A survey of berth allocation and quay crane scheduling problems in container terminals
Abstract
Due to the variety of technical equipments and terminal layouts, research has produced a multitude of optimization models for seaside operations planning in container terminals. To provide a support in modeling problem characteristics and in suggesting applicable algorithms this paper reviews the relevant literature. For this purpose new classification schemes for berth allocation problems and quay crane scheduling problems are developed. Particular focus is put on integrated solution approaches which receive increasing importance for the terminal management.
Keywords:Container terminal operations、Berth allocation、Quay crane assignment
Quay crane scheduling、Problem classification、Integrated planning
1. Introduction
In recent years, OR methods have received considerable importance for the operations management in container terminals (CTs). Comprehensive overviews on applications and optimization models in this field are given by Meersmans and Dekker, 2001, Vis and de Koster, 2003, Steenken et al., 2004, Vacca et al., 2007, Stahlbock and Voszlig;, 2008. A significant amount of papers dealing with the application of OR methods addresses the planning of the seaside transshipment operations. Fig. 1 shows important relations of the strategic planning and the operations planning at the seaside area, the yard, and the landside area.
One issue of seaside operations planning is the assignment of quay space and service time to vessels that have to be unloaded and loaded at a terminal. This problem is commonly referred to as the berth allocation problem (BAP). The transshipment of containers between a vessel and the quay is generally performed by specialized cranes, which are mounted on rail tracks alongside the quay. The assignment of these quay cranes (QCs) to vessels and the determination of work plans for the cranes addresses two further problems, namely the quay crane assignment problem (QCAP) and the quay crane scheduling problem (QCSP). Solutions to these problems must respect the berth layout and the used equipment, whereas they impact the yard operations and the workforce planning, see Fig. 1.
Due to the variety of technical equipments and terminal layouts, research has produced a multitude of optimization models for the BAP, the QCAP, and the QCSP. Moreover, a trend towards an integrated solution of these problems is observed in the recent literature. The large number of available models and proposed solution methods prevents an easy choice of a suitable approach in a specific situation. To provide a support in modeling problem characteristics and in suggesting applicable algorithms this paper develops classification schemes for BAPs, QCSPs, and integrated approaches.
The paper is organized as follows. In Section 2 the focused operational planning problems are described in detail against the background of different terminal properties and objectives. A literature survey of BAP and QCAP formulations is presented in Section 3 which is derived from a new classification scheme for these problems. Accordingly, a classification scheme and a literature survey are presented for QCSP formulations in Section 4. Since future advances in the field are expected from integrated solution approaches, Section 5 provides a literature review of the state-of-the-art integration concepts. The paper is summarized in Section 6.
2. Planning of seaside operations
2.1. Berth allocation problem
In the BAP we are given the berth layout of a CT together with a set of vessels that have to be served within the planning horizon. For each vessel additional data like the vesselrsquo;s length including clearance, its draft, the expected time of arrival, and the projected handling time can be given. All vessels must be moored within the boundaries of the quay. They are not allowed to occupy the same quay space at a time. The problem is to assign a berthing position and a berthing time to each vessel, such that a given objective function is optimized. An example for the graphical representation of a berth plan with five vessels is shown in Fig. 2a. Berth planning has been shown to be an NP -hard problem by relating it to the set partitioning problem (集装箱码头泊位分配与码头起重机调度问题综述
在泊位分配中可能会有进一步的限制,这会导致许多BAP公式。空间约束根据码头预设的泊位划分来限制船舶的可行停泊位置。据Imai等人说。(2005)区分下列情况:
(2)连续布局:码头没有分隔,即船只可以在码头边界内的任意位置停泊(图3c)。对于连续布局,泊位规划比离散布局更为复杂,其优点是能更好地利用码头空间。
(2)动态到达:船舶的到达时间是固定的,因此,船舶不能在预期到达时间之前停泊。
在绝大多数已发表的BAP模型中,船舶装卸时间被假定为确定性的。然而,文献以不同的方式论述船舶装卸时间:
(3)可规定在整个装卸期间为船舶服务的起重机的最少数量。这个号码通常是船舶经营人和CT经营人之间合同的一部分。
在QCSP上计划的任务描述了在QCSP模型中考虑船只工作负载的粒度。任务可以基于间隔区域或单个间隔(图4a)或基于容器堆栈、容器组或单个容器(图4b)定义:
(4)组:任务是指存储在间隔相邻插槽中的一组容器。分组容器通常有一个共同的目的地等。
(2)时间窗口:对于每台起重机,可以使用一个或多个时间窗口来指定起重机可以为所考虑的船舶服务的时间跨度。这些时间窗通常是时间起重机分配变量的结果。 (3)位置:起重机的初始和最终位置是规定的。
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