Optimization Process for Berth and Quay-Crane Assignment in Container Terminals with Separate Piers. By Neven Grubisic Livia Maglic

Transcription

1 Athens Journal of Technology and Engneerng March 2018 Optmzaton Process for Berth and Quay-Crane Assgnment n Contaner Termnals wth Separate Pers By Neven Grubsc Lva Maglc The objectve of ths research s the study of contaner termnals wth two separated pers wthn the same port basn. The man problem s how to optmze the berth and crane allocaton and to mnmze the overall servce tme for the vessels and to mprove the utlzaton of the termnal assets. The optmzaton of the seasde subsystem of the contaner termnals combnes three typcal operatonal problems: shp-to-berth allocaton, quay-crane to shp assgnment and quay-crane schedulng. Due to ther characterstcs, they have a hgh correlaton and should be consdered together. The problem can become even more complex n the Contaner termnals wth a dfferent layout where quays and berths are not placed n the lne or where berths are stuated n dfferent pers. In ths paper, a specfc methodology s presented wth a focus on the optmzaton process. Ths process conssts of three stages namely: ntaton, allocaton and adjustment. The core of the problem solutons n stage 1 s the executon of crane schedulng problem accordng to cargo volume and contaner dstrbuton on the vessel. The result of ths stage s three operatonal scenaros that set out two key varables: duraton of the handlng process and the number of cranes requred. Accordng to the results from stage 1, shp-to-berth assgnment and allocaton of cranes sexecuted. The practcal approach mplemented here, targets to hgh predcton, relablty and effcency of the operatonal plans to satsfy the requrements of the shppng companes. Ths approach requres a fxed number of quay-cranes durng the handlng operatons and hgh utlzaton rate of the cranes. The results of the overall optmzaton have been shown on the few examples. Keywords: Berth allocaton problem, Contaner termnal optmzaton, CT logstcs, QC schedulng problem. Introducton On the large contaner termnals, harbor quays are usually placed n a straght lne n order to ensure good connecton wth contaner stackng area and to ensure better berth utlzaton. However, port quays may be desgned n dfferent layout such as L or U shape or vessel berths may be placed on separate pers. Such s the case wth port basns, where both sdes of the basn are used for berthng the vessels and for handlng operatons (Fgure 1). In such a case, we have two termnal areas wth ndependent operatons wthn the same contaner termnal. Each termnal area has ts own resources, whch do not correlate wth those on the other sde. Due to ths fact, the optmzaton should be Assstant Professor, Unversty of Rjeka, Croata. Senor Research Assstant, Unversty of Rjeka, Croata. 53

2 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane approached n a dfferent way, where the man goal remans the mnmum tme the shp n the port wth equal capacty utlzaton of quay-cranes. Ths confguraton of the contaner termnal s more approprate for small and medum sze termnals where dfferent sze of vessels may be expected. Basn termnal type s less sutable for maneuverng large contaner shps, therefore ports wth large annual turnover of contaners, may prefer constructon of straght-lne quays f avalable. Fgure 1. Layout of Contaner Termnal wth Separate Quays In relaton to the sze of the termnal, Beskovnk & Twrdy (2009) suggested four groups of contaner termnals: small termnals to 500,000 TEUs, a medum-szed termnal from 500 thousand to one mllon TEUs, large termnals from 1 to 3,000,000 TEUs and largest more than 3 mllon TEUs. When evaluatng the productvty of the medum-szed termnals authors stated the average value of 99,762 TEUs per year per quay-crane and 699 TEUs/1m of the quay length. Ths would correspond to the termnal confguraton wth a total quay length of approxmately 1430 meters wth 10 quay-cranes n the seasde operaton system. Therefore, n the focus of ths research are contaner termnals wth two separate quays wthn the same port basn. The man objectve s to how to solve the typcal logstc problems n seasde operatons to mnmze the overall servce tme for vessels n port and to mprove utlzaton of termnal resources. A port contaner termnal may be consdered a logstc system (Steenken et al., 2004), where several dfferent technologcal processes occur wth ts own tasks, resource assgnments and schedulng of operaton. There are several tactcal logstc problems n the contaner termnal that must be consdered (Rashd & 54

3 Athens Journal of Technology and Engneerng March 2018 Tsang, 2006; Murty et. al., 2005). Among them Mesel (2009) grouped three logstc problems targetng seasde operatons: Berth Allocaton Problem (BAP), Quay Crane Assgnment Problem (QCAP) and Quay Crane Schedulng Problem (QCSP). The Berth Allocaton Problem (BAP) s one of the well-known tactcal logstc problems n transport process optmzaton on the contaner termnals. The problem s to fnd the optmal assgnment of berths to the vessels and to adjust vessel arrvals to the preselected tme wndows. The objectve s to maxmze berth capacty and mnmze the watng tme for the vessels n the port. The frst authors who publshed papers related to dscrete berth problem were Ima et al. (2001) and Nshmura et al. (2001). Lm (1998) carred out research wth contnuous berth layout. Another nterestng ssue s to put varous attrbutes nto the objectve functon accordng to the termnal busness strategy, techncal or organzatonal lmtatons. Thereby, Km & Moon (2003) ncluded a poston preference attrbute nto the model. On the other hand, Guan and Cheung (2004) ncluded a prorty coeffcent nto the model, whch vares dependng on the vessel characterstcs or shppng company. Consderng publc ports, Ima et al. (2005; 2007) presented the prorty model based on techncal attrbutes of the termnal subsystems rather than based on partcular shppng company. Grubsc (2015) propose modfcaton of the BAP consderng draft restrctons. Quay Crane Assgnment s another optmzaton problem wth objectve to allocate avalable cranes to vessels accordng to the handlng demand of the partcular vessel. QCAP s closely related to BAP, snce the poston and tme of berthng are nput parameters for the crane-to-vessel assgnment. Ths s more elaborated by Zhou & Kang (2008), and Mesel (2009). However, the problem wth separated or ndependent quays s not adequately represented n the lterature. Only the work of Hendrks et al. (2011) s found correspondng at some extend to ths problem. The objectve was more balanced quay-crane workload and mnmzaton of the contaner movement among the termnals. However, authors dd not deeply consder the relaton between the crane allocaton and cargo dstrbuton on board, but approxmate the capacty avalablty. In the followng chapters, we wll present an overall approach of the optmzaton process for berth and quay crane assgnment takng nto consderaton termnal quays layout, cargo dstrbuton on board and varaton n vessel handlng demand. The goal s to mprove the relablty and plannng of the operatons. Methodology Optmzaton of the seasde system of the port contaner termnal combnes three separate optmzaton problems n theory known as the berth allocaton problem, the quay-crane assgnment problem and the quay-crane schedulng problem. 55

4 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane The berth allocaton problem determnes the poston and tme of berthng the vessel. The man challenge for BAP solvng s how to determne the requred processng tme of the vessel n order to setup an arrval/departure plan for the plannng horzon. Ths processng tme ncludes preparaton for handlng operatons, tme for loadng/unloadng operatons and preparaton tme for departure. Tme for loadng/unloadng operatons s prmarly mportant factor and t depends on two key features: - avalablty of quay cranes (number of QCs to be assgned) - transport demand (number of contaners) and dstrbuton of contaner across the shp holds/bays. The man weakness of many BAP models s the predcton of processng tme and mplcaton of that assumpton on problem soluton. Ths assumpton s closely connected to avalablty of resources. The schedule of vessels arrvals s dynamc wth varatons n regular servce operatons and t s not always possble to guarantee the avalablty of the crane at the assgned tme-wndow. If delay occurs for one vessel, most probably t wll have mpact on overall handlng process on the termnal, ncludng crane tme-wndow assgnment for other vessels. In that case, the result of the optmzaton functon s not applcable and t s necessary to make reengneerng of the process. Consderng ths problem, Mesel (2009) proposed an ntegrated model that solves the BAP and QCAP problem at once. Handlng processng tme s varable, whch value depends on number of assgned cranes and depends on avalablty of cranes. Moreover, t assumes that the crane capacty s fully exploted. Agan, ths s not enough because the productvty of the handlng and a crane tself depends on the cargo dstrbuton on board. It s not possble to utlze crane capacty and evenly arrange the workload of cranes for partcular shp f we use only one model approach. Therefore, Mesel ncluded the quaycrane schedulng problem n the optmzaton process to be performed before the berth/crane assgnment based on cargo dstrbuton data and cargo plans. Regardng the propertes of the ndvdual models for BAP, QCAP and QCSP we have developed the methodology by whch t would be possble to provde a complete soluton as a result of the optmzaton process, not a sngle model. Because of the nterdependence of the result of the decson varables and nput parameters, ndvdual models that have, a hgh correlaton wth each other should be consdered together. Ths optmzaton process s based on the ntegraton and nterdependence of ndvdual optmzaton problems (Fgure 2). The feature of ths optmzaton process s operatonal functonalty of targeted medum-sze contaner termnals wth separated quays. The process conssts of three man stages: ntaton, allocaton and adjustment. In the ntaton stage, handlng sequences and crane arrangement are modeled based on vessels and cargo data. The result of the ntaton stage, are three optons of QC arrangement for each vessel, whch are chosen as relable and possble after solvng the quay-crane schedulng problem. The results strctly follow contaners dstrbuton on board each vessel. 56

5 Athens Journal of Technology and Engneerng March 2018 The core of the second stage s an optmal soluton fndng for shp to berth and crane to shp allocaton. Therefore, the models for solvng BAP and QCAP for separate quays are generated where the relocaton of resources s performed by the verfcaton of three possble optons resultng from the ntaton stage. The objectve of ths stage s to fnd the overall optmal soluton for the mnmzaton of the vessels servce tme n port and maxmum utlzaton of cranes servce tmes. The last stage of the process s the adjustment and algnment of the vessel arrval schedule where tme-wndow reservaton prncple may be mplemented accordng to mutual agreement wth shppng companes and a termnal operator (Zuskn et al., 2015). In addton, n ths stage t s possble to rearrange the berthng plan n case the two adjacent plannng horzons are overlappng. The fnal tactcal-operatonal plan ntegrates berth allocaton to vessels, tmetable for berthng, assgnment of fxed number of quay cranes per each vessel, quay-crane tmetable of workload and tasks sequencng. Fgure 2. Optmzaton Process for Seasde Operatons on CT 57

6 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane Model Formulaton Intaton Handlng Scenaro Determnaton The optmzaton process begns wth the ntaton stage. Based on the vessel arrval data and cargo dstrbuton on board, three-operaton scenaros are developed accordng to the results of the quay-crane schedulng problem solutons. For the quay-crane schedulng modelng two dfferent models are used, developed n the prevous work (see Grubsc & Dundovc, 2014). Each opton s defned by varable O(q,p) where q and p are parameters descrbe number of reserved cranes and servce tme necessary for loadng/unloadng operatons. Input and output varables for ntaton are shown on Fgure 3. Fgure 3. Operatonal Scenaro as Results of QCSP Soluton Intaton A, R, R' QCSP O1 m, p(a), h(a) wth sngle task algorthm O2 Q(q=n) QCSP wth task sharng algorthms O3 For each QCSP problem soluton, t s necessary to defne q beforehand. The mnmum number of quay cranes q mn avalable for each vessel s usually subject to a contract between termnal operator and shppng company whle the maxmum number of quay cranes q max depends on cargo dstrbuton. In cases where q=1 the problem s lmted to solvng a task sequence only. In other cases, QCSP soluton determnes task-to-crane assgnment and total makespan p requred for completon of handlng operatons. For each vessel operatonal scenaro s defned by the expresson: q1 p1 O q2 p 2 (1) q3 p 3 Accordng to the three dfferent processng tmes p are obtaned dependng on the number of quay-crane assgnment q. Whch opton would be the best opton depends on results of forthcomng optmzaton process n allocaton stage. In ntaton stage, t s mportant to carry out the QCSP solvng for each q n nterval [q mn, q max ]. The key feature of the proposed model are the output values that have three possble optons for crane assgnment determnng the total duraton of the handlng process. It should be ponted out that these three optons have balanced the operaton tme and at most even dstrbuton of workload. Ths s acheved by mplementaton of task sharng algorthm for QCSP soluton (Grubsc & Dundovc, 2014). Ths specfc feature ensures a hgh utlzaton 58

7 Athens Journal of Technology and Engneerng March 2018 rate of quay cranes and allows the smplfcaton of the optmzaton problem as we can consder fxed number of quay cranes durng entrely handlng process. It s only necessary to choose between the three optons. Ths smplfes the overall optmzaton process and avods the uncertanty that occurs when crane to shp allocaton s based on tme-wndows assgnment. On the other hand, from the shppng company pont of vew, the approach when a number of cranes s fxed durng the entrely loadng/unloadng process s much more acceptable and port servces much more relable. Allocaton Quay, Berth and Crane Assgnment In ths stage, we are solvng ntegrated BAP and QCAP model adapted for termnals wth separate quays layout confguraton. Input parameters for the model are the length and arrval tme of the vessels together wth values of output varables from the ntaton stage. In addton, for quay choce we defne set of quays W W 1, W2,..., WK wth ndex k K each wth total quay length QL k and total number of cranes QC k. In practce, shppng companes have preferences over the partcular quay choce. Before vessel arrval, contaners are prepared n blocks near the berth postons located at the preferred quay. If there s a change n quay assgnment, t wll more lkely result n more resources engagement for reposton of the contaners and consequently generate addtonal costs. In order to satsfy the requrements of preference-based selecton of quay, t s necessary to penalze berth at the quay, whch s less favorable for the vessel or would lead to an ncrease of the cost for reposton of the contaners on the termnal. If the cost of reposton s marked wth cp and the unt cost per tme unt of the shp watng for the free berth s marked wth cw, then the rato cp/cw s quay weght factor marked wth ω k. Its value s determned dependng on the vessel preference, based on costs cp and cw, accordng to the followng expresson: cpk k za V, k W (2) cw Quay weght factor s relatve dmenson ndcates the rato of cost for the shp repostonng n relaton to the cost of the shp watng for the free berth. The ntegrated model for BAP and QCAP optmzaton for separate quays s shown below. We defne the followng sets: V V1, V2,,..., VN s set of vessels wth ndex : N, where N s total number of vessels n the system. T T 1, T2,..., TH s set of tme wndows wth ndex t : t H, where H s plannng horzon. W W W W,,..., K

8 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane s set of quays wth ndex k : k K set of handlng scenaro (optons) wth ndex v. Followng notaton s appled:, where K s number of quays. O O, O, O w watng tme of vessel for free berth p duraton of handlng process for vessel n scenaro v v quay weght factor for vessel to be docked at quay k k Bnary varable used n the model are: s o x v k 1, f scenaro vs chosen for vessel 0, otherwse 1, f vessel s assgned to quay k 0, otherwse The objectve functon mnmzes port servce tme for the vessels to be processed at the contaner termnal wth separate quays and read: (3) MnZ w p o x v v k k V V v O V k W The allocaton of resources s acheved by selectng one among the three predefned scenaro wth objectve to get mnmum value of the functon. Shpto-berth assgnment s optmzed on the same manner as n conventonal BAP problem solutons. The dfference s n vessel-processng tme that s not fxed but depends on the chosen handlng scenaro. The model s desgned such a way that the best opton for the vessel s always taken at frst. That s the one wth the hghest number of quay cranes and the shortest processng tme. In ths way, the QCAP soluton comes down to the selecton of the scenaro rather than ndvdually assgnment of the cranes. As the bass for QCAP soluton s outcome of QCSP soluton, together wth the mplementaton of the splt task algorthm, the uncertanty resultng from the crane demand approxmaton s suppressed. The best scenaro selecton for the partcular vessel typcally leads to the lack of a real soluton f resources (quay cranes) are lmted. In that case, the model selects another operatng scenaro for each vessel to get ntegrated and optmal soluton for the plannng horzon. Adjustment Two stuatons durng the plannng horzon may occur, both as result of varaton n vessel schedule. Frst, t may happen that the vessel arrval s scheduled at the end of the plannng perod. If ths happens and the vessel 60

9 Athens Journal of Technology and Engneerng March 2018 handlng process contnues after the end of the plannng horzon, adjustments should be made n order to avod the double allocaton of berths to vessels that are schedulng at the begnnng of the next plannng perod. The second stuaton s when t s possble to adjust the schedule of the vessel accordng to a mutual agreement between the shppng company and termnal operator. The dea behnd s that the optmzaton result may be mproved by speed-up or slow-down the vessel voyage n order to ft her ETA nto the reserved tmewndows. If applcable, adjustment means that optmzaton process need to restart wth the adjusted nput values of vessels parameters. To perform the adjustment based on mutual agreement between a termnal operator and a shppng company t s necessary to modfy the objectve functon so that t reads: wat arr MnZ ( w e ) pvov xk k V v O k W where new notatons are: (4) e tme savng or dfference between estmated and earler tme of arrval weghted coeffcent of watng for free berth wat arr weghted coeffcent of the vessel earler arrval at the port Applcaton Example In the followng examples we demonstrate how to solve BAP and QCAP problems on the contaner termnal wth two separate quays (or pers) when 7 shps are scheduled for arrval durng the plannng horzon. Plannng horzon may be arbtrary selected, usually on the weekly bass. Each vessel competes equally for avalable berths but wth preference of quay 1 over the quay 2 ( 1 1, 2 5). Both weghted coeffcents, for watng and for earler arrval, are the same for all vessels n ths smple example wat arr ( 1, 2 ). For both quays, the total length s expressed n the number of berth segments and s set to 15. Let us say each berth segment has a length of 50 meters that corresponds to 750 meters. There are 5 quay cranes avalable on each quay. Values for p k and q k for scenaros o v are calculated after QCSP soluton s found n ntaton stage. Processng tme for handlng operatons p k are expressed n tme-wndow segments. The nput parameters are shown n Table 1 and soluton based on objectve functon (4) s shown n Table 2 and Fgure 4. 61

10 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane Table 1. Example 1: Input Data V wat arr l a a ' p 1 / p 2 / p 3 q 1 / q2 / q 3 1 / 2 1 A /6/10 4/3/2 1/5 2 B /5/8 3/2/1 1/5 3 C /13/25 3/2/1 1/5 4 D /10/20 3/2/1 1/5 5 E /7/10 5/4/3 1/5 6 F /8/1000 2/1/1000 1/5 7 G /7/11 4/3/2 1/5 k WL QC k k The followng notatons are used n the Table 1: V vessel name l length of the vessel (expressed n quay segments) a estmated tme of vessel arrval (ETA) a ' the earlest possble estmated tme of the vessel arrval arr, weghted coeffcents related to cost wat p / p / p processng tme for handlng operatons for three scenaros q / q / q number of QCs assgned to vessel for three scenaros / quay weght factor for vessel for a correspondng quay 1 2 WL total quay length (n the number of berth segments) k QC total number of quay cranes located at the quay k k Table 2. Example 1: Results of Integrated Optmzaton Model V b s d w e 1 / 2 x x o 1 / o 2 / o 3 1 A /0 0/1/0 2 B /0 0/1/0 3 C /0 1/0/0 4 D /1 1/0/0 5 E /1 1/0/0 6 F /0 1/0/0 7 G /0 1/0/0 Mn Z = 62 62

11 Athens Journal of Technology and Engneerng March 2018 Followng notatons are used n the Table 2: b berth poston (number of frst segment assgned to vessel ) s berthng tme (frst tme-wndow assgned to vessel ) d departure tme of vessel w watng tme of vessel e tme savng for earler arrval of vessel Fgure 4. Graphcal Representaton of Soluton for Example 1 The graphcal soluton of the ntegrated optmzaton problem s presented n Fgure 4. Vessels are represented by the rectangle wth tme-wndows on x- axs and berth segments on y-axs. The number of assgned cranes s shown n down-left corner of the rectangle. The optmal soluton of the objectve functon (4) s 62. Vessels D and E are berthed alongsde the quay number 2 where maxmum number of QCs s assgned to both of them accordng to the best of three possble handlng scenaros. Vessel C s only one who has to wat for a free berth at the quay 1, but after 63

12 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane berthng maxmum number of QCs wll be assgned n order to speed-up the processng tme for handlng operatons. Earler berthng tme for vessel C would not result n optmal soluton because t would be not beng possble to allocate 3 but only 1 or 2 cranes, that wll prolong the processng tme from 9 to 13 or even 25 tme wndows, accordng to QCSP soluton. Fgure 4 shows that number of assgned cranes corresponds to the selected scenaros for each vessel and does not exceed the maxmum number of QCs at the quay. The number of cranes assgned to the vessels s constant durng the overall handlng process. Ths has avoded the mpact of the handlng operatons takng place on other vessels nearby on avalablty of QCs that may occur n case when the number of QCs assgned to the vessel s varable. Let us consder the second example that explans the thrd stage of the optmzaton process the adjustment stage. In addton to the prevous example, we put three more vessels n the system, namely P, R and S whch arrvals are scheduled n next plannng horzon, whch s arbtrary selected at tme wndow 16 (see Fgure 5). The nput data for these vessels are shown n Table 3. Table 3. Example 2: Input Data V wat arr l a a ' p 1 / p 2 / p 3 q 1 / q2 / q 3 1 / 2 1 P /6/10 3/2/1 1/5 2 R /5/8 3/2/1 1/5 3 C /13/25 3/2/1 1/5 4 S /8/10 3/2/1 1/5 5 E /7/10 5/4/3 1/5 6 F /8/1000 2/1/1000 1/5 Consderng the optmal soluton obtaned from prevous stages, we can notce that vessels C, E and F exceed the actual plannng horzon and should be ncluded n the next one. However, they are already berthed and the handlng operatons contnue at the begnnng of the second plannng horzon. Therefore, we must take nto account the tme remanng for completon of handlng operatons and fx ther postons n tme-space dagram. Ths has been done by settng fxed values for varables b, a and s such thatb 3 5, b 5 9, b6 1, a3 a5 a6 1, and s3 s5 s6 1. Bnary decson varables must be fxed such that x3,1 1, x5,2 1, and x 6,1 1. Values for p3,1, p 5,1, p 6,1 should be adjusted accordngly. 64

13 Athens Journal of Technology and Engneerng March 2018 Table 4. Example 2: Output Data V b s d w e 1 / 2 x x o 1 / o 2 / o 3 1 P /1 1/0/0 2 R /0 0/1/0 3 C /0 1/0/0 4 S /0 1/0/0 5 E /1 1/0/0 6 F /0 1/0/0 Mn Z = 44 Fgure 5. Graphcal Representaton of Soluton for Example 2 65

14 Vol. 5, No. 1 Grubsc et al.: Optmzaton Process for Berth and Quay-Crane It can be concluded that the results fully correspond to the gven condton n terms of allocaton of the vessels from prevous plannng horzons and berth and tme-wndow assgnment of new vessels enterng the system n new plannng perod (Table 4). For example, vessel P has to wat completon of operatons on vessel E because there s no QC avalable for operatons. None of the vessels P, R or S s allocated to the berthng postons occuped by the vessels C, E and F or volates the rule of maxmum number of QCs at the quays (Fgure 5). Vessel S n ths example must wat three tme-wndows because t s not possble to fnd better soluton. If we place S on the quay number 2, above the P mmedately after the arrval, due to quay weght factor the total value of objectve functon wll be hgher. On the other sde, lookng at the vessel R, only 2 QCs are possble to be assgned choosng the scenaro 2 for the handlng operatons. Conclusons Typcal logstc problems on contaner termnals known as BAP, QCAP and QCSP can be ntegrated to solve dfferent ssues and requrements of optmzaton. The model proposed n ths research target dfferent termnal layouts tryng to solve complex correlaton between those three problems. From the present experence, that ntegraton s possble wth some assumptons regardng the quay crane capacty plannng. One may notce that fxed number of cranes per vessel durng the entrely handlng process s weak pont of the model. However that s a queston of termnal polcy where both sdes, termnal operator and shppng companes, may beneft from better predcton of the servce tme and the servce relablty. The key for the model success s hgh utlzaton rate and good balance between workloads of quay cranes assgned to each vessel that need to be acheved by mplementaton of splt-task algorthm developed n prevously research. Further acton should be drected to the model testng for dfferent ntervals of vessel's arrval and for dfferent contaner dstrbuton on board the vessel. References Beskovnk, B. & Twrdy, E. (2009) Productvty smulaton model for optmzaton of Martme Contaner Termnals. Transport Problems. 4 (3), pp Grubsc, N., Dundovc, C. (2014) A Soluton for Contaner Termnal QC Schedulng Consderng Grouped Tasks and Operatve Zone Lmts. ICIL 2014 Conference Proceedngs/Lesar, Maro (ed.). Internatonal Conference on Industral Logstcs, Bol, Croata. Grubsc, N. (2015) A Contrbuton to Berth Allocaton Problem Soluton wth Draft Restrctons. Pomorsk zbornk (1), pp Guan, Y. & Cheung, R.K. (2004) The berth allocaton problem: models and soluton methods. OR Spectrum. 26 (1), pp

15 Athens Journal of Technology and Engneerng March 2018 Hendrks, M.P.M., Armbruster, D., Laumanns, M., Lefeber, E. & Uddng, J.T. (2011) Strategc allocaton of cyclcally callng vessels for mult-termnal contaner operators. Flexble Servces and Manufacturng Journal. Ima, A., Nshmura, E. & Papadmtrou, S. (2001) The dynamc berth allocaton problem for a contaner port. Transportaton Research Part B: Methodologcal. 35 (4), pp Ima, A., Sun, X., Nshmura, E. & Papadmtrou, S. (2005) Berth allocaton n a contaner port: usng a contnuous locaton space approach. Transportaton Research Part B: Methodologcal. 39 (3), pp Ima, A., Nshmura, E., Hattor, M. & Papadmtrou, S. (2007) Berth allocaton at ndented berths for mega-contanershps. European Journal of Operatonal Research. 179 (2), pp Km, K.H. & Moon, K.C. (2003) Berth schedulng by smulated annealng. Transportaton Research Part B: Methodologcal. 37 (6), pp Lm, A. (1998) The berth plannng problem. Operatons Research Letters. 22 (2-3), pp Mesel, F. (2009) Seasde Operatons Plannng n Contaner Termnals. Sprnger. Murty, K.G., Lu, J., Wan, Y. & Lnn, R. (2005) A decson support system for operatons n a contaner termnal. Decson Support Systems. 39 (3), pp Nshmura, E., Ima, A. & Papadmtrou, S. (2001) Berth allocaton plannng n the publc berth system by genetc algorthms. European Journal of Operatonal Research. 131 (2), pp Rashd, H. & Tsang, E.P.K. (2006) Contaner Termnals: Schedulng Decsons, ther Formulaton and Solutons. Steenken, D., Voss, S. & Stahlbock, R. (2004) Contaner termnal operaton and operatons research - a classfcaton and lterature revew. OR Spectrum. 26 (1), pp Zhou, P. & Kang, H. (2008) Study on Berth and Quay-crane Allocaton under Stochastc Envronments n Contaner Termnal. Systems Engneerng - Theory & Practce. 28 (1), pp Zuskn, S., Grubsc, N., Sumner, M. (2015) Shpowner management n accordance wth mutual agreement. Pomorstvo: Scentfc Journal of Martme Research. 29 (1), pp

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