Available online at www.sciencedirect.com Procedia Social and Behavioral Sciences 20 (2011) 994–1003 14th EWGT & 26th MEC & 1st RH Optimizing the stacking of the Intermodal Transport Units in an inland terminal: an heuristic procedure Stefano Carresea*, Luigi Tatarellia a University Roma Tre, Via Vito Volterra 62, 00146 Roma, Italy Abstract The actual system structure of the mobility of the goods, self-regulated from spontaneous phenomena rather than coherent and uniform managerial approach, is not compatible with the sustainable development, the optimization of the resources, the quality of the services and the respect of the atmosphere. In this context, the combined transport represent an alternative to all-road transport. Inside the transport chain, the node dedicated to the modal change represents the critical element in which, due to a wrong political organizational, design or operational procedures, it’s possible to make useless the benefits acquired in the phases of transport. This research, aims to develop an heuristics procedure for the optimization of the stacking activities in an inland intermodal terminal with the aim of increasing total efficiency in the whole transshipment node. © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of the Organizing Committee. Keywords: combined transport; inland terminal; reshuffles; optimization; heuristic procedure; genetics algorithms 1. Introduction The ECMT (United Nations, 2001) – European Conference of Ministers of Transport – defines: x intermodal freight transport as “the movement of goods in one and the same loading unit or road vehicle, which uses successively two or more modes of transport without handling the goods themselves in changing modes”; x combined transport as “intermodal transport where the major part of European journey is by rail, inland waterways or sea and any initial and/or final legs carried out by road are as short possible”; x Unaccompanied Combined Transport (UCT) as “transport of a road vehicle or an Intermodal Transport Unit (ITU), not accompanied by the driver, using another mode of transport. In the UCT a distinction can be done between unaccompanied inland combined transport (UnAICT) and unaccompanied maritime combined transport (UnAMCT). In the first case the transport arise exchange between couples of industrial sites or exchange between an industrial site and a consumption center (for example a warehouse located nearly an urban area). In the second case the origin or destination of the traffic is always constituted from a harbour system, which interfaces with an industrial system (transport of raw materials or * Corresponding author. Tel.: + 39-06-57333410 ; fax:+39-06-57333441 E-mail address carrese@uniroma3.it 1877–0428 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and/or peer-review under responsibility of the Organizing Committee doi:10.1016/j.sbspro.2011.08.108 Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 995 semifinished products) or with a consumption center. The ITU utilized in the unaccompanied combined transport are: x containers, boxes to carry freight usually stackable and top-lifted which mainly arise the UnAMCT; x swap bodies (freight carrying units optimized to road vehicle dimension that usually are not capable of being stacked and not capable to be top-lifted); x semi-trailers (non-powered vehicles fro the carriage of goods, intended to be coupled to a motor vehicle in such a way that a substantial part of its weight and of its load is borne by the motor vehicle. Semi-trailers are not capable of being stacked and not capable to be top-lifted). Swap bodies and semi-trailers arise UnAICT. ITU type then determines the needs of space for the stacking activities (the possibility to overlap ITUs one over the other in the storage area reduces the requested surfaces) and influences the choice of the handling techniques and technologies and the average period of dwells in the terminals. Generally the logistic chains of the UnAMCT and of the UnAICT are independent from each other and their attributes would need a functional specialization of the transhipment node (a place equipped for the transshipment and storage, that we will define, for simplicity, terminal or intermodal terminal) for this purpose dedicated. The recent evolutionary tendencies, make evidence a crescent promiscuity of the two components of traffic because: x in the European context (but not only), more of the terminals derive from the adaptation of railway areas conceived for other uses (conventional rail freight transport or freight wagons maintenance/parking); x only in recent times, with the increase of the traffic, dedicated infrastructures have been designed and constructed, in exclusive way for the combined transport; x high volumes of traffic, as results of the joining between UnAICT and UnAMCT create scale economies and synergies in order to optimize the activities of the terminal. For these reasons the managers of the terminals located in the inland areas – in the following indicated as IIT (Inland Intermodal Terminal) – differently from the managers of the terminals located in the port areas that manage only containers, aim to identify cohabitation forms to that concur with the two segments of the combined transport of being managed in mixed way in the IITs, mainly about the stacking activities. Therefore in the present research a procedure has been developed in order to optimize the phases of stacking in a IIT in which containers, swap bodies and semi-trailers are managed at the same time. The research starts from a Doctoral Thesis developed in Roma Tre University (Tatarelli, 2006). 2. The stacking activities in an IIT As highlighted by KombiConsult (2010), while IITs serving maritime containers generate a considerable share of their revenues from interim storage and depot services, the majority of “conventional” rail/road IITs rather suffer from loading units remaining on their premises longer than 12 to 24 hours prior to or after the rail journey, because these terminals were primarily designed to enable the transhipment of ITUs directly from wagon to truck and vice versa. The delayed trains, the exchange of trains between transhipment area and parking tracks, the shunting of damaged wagons, and the pick-up and delivery behaviour of road operators require many times the intermediate buffering of loading units. In addition, some terminals experience that their terminals are used for parking loading units according to typical intermodal supply chain. In this context, the storage of the ITUs in a IIT lacking in surfaces implies very expensive activities, whose the most relevant aspects are summary described in following subparagraphs. 2.1. The Reshuffles The analysis of the scientific references and the analysis of the operating practice evidence that in the area of the storage of the ITU, the main problem is determined from the phenomenon of the rehandling or reshuffling, it means the necessity to operate a rehandling of the units in dwell. As Murty et al. (2005) also evidenced, it is opportune to distinguish between: x productive move which are those associated to the transshipment of the ITUs (between train and train or train and trucks) or to the direct moves of the loading units from/to the storage area; x unproductive or reshuffling move. Given a generic ITUth to be handled, all the movements of other dwelling ITUs that become necessary in order to operate the movement of the ITUth. 996 Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 The reason why unproductive moves are generated are essentially two: the scarcity of available spaces that need to place the ITU on more levels (in height); the deficiency of information about the forecasted moment of departure from the IIT of the generic ITU, that makes difficult any process of programming the handling. Steenken et al. (2004) present their first papers on the problem connected to the minimization of the unproductive movements, only in the first 90’s relatively to harbour terminals (that differ from the IIT for the typology of ITU, the dimensions and the shape of the available spaces, the handling technologies). They have put in evidence a direct relationship between increment of height of storage and increment of the average number of unproductive moves. De Castilho and Daganzo (1993), show that, for an increment in the exploitation of the available spaces, an elevated height of storage (number of levels) requires the necessity to operate reshuffles in the ITU located in the inferior levels. Kim (1997) has operated the comparison between 4 analytical methods for the determination of the expected number of reshuffles in a generic configuration of the storage area, in which the mix between ITU of various dimensions is excluded however (containers located in different column are not influenced mutually during the movements): Kim and Kim (2002) have developed a calculation model of the costs of the various activities in a terminal harbour. The authors have also put in evidence that the variability of the time associated to the reshuffle operations can be estimated with reasonable approximation from a Gamma distribution. Murty et al. (2005), developing a DSS dedicated to the harbour areas, have many times underlined the necessity to minimize the number of reshuffles through a correct allocation of the position of every container in the storage area. It is possible to conclude that the main factors that increase the number of reshuffles are: x variability in the typology of ITUs; x variability in the dimensions of the ITUs; x performance limits in the handling equipment; x variability in the time of leaving the terminal by the ITUs. The reduction of the reshuffles can be reached by using an intelligent system able to acquire data about incoming and outcoming ITUs and to determine the optimal allocation of each in the stack or by installing more expensive solutions, still in experimental phase, as the TEUSTACK system. As showed in figure 1, TEUSTACK allows to avoid the reshuffles by storing the ITUs in a sort of large scale automatic warehouse. It is clear that a similar solution could be very interesting only in presence of relevant ITUs flows, but in most cases the volumes of ITUs could be not sufficient to justify the relevant investments and operational costs required to install and to manage it. Then the information and technology applications, based on algorithms to minimize the number of reshuffles, can represent the optimal solution for small and medium size IIT (in a preliminary estimation, for traffic lower than 200.000 ITUs/year). Figure 1. TEUSTACK (source Promit, 2007) Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 997 2.2. The dwelling time In the UnAICT the generic ITU remain generally in the terminal only for some hour, because: x for the units entering in the IIT by rail, the trucks are arranged in coincidence with the train arrival; x for the departure by rail, the delivery to the terminal is organized within the time limit of closing the train load. It is interesting to evidence that the entity of the phenomenon depends also from the organization of the road transport and from the typology of goods contained in the ITU. An analysis carried out by Mariani (2006) about the activities of the Pomezia-Santa Palomba terminal, on of the italian IIT located nearly to Rome, has confirmed the importance of the content of the ITU. Those dedicated to the transport of chemicals or dangerous goods (tank containers) introduce an average dwelling time to the terminal, shorter of approximately 45% regarding the swap bodies dedicated to the transport of products that have less necessity of an express delivery to destination [7]. In the UnAMCT, also due to the reduced spaces of storage in the harbour terminals, the use of the rail-road terminal has the double purpose to guarantee the transfer of the ITU and to act as dwell place. Since the entire cycle of the terrestrial transport of container is based on the requirement of synchronize with the port calls, the storage of the container in the IIT is characterized for [8]: x full import and export containers: the medium lay time of the containers full in arrival to the IIT terminal from the port or vice versa is generally limited to few days; x empty containers: either in export or in import, the lying can be extended also till various weeks. These general tendencies, characterized from hypothesis formally corrected, often depend also from the single operating experience. It is therefore obvious that the dwelling time of the ITU in the IIT is a complex phenomenon, influenced from numerous parameters and that it contributes to increase inefficiencies in the storage operations. KombiConsult (2010) highlights how to prevent the very extensive dwells some IIT i.e. Busto Arsizio, KTL Ludwigshafen, Duisburg-Ruhrort Hafen and Köln-Eifeltor experiences a bonus/malus system aimed at the management of the interim storage space. This systems foresee a reward (“bonus”) for a customer who picks up his shipment early for example in the first three hours after the time of availability of the train (maximum reduction 8 Euro/ITU), and a penalty (“malus”) if the shipment is collected e.g. 24 to 48 hours after the arrival (maximum increase about 29 Euro/ITU). The terminal managers show that the results of applying similar pricing schemes are very encouraging and in possible to estimate that such a measure ensures a total capacity increase effect of about 5 per cent depending on the initial pick-up and delivery behaviour of the customers. 2.3. The lack of space The UnAICT involves ITUs with a wide range of typologies (container, swap bodies and semi-trailers) and dimensions (20, 30, 40 and more foots) and then the process to allocate each ITU in the storage area is more difficult with respect the maritime terminals, where type and dimensions of loading units are more uniform (generally 20 or 40 foots containers). Most IITs manage the spaces by a “segregation” policy which foresees to store the ITUs in well defined and rigid areas according to the origin or destination of the train which the ITUs arrive or depart. In addition, when possible, terminal managers prefer to collect the ITUs on the basis of dimension or type. This is possible only in presence of a sufficient extension of the yards storage dedicated, but in some and not isolated cases, due a large number of spatial constraints (i.e. IITs located in an urban or sub-urban areas often cannot enlarge its surfaces), could not be possible to separate the different ITUs (by dimension and type) and then to store its in dedicated areas. Is therefore necessary to stack the ITUs sometimes creating, if necessary, a series of joints and then increasing the number of rehandles. 2.4. The handling technologies Reach-stackers or front-loaders, the mobile cranes currently employed in the IITs (rail mounted or rubber tired gantry cranes are typically of the hub or gateway terminals, , while straddle carriers are in practice exclusive of port terminals) access the ITUs from the side of the stack whit different capacity of penetration in the internal areas. 998 Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 Figure 2. Stack approach for a Front-loader (on the left) and a Reach-stacker (on the right) It may thus be necessary to rehandle many ITUs - located on the top or nearly - to reach the target ITU. As in Figure 2, the reach-stacker allows to manage ITUs located in the second or third row while the front-loader allows to manage only the ITUs in the first row. Obviously the second crane in less expensive than the first one but his utilization can generate a large number of reshuffles. Referred to a stack with two or more row, employing a gantry crane or a straddle carrier, which handle the ITUs by top-lifting, the number of reshuffles can be reduced. Optimal choice of the handling technologies is then a trade-off between investment/operative costs and reshuffles costs. Finally the lack of climbing other parked ITUs to access the stack causes an increase in the number of rehandles. For the purpose of the present research, climbing power (the ability to handle an ITU located in second or more row – the target row - remaining in the front of the stack) can described by 2 components: x vertical, the maximum number of the ITUs top-stacked in the rows before the target row; x horizontal, the maximum number of row with stacked ITUs before the target row. Both the parameters are equal to infinite for a gantry-crane and are equal to 0 for a front-loader, while a reachstackers can be defined by its combination (each variable from 0 to infinite). 3. Formalization of the problem This research deals with the problem of allocating a group ITUs, arrived in the IIT by rail, in a stack minimizing the total operating cost, i.e. the cost required for storage and reshuffling the ITUs. It consists in the process, daily experienced by an IIT manager, to decide the best set of available positions to store each ITU. To clarify the problem, next paragraphs present its parameters hypotheses, objectives and constraints. 3.1. Parameters and Hypotheses The following parameters were taken into account: x the layout of the storage yard composed, in a tri-dimensional space, of F lines, R rows and L levels (a sequence of three elements f, r, l – respectively in the sets F, R, L - defines a “cell” in the storage yard); x the set of ITUs to be stored U1; x the set of ITU already in the stack U2; x the set of positions of the ITUs on the rail wagons I ; x the set of point corresponding the access points to the stack by the crane J; x the set of available cells in the storage space AP. Each ITU u (in U1 or in U2) is characterized by: x the dimensions du (expressed in terms of number of cells needs to store the ITU). x the expected times to leave the IIT, following indicated ltu. x the overlap index Su (number of full ITUs which can be stacked on top of ITU u). This parameter depending by the mechanical resistence of the structure, is equal to 0 for conventional swap-bodies and semi-trailer; 999 Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 According to the paragraph 2.4, the crane is outlined by the 2 climbing parameters, H for the vertical component and K for the horizontal component; by using this parameters it is possible to model a wide range of cranes (i.e. front loaders have K = 0 while gantry cranes have H and K = ∞). Main hypotheses are: x only a crane is used (that is in more operative contexts) to handle the ITUs; x the ITUs already stacked on the storage yard before the arriving of the train cannot be handled. 3.2. Objective function The objective of the present research is to determine a feasible sequence of stacking operations that minimize the costs associated to the storage of the ITU considering spatial and operative constraints. Set α and β two real number with sum 1, the objective function results: · § U F R L u Min¨¨ D ¦¦¦ ¦T frl * xufrl  E ¦¦ cij xij ¸¸ iI jJ ¹ © u 1 f 1r 1 l 1 (1) where Tufrl represents the cost of the reshuffles associated to stacking the ITU u in the cell defined by line f, row r and level l and cij represents the cost for the crane running in the graph defined by arcs and nodes from I and J. Present is an integer Boolean programming problem (Tadei & Della Croce, 2022), with the decision variables xufrl and xij which can be assume only value 0 or 1: x xufrl = 1 if the ITU u is assigned to cell defined by line f, row r and level l; x xij =1 if the link ij, following defined, is in the optimal cycle for the crane. There are 2 sub-problems: x the reshuffles problem: to minimize the sum of costs associated to the rehandling; x the path optimization problem (to minimize the movements of the crane around the yard), adding any constraints about the sequence of positions to a classical TSP (following indicated TSP*). First sub-problem supplies the assigned positions in the stack to minimize the reshuffling costs, while the second supplies the sequence of operations for the crane (c ij represents the crane cost to run on the link ij) . Tufrl is a sum of 4 terms respectively representing: x the cost of the reshuffles generated to handle the ITUs stored underneath the ITU u and which have a smaller leaving time; x the cost of the reshuffles generated to stack the ITU u in the assigned cell, and caused by the limits on the climbing power (to access the assigned cell, could be needed to shift some ITUs already stacked); x the cost of the reshuffles generated to take off the ITU u leaving the IIT if the assigned position, due the limits on the climbing capability, needs to reshuffle some ITUs with a largest leaving time; x the cost of the reshuffles generated by taking the ITUs adjacent to the ITU u (located at the same level l) and with a smaller leaving time. These rehandles can be caused by limits on the climbing power. 3.3. Constraints Problem constraints can be grouped into two categories, each one related to one of the sub-problems. Reshuffles problem: xufrl  ^0,1` (2) x ufrl  x ufrl' 1u z u'; u, u'U (3) xufrl  xufrl' 1u z u'; u, u'U ; r ' r...r  d u (4) 1000 Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 Ld u ¦x 1u 1..U ; f 1..F ; l 1..L u frl (5) r 1 r d u U ¦ ¦x u f ' r 'l ' 1f ' f ; l' l 1 (6) u 1 r ' r d u min s u ' x uf ''r 'l ' d lu' z u; u, u'U ; r ' r..r 'd u ; f '1.. f ; l '1..l (7) Equation (2) impose that the variable xufrl can assume only integer values 0 or 1, (3) impose that only one ITU can be stored in a cell, (4) defines the space constraints (the assigned position must be able to contain the ITU). (5) is relative to the border positions (the ITU must be stored avoiding situation #4 in the Figure 3) , and (6) defines a safety constraint to avoid empty cells underneath the ITU u (no bridges or jumps). Constraints (7) aim to avoid the overlaps. Figure 3 shows the illegal position in the stack avoided by the constraints from (3) to (7). 1 Swap Body 2 Container 3 Container 4 Container Figure 3. Illegal positions in the stack: (1) overlap of a swap body or a semi-trailer; (2) bridge between two ITUs; (3) jump; (4) ITUs over the border of the stack. TSP* problem. The modified Traveling Salesman Problem is obtained by adding two constraints relative the sequence of operations from the pick-up point on the wagons (set of points I) and the drop-off points on the storage yard (set of points J) defining a complete graph. ¦x ij ( i , j )E (U ) d U  1U  N xij  ^0,1`i  I , j  J (8) (9) ¦x 0j  I (10) ¦x 0j  J (11) ¦x 0j  I (12) ¦x 0j  J (13) jJ jJ iI iI ij ij ij ij Then equations from (8) to (13 ) constitute the well known set of constraints of the TSP, while (12) and (13) are the added constraints which defines the TSP*. 4. The solving procedure based on the genetic algorithms The problem defined in paragraphs 2 and 3 is NP-hard and is an intractable highly combinatorial optimization problem (the problem is hard as much as the TSP* within it). Due to this, we propose an heuristic solving procedure Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 1001 based on a double string genetic algorithm integrated by a support algorithm able to estimate the number of reshuffles. The first population of solutions is generated by a guided procedure which foresees, for each ITU in U1, the assignment of a cell that is able to respect the constraints. The Chromosome represents the generic solution and is defined by a double integer string (top and down) simultaneously managed in each iteration (see figure 5). Genes sequence defines the handling order of the ITUs coded in the top string and stored in the stack cells coded in the down string. Chromosome structure allow to calculate the fitness value. Figure 4 illustrates an example of solution. 2015 3027 40556 56090 29054 6845 302 401 450 660 780 22 Figure 4. Example of double-string chromosome. The solution in figure 4 defines the following operations to stack for the six ITUs (in top string) simultaneously arriving by rail in the IIT: firstly to store ITU 2015 in the stack cell 302; secondly to store ITU 3027 in the stack cell 401 and so on. Mutation is based on the random variations of the assigned position (cell code) respecting the constraints and fixing the handling sequence. The choice of the modified genes is random. Crossover is performed with a two-point strategy with random choice of the cut points. To avoid the inadmissible solutions, a Sakawa and Kato (2003) idea has been developed and adapted to the problem. Fitness function coincides with the objective function. To evaluate the fitness we need to calculate the reshuffles costs and the crane paths. The first value is obtained by an algorithm, based on the concept expresses in the preceding paragraphs, accounting the effects of the dimension and leaving time for the ITUs and the limits on the climbing power for the cranes. Cost in the TSP* is calculated by an O/D matrix containing the minimum travel costs for the origin-destination couples in the sets I and J. 5. Computational results The algorithm has been implemented in a simple software developed in C++ language and the validation tests has demonstrated the capability of the procedure to reach a good solution for the stacking in more situations. As example, in a test in presence of storage yard with 32 row, 4 lines, 3 levels and 50 ITU already in the stack, the proposed allocation of a series of 25 ITU arriving with the same train in the terminal was found within 5 minutes 36 seconds using a Pentium IV 1,5 GHz . Table 1 shows the test conditions. Considering the dimensions of the 50 ITUs to already in the stack, the starting index of saturation of the stack is about the 40%. The analysis of the percentile of the dwell time, as in figure 5, allows to evidence that all the ITUs already in the stack leave the terminals not more of 212 days, while this parameter for the ITUs to be stacked is less than 150 days. Algorithm reaches 10.000 generations in 12’-33’’ and the total cost linked the allocation of the 25 ITUs on exams, as highlighted in Figure 6, can be reduced of about the 13% with respect the first solution. A preliminary estimation of the amount of the saving that can be allowed by the optimization procedure, can be conducted by introducing the prudential hypotheses of an average production cost of 5 Euro for a single handle and of an average number of 2,5 handles for each ITUs during the permanence in the terminal (25% of reshuffles). In the test case the total cost of handling the total 75 ITUs (50 already in the stack and 25 to be stacked) can be reduced of about 100 Euro. 1002 Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 Table 1. Test conditions ITUs already in stack ITUs to be stacked Number 50 25 Dimension 2 TEU: 26%; 1,5 TEU: 40%; 1 TEU: 34% 2 TEU: 12%; 1,5 TEU: 52%; 1 TEU: 26% Overlap index 2: 68%; 1: 12%; 0: 20% 2: 52%; 1: 28%; 0: 20% Dwell time [days] mean value 24,4 23,5 median 11 2 standard deviation 38,8 34,6 variance 1509 1200 Index of saturation Stack (average) Level 0 Level 1 Level 2 38% 70,3% 34,4% 9,3% Dwell time [days] 200 150 100 50 0 0 10 20 30 40 50 60 70 80 90 100 percentile ITUs already in stack ITUs to be stacked 100,00% 14,00% 99,00% 13,00% 98,00% 12,00% 97,00% 11,00% 96,00% 10,00% 95,00% 8,00% 93,00% 7,00% 92,00% 6,00% 91,00% 5,00% 90,00% generations Current Cost vs Initial cost Figure 6. Evolution of costs and savings (% with respect the first solution). Saving 9.600 10.000 9.200 8.800 8.400 8.000 7.600 7.200 6.800 6.400 6.000 5.600 5.200 4.800 4.400 4.000 3.600 3.200 2.800 2.400 0,00% 2.000 1,00% 85,00% 1.600 2,00% 86,00% 800 3,00% 87,00% 1.200 4,00% 88,00% 0 89,00% Saving 9,00% 94,00% 400 Current Costs Vs Initial Cost Figure 5. Dwell time percentiles Stefano Carrese and Luigi Tatarelli / Procedia Social and Behavioral Sciences 20 (2011) 994–1003 1003 6. Conclusions The proposed procedure aims to the rationalization of the handling operations through the reduction of the unproductive moves (moreover generated from an incorrect positioning of the ITU in the storage area). The procedure developed, even though calibrated and tested on a special operating case like a terminal for not accompanied inland combined transport, can be easily reused in the rationalization of the operations in a harbour container terminal, with the opportune modifications (moreover simplifier) on constraints and parameters. The choice to employ genetic algorithms has been dictated from a references analysis of the result of the applications to analogous problems and from the versatility and conceptual simplicity of their application. Further developments of the present research can be suggested: x elimination of the hypothesis of employment of a single crane for the movements, and therefore integration, in the procedure of calculation, of an algorithm for the resolution of the problem of allocation of the cranes to the several operations; x appraisal of the effects of the variability in the time of departure of the ITUs, by means of the introduction of probabilistic elements in the estimation of the associate values; x introduction of the possibility to vary the position of the ITUs already in dwell at the beginning of the operations of allocation of the ITUs in arrival; x introduction of the possibility to manage at the same time ITUs arriving and ITUs leaving the terminal. References De Castilho B., & Daganzo, C.F. (1993). Handling Strategies for Import Containers at Marine Terminals. Transportation Research Part B, 27 no. 2, 151-166. Freight Leaders Club (1999). Il trasporto Combinato delle merci. Quaderni FLC. 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