AN INTEGRATED SIMULATION AND OPTIMIZATION APPROACH FOR SEASIDE TERMINAL OPERATIONS

Transcription

1 AN INTEGRATED IMULATION AND OTIMIZATION AROACH FOR EAIDE TERMINAL OERATION Daniela Ambroino Elena Tànfani Department of Economic and Quantitative Method (DIEM) Univerity of Genova Via Vivaldi 5, 16126, Genova, Italy KEYWORD Dicrete Event imulation, 0/1 MI optimiation model, container terminal, eaide operation planning, performance analyi. ABTRACT In thi paper we focu our attention on the operational deciion problem related to the eaide area of maritime container terminal. In particular, we face the Quay Crane Aignment roblem (QCA) and Quay Crane cheduling roblem (QC) with an integrated imulation-optimiation approach. A 0/1 MI model i developed in order to determine the optimal aignment, on a hift bai, of QC to bay of each hip erved by the terminal during a given planning horion, referred a Bay_QCA. The optimiation model olution are ued a input parameter for a Dicrete Event imulation (DE) model able to reproduce the ytem behaviour taking into account it tochatic nature and complexity. The framework can be ued for evaluating the impact on the eaide terminal performance of the optimied olution and the effect of different operative deciion related to the cheduling of QC. The framework i going to be applied to a real cae tudy pertaining to the outhern European Container Hub (ECH), ited in the ort of Genoa, Italy. INTRODUCTION The competitivene of a marine container terminal i baed on different factor, uch a tranhipment time combined with low rate for loading and dicharging and fat turnover of container, which correpond to a reduction of the berthing time and, conequently, of the cot of the whole tranportation proce. A marine terminal mut be managed in uch a way to optimie the flow of container that arrive and leave it in variou way, a, for intance, by truck, train and veel. A terminal can be viewed a made up of many interrelated logitic procee a treed in Vi and De Koter (2003) and teenken et al. (2004). In thee intereting overview paper the author give a claification of the deciion problem at marine container terminal in accordance with the following logitic procee: i) arrival of the hip, ii) dicharging and loading of the hip, iii) tranport of container from hip to tack and vice vera, iv) tacking of container, and v) inter-terminal tranport and other mode of tranportation. In thi paper we focu our analyi on the dicharging and loading of the hip proce. In particular, we are intereted in the tactical and operational deciion problem related to the organiation of the loading and unloading operation. Gunther and Kim (2006) propoe a claification of the problem ariing in terminal following the planning level of deciion. In particular, the trategic level refer to long-term deciion pertaining to layout, connection, equipment, berthing and yard capacity, the tactical level regard mid-term deciion pertaining to berth and yard planning and policie, while the operational level refer to hort-term deciion pertaining to quay ide and land ide operation. It i worth mentioning that there are trong relation among trategic, tactical and operation planning at the eaide area, a at the yard and the landide area. Focuing on the eaide terminal management operation the main problem and their interrelation (ee Figure 1) are decribed in detail in a recent urvey of Bierwirth and Meiel (2010). BA (Berth Aignment roblem) Available berthing poition hould be allocated to the arriving hip QCA (Quay Crane Aignment roblem) How many QC hould be aigned to each berthing hip during the planning horion QC (Quay Crane cheduling roblem) tage 1 Allocation of QC to ection/bay of the hip QC (Quay Crane cheduling roblem): tage 2 equencing order in which hip ection hould be handled Figure 1: eaide Deciion roblem Work force planning taffing and roatering of terminal work force towage planning # of cntr to be unloaded/loaded from/to each bay/hip The Berth Allocation roblem (BA) concern the aignment of quay pace to veel that have to be unload and loaded at the terminal. The Quay Crane Aignment roblem (QCA) define how many QC aigning to each berthing hip, while the Quay Crane cheduling roblem (QC) determine the allocation roceeding 26th European Conference on Modelling and imulation ECM Klau G. Troitch, Michael Möhring, Ulf Lotmann (Editor) IBN: / IBN: (CD)

2 of tak to QC (tage 1) and tak chedule of each QC (tage 2). Note that tak can be related to a bay area, a bay, tack, or group of container. Generally, reearcher decompoe the eaide ytem into ub-ytem and approach the above mentioned problem eparately a ingle deciion problem. Anyway, a pointed out by the recent literature, the interrelation among the deciion problem ariing in the terminal eaide planning hould not be ignored. In fact, only to give an example of thee interrelation, we can note the QC ha a direct connection with the QCA that define the exact number of quay crane operating a veel; in QC tak mut be plit and cheduled among the aigned quay crane. The main aim of QC uually regard the minimiation of the makepan of the quay crane chedule that repreent the handling time of a veel. Thi time i trictly connected with the number of aigned quay crane, and finally the BA depend on the handling time neceary for erving each veel. The number of available quay crane to aign to veel i directly affected by the quay crane deployment problem (i.e. ee Legato et al. 2008) and by the ground crew planning problem (ee Legato and Monaco 2004 for detail on thi problem). Moreover, the tak to be cheduled in the QC are alo affected by the towage plan (ee Ambroino et al for detail on thi problem). Due to the impact of QCA on the handling time, in the recent literature it i quite frequent to find integrated approache for QCA and BA. In Bierwirth and Meiel (2010) a claification cheme for integrated eaide operation planning i reported. Thi cheme follow two different integration concept propoed by Geoffrion (1999), i.e. deep and functional integration. In the deep integration a whole model include interrelation among deciion, while in functional integration there i a equence of olution of ubproblem and a data exchange between bae level and top level. Approache baed on functional integration between the BA and QC, between BA and QCA are reported i.e. in Lee et al (2006), Lokuge and Alahakoon (2007). Approache baed on deep integration between BA and QCA are decribed, among other, in Giallombardo et al. (2008), Imai et al. (2008), Theofani et al. (2007) and ark and Kim (2003). In Tavakkoli Moghaddam et al. (2009) an approach baed on deep integration between QCA and QC i preented. Finally, ome paper deal with integrated approache among the three problem ariing in the eaide planning (BA-QCA-QC), and ometime deep and functional integration are jointly ued. The intereted reader can ee for example Ak and Erera (2006), Liu et al. (2006) and Meiel (2009). By more holitic point of view, imulation approache have been quite often ued to analye the eaide terminal operation performance. Nam et al. (2002) examine the optimal number of berth and quay crane for a terminal in Buan (Korea), while Legato and Maa (2001) develop a imulation model for the arrival-departure proce of veel at the container terminal of Gioia Tauro (Italy) that i ued for optimiation cenario analyi of the berth planning problem. Kia et al. (2002) decribe the role of imulation for evaluating the performance of a terminal eaide equipment and capacity in Melbourne by uing intereting performance criteria and model parameter. In thi paper, we tart tudying the challenging problem of integrating imulation and optimiation (Fu 2002; Fu et al. 2005) in order to put together the capability of imulation to decribe the dynamic of the ytem conidered and perform cenario analyi (what-if analyi), with the deciional advantage of optimiation, i.e. what-bet analyi. The potentialitie of an integrated imulation and optimiation approach are herein exploited in order to analye the performance of the eaide planning at an import/export container terminal. In particular, we focu our attention on the QCA and QC and propoe an integrated imulationoptimiation approach to olve in a concie framework the two problem (Figure 1). More preciely, we ue a deep integration to olve the QCA and QC (tage 1) by mean of an ad hoc optimiation model, called Bay_QCA. Afterward, applying a functional integration, the optimiation model olution i ued by a Dicrete Event imulation (DE) model deigned to reproduce and evaluate alternative cheduling rule and olution of the QC (tage 2) introducing in the analyi ome tochatic element (e.g. QC breakdown). The paper i organied a follow. Firtly the main characteritic of the modelling approach are decribed, with particular attention to the performance indexe to be computed. Afterward, more detail on both the optimiation model Bay_QCA and the DE model are reported. Finally, the main characteritic of the cae tudy we are going to invetigate are preented and ome concluion and further work are given. ROBLEM ADREED AND MODELLING AROACH A decribed in the previou ection our analyi i focued on the eaide area at container terminal with particular attention to the operational deciion problem related to the organiation of the loading and unloading operation. In particular, given: i) the expected time of arrival (ETA) and berthing poition of the hip erved by the terminal in a given planning horion, i.e. the olution of the BA; ii) the number of import and export container to be handled and their poition on board, i.e. the olution of MB; iii) the taffing and roatering of terminal work force; we are involved in the QCA and QC, a decribed in previou ection. In more detail, we have to define the aignment of quay crane to the veel erved by the terminal, and,

3 more preciely, determine both the aignment of quay crane to the bay of the veel (QCA) and the chedule of tak of each quay crane (QC), in uch a way to minimie the berthing time of the hip and the quay crane cot. The problem herein addreed are olved with an integrated imulation-optimiation approach, whoe main characteritic are depicted in Figure 2. A optimiation i referred, we focu our attention on the QCA and QC (tage 1). A 0/1 MI model ha been developed in order to olve the Bay_QCA and give the optimal number of QC to be aigned to each hip a well a the aignment of QC to the bay of the hip. The optimiation model olution i ued a input parameter for a Dicrete Event imulation (DE) model deigned to imulate the QC (tage 2). The DE model i able to manage the non-determinitic and dynamic behaviour of the ytem and it complexity and can be ued to evaluate the impact on the eaide terminal performance of the optimied olution. The model can alo be ued to introduce many caue of variability in the ytem, uch a breakdown and hift et-up time for the QC and truck, unplanned delay, meteorological advere condition, etc. INUT DATA for the Bay_QCA opt MODEL Berth Aignment (BA) # import cntr to be unloaded from each hip/bay # export cntr to be loaded in each hip/bay QC Aignment to each hip/bay (olution of the Bay_QCA) INUT DATA for the IMULATION MODEL Figure 2: Integration between DE and QCA opt model Moreover, the major advantage of the integrated approach herein propoed i it ability to face in a concie and tractable framework both the QCA and QC, uing both deep and functional integration. More detail on the Bay_QCA and DE model are given in the following ection. erformance Indexe A major characteritic of the framework herein analyed i it ability to perform a very informative bottom-up performance analyi (Figure 3). In particular, we tart by the aement of the productivity of the reource involved in the eaide operation, i.e. gang and QC. Note that, a gang i defined a a team of human and aociated handling equipment, generally, compoed of one quay crane driver, one deck man, one checker, one to three yard crane driver, three track driver, two twit handler (for the entire hip) and three to eight lahing and unlahing operator (for the entire hip). Note that each gang i aigned to one or more working period (hift); generally, a hift i 6 hour long. ERVICE oriented TERMINAL ERFORMANCE HI/ERVICE QC GANG/HIFT Figure 3: Bottom-up performance analyi Afterward, the indexe for each hip/ervice and for the whole terminal are computed a average. Moreover, we focu our attention on the evaluation of two erie of performance indexe. The firt are the o-called productivity-oriented indexe () that meaure the container traffic volume internal performance of the reource involved, while the econd are the erviceoriented indexe that meaure the ervice level () provided to client and are computed for each ervice/hip and a a macro level terminal point of view. In Table 1 the whole et of indexe included in the performance analyi i reported. With reference to the productivity oriented indexe, we decided to ue: 1) the berth utiliation level, expreed in term of percentage time of berthing area utiliation; 2) the QC utiliation, expreed in term of percentage of utiliation of the QC involved in the eaide operation; 3) the QC and gang productivity computed a the ratio between the container move and the berthing time and total hift time, repectively; 4) the gang utiliation rate expreed in term of utiliation (in percentage), i.e. buy time, of the hift, involved in the loading and unloading operation of each hip; 5) the gang ued and related cot. The productivity level indexe hould be computed for a macro level/terminal point of view, but more importantly they are alo aeed for each hip/ervice, for each QC and for each gang (i.e. for each hift working period). The ervice indexe are uually computed for each hip or ervice berthing the terminal. Among thi group the mot important are the berthing time and the o-called terminal performance index, expreed a the ratio between the total number of container moved and the total berthing time. The above indexe can alo be aeed a average, computing the above indexe for RODUCTIVITY oriented

4 the whole et of hip erved by the terminal during a given planning horion. The propoed bottom-up performance analyi can allow the terminal to better undertand bottleneck in the eaide proce, major cot and productivity gap in the ytem. hift move Table 1. erformance indexe GANG/hift hift working time Gang productivity=hift move/hift length Gang utiliation= Gang working time/hift length QUAY CRANE QC move Crane working time # gang (hift) ued Crane productivity=qc move/crane working time Crane utiliation= Crane working time/berthing time Gang productivity=qc move/(# gang ued*hift length) Gang utiliation= Crane working time/(# gang ued*hift length) HI/ERVICE hip move Berthing time Veel operation time (Gang on - ahore) (=loading time) Terminal performance index=total move / Berthing time % of berth utiliation = Berthing time / Total time Crane productivity = hip move / Crane working time Crane utiliation = Avg crane working time/berthing time Gang productivity=hip move/(# gang ued*hift length) Gang utiliation= gang working time/(# gang ued*hift length) # gang (hift) ued hip gang cot TERMINAL Total move Total Berthing time Veel operation time (Gang on - ahore) (=loading time) Terminal performance index=total move / Berthing time Berth utiliation = Total Berthing time / Total time Crane productivity = Total move / Crane working time Crane utiliation = Avg crane working time/berthing time Gang productivity=total move/(# gang ued*hift length) Gang utiliation= Gang working time/(# gang ued*hift length) # gang (hift) ued Total terminal gang cot Bay_QCA MODEL Type The model herein developed i deigned to determine the amount of reource (gang) needed to perform the loading and unloading operation of each hip entering the terminal in a given time horion with the aim of minimiing a multi-objective function that take into conideration both the overall gang cot (terminal point of view) and the hip cot related to the time the hip pend on berth (maritime company point of view). A already aid, each gang i aigned to one or more working period (hift); generally, a hift i 6 hour long. The cot of a gang i different in accordance with the working hift, i.e. hift at night and on unday are more expenive. The aignment of a gang to a hift implie a fixed cot that i charged even if the hift i not completely ued. The maximum number of team/gang available in each hift i derived by the olution of the Ground Crew lanning problem. ometime it i poible to obtain a higher number of gang thank to the poibility of activating ome external contract. In thi cae it i neceary to ditinguih between the maximum number of internal gang and the maximum number of external one (i.e. more expenive gang). Often, alo the minimum and maximum number of QC to be ued for each hip i known in advance. The firt i determined by contractual agreement with each maritime company, while the latter i due to phyical (i.e. length of the veel) and logical contraint (interference between crane boom). It i generally required that there are not hift unworked between the firt and the lat one (pairing contraint). Crane are lined up along the quay and can be moved to every veel but cannot pa each other (patial contraint). More preciely, given: i) a planning horion T, plit into a given number of hift period; ii) the olution of the BA and MB; iii) the ETA of each veel; iv) the number of QC available in the terminal for each hift; the Bay_QCA herein addreed conit in determining the aignment of QC to the bay of the veel and the amount of work executed by each QC. The aim i to minimie the berthing time of the hip and the QC cot, while atifying the hip demand, the QC capacity and other operative contraint. The Bay_QCA differ from the claical QCA (that define how many QC hould be aigned to each berthing hip during a given planning horion) becaue it alo define which bay mut be operated by each QC and the aignment of QC to the hip in each hift of the berthing period; moreover, QC cot are alo included in Bay_QCA model. In thi firt attempt to face thi problem, the following aumption are conidered: there i a fixed maximum number of gang available for each hift; there i no minimum number of QC to ue for each hip, even if it i required that there are no hift unworked between the firt and the lat one (pairing contraint); the maximum number of QC working a hip derive from operational contraint that, in accordance with the type of QC, require a one-bay or a two-bay ditance between QC working; QC aignment aumption: a1. a QC hould be aigned to more than one hip for each hift; a2. a QC hould be aigned to more than one bay for each hift; a3. a bay hould not be erved by more than one crane in each hift; A mathematical formulation for the Bay_QCA decribed above i now introduced. Let: = {1,2, l} the et of hift of the given planning horion T; V = {1,2, m} the et of veel of the given BA;

5 B = {1,2, n} the et of bay; QC = {1,2, o} the et of quay crane/gang; d b the demand, i.e. time neceary for loading/unloading container in bay b of veel b B, (in minute); d v the total demand of veel (in minute); Q maximum number of QC available in hift ; K q hift capacity of QC, C (in minute); cf gang fixed cot for uing quay crane q in hift, C, ; cv b cot for erving bay b by QC C, b B; cb hip berthing cot for veel v in hift,,. Let u introduce the following deciion variable: x The reulting 0/1 MI model i the following: Min ubject to 1if bay b of veel v i aigned to crane q in hift = 0 otherwie 0 quantity of work executed by crane q in bay b of veel v in hift 1 if crane q i ued in hift q, = 0 otherwie y 1 if veel v i berthed in hift v, = 0 otherwie w x Kq y b B x = d b x q M, C cb y Q w + C, 0 cf b B, (1) (2) (3) C, b B,, (4) C C b B (5) + q', b+ 1, + q', b+ 2, q': q' q q': q' q d v b B ' : ' < w b B 1 y + C, b B, (6) v x Mw V, (7) b < ( b + i) q+ 1, b+ i,, (8) b B, (9), b B, i=1,... B - q=1,...o-1. (10) 1 cv b The objective function minimie berthing cot and QC cot; moreover, it include a third term aimed at reducing the movement of QC in the quay. The lat term alo reduce the poibility of obtaining olution in which QC pa other one, even if for avoiding croing of crane patial contraint are neceary (10). Berthing cot are computed in accordance with the number of hift veel are berthed; anyway the minimiation of berthing time doe not grant that there are no hift unworked between the firt and the lat one. For thi aim pairing contraint (8) are neceary. The capacity contraint (2) enure that the total amount of work executed by a QC in a hift mut be le than the maximum hift capacity of the QC. The demand of each veel, and more preciely of each bay of each veel, mut be atified a required by contraint (3). Contraint (4) are related to the definition of the aignment variable of QC and link variable and x. Contraint (5) guarantee not to exceed the maximum number of QC available for erving veel in each hift. Contraint (6) guarantee to have two bay ditance between two quay crane working a veel. Thank to contraint (7) variable w are fixed to one when the global demand of a veel i not yet completely atified, thu veel v remain in the port during hift, while thank to contraint (8) veel i worked in hift. In fact, pairing contraint (8) aign at mot one QC to veel v until the veel i completely erved. Contraint (9) enure that in each hift a bay i worked at mot by one crane. If a QC can be aigned to at mot one hip in each hift, i.e. the QC aignment aumption a1) doe not yet hold, the following contraint hould be alo included in the model: a 1 C, (11) where: 1if crane q i aigned veel v in hift a q, v, = 0 otherwie and the new et of variable i defined by: B a b B C,, (12) If a bay can be erved by more than one crane in each hift, i.e. the QC aignment aumption a3) doe not yet hold, the following contraint mut be included in the model to check that the total amount of work in a bay i le than the length of a hift: x l b B,, (13) where l repreent the length of hift. Finally, the model can be eaily extended to include external gang. Thi mathematical model ha been implemented in ML and ha been olved with the commercial olver Cplex 11.0.

6 DE MODEL The DE model i deigned to repreent the flow of container related to the unloading and loading operation of the terminal for a given planning horion. In Figure 4 the model overview related to the et of operation to be performed for a given hip i reported. In the operative cenario herein conidered, container are unloaded (import cntr) and loaded (export cntr) by QC and internal non-lifting vehicle (truck) tranport container from the quay to the yard and vice vera. Note that we aume that QC move bay to bay in the ame direction along the hip (i.e. unidirectional chedule) and after finihing unloading all the bay aigned a QC tart loading bay by bay working the other way round. Thi mean that the unloading and loading procee of each hip are managed in a equential logic, even if mixed handling technique can alo be analyed. The model tart at the beginning of the planning horion (uually a week). A dicued above, the model read the olution of the BA that give the time of arrival and berth poition of the et of hip expected to arrive during the period. The number of bay in each hip i known in advance. The number of import and export container for each hip i generated together with their ditribution over the bay of the hip. Afterward, the number of QC aigned to each hip, a well a the et of bay to be handled by each QC, are read by the olution of the Bay_QCA optimiation model. The number of truck aigned to each QC/gang are imulation parameter known in advance. When a hip arrive, the QC aigned to it tart to unload the container from the firt aigned bay following a given equencing (could be right to left, left to right or other handling technique). After unloading a container from it bay poition on board the QC drop it to a truck ready on quay. If no truck are available to tranport the unloaded container the QC i blocked and mut await a truck to deliver the container and to tart another job. Thee delay mut be obviouly reduced in order to improve the eaide performance by deciding the right number of truck to aign to each QC/gang. The truck tranport the container to the torage area where they will then be tacked by the yard equipment. The truck ervice time include the time needed to tranport a container to it yard poition and the time needed to RMG or RTG crane to pick up the container and releae the truck to tart a new tranportation job. Thi mean that we are not intereted in what happen to import container after the internal vehicle have tranported them to the yard poition. After unloading all container in a given bay the QC mut move to the next bay but delay can occur if there i not the ecurity ditance of two bay, needed to avoid interference among QC working. The QC unload import container bay by bay and when they finih unloading tart the loading proce working the other way round bay by bay. Note that the ame pool of internal tranport vehicle are devoted to firtly tranport import container to the yard and, afterward, to deliver the export container to be loaded under the aigned QC. The terminating imulation run top at the end of the planning period (uually a week), when all operation have been performed to the et of hip planned to arrive and all the tatitic and performance indexe introduced above are recorded. ALICATION TO A REAL CAE TUDY The propoed framework i going to be applied to a real cae tudy referred a the outhern European Container Hub (ECH) terminal container ited in the ort of Genoa, Italy. The terminal ECH i a medium-ied import export container terminal which cover a qm total urface ground and ha a quay length of 526 m. The terminal i baed upon the Indirect Tranfer ytem (IT) in which a fleet of huttle vehicle (Reach tacker, Fork lift and Internal truck) tranport the container from a veel to the tack area while dedicated crane (i.e. rail mounted gantry crane (RMG) or rubber-tired gantry crane (RTG)) tack container in the yard lot. In the ame way, export container arriving by road or railway at the terminal are handled within the truck and train operation area, picked up by the internal tranportation equipment and ditributed to the repective tack in the yard by uing dedicated equipment. 5 QC are available for the loading and unloading operation and 27 internal truck are ued to tranport the container from quay to yard and vice vera. Intereted reader can refer to the web ite for getting more information about the terminal ECH. The DE model preented ha been already implemented for the ECH cae tudy uing the imulation oftware environment Witne (Witne, 2010). At preent the main effort are concentrated on getting the information related to the ytem parameter to be ued in the DE model, with a particular attention to the hip berthing time and number of container movement and to the quay crane and internal tranport ervice time. A far a the optimiation model i conidered, preliminary tet for olving real intance of terminal ECH are characteried by a planning horion of 7 day plit into 28 hift, 5 QC and a berth 35 bay long. A deeper analyi on the model i under invetigation. Note that, the propoed approach can be eaily adapted for being applied to other terminal characteried by different equipment and facilitie.

7 Figure 4. imulation model overview

8 CONCLUION AND FURTHER REEARCH In thi paper we propoe an integrated ue of optimiation and imulation to tudy the eaide operation at terminal container. In particular, we introduce the Bay_QCA optimiation model that generate crane and gang allocation plan to be ued a input data for a DE model. Afterward, a imulation model, baed on a more realitic repreentation of the terminal than the one aumed in the Bay_QCA model, i implemented to olve the reource allocation problem and ae the validity of the generated olution. At preent, the main effort are aimed at collecting the main data, debugging and tuning the model for a real cae tudy. Afterward, particular attention will be given to the validation of the model comparing the model' output with hitorical data (parametric tet) and verifying the reult together with the terminal operator involved in the data collection (face validity). We expect to give the firt finding of the application of the framework to the ECH terminal during the conference. Note that, the propoed approach can be eaily adapted for being applied to other terminal characteried by different equipment and facilitie. The main expected reult regard the poibility to contrain the reource (in particular truck vehicle and gang) and compute variou performance tatitic including: berth and quay utiliation, average hip berthing time, QC delay time, truck utiliation rate, etc. The validated model could be ued to identify the critical component of the ytem that repreent the proce bottleneck, and perform a cenario analye aimed at evaluating the impact of organiational change or alternative operative rule for the quay area, alternative gang work plan for each hip entering the terminal and work equence on each QC with relevant cot aving. REFERENCE Ak, A. and A.L. Erera imultaneou berth and quay crane cheduling for container port. Working paper, H. Milton tewart chool of Indutrial and ytem Engineering, Georgia, Atlanta. Ambroino, D., A. ciomachen and E. Tanfani towing a containerhip: the mater bay plan roblem. Tranportation Reearch art A: olicy and ractice, 38, No.2, Bierwirth, C. and F. Meiel A urvey of berth allocation and quay crane cheduling problem in container terminal. European Journal of Operational Reearch 202, No.3, Fu, M.C Optimiation for imulation: Theory v. practice. INFORM Journal on Computing 14, No.3, Fu, M.C., Glover F.W. and J. April imulation optimiation: a review, new development, and application. In roceeding of the 2005 Winter imulation Conference. IEEE, icataway, N.J., Geoffrion, A tructured modelling: urvey and future reearch direction. Interactive Tranaction of OR/M 1, No.3. Giallombardo, G., L. Moccia, M. alani and I. Vacca The tactical berth allocation problem with quay crane aignment and tranhipment-related quadratic yard cot. In roceeding of European Tranport Conference (ETC), Günther, H.O and K.H. Kim Container Terminal and terminal operation. OR pectrum 28, Imai, A., E. Nihimura and. apadimitriou The imultaneou berth and quay crane allocation problem. Tranportation Reearch art E: Logitic and Tranportation Review, 44, No.5, Kia, M., E. hayan and F. Ghotb Invetigation of port capacity under a new approach by computer imulation. Computer & Indutrial Engineering 42, Lee, D.H., L. ong and H. Wang Bilevel programming model and olution of berth allocation and quay crane cheduling. In roceeding of 85 Annual meeting of Tranportation Reearch Board. Wahington DC. Legato,., D. Gulli and R. Trunfio The quay crane deployment problem at a maritime container terminal. In roceeding of the 22 European Conference of modelling and imulation (ECM 2008), Legato,. and R.M. Maa Berth planning and reource optimiation at a container terminal via dicrete event imulation. European Journal of Operational Reearch 133, Legato,. and F. Monaco Human Reource management at a maritime container terminal. European Journal of Operational Reearch 156, Liu, J., Y.W. Wan and L. Wang Quay crane cheduling at container terminal to minimie the maximum relative tardine of veel departure. Naval reearch logitic 53, No.1, Lokuge,. and D. Alahakoon Improving the adaptability in automated veel cheduling in container port uing intelligent oftware agent. European Journal of Operational Reearch 177, No.3, Meiel, F eaide operation planning in container terminal. hyica- Verlag. Berlin. Nam, K.C., K.. Kwak and M.. Yu imulation tudy of container terminal performance. Journal of Waterway, ort, Coatal and Ocean Engineering 128, No.3, ark, Y.M. and K.H. Kim A cheduling method for berth and quay crane. OR pectrum 25, No.1, teenken, D.,. Vo and R. tahlbock Container terminal operation and operation reearch - a claification and literature review. OR pectrum, 26, Tavakkoli-Moghaddam R., A. Makui,. alahi, M. Baai and F. Taheri An efficient algorithm for olving a new mathematical model for a quay crane cheduling problem in container port. Computer & Indutrial Engineering 56, No.1, Theofani,., M. Golia and M. Boile Berth and quay crane cheduling: a formulation reflecting ervice deadline and productivity agreement. In roceeding of the International Conference on Tranport cience and Technology (TRANTEC 2007), rague, Vi, I.F.A. and R. de Koter Tranhipment of container at a container terminal: an overview. European Journal of Operational Reearch 147, Witne imulation oftware (2010 Edition). Uer Guide, Lanner Group.