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Two-stage stochastic programming model for generating container yard template under uncertainty and traffic congestion

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Abstract

Yard template is a space assignment at the tactical level, which is kept unchanged within a long period of time and significantly impacts the handling efficiency of a container terminal. This paper addresses a yard template planning problem considering uncertainty and traffic congestion. A two-stage stochastic programming model is formulated for minimizing the risk of containers with no available slots in the designated yard area and minimizing total transportation distances. The first-stage model is formulated for assigning vessels in each block without considering the physical location properties of blocks, and the second-stage model is formulated for designating physical locations to all blocks. Subsequently, a solving framework based on genetic algorithm is proposed for solving the first-stage model, and the CPLEX (a commercial solver) is used for solving the second-stage model. Finally, numerical experiments and scenario analysis are conducted to validate the effectiveness of the proposed model and the efficiency of the proposed solution approach.

Introduction

Maritime transportation plays an important role in driving economy growth and energizing the process of globalization, since its trade volume accounts for four fifths of the world’s total merchandise trade [1]. A total amount of the throughput of global container ports has achieved 781.6 m TEU in 2018, and it is expected to reach 850 m in 2020 [2]. The growth in ship transportation volumes not only poses greater challengers to port management, but also breeds uncertainty and congestions in the terminal operations [3]. Generally, the working areas of container terminals are divided into two main parts, namely, the seaside for vessel berthing and landside where containers are stored [4]. With the improvement of quay crane (QC) handling efficiency, the bottleneck of port operation has moved from the quay side to yard side [5]. Therefore, an optimal yard management is critical to maintain and upgrade the service level of a container terminal and help meet the demands of high-efficiency handling of containers for mega-vessels.

Yard template is a concept applied in container terminals under the framework of consignment strategies. Containers for export and transshipment that will be loaded on the same departing vessel are stacked at the same storage area in the yard [6]. Yard template planning in a container terminal pertains to the assignment of yard storage sub-blocks to vessels, in the process of which sub-blocks reserved for each vessel are determined. It is a space assignment at the tactical level and keeps unchanged within a long period of time. After yard template is completed in a container terminal, yard plans for the operational level can be easily made within the framework of the template. Moorthy and Teo [7] first proposed the concept of yard template, but only the berth allocation planning in container terminals is studied in particular. Han et al. [8], Zhen et al. [9], Jiang et al. [10] and Tan et al. [11] conducted in-depth researches from different aspects, pertaining to yard template generating, multi-period yard template generating and yard template regenerating in container terminals.

It is worth noticed that many uncertainties, such as periodic and non-periodic fluctuations of global maritime markets and the on-changing of container collection patterns according to the relative proportion between the volumes of the arriving and departing containers within each planning period, has formulated great challenges in generating a yard template. In particular, the maritime market determines the demand of vessels for space in the yard area, and container collection patterns affect the storage allocation of each period [11]. Another factor that should be concerned in container terminals is the traffic congestion, which can significantly impact the efficiency of landside processes [12], and results in longer processing time for vessels at ports [8].

This study investigates a yard template planning problem considering uncertainty and traffic congestion based on space sharing among adjacent sub-blocks [10]. For reducing the computational complexity of the problem, a two-stage stochastic programming model is formulated by two steps: assigning vessels in each block without considering the physical location properties of blocks, and then designating physical locations to all blocks. A solving framework based on the genetic algorithm and the CPLEX is proposed for solving the model. Numerical experiments are conducted to validate the effectiveness of the proposed model and the efficiency of the proposed solution approaches.

The remainder of this paper is organized as follows. An overview of related works is presented in Section 2. The problem background is described in Section 3. Mathematical models and the solution approaches are established and proposed in Sections 4 and 5, respectively. Numerical experiments and the results analysis are presented in Section 6. Concluding remarks are presented in the last section.

Section snippets

Literature review

The port operation research spans a very wide range of concerns and methods, such as space assignment, production scheduling, handling equipment dispatching and routing planning [13], [14]. For a comprehensive overview on the yard management, see the review work given by Carlo et al. [15]. This work is mainly related to the yard template planning problem, which has attracted large attention in academic researches, e.g. [5], [8], [10], [16], [17], [18]. In this section, we mainly reviews the

Two-level space sharing strategy

The space sharing strategy is considered in yard template planning to increase the sharing feasibilities among adjacent sub-blocks. Most previous studies only enabled one-level space sharing, i.e., the space assigned to vessels can be shared by their adjacent sub-blocks. The space sharing strategy is utilized based on the pairing of vessels with different container collection patterns. When the maritime market is deterministic, and this one-level space sharing could be an optional method to

Model formulation

Considering the advantages by formulating the integrated problem into a two-stage stochastic program [26], a two-stage stochastic programming model is formulated for the yard template planning problem. The first-stage model is formulated for assigning vessels in each block without considering the physical location properties of blocks, and the second-stage model is formulated for designating physical locations to all blocks.

Before formulating the mathematical models, some assumptions are

Framework for solving the proposed model

Although, mathematical programming could yield a solution that is proof of optimum [27], [28]. However, the proposed mathematical model [M1] in this paper is too intractable to be solved by commercial software (e.g., CPLEX, LINGO) for large size problems. While, the heuristics and meta-heuristics can yield a close to optimal solution [29]. Thus, a GA-based framework combined with two-stage meta-heuristic algorithm is proposed for solving this problem. To precisely evaluate the performance of

Computational experiments

To verify the effectiveness of the proposed model and solution approaches, a series of experiments are performed on a computing server with 12 dedicated 2.3 GHz processors and 128 GB RAM. The experiments include three major parts: (1) performance analysis of the proposed solution approach, (2) effectiveness analysis of the proposed models, and (3) scenario analysis.

Conclusions

A well-performed yard planning template is essential in port management whereby the challenges of yard management can be readily faced. Once a yard planning template is generated, the daily yard operations are going to be easier. It is required in particular that the yard planning template should have the ability to deal with uncertainty. Therefore, this paper addresses the problem of yard template planning considering uncertainty and traffic congestions. A two-stage stochastic programming

Declaration of Competing Interest

The authors declare that they have no competing interests, and the first two authors contributed equally to this work.

Also declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

Acknowledgement

This work is sponsored by the National Natural Science Foundation of China [grant number 71602114, 71974122]; Shanghai Science & Technology Committee Research Project [grant number 17040501700]; Shanghai Rising-Star Program [grant number 19QA1404200], Shanghai Sailing Program [grant number 19YF1418800] and Shanghai Special Research Project [grant number 17DZ2280200].

References (30)

  • K.K.H. Ng et al.

    Robust aircraft sequencing and scheduling problem with arrival/departure delay using the min-max regret approach

    Transport. Res. Part E: Logist. Transport. Rev.

    (2017)
  • K.K.H. Ng et al.

    Review on meta-heuristics approaches for airside operations research

    Appl. Soft Comput.

    (2018)
  • Y. Xu et al.

    Berth scheduling problem considering traffic limitations in the navigation channel

    Sustainability

    (2018)
  • Drewry, Container Forecaster Quarter 1·2019, London,...
  • F.F. Zheng et al.

    A two-stage stochastic programming for single yard crane scheduling with uncertain release times of retrieval tasks

    Int. J. Prod. Res.

    (2019)
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