. Radom allocatio algorithm (RAA) Imbalace amouts Overlappig amouts Imbalace amouts Overlappig amouts GAP 1 GAP % 77.8% % 42.9% % 33.3% % 41.2% Notes: GAP 1 = (imbalace amouts obtaied from RAA imbalace amouts obtaied from ) 1/imbalace amouts obtaied from RAA. GAP 2 = (overlappig amouts obtaied from RAA overlappig amouts obtaied from ) 1/overlappig amouts obtaied from RAA. Based o the computatioal example above, experimet is coducted, ad a compariso betwee our approach () ad radom allocatio algorithm (RAA) is made to evaluate the performace of o space allocatio problem of iboud cotaier i railway cotaier termial. The computatioal results are show i Table 4 ad Figure 4. As observed i Table 4 ad Figure4, the imbalace amouts ad overlappig amouts obtaied by are both fewer tha the amouts obtaied by, the average GAP of imbalace amouts is 42.7%, ad the average GAP of overlappig amouts is 48.8%. I order to evaluate the effectiveess ad practicability of our approach, umerical experimets of 7 days ad 3 days are coducted. The computatioal results of 7 days are show i Table 5 ad Figure 5 ad of 3 days are show i Figure 6. As observed i Table 5 ad Figures 5 ad 6, theperformace of our approach is satisfactory i solvig differet size istaces. The results of computatioal experimets idicate that our approach is efficiet to solve space allocatio problem of iboud cotaier i railway cotaier termials.

9 Mathematical Problems i Egieerig 9 Table 5: Compariso betwee ad RAA i 7 days. Plaig Our approach () Radom allocatio algorithm (RAA) period Imbalace amouts Overlappig amouts Imbalace amouts Overlappig amouts GAP 1 GAP % 77.8% % 42.9% % 33.3% % 41.2% % 75.% % 56.% % 31.6% % 27.3% 9.%.% % 72.7% % 47.1% % 53.3% % 1.% % 72.7% % 44.4% % 54.2% % 1.% % 45.5% % 26.3% % 63.2% % 1.% % 61.5% % 34.6% % 75.%.%.% % 44.4% % 56.5% % 53.3% Notes: GAP 1 = (imbalace amouts obtaied from RAA imbalace amouts obtaied from ) 1/imbalace amouts obtaied from RAA. GAP 2 = (overlappig amouts obtaied from RAA overlappig amouts obtaied from ) 1/overlappig amouts obtaied from RAA. 7. Coclusio I this paper, we cosidered the space allocatio problem of iboud cotaier i railway cotaier termials with the arrival-departure time ad operatio sequece of cotaiers kow. Two-stage optimizatio models were proposed; the first stage is workload balace model, whose objective is to balace workloads of iboud cotaiers amog blocks ad evely allocate iboud cotaiers to each block. The secod stage is cotaier slot allocatio model, whose objective is to miimize overlappig amouts of ICT. A algorithm implemet process based o rollig horizo approach is desiged to solve the proposed models. Computatioal experimets o a actual railway cotaier termial show that the models ad algorithm proposed i this paper are effective to balace workloads of iboud cotaiers ad reduce the overlappig amouts. I future, proposig a stochastic programmig model for cotaier slot allocatig problem by cosiderig radom factors is a possibility for further research. Coflict of Iterests The authors declare that there is o coflict of iterests regardig the publicatio of this paper. Ackowledgmets This research was supported by the Natioal Natural Sciece Foudatio of Chia (Grat o ), the Specialized Research Fud for the Doctoral Program of Higher Educatio (Grat o ), ad the Major Research pla of the Natioal Natural Sciece Foudatio of Chia (Grat o ). Refereces [1] M. Bazzazi, N. Safaei, ad N. Javadia, A geetic algorithm to solve the storage space allocatio problem i a cotaier termial, Computers ad Idustrial Egieerig, vol.56,o.1, pp.44 52,29.

10 1 Mathematical Problems i Egieerig [2] C. Zhag, J. Liu, Y. Wa, K. G. Murty, ad R. J. Li, Storage space allocatio i cotaier termials, Trasportatio Research B: Methodological,vol.37,o.1,pp ,23. [3] K. H. Kim, Y. M. Park, ad K. Ryu, Derivig decisio rules to locate export cotaiers i cotaier s, Europea Joural of Operatioal Research,vol.124,o.1,pp.89 11,2. [4] K. H. Kim ad K. T. Park, A ote o a dyamic spaceallocatio method for outboud cotaiers, Europea Joural of Operatioal Research,vol.148,o.1,pp.92 11,23. [5] L. Che ad Z. Lu, The storage locatio assigmet problem for outboud cotaiers i a maritime termial, Iteratioal Productio Ecoomics,vol.135,o.1,pp.73 8,212. [6] Y. J. Woo ad K. H. Kim, Estimatig the space requiremet for outboud cotaier ivetories i port cotaier termials, Iteratioal Productio Ecoomics,vol.133,o.1,pp , 211. [7] M. Rodriguez-Molis, M. A. Salido, ad F. Barber, Itelliget plaig for allocatig cotaiers i maritime termials, Expert Systems with Applicatios, vol.39,o.1,pp , 212. [8] M. Yu ad X. Qi, Storage space allocatio models for iboud cotaiers i a automatic cotaier termial, Europea Joural of Operatioal Research,vol.226,o.1,pp.32 45,213. [9] O. Sharif ad N. Huyh, Storage space allocatio at marie cotaier termials usig at-based cotrol, Expert Systems with Applicatios,vol.4,o.6,pp ,213. [1] A. R. McKedall Jr. ad J. R. Jaramillo, A tabu search heuristic for the dyamic space allocatio problem, Computers ad Operatios Research,vol.33,o.3,pp ,26. [11] A. R. McKedall Jr., Improved Tabu search heuristics for the dyamic space allocatio problem, Computers ad Operatios Research,vol.35,o.1,pp ,28. [12] D. Lee, J. X. Cao, Q. Shi, ad J. H. Che, A heuristic algorithm for truck schedulig ad storage allocatio problems, Trasportatio Research Part E: Logistics ad Trasportatio Review,vol.45,o.5,pp.81 82,29. [13]T.Park,R.Choe,Y.HuKim,adK.RyelRyu, Dyamic adjustmet of cotaier stackig policy i a automated cotaier termial, Iteratioal Productio Ecoomics, vol. 133, o. 1, pp , 211. [14] M. A. Salido, M. Rodriguez-Molis, ad F. Barber, A decisio support system for maagig combiatorial problems i cotaier termials, Kowledge-Based Systems, vol.29,pp.63 74, 212. [] G.C.daSilva,L.Bahiese,L.SatoruOchi,adP.O.Boavetura- Netto, The dyamic space allocatio problem: Applyig hybrid GRASP ad Tabu search metaheuristics, Computers ad Operatios Research,vol.39,o.3,pp ,212. [16] L. Wag, Key resources schedulig optimizatio theory ad method of railway cotaier termial [Ph.D. thesis], Beijig Jiaotog Uiversity, Beijig, Chia, 214, (Chiese).

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