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文献出处：Bierwirth, Christian, and Frank Meisel. \follow-up survey of berth allocation and quay crane scheduling problems in container terminals.\European Journal of Operational Research (2014).

原文

A follow-up survey of berth allocation and quay crane

scheduling problems in container terminals

Bierwirth；Christian；Meisel.

Berth allocation problems Scope and classification scheme

In berth allocation problems, we are given a berth layout together with a set of vessels that have to be served within a planning horizon. The vessels must be moored within the boundaries of the quay and cannot occupy the same quay space at a time. In the basic optimization problem, berthing positions and berthing times have to be assigned to all vessels, such that a given objective function is optimized. A variety of optimization models for berth allocation have been proposed in the literature to capture real features of practical problems. In Bierwirth and Meisel (2010), we have proposed a scheme for classifying such models according to four attributes, namely a spatial attribute, a temporal attribute, a handling time attribute, and the performance measure addressed in the optimization. The values each attribute can take are listed in Fig. 1

2.1.1. Spatial attribute

This attribute concerns the berth layout, which is either a discrete layout (disc), a continuous layout (cont), or a hybrid layout (hybr). In case of disc, the quay is partitioned into berths and only one vessel can be served at each single berth at a time. In case of cont, vessels can berth at arbitrary positions within the boundaries of the quay. Finally, in case hybr, the quay is partitioned into berths, but vessels may share a berth or one vessel may occupy more than one berth. A particular form of a hybrid berth is an indented berth where large vessels can be served from two oppositely located berths. The spatial attribute is extended by item draft, if the BAP-approach additionally considers a vessel’s draft when deciding on its berthing position. 2.1.2. Temporal attribute

This attribute describes the arrival process of vessels. The attribute reflects static arrivals (stat), dynamic arrivals (dyn), cyclic arrivals (cycl), and stochastic arrival times (stoch). In case of stat, we assume that all vessels have arrived at the port and wait for being served. In contrast, in case of dyn, the vessels arrive at individual but deterministic arrival times imposing a constraint for the berth allocation. In case cycl, the vessels call at terminals repeatedly in fixed time intervals according to their liner schedules. In case stoch, the arrival times of vessels are stochastic parameters either defined by continuous random distributions or by scenarios with discrete probability of occurrence. Cyclic and stochastic arrival times are considered in a number of recent publications and, therefore, we have extended the original classification scheme with regard to these cases. The temporal attribute is completed by value due, if a due date

is preset for the departure of a vessel or if a maximum waiting time is preset for a vessel before the service has to start. Temporal attribute

This attribute describes the arrival process of vessels. The attribute reflects static arrivals (stat), dynamic arrivals (dyn), cyclic arrivals (cycl), and stochastic arrival times (stoch). In case of stat, we assume that all vessels have arrived at the port and wait for being served. In contrast, in case of dyn, the vessels arrive at individual but deterministic arrival times imposing a constraint for the berth allocation. In case cycl, the vessels call at terminals repeatedly in fixed time intervals according to their liner schedules. In case stoch, the arrival times of vessels are stochastic parameters either defined by continuous random distributions or by scenarios with discrete probability of occurrence. Cyclic and stochastic arrival times are considered in a number of recent publications and, therefore, we have extended the original classification scheme with regard to these cases. The temporal attribute is completed by value due, if a due date is preset for the departure of a vessel or if a maximum waiting time is preset for a vessel before the service has to start. Handling time attribute

This attribute describes the way how handling times of vessels are given as an input to the problem. It takes value fix, if the handling times of vessels are known and considered unchangeable. Value pos indicates that handling times depend on the berthing positions of vessels and value QCAP indicates that handling times are determined by including QC assignment decisions into the BAP. In case of

value QCSP, the handling times are determined by incorporating the QC scheduling within the BAP. In order to classify the recent literature properly, we have inserted case stoch as a new attribute for the scheme. Again, handling times can be subject to either discrete or continuous random distributions. A similar extension of our scheme is also suggested by Carlo et al. (2013), who also open it to further sources of influence on vessel handling times, like operations of transfer vehicles and yard cranes. However, as we hardly find instantiations of these cases in the literature, we refrain from extending the scheme in further directions. Performance measure

This attribute considers the performance measures of a berth allocation model. Most models consider to minimize the port stay time of vessels. This is reached by different objective functions, e.g. when minimizing waiting times before berthing (wait), minimizing handling times of vessels (hand), minimizing service completion times (compl), or minimizing tardy vessel departures (tard). If soft arrival times are given, also a possible speedup of vessels (speed) is taken into consideration at the expense of additional bunker cost. Other models aim at reducing the variable operation cost of a terminal by optimizing the utilization of resources (res) like cranes, vehicles, berth space, and manpower. An often considered feature is to save horizontal transport capacity by finding berthing positions for vessels close to the yard, which is why we include this goal by its own value pos. Rarely met performance measures are summarized by value misc(miscellaneous). The introduced measures are either summed up for all vessels in the objective function. Alternatively, if the minimization

of the measure for the worst performing vessel is pursued, i.e. a min–max objective is faced. Vessel-specific priorities or cost rates are shown by weights. Different weights w1 to w4 address combined performance measures. Literature overview

In the relevant literature, we have found and classified 79 new models for berth allocation, most of them published after 2009. Fig. 2 shows the BAP models developed by researchers since 1994 by year of their publication, including also those approaches reviewed in Bierwirth and Meisel (2010). The figure shows that the interest in berth allocation started with the early papers of Hoffarth (1994) and Imai, Nagaiwa, and Tat (1997). However, the growth of publications followed the pioneering paper of Park and Kim (2003), who combined berth allocation and QC assignment for the first time, and the early survey on container terminal operations by Steenken et al. (2004). In particular, journal publications scaled up to ten and more per year after 2010. To the mid of 2014, already 13 new journal papers have been published or accepted for publication. The continuous effort spend on research in berth allocation confirms it as a well-established field today, which still shows potential for future research.

With Table 1, we also provide an overview of the methods that are used for solving the BAP models. Note that only the most successful method presented in a paper appears in the table. It is not surprising that heuristic approaches dominate as the BAP is known to be NP-hard in both, the discrete and the continuous case, see e.g. Lim (1998) and Hansen and O?uz (2003). Exact methods are applied in only one

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