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Modeling berth allocation and quay crane assignment considering QC driver cost and operating efficiency

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Abstract

Due to high labour costs and difference of QC driver’s handling efficiency existing between day and night, factors concerning QC drivers can significantly impact the schedule of berth allocation and quay crane assignment. This paper tackles the berth allocation and quay crane assignment problem considering QC driver cost, difference of the operating efficiency and performance-related pay between day and night. How QC driver-related factors affect the schedules is analyzed, and the objective composition including QC driver cost is given. A mixed integer programming model with model acceleration algorithms is developed for the proposed problem, and a meta-heuristic framework including a three-stage algorithm is proposed for solving the problem. Numerical experiments are conducted to validate the effectiveness of the proposed model and performance of the meta-heuristic approach, leading to a multitude of managerial insights.

Introduction

The consensus has been that maritime transportation undertakes 90% freight volume of global merchandise trade [1]. Container terminals govern as a hub connecting shipping and land transportation. Although still under the influence of the COVID-19 pandemic and the ongoing adjustment of global trade structures, the world container throughput still will maintain a growth rate of about 4%-6% in the next four years as predicted [2]. In recent years, the labor cost is on the rising trend. Quite a few of ports invest automated container terminals for reducing labour costs [3]. However, as a result of the high investment cost of automated container terminals, most of the existing container terminals can hardly be transformed into automated container terminals. Human resource plays as an important role in container terminal operations, and a good human resource management will contribute to labor cost control. However few works takes human resource into account in previous studies on container terminal’s operations, such as berthing allocation problem (BAP), berthing allocation and quay crane assignment problem (BACAP), quay crane (QC) scheduling problem, yard allocation problem, yard crane (YC) scheduling problem and yard truck (YT) scheduling problem. In addition, due to factors of the degree of tired and operating level, human resource can significantly impact the operational efficiency, energy consumption and operational cost of container terminals.

As for BACAP, the influence of worker is more evident. Even if in automated container terminals, QC operations are completed by workers through remote operations. In traditional container terminals, QC drivers are the most valuable human resources, but the shortage of workforce keeps emerging and driver wages are higher than those of other type workers. Since berth and QC directly serve vessels, their schedules constrain the terminal’s service commitment for shipping liners. In traditional BACAP studies, schedules for the berth allocation and QC assignment are generated, but omitting the limit of the number of QC drivers and the facts that handling efficiency decreases and energy consumption increases at night. Taking higher levels of fatigue and working strength of QC drivers at night into account, the performance-related wage payof QC driver at night should be higher than that at day. This is another fact hardly explored in traditional BACAP studies. Therefore, this paper addresses the berth allocation and quay crane assignment problem considering QC driver’s factors (BACAP-D). In the proposed BACAP-D, four decisions of berthing time, berthing position, QC assignments in each period and the number of QC drivers dispatched in each shift are simultaneously considered. Beside pursuing higher efficiency goals, we pursue to lowering labour cost and energy consumption in the proposed BACAP-D.

The rest of this paper is organized as follows. Section 2 presents a literature review. Section 3 describes the proposed BACAP-D, analyzes QC driver factors, and gives objective compositions. The proposed BACAP-D is formulated as a mixed integer programming (MIP) model in Section 4, and a meta-heuristic is used to solve it in Section 5. A packet of numerical experiments and analysis are employed in Section 6, and conclusions are summarized in Section 7.

Section snippets

Literature review

The berth allocation problem (BAP) mainly optimizes the assignment of berthing resources and minimize the ship waiting and handling time illustrated by Imai et al. [4] and Imai et al. [5]. The efficient BAP is a critical issue for both port operators and shipping companies [6] that had been well documented in the past decades. A traditional BAP is modeled as discrete berths with several fixed positions [4], [5] or continuous [7] berths with no fixed positions. These studies are efficient to

Problem description

For the traditional BACAP, there are three decisions to be made: berthing time, berthing position and QC assignments in each period. However, the number of QCs that can be assigned in each period is limited by the number of QC drivers dispatched in each shift, and herein this needs to be determined as well. For a container terminal, a planning horizon includes two types of time windows, one is the working shift and the other is the planning period. In most container terminals, quay crane

Modeling the BACAP-D

The following MIP model in this study considers the QC driver cost, the difference of handling efficiency and handling energy consumption between day and night, and the difference of QC driver’s performance-related pay between day and night.

Meta-heuristic framework

Due to the computational intractability of large-size BAP [19], it is more comprehensive for the large-size BACAP-D to be solved by commercial software than for the traditional BAP. Hereby we propose a GA-based meta-heuristic to solve the BACAP-D.

We then refer to the proposed framework by He [40]. GA-based meta-heuristic framework is used for a global search and evolving. A three-stage algorithm is proposed to decode the berthing sequences into BACAP-D schedules. In the first stage, a

Numerical experiments and analysis

In this section, numerical experiments are conducted to validate the effectiveness of the proposed model, evaluate the performance of the meta-heuristic approach, analyze the impact of some parameters and generate a multitude of managerial insights. Numerical experiments consist of three parts: (1) performance analysis of the proposed meta-heuristic approach, (2) effectiveness analysis of the proposed model and (3) sensitivity analysis of QC driver cost and managerial insights. Performance

Conclusions

This paper addresses the BACAP-D for pursing the minimization of comprehensive cost, besides optimizing departure delay. Impact analysis of QC driver-related factors on schedules of the BACAP-D is conducted, and the cost composition of the proposed BACAP-D is illustrated. The proposed BACAP-D is formulated as a MIP, and a meta-heuristic is employed to solve it. Numerical experiments are performed to validate the effectiveness of the proposed model and the performance of the meta-heuristic

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgement

This work is sponsored by the National Natural Science Foundation of China [grant numbers 72072112, 71602114, 72002125, 72001135], Shanghai Rising-Star Program [grant number 19QA1404200], Shanghai Sailing Program [grant numbers 20YF1416600, 19YF1418800] and Shanghai Science & Technology Committee Research Project [grant number 17040501700].

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