Baixe Container - Terminal - Operation - and - Operations - Research - A-Classification - and - Literature - Review e outras Notas de estudo em PDF para Cultura, somente na Docsity! DOI: 10.1007/s00291-003-0157-z OR Spectrum (2004) 26: 3–49 c© Springer-Verlag 2004 Container terminal operation and operations research – a classification and literature review Dirk Steenken1, Stefan Voß2, and Robert Stahlbock2 1 Hamburger Hafen- und Lagerhaus AG, IS – Information Systems/Equipment Control, Bei St. Annen 1, 20457 Hamburg, Germany (e-mail: steenken@hhla.de) 2 Institute of Information Systems (Wirtschaftsinformatik), University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany (e-mail: stefan.voss@uni-hamburg.de; stahlboc@econ.uni-hamburg.de) Abstract. In the last four decades the container as an essential part of a unit- load-concept has achieved undoubted importance in international sea freight trans- portation. With ever increasing containerization the number of seaport container terminals and competition among them have become quite remarkable. Opera- tions are nowadays unthinkable without effective and efficient use of information technology as well as appropriate optimization (operations research) methods. In this paper we describe and classify the main logistics processes and operations in container terminals and present a survey of methods for their optimization. Keywords: Container terminal – Logistics – Planning – Optimization – Heuristics – Simulation 1 Introduction/historical overview Containers came into the market for international conveyance of sea freight almost five decades ago. They may be regarded as well accepted and they continue to achieve even more acceptance due to the fact that containers are the foundation for a unit-load-concept. Containers are relatively uniform boxes whose contents do not have to be unpacked at each point of transfer. They have been designed for easy and fast handling of freight. Besides the advantages for the discharge and loading process, the standardization of metal boxes provides many advantages for the customers, as there are protections against weather and pilferage, and improved and simplified scheduling and controlling, resulting in a profitable physical flow of cargo. Regarding operations, we need to distinguish whether we refer just to a container (which in that sense is called a box) or we specify the type of container Correspondence to: S. Voß 4 D. Steenken et al. under consideration. The most common distinction refers to a so-called standard container as one which is twenty feet (20’) long, describing the length of a short container. Other containers are measured by means of these containers, i.e., in twenty feet equivalent units (TEU) (e.g., 40’ and 45’ containers represent 2 TEU). Additional properties of containers may be specified whenever appropriate (e.g., the weight or weight class of a container, the necessity of special handling for reefer containers or oversized containers). First regular sea container service began about 1961 with an international con- tainer service between the US East Coast and points in the Caribbean, Central and South America. The breakthrough after a slow start was achieved with large investments in specially designed ships, adapted seaport terminals with suitable equipment, and availability (purchase or leasing) of containers. A large number of container transshipments then led to economic efficiency and a rapidly growing market share. In this context, transshipment describes the transfer or change from one conveyance to another with a temporarily limited storage on the container yard. Today over 60 % of the world’s deep-sea general cargo is transported in con- tainers, whereas some routes, especially between economically strong and stable countries, are containerized up to 100 % [140,78]. An international containeriza- tion market analysis shows that in 1995 9.2 million TEU were in circulation. The container fleet had almost doubled in ten years from a size of 4.9 million TEU in 1985. Figure 1 shows the container turnover for the ten largest seaport terminals in the world from 1993 to 2002 [16,17,3,4,148]. Due to the positive forecast for con- H on g K on g S in ga po re B us an S ha ng ha i K ao hs iu ng S he nz he n* R ot te rd am Lo s A ng el es H am bu rg A nt w er p 1993 1995 1997 1999 2001 0 2 4 6 8 10 12 14 16 18 20 Million TEU * Shenzen: includes Yantian, Shekou & Chiwan Fig. 1. Container turnover of the ten largest seaport terminals in the world from 1993 to 2002 (ranking 2002) Container terminal operation and operations research 7 It should be noted that the quayside operation or container transshipment as well as the container movement to and from the wharf is sometimes also referred to as wa- terside transshipment process. Correspondingly, one may find the terms hinterland transshipment processes and landside transshipment processes. Different types of ships have to be served at the quayside. The most important ones are deep-sea vessels with a loading capacity of up to 8.000 container units (TEU) which serve the main ports of different countries and continents. Such vessels are about 320 m long with a breadth of 43 m and a draught of 13 m; on deck containers can be stowed 8 tiers high and 17 rows wide, in the hold 9 high and 15 wide. The ships’ data call for respective dimensions of the cranes’ height and jib length. Loading of about 2.000 boxes is common in large ports; the same is valid for unloading. Feeder vessels with a capacity of 100 to 1.200 TEU link smaller regional ports with the oversea ports delivering containers for deep-sea vessels. Inland barges are used to transport containers into the hinterland on rivers and channels. Functionally, barges are means of hinterland transportation (like trucks and trains), operationally they are ships which are served by quay cranes. Trucks have a capacity of up to three TEU. At container terminals they are directed to transfer points where they are loaded and unloaded. To serve trains, railway stations with several tracks may be part of container terminals. The capacity of one train is about 120 TEU. Shuttle trains connecting a terminal with one specific hinterland destination obtain increased importance. The modal split of hinterland transportation is very specific for different ports which has a direct impact on the terminals’ layout and type of equipment.3 The container storage area is usually separated into different stacks (or blocks) which are differentiated into rows, bays and tiers. Some stack areas are reserved for special containers like reefers which need electrical connection, dangerous goods, or overheight/overwidth containers which do not allow for normal stacking. Often stacks are separated into areas for export, import, special, and empty containers. Besides in these general functions some terminals differ also in their operational units. For example, if railway stations do not exist inside the terminal, containers have to be transported by trucks or other landside transportation means between the external station and the terminal. This results in additional logistic demands. Other differences occur if sheds exist within the terminal area. At sheds con- tainers are stuffed and stripped, and goods are stored. Additional movements have to be performed connecting the yard stacks with the sheds. The same applies to empty depots where empty containers are stored according to the needs of shipping lines. 3 The figures for Hamburg, Rotterdam, Hong Kong and Singapore illustrate this quite clearly (see, e.g., [184] for Rotterdam): Hamburg: about 47 % truck, 35 % feeder and 18 % rail; Rotterdam: about 50 % truck, 40 % feeder, 10 % rail; Hong Kong: more than 90 % truck, less than 10 % feeder, no rail; Singapore: 20 % truck, 80 % feeder, no rail. 8 D. Steenken et al. 2.1 Handling equipment Usually, container terminals are described very specifically with respect to their equipment and stacking facilities. From a logistic point of view, however, terminals only consist of two components: stocks and transport vehicles. The yard stacks, ships, trains, and trucks belong to the category ‘stock’. Stocks are statically defined by their ability to store containers while from a dynamic point of view a stowage (or loading) instruction is necessary defining the rules how and where containers have to be stored. There is no principal difference between these different types of stocks but only a difference in capacity and complexity. Routing and scheduling of ships, trains and trucks do not belong to container terminal operation. Therefore, they can be considered statically as storage entities whereas a stowage instruction exists in any case even for trucks where at least the position of the containers to be loaded has to be defined. For specific stowage, ships and trains need instructions defining the position for every container. Transport means either transport containers in two or three dimensions. Cranes and vehicles for horizontal transport belong to this category. Their logistical specifics are that transport jobs have to be allocated to the means of transport and sequences of jobs have to be performed. The calculation of sequences is typical for the transportation means and defines a principal difference to the stocks categorized above. Not looking for these identities but being fixed on the specifics of each component and equipment applied at container terminals results in a variety of operations research approaches and solutions. 2.1.1 Types of cranes. Concerning cranes, different types are used at container terminals. The quay (or gantry) cranes (Fig. 4a) for loading and unloading ships play a major role. Two types of quay cranes can be distinguished: single-trolley cranes and dual-trolley cranes. The trolleys travel along the arm of a crane and are equipped with spreaders, which are specific devices to pick up containers. Modern spreaders allow to move two 20’ containers simultaneously (twin-lift mode). Conventionally single-trolley cranes are engaged at container terminals. They move the containers from the ship to the shore either putting them on the quay or on a vehicle (and vice versa for the loading cycle). Single-trolley cranes are man-driven. Dual-trolley cranes represent a new development only applied at very few terminals. The main trolley moves the container from the ship to a platform while a second trolley picks up the container from the platform and moves it to the shore. The main trolley is man-driven while the second trolley is automatic. At modern cranes, the crane driver is supported by a semi-automatic steering system; this is both the case for one and two-trolley cranes. The maximum performance of quay cranes depends on the crane type. The technical performance of cranes is in the range of 50–60 boxes/h, while in operation the performance is in the range of 22–30 boxes/h. A second category of cranes is applied to stacks. There are three types of cranes, either rail mounted gantry cranes (RMG) or rubber tired gantries (RTG) and over- head bridge cranes (OBC). Rubber tired gantries are more flexible in operation while rail mounted gantries are more stable and overhead bridge cranes are mounted on Container terminal operation and operations research 9 a b Fig. 4a,b. Quay cranes and stacking crane. a Quay crane (here: dual-trolley cranes). b Stacking crane (here: Double-RMG) concrete or steel pillars. Commonly gantry cranes span up 8–12 rows and allow for stacking containers 4–10 high. To avoid operational interruption in case of technical failures and to increase productivity and reliability, two RMGs are often employed at one stack area (block). Containers which have to be transported from one side of the block to the other then have to be buffered in a transition area of the block. Double-RMG systems represent a new development. They consist of two RMGs of different height and width able to pass each other thus avoiding a handshake area (Fig. 4b). This results in a slightly higher productivity of the system. Although most of the gantry cranes are man-driven, the tendency is for automatic driverless gantry cranes which are in use at some terminals (e.g. Thamesport, Rotterdam, Hamburg). The technical performance of gantry cranes is approximately 20 moves/h. Similar cranes are used for loading and unloading trains. They span several rail tracks (about six). Containers to be transferred from/to trains are pre-stowed in a buffer area alongside the tracks. Forklifts and reachstackers are used to move and stack light containers – espe- cially empty ones. 2.1.2 Horizontal transport means. A variety of vehicles is employed for the hori- zontal transport both for the ship-to-shore transportation and the landside operation. The transport vehicles can be classified into two different types. Vehicles of the first class are ‘passive’ vehicles in a sense that they are not able to lift containers by themselves. Loading and unloading of these vehicles is done by cranes, either quay cranes or gantry cranes. Trucks with trailers, multi-trailers and automatic guided vehicles (AGV, Fig. 5a) belong to this class. AGVs are robotics able to drive on a road network which consists of electric wires or transponders in the ground to control the position of the AGVs. AGVs can either load one 40’/45’ container or two 20’ containers – in the latter case multiple load operation is possible. As AGV systems demand for high investment, they are only operated where labour costs are high; they are now in operation at ECT/Rotterdam and at the HHLA/Hamburg – in combination with automatic gantry cranes. 12 D. Steenken et al. Literature review General information about technical equipment for container terminals can be found in engineering oriented journals as well as specialized outlets (see, e.g., http://www.porttechnology.org/). For different types of cranes and their use see, e.g., [147,180]. Mobile vehicles or crane installations are also described in [127, 140,147]. A more general insight into transport vehicles or gantry cranes is pro- vided by, e.g., [127,140,106]. For a detailed overview of current state of the art handling technologies for terminal operations – like Automated Storage and Re- trieval Systems (AS/RS) or AGVs – see, e.g., [85,84,83]. The use of DGPS at a container terminal is reported in [179]. Embedding handling equipment into more general aspects of innovation management at container terminals is considered in [199]. An interesting comparison between different types of container terminals based on specific types of equipment is provided in [168]. The authors compare the waterside productivity in different scenarios for manually operated SCs, AGVs and ALVs in a system set with yard stacking cranes. In addition they provide cost estimates based on simulation studies. An overview of research on the potential of an integrated approach with usage of AS/RS and an AGV system is given in, e.g., [87,5,6]. Variations with different technical equipment – new in the field of container terminals – are shortly discussed. Effectiveness of such systems is compared with performance of current conven- tional systems by simulation experiments. For example, a ‘Grid on Rail’ concept is proposed: conventional container blocks are served by an overhead grid network of rails and a fleet of shuttle cranes moving on it. Effects are better space utiliza- tion by a more compact yard without necessity of roads between blocks and faster storage/retrieval operations than in conventional approaches with gantry cranes or straddle carriers. A pilot design is located in Hong Kong. Details about assisting systems (without any planning functionality) can be found, e.g., on the web pages of service companies. This also includes detailed handbooks for electronic data interchange (EDI and EDIFACT) or hints for con- tractual agreements (see, e.g., http://www.dakosy.de and [79]). 2.2 Container terminal systems A great variety of container terminals exists mainly depending on which type of handling equipment is combined to form a terminal system. All terminals use gantry cranes, either single- or dual-trolley, manual or semi-automatic. The transport be- tween quay and stack can be performed either by trucks with trailers, multi-trailers, AGVs or straddle carriers. These vehicles can also serve the landside operation – except AGVs which nowadays are exclusively engaged at the quayside. Container stacking is either performed by gantry cranes or by straddle carriers. Despite the variety of equipment combinations, two principal categories of terminals can be distinguished: pure straddle carrier systems and systems using gantry cranes for container storage. Container terminal operation and operations research 13 Terminals with gantry cranes for container storage apply any kind of transport vehicles mentioned above. Even mixed systems of transport vehicles occur; e.g., multi-trailers for the quayside and straddle carriers for the landside operation. Up to now AGV terminals only exist in combination with automatic gantry cranes. Trains are normally loaded and unloaded by gantry cranes even in case of straddle carrier terminals, although in some cases straddle carriers are also used for this purpose (see Fig. 6). Stack with RMG Quay Crane Trucks, Train Vessel Vehicles Quayside Landside Vehicles Fig. 6. Container terminal system (schematic side view, not true to size) The decision on which equipment is used at container terminals depends on several factors. Space restrictions, economical and historical reasons play an im- portant role. A basic factor is the dimension of the space which can be used for a terminal. If space is restricted, gantry cranes to store containers are preferred. A decision for AGVs and automated gantry cranes can be made in case of high labour costs and new terminal construction. Historical and cultural reasons have to be considered if container terminals are enhanced or modernized. Because space is becoming a scarce resource, a tendency for higher storage is to be foreseen. Besides the mentioned two main categories, common in Europe and Asia, a third type, quite often in North America, is an on-chassis system, in which containers are stored on chassis instead of being stacked on top of each other. This system lacks of special stacking cranes, has simpler stacking logistics and is more space demanding. Its logistic aspects are covered by the other two systems. Literature review Container terminal operations are becoming more and more important. Therefore, an ever increasing number of publications on container terminals have appeared in the literature. While we refer to most of them in the subsequent chapters, some deserve special mention due to some of their general perspectives. Decision problems at container terminals are comprehensively described by Vis and de Koster [196] (with some 55 references up to 2001). An overview of relevant literature for problem classes like arrival of the ship, (un)loading of a ship, 14 D. Steenken et al. transport of containers from/to ship to/from stack, stacking of containers, inter- terminal transport and complete terminals is provided. Kozan [112] discusses major factors for the transfer efficiency of multimodal container terminals. A network model reflecting the logistic structure of a terminal and the progress of containers is shown. Its objective is the minimization of the total throughput time as the sum of handling and travelling times of containers. Earlier work of the same author is [111]. Meersmans and Dekker [132] present an overview of the use of operations research models and methods in the field of design and operation of container terminals with its decision problems on strategic, tactical and operational level. Fung [50] presents a three-player oligopoly error-correction model for fore- casting demand for Hong Kong’s container handling services. Due to increasing demand and necessity of higher throughput, early construction of new terminals is suggested. Murty et al. [141] describe various interrelated complex decision problems occurring daily during operations at a container terminal. They work on decision support tools and discuss mathematical models and algorithms. Steenken [180] presents a comprehensive description of logistics and optimiza- tion systems in container terminals – shown by example of ‘Burchardkai’ (Ham- burg). For an early work on berth assignment and berth investment decisions see [45]. A general discussion of different productivity related objectives regarding transshipment terminals can be found, e.g., in [49,62]. Additional works giving more or less general descriptions of container terminals are, e.g., [34,130]. In [34] the authors view a container terminal as a production system that is represented as a network of complex substructures or platforms. The idea of platform capacity is used to represent operational aspects of a container terminal in a mathematical model for tactical planning. The problem is to allocate resources in each platform in order to minimize the total delay on the overall network and time horizon. Konings [108] presents a survey of the possibilities for an intermodal transport concept of high quality. Conditions for best development of centers, that integrate transshipment, storage, collection and distribution of goods, are outlined. The in- ternal transport system is identified as key element. The topic is discussed in detail for the harbour of Rotterdam. Nam and Ha [142] investigate aspects of adoption of advanced technologies such as intelligent planning systems, operation systems and automated handling systems for container terminals. They set criteria for evaluation of different handling systems and apply them to examples in Korea. Results show that automation does not always guarantee outperformance (e.g. higher productivity) – it depends on terminal characteristics such as labour costs. Four different types of automated container terminals are designed, analyzed and evaluated in a simulation model with very detailed cost considerations by Liu et al. [126]. The performance criteria that are used in this study to evaluate and compare different terminal systems are summarized as follows: Throughput: number of moves/hour/quay crane; throughput per acre; ship turnaround time: time it takes for a ship to get loaded/unloaded; truck turnaround time: average time it Container terminal operation and operations research 17 3.1 The ship planning process Ship planning consists of three partial processes: the berth planning, the stowage planning and the crane split. 3.1.1 Berth allocation. Before arrival of a ship, a berth has to be allocated to the ship. The schedules of large oversea vessels are known about one year in advance. They are transferred from the shipping lines to the terminal operator by means of EDI. Berth allocation ideally begins before the arrival of the first containers dedicated to this ship – on average two to three weeks before the ship’s arrival. Besides technical data of ships and quay cranes – not all quay cranes can be operated at all ships – other criteria like the ship’s length and the length of the crane jib have to be considered. All ships to be moored during the respective time period have to be reflected in berth allocation systems. Several objectives of optimized berth allocation exist. From a practical point of view the total sum of shore to yard distances for all containers to be loaded and unloaded should be minimized. This corresponds to maximum productivity of ship operation. Automatic and optimized berth allocation is especially important in case of ship delays because then a new berthing place has to be allocated to the ship whereas containers are already stacked in the yard. Literature review Berth planning problems may be formulated as different combinatorial optimiza- tion problems depending on the specific objectives and restrictions that have to be observed. As an example we mention the possibility to model berth planning by means of the resource constrained project scheduling problem. Restrictions may refer to special equipment that is needed for certain operations, as it is the case, e.g., for unavailability due to maintenance or for RoRo-ships5 where tractor trailers need to drive into the ship. Connections of berth planning to assignment problems and especially to the quadratic semi-assignment problem are emphasized in [75]. Due to the large interdependency, berth and yard planning are frequently considered in a common optimization model [54,19,183]. Li et al. [120] discuss the more general problem of ‘scheduling with multiple- job-on-one-processor pattern’ with the goal of minimizing the makespan of the schedule. Vessels can represent jobs, a processor can be interpreted as a berth. Computational experiments show the effectiveness of a heuristic method with near- optimal results. Lim [122] reformulates the problem as a restricted form of the two-dimen- sional packing problem and explores a graph theoretical representation. For this reformulation it is shown that this specific berth planning problem is NP-complete. An effective heuristic algorithm for solving the problem – applied to historical test data – is proposed. 5 A RoRo-ship is a Roll-On Roll-Off ship, i.e., transport vehicles can enter the ship via a stern ramp. 18 D. Steenken et al. Legato and Mazza [117] present a queuing network model and a simulation experiment of the logistic processes (arrival, berthing and departure of vessels) at a container terminal. Nishimura et al. [146] focus on the problem of dynamic berth assignment to ships in the public berth system (not especially container ports; it is emphasized that these systems and, therefore, the shown results ‘may not be suitable for most container ports of major countries’). A heuristic procedure, based on a genetic algorithm (GA), is developed – ‘adaptable to real world applications’. Similar to [146], Imai et al. [81] study berth allocation and optimization of berth utilization using a heuristic procedure, which is based on a mixed-integer program- ming (MIP) formulation of static and dynamic versions of the allocation problem and its Lagrangian relaxation. The same authors develop a GA-based heuristic procedure for solving the nonlinear problem of berth allocation for vessels with different service priorities [82]. Imai et al. [80] relate berth allocation to machine scheduling problems and discuss a bi-objective nonlinear optimization problem considering ship waiting times and terminal utilization. Based on [136], Kim and Moon [98] formulate a MIP-model for determining berthing times and positions of vessels in container ports with straight-line shaped berths. They develop a simulated annealing (SA) algorithm and show near-optimal results. Guan and Cheung [60] propose a tree-search procedure and composite heuristics for large size problems in order to minimize total weighted flow time. Efficiency of the methods is shown by computational experiments. Park and Kim [154] combine a berth assignment approach with consideration of quay crane capacities. Additional references dealing with berth planning are, e.g., [115,61,153]. 3.1.2 Stowage planning. Stowage planning is the core of ship planning. Planning a ship’s stowage is a two-step process. The first step is executed by the shipping line. The shipping line’s stowage plan has to be designed for all ports of a vessel’s rotation. The positions for all containers and all ports of a rotation have to be selected within the ship. Stowage planning of a shipping line usually does not act with specific containers identified by numbers, but on categories of containers. These categories or attributes are: the length or type of a container, the discharge port and the weight or weight-class of containers. Containers of these attributes are assigned to specific positions within the ship. The objective of optimization from the shipping line’s point of view is to minimize the number of shifts during port operation (ship to ship or ship to shore shifts) and to maximize the ship’s utilization. Constraints to be satisfied mainly result from the stability of the ship. The stowage plan of the shipping line is transferred to the terminal operator by EDI. The stowage instruction of the shipping line is filed into the terminal’s system and serves as a working instruction or pre-plan for the terminal’s ship planner. The stowage instruction of the shipping line is characterized by the assignment of con- tainers of special attribute sets to ship slots. Based on this instruction the terminal planner then assigns dedicated containers identified by numbers to the respective slots. The attribute set of the slot and the container selected in the yard have to Container terminal operation and operations research 19 match. The stowage planning systems of a container terminal, therefore, display both the ship’s sections to be planned and the yard situation. Some of the systems allow for automatic assignment and optimization. Different objectives of optimiza- tion are possible, e.g., maximization of crane productivity, cost minimization, or minimization of yard reshuffles. From a practical point of view the minimization of yard reshuffles plays an important role. Reshuffles occur when a container has to be accessed while others on top of it have to be removed first. Reshuffling consumes time which is an offset to the transportation time between stack and shore reducing the productivity of ship operation. Because the stowage plan is generated before the ship’s loading has started, this kind of optimization is offline optimization. Although stowage planning in real terminal operation is either a manual or an offline optimization process, the process structure of ship loading applies for online optimization. This is because the loading process and the stack-to-shore transport are more complex than yet described. To achieve a high productivity for the crane operation containers have to arrive at the quay in the right time and in the order of the loading sequence; i.e., loading sequence and sequence of horizontal transport have to correspond with each other. Otherwise crane waiting times and/or queuing of transport vehicles occur. Both reduce crane productivity and extend the ship’s berthing time. As a common feature, containers are more or less spread in the yard and have different distances to the crane; special containers like overheight containers need special equipment which has to be mounted before they can be transported, reefer containers have to be disconnected from the electrical circuit, and yard reshuffles occur to a respective percentage. All this consumes additional transportation time. In manually driven systems the performance additionally de- pends on the driver’s skill and decision which path he travels. Even technical or operational disturbances of the crane operation occur which enforce to change the loading sequence. Therefore, transportation times cannot be calculated exactly even if automated equipment is in use. All reasons together mean that the stowage plan prepared in advance can be sub-optimal. Online stowage planning is a solution to omit or at least reduce these problems. In online stowage planning a stowage plan which assigns specific containers to ship positions is no longer prepared. Instead containers are selected for transportation according to the attributes assigned to ship positions in the stowage instruction of the shipping line. Containers with the same attributes are considered as equal. They are then loaded according to their arrival time at the quay crane. Thus the specific stowage plan addressing specific container data to specific ship positions is generated simultaneously to the loading activity. Online stowage planning is not yet in use at container terminals but is a future need to enhance the performance of ship loading. Literature review In practice, stowage planning usually is a manual or offline optimization process using respective decision support systems (see, e.g., [176]). Most of the papers below describe research work applicable to enhance existing systems by appropriate optimization functionality. Container data are assumed to be given, i.e., we do not consider the problem of loading containers (see, e.g., [26,33,171,47]). 22 D. Steenken et al. Peterkofsky and Daganzo [155] study a branch and bound method for minimiz- ing delay costs. Exact solutions for problems described in [32] are given in order to speed up the time-intensive and, therefore, cost-intensive (un)loading process. Gambardella et al. [52] present a solution for the hierarchical problems of resource allocation – namely the allocation of quay cranes for (un)loading vessels and yard cranes for stack operations – and scheduling of equipment (i.e. (un)loading lists for each crane). Simulation results show reduction of equipment conflicts and of waiting times for truck queues. (See also related earlier papers of members of the same group of authors: [54,129,210,166,165,53].) The crane split as part of an integrated stowage and transport planning problem is discussed in [204,182] as mentioned in Section 3.1.2. Bish [12] develops a heuristic method for minimizing the maximum turnaround time of a set of ships in the so called ‘multiple-crane-constrained vehicle scheduling and location problem (MVSL)’. The problem is threefold: determination of a stor- age location in the yard for unloaded containers, dispatching vehicles to containers and scheduling of (un)loading operations to cranes. Park and Kim [154] discuss an integer programming model for scheduling berth and quay cranes and propose a two-phase solution procedure. A first near-optimal solution for finding a berth place and time for each vessel and assigning the number of cranes is refined by a detailed schedule for each quay crane. 3.2 Storage and stacking logistics Stacking logistics has become a field of increasing importance because more and more containers have to be stored in ports as container traffic grows continuously and space is becoming a scarce resource. Generally containers are stacked on the ground in several levels or tiers and the whole storage area is separated into blocks. A container’s position in the storage area (or yard) is then addressed by the block, the bay, the row and the tier. The maximum number of tiers depends on the stacking equipment, either straddle carriers or gantry cranes. According to operational needs the storage area is commonly separated into different areas. There are different areas for import and export containers, special areas for reefer, dangerous goods or damaged containers. The average daily yard utilization of large container terminals in Europe is about 15.000–20.000 containers resulting in about 15.000 movements per day. The dwell time of containers in the yard is in the range of 3–5 days at an average. A storage planning or stacking decision system has to decide which block and slot has to be selected for a container to be stored. Because containers are piled up, not every one is in direct access to the stacking equipment. Containers that are placed on top of the required one have to be removed first. Reshuffles (or rehandles) may occur due to several reasons; the most important ones result if data of containers to be stacked are wrong or incomplete. At European terminals 30–40 % of the export containers arrive at the terminal lacking accurate data for the respective vessel, the discharge port, or container weight – data which are necessary to make a good storage decision. Even after arrival, vessel and discharge port can be changed by the shipping line. For import containers unloaded from ships the situation is even Container terminal operation and operations research 23 worse: the landside transport mode is known in at most 10–15 % of all cases at the time of unloading a ship, e.g., when a location has to be selected in the yard. To ease the situation and to ensure a high performance of ship, train and truck operation, containers sometimes are pre-stowed near to the loading place and in such an order that it fits the loading sequence. This is done after the stowage plan is finished and before ship loading starts. Because pre-stowage needs extra trans- portation, it is cost extensive and terminals normally try to avoid it by optimizing the yard stacking, but it is executed when ship loading has to be as fast as possible. Storage and stacking logistics are becoming more complex and sophisticated; they play an important role for the terminals’ overall performance. Two classes of storage logistics can be distinguished. In storage or yard planning systems, stack areas and storage capacities are allocated to a ship’s arrival in advance according to the number of import and export containers expected. An appropriate number of slots in blocks and rows are reserved for a special ship. Depending on the planning strategy, the reservation for export containers can be split for discharge port, container type/length, and container weight. A common strategy for export planning is to reserve slots within a row for containers of the same type and discharge port while heavier containers are stacked on lighter ones assuming that they are loaded first because of the ship stability. For import containers only a reservation of yard capacity of respective size is done without further differentiation. This is because data and transport means of delivery generally are unknown at the time of discharge. If the transport mode is known, import areas can be subdivided according to them. Common strategies for import containers are either selecting any location in the import area or piling containers of the same storage date. Yard or storage planning seldom matches the real delivery because container delivery is a stochastic process not exactly to be foreseen. The quality of this yard concept mainly depends on the strategy how to determine a good stack configuration and a good forecast of the container delivery distribution. Both factors are hard to solve, the result is a comparatively high amount of yard reshuffles. In addition, the reservation of yard locations occupies stack capacity. Because of these disadvantages some terminals installed an alternative stacking concept, called scattered stacking. In scattered stacking, yard areas are no longer assigned to a specific ship’s arrival but only once to a berthing place. On arrival of a container the computer system selects the berthing place of the ship from the ships schedule and automatically searches for a good stack location within the area assigned to the berth. A stack position is selected in real-time and containers with the same categories – ship, type/length, discharge port, and weight – are piled up one on top of the other. Containers for one ship are stochastically scattered over the respective stack area; reservation of yard slots is no longer necessary. This concept results in a higher yard utilization – because no slots are reserved – and a remarkable lower amount of reshuffles – because the stacking criteria merge the ship’s stowage criteria. Although the container attributes play a major role in yard stacking concepts, additional parameters have to be taken into account for improving logistic pro- cesses. Evidently, containers have to be stacked near to the future loading place, e.g., the transport distance should be minimal to ensure a high performance of the 24 D. Steenken et al. future operation. The performance of quay cranes is a multitude higher than the per- formance of stacking and transport equipment. Therefore, containers with the same categories have to be distributed over several blocks and rows to avoid congestions and unnecessary waiting times of vehicles. The actual workload of a gantry crane or other stacking equipment also has to be considered because allocating additional jobs to highly utilized equipment provokes waiting times. All these factors can be integrated into an algorithm while the weight of each factor is measured by param- eters. The objective of yard optimization is to minimize the number of reshuffles and to maximize the storage utilization. Literature review Cao and Uebe [22] propose a tabu search based algorithm for solving the trans- portation problem with nonlinear side constraints – a general form of the problem of assignment of storage positions for containers with minimized searching and/or loading costs and satisfaction of limited space and other constraints. Kim [89] investigates various stack configurations and their influence on ex- pected number of rehandles in a scenario of loading import containers onto outside trucks with a single transfer crane. For easy estimation regression equations are proposed. Kim and Bae [90] propose a methodology to convert a current order of export containers in the yard into a bay layout which is best from the point of view of operations for loading a vessel. The goal is to find the fewest possible number of containers and/or shortest possible travel distance in order to minimize the total turn-around time of a vessel in a port. The problem is decomposed, mathematical models (dynamic programming, transportation problem) for the three subproblems are suggested, and a numerical example is given. The authors demand heuristic algorithms due to time consuming computations. Kim and Kim [92–94] discuss the determination of optimal amount of storage space and optimal number of transfer cranes for import containers. The decision is based on a cost model including fixed investment costs and variable operation costs. A simple solution procedure and sensitivity analysis is illustrated with a numerical example. Two different objectives are considered: minimization of the costs of only the terminal operator and minimization of these costs combined with the costs of the customers. Deterministic and stochastic models and simple solution methods are provided and illustrated using numerical examples. In [93] the authors focus on strategies for storage space allocation. Cases with constant, cyclic and dynamic arrival rates of import containers are analyzed. The objective is minimization of the expected total number of rehandles. Mathematical models and solution procedures are shown and illustrated by numerical examples. Kim et al. [100] formulate a dynamic programming model for determination of the storage location of export containers in order to minimize the number of reshuffles expected for loading movements. The configuration of the container stack, the weight distribution of containers in the yard, and the weight of an arriving container are considered. For real-time decisions a fast decision tree is derived from the set of optimal solutions provided by dynamic programming. Container terminal operation and operations research 27 load mode is possible. Multiple load for AGVs contains potential for optimization, but it rarely occurs in practice because it is hard to organize. If unmanned equipment like AGVs or ALVs for transportation and automated gantry cranes for stacking are used, a main task of the control system is to synchronize the equipment in a way that the containers arrive ‘in-time’ at the interfaces (of the equipment such as, e.g., cranes and AGVs) and the idle times (of the cranes) are minimized. Ship operation in practice is dynamic and, therefore, demands online optimiza- tion. For import containers, e.g., the precise yard location cannot be selected before the container is unloaded and its data and condition is physically checked. Distur- bances occurring during ship operation often force to alter the loading or unload- ing sequence immediately. Such disturbances are: interruption of crane operation because of operational or technical problems, change of (un)loading sequences de- cided by the crane driver because of ship stability reasons or problems occurring during the horizontal transport. Such reasons force (re)calculating sequences only for few containers. The objective of optimization in any case is to minimize the lateness of container deliveries for the cranes and the travel times of the transport vehicles. Literature review A literature review regarding quayside transport is almost a dime a dozen and may be distinguished mainly based on the means of transport, i.e., AGVs, straddle carriers, etc. Even within the first category (AGVs) the number of references is enormous as AGVs are commonly used in warehouse operations and flexible manufacturing systems (see, e.g., [162] for a survey). In the sequel we first provide a wealth of references regarding AGVs before we are considering other means of transport. Evers and Koppers [48] focus on movements of AGVs over the physical in- frastructure with their model of an AGV traffic control system and the so-called semaphore technique. Bruno et al. [18] focus on the control problem of dynamic determination of waiting positions for idle AGVs in order to reach good overall performance of the system (the paper deals with general material handling systems). Two fast effective heuristic algorithms are discussed and tested in real-world scenarios. The shown approach (without taking into account any information about future events) has better results than the traditional point-of-release-positioning rule. Gademann and van de Velde [51] determine the waiting locations for idle AGVs in a loop layout with uni- or bidirectional flow system. The problem is restricted to a static setting, in which all AGVs are assumed to be idle at the same time. Objective functions are functions of travel times from the nearest waiting location of an AGV to a pickup point. Wallace [200] presents an agent based AGV controller in order to provide effective flow even in complex designs. Agents allow AGVs to allocate only small possible segments or points on their paths. The agent approaches are tested in computational experiments with two layouts and are compared with an ‘AutoMod’ simulation. Results show higher efficiency without any deadlock situation. 28 D. Steenken et al. Van der Heijden et al. [72] develop rules for management of empty AGVs in (general) automated transportation systems. Their performance (in terms of service levels, AGV requirements and empty travel distances) is evaluated by simulation. Look-ahead rules outperform the simple first-come-first-served rule. Leong [119] develops an efficient dynamic deployment algorithm scheme for AGVs, that dispatches AGVs to containers in order to minimize the (un)loading time for a vessel. A deadlock prediction and avoidance algorithm – developed in [137] and also discussed later in [138] – is integrated. The new scheme is compared with the current scheme (used at a terminal in Singapore) in a simulation experiment. Analysis of results shows improvements, since the throughput is increased by the new scheme. In a similar paper concerning the same project as in [119], Chan [25] models a network flow in order to develop an efficient dispatching strategy for AGVs. Constraints describe disparate instances of AGVs carrying one container or two containers. The performance of the proposed heuristic algorithms is tested and – in case of single load – compared with the current deployment strategy, that is outperformed by the new one. Reveliotis [164] proposes a robust conflict resolution strategy for flexible ope- rations on arbitrarily structured path networks. A dynamic closed-loop control scheme is developed, which organizes dispatching and routing of AGVs on basis of real-time feedback on the system traffic. Although the paper does not focus on automated container terminals, results may be transferred to this field. Qiu and Hsu [158–161] address scheduling and routing problems for AGVs. They develop conflict-free routing algorithms for two different path topologies and two scheduling strategies. The methods are applied together in a case study. Qiu et al. [162] provide a survey of scheduling and routing algorithms for AGVs. They show similarities and differences between scheduling and routing of AGVs and related problems like the vehicle routing problem, the shortest path prob- lem, scheduling problems or others. They classify algorithms in groups for general path topology (static/time-window based/dynamic methods), for path optimization (0-1-integer-programming model, intersection graph method, integer LP model), for specific path topologies (linear/loop/mesh topology) and dedicated scheduling algorithms. Grunow et al. [58,59] focus on dispatching multi-load AGVs. A flexible priority rule based approach is proposed and compared to an alternative MIP formulation in different scenarios. Reduction of AGVs’ lateness in case of multi-load mode is shown and an improvement of the terminal’s overall performance is expected. In addition, a MIP is developed that allows determining optimal solutions for small problem instances. For real applications a hybrid approach using the MIP combined with fast heuristics on some special dispatching requests is suggested. A different MIP formulation can be found in [172]. Hanafi et al. [67] extend the simple multi-load case to the following problem related to container terminal logistics. Given a pool of containers, the container assignment problem consists of determining on which barges containers have to be loaded to minimize the total number of barges used while satisfying a number of Container terminal operation and operations research 29 side constraints. Different models and methods are compared on data provided by the Port of Lille. Hartmann [68] develops a general scheduling model consisting of assignment of jobs to resources and (temporal) arrangement of the jobs with consideration of constraints. This model can be applied for scheduling of AGVs, straddle carriers, gantry cranes and even workers. A heuristic method based on priority rules and a GA for solving the problem are discussed and compared in a computational experiment, that shows promising results for the GA. Yang et al. [207] analyze an increase of terminal productivity due to using ALVs rather than AGVs – based on the observation of unproductive and costly waiting of AGVs under quay cranes and in the blocks compared to that of ALVs. By means of a simulation model it is demonstrated, ‘that the ALV is superior to the AGV in both productivity and economical efficiency principally because the ALV eliminates the waiting time in the buffer zone’. Similar findings are reported by [195]. Lim et al. [123] do not especially focus on container terminals, but suggest an auction algorithm as dispatching method for AGVs in a general context. The method implements a distributed decision process with communication among related ve- hicles and machines for matching multiple tasks with multiple vehicles. Future events are taken into account as well. Outperformance is shown by a simulation study. Ulusoy et al. [188] address the problem of simultaneous scheduling of machines and a number of identical AGVs in a flexible manufacturing system in order to minimize the makespan. The discussed ideas and the GA may be transferred to problems arising at container terminals, especially the simultaneous scheduling of RMGs and AGVs. Routing of straddle carriers for loading export containers is discussed by Kim and Kim [96]. The objective is the minimization of total travel distance of straddle carriers in the yard. The routing problem is composed of the container allocation problem – formulated as a transportation problem – and a carrier routing problem with given sequence of yard-bays to be visited by a carrier. The routing problem is solved by a beam search algorithm, that is evaluated in numerical tests. In [103] the number of containers picked up by a straddle carrier at each bay and the se- quence of bay visits are determined in order to minimize total travel distance/time of the carrier. The proposed integer programming model is solved by a two-phase procedure. Sequencing of individual containers is not studied. Böse et al. [15] investigate different dispatching strategies for straddle carriers to gantry cranes in order to reduce vessel’s turnaround time at port by maximizing productivity of gantry cranes achieved by an efficient schedule of given straddle carriers. The potential of evolutionary algorithms for solving the considered allo- cation problem is shown in computational experiments based on real data (without taking stochastic influence into account). Different vehicle assignment strategies are suggested. The first approach suspends the static binding of carriers to gantry cranes using a dynamic strategy where a predetermined number of carriers perform container transports for several gantry cranes (straddle carrier pooling). Depending on the number of loading and discharging processes (structure of the waterside transshipment process), the carriers can be used in a double-cycle mode such that 32 D. Steenken et al. In general these kinds of transports are not as time critical as those for the ship or truck operation. Therefore, terminals try to execute them at times of less workload. The objective is to minimize empty and loaded travel times. Literature review Powell and Carvalho [156] propose a dynamic model for real-time optimization of the flow of flatcars considering constraints for assignment of trailers and containers to a flatcar. A smaller flatcar fleet is possible due to useful information for decision makers provided by the developed global logistics queueing network model. Steenken [178] investigates methods to optimize the straddle carrier operation at the truck working area. The problem of assigning jobs to straddle carriers is solved with linear assignment procedures combining movements for export und import containers. Steenken et al. [181] deal with the optimization for the rail operation and internal moves. Different algorithmic approaches are used to solve the routing problems, as they can be found in machine scheduling, for solving the travelling salesman problem, the rural postman problem, etc. Both solutions were implemented in a real time environment and resulted in considerable gains of productivity. Results and architecture of implementation are presented in [180]. Kim et al. [97] discuss approaches and decision rules for sequencing pickup and delivery operations for yard cranes and outside trucks, respectively. Their goal is to maximize the service level of trucks by minimizing the turnaround time of them, both for automated and conventional terminals. A dynamic programming model for a static case (all arrivals of trucks are known in advance) is suggested. For a dynamic case (new trucks arrive continuously) a learning-based method for deriving decision rules is proposed besides several heuristic rules. The performances of the methods are compared in a simulation study. The rule of serving the truck with the shortest transfer time (sum of travel time and time for transferring the corresponding container to and from the truck, including occurring rehandling time) shows good, robust performance in various situations, whereas the learned rules outperformed other methods in case of non-uniform distribution of containers’ arrival locations. The authors conclude that their single crane based approaches can be extended to the multiple crane case. Koo et al. [109] present a two-phase fleet sizing and vehicle routing procedure for container ports with several yards. The goal is to find the smallest required fleet size and a route for each vehicle to fulfill all transportation requirements within a static planning horizon. A computational study shows solutions of good quality in comparison with two other existing methods. 3.3.3 Crane transport optimization. Another field of application of optimization methods are the transports of gantry cranes operating in stacks. The transport re- quirements do not differ from those of the horizontal transport described above. Sequences of jobs have to be calculated and jobs have to be assigned to the re- spective crane. Commonly the location of a container to be positioned in the stack is calculated by the yard module. This is also true for the containers which have Container terminal operation and operations research 33 to be reshuffled. Therefore, transport optimization for stack cranes reduces to the same requirements as for the horizontal transport and comparative algorithms can be applied. Priority of jobs have to be taken into account – as is the case for the horizontal transport. The objective of optimization is to minimize the waiting times of the transport vehicles at the stack interfaces and the travel times of the stacking cranes. Because the traffic at the interfaces changes rapidly online optimization is demanded for and job sequences have to be recalculated whenever a new job arises. Literature review Due to interdependencies of crane operations and quayside, landside and stack operations, references regarding crane transport optimization may be reviewed in either section as we have done above; see, e.g., [155,92–94,12,97]. Kim and Kim [102] present a routing algorithm for a single gantry crane loading export containers out of the stack onto waiting vehicles. The objective is to minimize the crane’s total transfer time including set-up and travel times. The model’s solution determines the sequence of bay visits for pick-up operations and the number of containers to be picked up at each bay simultaneously. The developed algorithm is named ‘efficient’ and shows solutions to problems of practical size ‘within seconds’. In a more detailed paper [95] the same algorithm is used for solving the MIP of a ‘practical problem of a moderate size’. The load sequence of individual containers within a specific bay remains undetermined. Kim and Kim [104] extend their problem shown in [102] and [95] to general yard-side equipment, such as gantry cranes or straddle carriers. Experiments show that the proposed beam search algorithm outperforms a GA. The pick-up sequence for individual containers in a bay remains undetermined as in [95]. Lin [124] deals with the problem of scheduling movements of RTGs among different storage blocks in order to balance the workload and minimize the total unfinished workload at the end of each time period. The complexity of the MIP is analyzed. Besides the Lagrangian decomposition solution procedure, a new ap- proach (‘successive piecewise-linear approximation’) is discussed. This solution method can be applied to large size problem instances since computational experi- ments show efficiency and effectiveness. The same results are published later by Cheung et al. [30]. Narasimhan and Palekar [144] consider the minimization of a yard gantry crane’s handling time for executing a given load plan with a given bay plan for export containers. An exact branch-and-bound based algorithm and a heuristic method are developed and tested by computational experiments on randomly gen- erated problem instances. Besides the algorithmic approaches the authors provide a mathematical programming formulation and also consider some complexity issues. Zhang et al. [212] describe the dynamic RTG deployment problem with fore- casted workload per block per planning period (4 hours). The objective is to find times and routes of RTG movements among blocks with minimization of total de- layed workload in the yard. For safety reasons a maximum of two RTGs per block is allowed. Only one transfer of a RTG in and out of a block can occur. The problem 34 D. Steenken et al. is formulated as a MIP model and is solved by a modified Lagrangian relaxation with excellent results. A similar group of authors [125] solve this RTG deployment problem in a different way. The size of the problem is reduced by sorting blocks into categories like ‘sink block’ (needs and can take additional help), ‘source block’ (can spend capacity of RTGs) and ‘neither block’ (needs help but cannot take help, because two RTGs currently work in the block, or it does not need help). Neither blocks are excluded in the model. A pre-sort step identifies eligible RTGs and sink blocks, a following deployment step (formulated as MIP model) results in the optimal RTGs’ deployment plan for source and sink blocks. The approach is tested with a set of real operation data (Hong Kong). Results demonstrate ‘an excellent capability and potential of the model in minimizing the crane workload overflow’. Routing and/or scheduling algorithms for multiple cranes are hardly addressed in literature. A simulation study on operational rules for Double-RMGs is shortly discussed by Kim et al. [101]. Crane dispatching rules with and without different roles for the different cranes and sequencing roles are tested. A second simulation study focuses on determining the storage location of arriving containers. In [46] we consider the case of Double-RMGs and develop possible solution approaches for specific sequencing and scheduling problems in order to take ad- vantage of using two cranes – which can overtake each other – instead of one crane and increase the terminal’s throughput. 3.4 Simulation systems In recent years, simulation has become an important tool to improve terminal oper- ation and performance. Three types of simulation can be distinguished: strategical, operational and tactical simulation. Strategical simulation is applied to study and compare different types of ter- minal layout and handling equipment in respect to efficiency and costs expected. It is mainly used if new terminals are planned or the layout or the equipment of existing terminals has to be altered. Strategical simulation systems allow for easy design of different terminal layouts and employment of different types of handling equipment. The chief goal of strategical simulation is to decide on terminal layout and handling equipment which promises high performance and low costs. To match reality, simulation systems allow to design realistic scenarios or to import data of existing terminals. Operational simulation is applied to test different kinds of terminal logistics and optimization methods. It has achieved growing acceptance at least at large terminals. Terminal operation and logistics at large terminals are already very complex and the effect of alternative logistics or optimization methods has to be tested with objective methods. Therefore, optimization methods are tested in a simulation environment before they are implemented in real terminal control and steering systems. Tactical simulation means integration of simulation systems into the terminal’s operation system. Variants of operation shall be simulated parallel to the operation and advices for handling alternatives shall be given especially if disturbances occur in real operation. Real data of operation then have to be imported and analyzed Container terminal operation and operations research 37 handshaking. Thus not all sources of optimization are exploited, but high perform- ing operations ask for it. An example shall be given which explains the problem: A solution for the crane split can allow that two (or more) cranes operate very close together at a ship. This can be optimal for the crane operation, but it will not be for the horizontal transport because then the cranes are not easily accessible by the vehicles and congestions are provoked. An integrated optimization of both the crane split and the horizontal transport is demanded for. Similar problems can be found for every transport or stowage process at container terminals. Up to now there are only a few studies on such ‘integrated problems’ – e.g., in [134] or in [74,73], presenting a multi-agent system approach with several agents (agents for ship, berth, yard, and gate and utility agents for quay crane, gantry crane and transport) – although they are important for enhanced terminal performance. Therefore, ‘integrated optimization’ should be a field of increased investigation. Besides the major research needs regarding the topics online optimization as well as integration, additional topics may become important. Operations research approaches for container terminals usually apply simulation when it comes to con- sideration of stochasticity. However, the area of stochastic optimization and sce- nario based planning may be applied, too. For instance, vehicle routing problems with time windows and stochastic travel times or with stochastic customers (see, e.g., [206,11]) may be important areas worth considering for container terminal operations. 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