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Yard crane scheduling problem in a container terminal considering risk caused by uncertainty

https://doi.org/10.1016/j.aei.2018.11.004Get rights and content

Highlights

  • The extra loss caused by uncertainty is measured.

  • A MIP model under uncertainty is formulated considering a lot of uncertain scenarios.

  • A GA-based framework combined with three-stage algorithm is proposed.

Abstract

In a container terminal, the arriving times and handling volumes of the vessels are uncertain. The arriving times of the external trucks and the number of containers which are needed to be brought into or retrieved from a container terminal by external trucks within a period are also uncertain. Yard crane (YC) scheduling is under uncertainty. This paper addresses a YC scheduling problem with uncertainty of the task groups' arriving times and handling volumes. We do not only optimize the efficiency of YC operations, but also optimize the extra loss caused by uncertainty for reducing risk of adjusting schedule as the result of the task groups' arriving times and handling volumes deviating from their plan. A mathematical model is proposed for optimizing the total delay to the estimated ending time of all task groups without uncertainty and the extra loss under all uncertain scenarios. Furthermore, a GA-based framework combined with three-stage algorithm is proposed to solve the problem. Finally, the proposed mathematical model and approach are validated by numerical experiments.

Introduction

Accompanied with the slowdown in trade growth, the volume growth of container shipping has been slowed down gradually. Container terminals are facing more challenges, such as fiercer and fiercer competition, attracting freight source, improving the service level, promoting operation efficiency, saving operation cost. The yard crane (YC) is the most important equipment for container yard operation, which can directly impact the entire operation efficiency. YC scheduling is one of the most important operation problems of a container terminal, which mainly refers to the handling sequence and starting service time of each YC for each task group (the concept of task group is referred to the core idea proposed by He et al. [17]. YC scheduling can directly impact the handling efficiency and cost of a container terminal.

As the result of the importance of YC scheduling, the operation efficiency of container terminals is most studied, and a lot of YC scheduling approaches for solely improving the efficiency are developed. To the best of our knowledge, most of the traditional researches on YC scheduling generally consider deterministic environment, where the arriving times and the handling volumes of the task groups are not uncertain. However, YC scheduling must face to various uncertain factors and unknown issues in reality. For example, because of the change of shipping liner's plan and weather reasons, the vessel may arrive at port earlier or later. As the result of handling equipment failure, the total served time of the vessel may be longer. The report of Drewry Shipping Consultants shows that the average arriving time of all ships at East-West route deviated from their estimated arrival time 1.9 days in January and February 2015 [7]. All of the uncertain factors impact the initial schedule. Once the uncertainty occurs, the planners should adjust or reschedule the initial schedule to satisfy the reality. But, this adjustment or rescheduling incur extra cost, and impact the other plans or schedules. If the uncertainty can be considered in the initial schedule, the risk of adjusting schedules will be reduced significantly. Therefore, container terminals need some models and methods for the YC scheduling problem with uncertainty. This paper mainly addresses the YC scheduling problem with uncertain arriving time and uncertain handling volume of task groups, which significantly impact the YC handling sequence . The main contributions of this work are: (1) the extra loss caused by uncertainty is measured, (2) a MIP model is formulated for minimizing the extra loss considering a lot of uncertain scenarios, and (3) a GA embedded three-stage algorithm is developed for obtaining enhanced solution.

The remainder of the paper is organized as follows. Literature review is addressed in Section 2. In Section 3, the YC scheduling problem with uncertain factors is described. In Section 4, the YC scheduling problem with uncertainty is modeled as a mixed integer programming (MIP). A three-stage optimization for solving this problem is proposed in Section 5. Section 6 validates the performance and the effectiveness of the developed model and algorithm by numerical experiments, and the last section concludes this work and gives the future research.

Section snippets

Literature review

Up to now, there are abundant studies focused on the operations of container terminals, such as handling equipment scheduling, storage space allocation, berth allocation and integrated scheduling of multi-resource [31], [30], [8]. Most of these works are devoted to port operation management under deterministic environment, whereas the uncertain factors are involved less. In this section, we mainly review the literatures highly related to port operation management under uncertainty and YC

Description of YC scheduling under uncertainty

YC scheduling problem mainly refers to two decisions: (1) the served sequence for each task group; and (2) the start served time of each task group. In order to reduce computational complexity, the scheduling object is not each container but task group. The construction approach of a task group is referred to the approach proposed by He et al. [17], [18]. Task group means a lot of tasks are belong to the same shipping line or the same carrier at adjacent bays in the same block, which volume

Notation

Parameters
iThe index of task groups
jThe index of YCs
kThe index of customers
TThe set of all task groups in the planning horizon.
YThe set of all YCs.
UU=TY0, where 0denotes virtual depot.
pThe loading and unloading speed of each YC (unit: h/move)
VkThe task number of Customer k(unit: move). If kY0,Vk = 0.
SkThe needed handling time of Customer k.Sk=Vk·p
akThe arriving time of Customer k. If kY0,ak = 0.
dpkThe planned ending time of Customer k. If kY0, dpk = 0.
tkkThe moving time between

Overall framework

As aforementioned, the YC scheduling problem under uncertainty is a VRP with high complexity caused by uncertainty. Generally, the large-size VRP with deterministic environment is hard to solve in a short CPU time using exact algorithms or commercial solvers such as ILOG CPLEX, not to mention the YC scheduling problem under uncertainty, especially with a lot of scenarios. Thus a GA-based framework combined with three-stage algorithm is proposed to solving the problem, where the GA is used for

Computational experiments

To validate the effectiveness of the proposed approach, we conduct a series of numerical experiments with different sizes. This section consists of three parts: (1) performance analysis, (2) extra loss analysis and (3) sensitivity analysis. In the performance analysis, the CPU time and solution quality between the proposed method and CPLEX are compared. In the extra loss analysis, we compare the completion delay costs and the extra loss costs between schedules obtained by the proposed model and

Conclusions

Since there are a lot of uncertain factors, such as the changes of shipping liner's plan, changes of weather, handling equipment failure and variations of requested service time, operation plans and schedules may have to be adjusted. We should reduce the adjustment caused by the uncertain factors. This paper addresses YC scheduling problem in a container terminal under uncertainty in reality. A mixed integer programming (MIP) model and three-stage optimization algorithm are proposed to handle

Declarations

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

Acknowledgement

This work is sponsored by National Natural Science Foundation of China (71602114) and Shanghai Science & Technology Committee Research Project (17040501700, 15590501700).

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