Elsevier

Knowledge-Based Systems

Volume 163, 1 January 2019, Pages 675-692
Knowledge-Based Systems

Bi-objective optimization for integrating quay crane and internal truck assignment with challenges of trucks sharing

https://doi.org/10.1016/j.knosys.2018.09.025Get rights and content

Abstract

Due to both the rapid growth of world and the expansion of the flow of container shipment, a maritime container terminal plays a vital role in global coverage of supply chain. In this market, because shipping is growing fast, container terminals should be able to serve the vessels in the shortest possible time. Alternatively, the limited availability of operational facilities, such as internal trucks, makes servicing more complicated in container terminals. Therefore, this study aimed to integrate the assignment of quay cranes in container terminals and internal truck sharing assignment among them. For this purpose, a bi-objective optimization model is developed. In the proposed model, several assignment phases, including the assignments of the vessel to container terminals, cranes to terminals, cranes to vessels and trucks to cranes are performed. The model also seeks to increase and improve the efficiency and effectiveness of internal trucks by sharing them among different terminals, so that there is an appropriate balance between the volume of workloads of the terminals and the trucks in question. The first objective function in the proposed model seeks to minimize operational costs and the second objective function seeks to minimize the maximum overflowed workload in the terminals. Furthermore, in order to solve the proposed model, two meta-heuristic multi-objective algorithms, including modified non-dominated sorting genetic algorithm-II (MNSGA-II) and modified multi-objective particle swarm optimization (MMOPSO) are presented. Several numerical examples have been investigated and analyzed to show the accuracy of the proposed model and the methods. In addition, the results demonstrated that the simultaneous consideration of the assignments and the sharing of trucks would reduce the remaining workload in the terminals.

Introduction

A Container terminal is a place where containers transported by various means such as vessels, trucks and trains. In the past years the function of maritime container terminals shows that this is a fast-growing transportation market. Recently, this way of transporting has received a lot of attention from shipping companies as a result of the development of container shipping and the use of vessels with the capacity to carry 10 to 12 thousand (TEU) [1]. Alternatively, today, the competition among the container terminals has increased very much so that almost all terminals are trying to attract more customers. Additionally, with the increase of the size of container vessels, terminals face another challenge, for example, increasing service speed to the vessels. Therefore, reducing service time to the vessels is very important to improve the service level at terminals [2].

However, today’s container terminals have faced with the new problems. On the one hand, they have to make themselves compatible with modern transportation, and on the other hand, the terminals rarely have the ability to purchase additional equipment and expand storage area because the cost of transport equipment including quay cranes (QCs), yard cranes (YCs) and trucks is high. In addition, competition among the container terminals, especially terminals that are geographically adjacent, cause the terminals to look for a solution to these problems [3]. Hence, improving the service level of container terminals is a major problem for marine operators. In the service level evaluation index, the duration of the service to the vessel that includes the service time of QC, YC as well as the transportation time of internal trucks between quayside and storage area are important [4]. In regard to the referred cases, careful planning to assign vessels to container terminals, cranes to terminals, cranes to vessels and trucks to cranes are required to enhance the service level.

It should be noted that QCs located at the terminal are used for unloading and loading containers from/to the vessels. Internal trucks are utilized for the transport of containers between the quayside and storage area. In addition, the YCs are used for placing containers in the storage area and restoring them from these places. Therefore, each uncounted program causing interruptions during the operation of the equipment prolong the delivery time of the goods until reloading. It is consequently essential to advance the service level at container terminals via a proper program for optimal use of the limited equipment [5].

It is important to have enough internal trucks, which are used as internal transportation equipment at container terminal because the truck should be constantly assigned to the QC to receive or transport containers, thereby eliminating the idle time for QCs. At times when workloads in a container terminal are high, there are not enough trucks to bring containers to/from the QC and YC from/to storage location which would stop the crane operation. One solution to prevent crane idleness is to buy more trucks. This would impose high costs on the system. Moreover, as there may be the imbalance of workloads among the terminals in multi-terminal ports considering the number of vessels assigned to them, there may be an imbalance between the trucks and therefore between the terminals. Accordingly, on the one hand, cost adjustment has created an appropriate balance between containers terminals, on the other hand, truck sharing at container terminals is raised. According to this approach, if there are not enough trucks at a container terminal and at the same time interval there are idle trucks in the adjacent terminals, the idle trucks can be shared between the adjacent terminals that are in short supply [6].

Due to the lack of research on the integration of the decisions mentioned in the literature, a new optimization model is presented in this study in order to coordinate the decisions related to assignments of the vessel to container terminals, cranes to terminals, QCs to vessels, trucks to cranes and truck sharing among the container terminals. The model proposed in this study has two objectives so that the first objective function minimizes the operating costs and the second objective function minimizes the maximum amount of overflowed workload at the terminals. Also, with the aim of solving the proposed model, two multi-objective meta-heuristic algorithms such as modified non-dominated sorting genetic algorithm-II (MNSGA-II) and modified multi-objective particle swarm optimization (MMOPSO) were used. Hence, the novelties of this paper, in comparison with the research conducted on subject, are summarized below:

  • Creating a new framework to coordinate the assignment of vessels to the container terminals, the assignment of trucks to cranes and sharing trucks in a multi-terminal port.

  • Establishing a balance between the different terminals of a port and preventing workload surpluses and shortages.

  • Applying two modified meta-heuristic algorithms for solving the proposed model.

The rest of this paper is organized as follows. Section 2 presents a brief review of the literature. In Section 3, the problem definition is deliberated and an optimization model is presented. The proposed solution approaches are deliberated in Section 4. Computational experiments are presented in Section 5. Finally, the paper is concluded in Section 6.

Section snippets

Literature review

Liang et al. [7] proposed the problem of determining theberthing location and time for each vessel and the number of cranes that should be assigned to each vessel. Their aim was to minimize the total time served, waiting time and latency for each vessel. They developed a mathematical model (MM) for both the allocation of berth and scheduling for cranes. Then, a genetic algorithm (GA) using a heuristic innovation was integrated to find an approximate solution. Cao et al. [8] presented a new

Problem statement and mathematical model

The present study seeks to integrate the assignment of QCs at container terminals and the sharing of internal trucks among them. The problem involves several assignment phases, including vessel assignments to container terminals, cranes to terminals, cranes to vessels and trucks to cranes. Therefore, in this study we faced with a model involving multiple assignments. In the survey, there is a port that includes several terminals for loading and unloading the goods in containers. First of all,

Solution approaches

In this section, because the proposed model belongs to Np-hard and multi-objective optimization problems (MOOPs), two modified multi-objective meta-heuristic algorithms named MNSGA-II and MMOPSO were used to solve this model in large sizes at a reasonable time [30], [31].

Computational results

With the aim of demonstrating the correctness of the proposed model and algorithms, 15 problems are considered. Input parameter values are presented in Table 4. Furthermore, in order to demonstrate validity of the proposed model, the computational results for one problem solving with GAMS are graphically depicted in Fig. 9. Because the presented MM is multi-objective, the LP metric technique was utilized to convert it into a single-objective. With the aim to investigate the computational

Conclusion and future direction

The container terminals have witnessed fast growth andprogress during the last decade, so that condition lead to designing container terminals which were trustable, energy and cost efficient, responsive at terminal requirements and ultimately automatic. The problem to be investigated in this research was the emergence of new considerations regarding container terminals and operation research models and review of the literature related to it. In this study, we sought to integrate the assignment

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