## 1 Introduction  
Container terminals (CTs), connecting seaside and landslide transportation, are an essential part of the global transportation system. Over the past two decades, the demand for maritime transport has increased dramatically [1]. The number of container shipments between 1990 and 2008 has increased from 28.7 million to 152 million, representing a 9.5% average annual compound growth rate [2]. In addition, about 60% of the maritime transports employed containers, with a growth rate of 6.4% each year. This figure even approaches 100% for developed countries [3]. The above figures show the need to improve the efficiency of CTs. One effective way to improve the efficiency of a CT is to directly improve its operations, which are usually separated into three areas: seaside, yard, and landslide [4, 5]. The seaside operations are particularly critical as they employ berths and quay cranes (QCs), two scarce resources that can affect the CT performance considerably [6]. For the seaside operations, there are three well known operational problems, i.e., berth assignment problem (BAP), quay crane assignment problem (QCAP), and quay crane scheduling problem (QCSP). Essentially, the BAP is a problem of allocating berths to ships. The QCAP focuses on assigning QCs to ships whereas the QCSP focuses on the further assignment of QCs to the tasks of ships, where each task consists of a group of containers from a same ship to be loaded and unloaded, so that the QC schedules can be finally settled down. A solution to the QCSP should clarify which task is handled by which QC and what are the starting and ending times of each task. To solve the QCAP, it usually needs to solve the QCAP first. The solution found for the QCAP can affect the solution found for the QCSP, thus the two problems are related. In our approach, we use an indirect approach to assign QCs to ships, i.e., QCs are first assigned to berths based on the workload of the berths and then the QCs assigned to a berth are used to serve the ships that moor that berth. After a literature review, it was found that the three seaside operational problems have often been solved separately or partially [7; 8; 9]. The drawback of a separate study is that it tends to result in a poor overall system performance while neglecting the interrelationship between the various levels of seaside operational problems. Thus, it has been suggested to solve the three operational problems in an integrated way [5]. Various approaches have been proposed to deal with the three seaside operational problems separately or simultaneously. For example, Mixed Integer Programming (MIP) has been used to solve BAP [10; 11], QCSP separately [12; 13], and BAP and QCAP simultaneously [8]. Simulation has been used to solve BAP [14], QCSP [11; 15], and as an evaluation tool for terminal operations [16]. Genetic algorithms (GAs) have been used to solve dynamic QCAP [17], QCSP [1; 18], simultaneous BAP and QCAP [19; 20; 21], and simultaneous BAP and QCSP [7; 22; 23; 24]. Heuristic rules have been employed to solve QCSP [25]. The branch and bound (B & B) approach has been applied towards QCSP [23]. Timed Petri net (PN) has been used to deal with QCSP [26], and stochastic PNs have been applied for the modeling and analysis of the activities of human operations [27] and logistic systems [28] for a container terminal. Decision support systems (DSSs) have been used to solve both BAP and QCAP [2], and as a tool for decision making [3; 29]. While exact approaches, such as Mixed Integer Programming (MIP), have the capability to solve a problem to optimality, they are usually computationally intractable when dealing with problems of practical size [12; 25; 30], due to non-deterministic polynomial-time hard (NP-hard) [2]. Approximate approaches, such as heuristics, meta-heuristics and Genetic Algorithms (GAs), and PN-based approaches [31; 32; 33] have thus been widely used to find near-optimal solutions within an acceptable time.