Integrated operations planning in highly electrified container terminals considering time-of-use tariffs

https://doi.org/10.1016/j.tre.2023.103034Get rights and content

Highlights

  • We address an integrated operations planning problem under time-of-use tariffs.

  • We propose a LBBD algorithm with valid inequalities to solve the problem accurately.

  • We design a tailored genetic algorithm to solve practical-sized instances.

Abstract

With the electrification of port equipment, container terminals have become electricity-intensive consumers. The time-of-use (TOU) pricing policy has prompted container terminals to reoptimize their operations planning to decrease electricity costs. However, it is an essential challenge to optimally plan highly correlated operations of a container terminal in response to TOU tariffs. Traditional operations planning of a container terminal focuses on improving operational efficiency under flat electricity tariffs. The obtained solution under flat electricity tariffs may be far from optimal when the TOU pricing policy is involved. To this end, this paper addresses an integrated operations planning problem from container terminals under TOU tariffs. In particular, several vital resources, including quay cranes, yard cranes, and berths, are jointly scheduled to handle tasks from vessels and external trucks. The objective is to minimize the total costs. We formulate the integrated optimization problem as a mixed-integer linear programming (MILP) model. We then propose a logic-based Benders decomposition (LBBD) algorithm for the problem. The proposed LBBD method uses valid inequalities to speed up the solution procedure. To address practical-sized instances, we design a tailored genetic algorithm (GA) with several acceleration techniques. We demonstrate the performance of the LBBD method and tailored GA through numerical experiments. Results indicate that the proposed integrated approach yields a better solution than its decentralized counterpart, demonstrating that the total operational cost can be significantly reduced by applying the developed model. We also discuss managerial implications drawn from our results for the integrated operations planning under TOU tariffs, which help port operators make critical decisions.

Introduction

Facing the energy crisis and environmental issues, the world is in a critical period of the energy transition to reduce carbon emissions (Poudyal et al., 2019). Electricity is widely regarded as a cleaner alternative to traditional energy. Various industries are forced to promote the electrification of equipment, significantly increasing electricity consumption and posing a vital challenge to the power grid (Butt et al., 2021). Recently, many countries are suffering from power shortages. In the summer of 2022, the Sichuan province of China even limited the supply to industries. To alleviate this dilemma, electricity companies usually implement the time-of-use (TOU) tariff paradigm to regulate peak electricity consumption (Cheng et al., 2017b). The TOU tariff gives economic incentives to electricity-intensive users to establish demand-responsive mechanisms. Container terminals are among those electricity-intensive users.

Given the increasingly fierce competition in global maritime markets, container terminals face considerable pressure to save costs and provide high-quality services. With the electrification of port equipment, container terminals consume huge quantities of electrical energy and thus suffer high electricity costs. For example, the electricity consumption of container terminals in Qingdao port in 2020 was around 13,800 MW h and resulted in about 12 million yuan in electricity bills. In highly electrified container terminals, electricity costs contribute to a large proportion of the total operational costs (Budiyanto et al., 2021). The electricity consumption of a container terminal largely depends on the operational efficiency of various types of equipment. As shown in Fig. 1, the primary electricity consumers are power supply equipment for vessels and reefer containers ([1] and [4] in Fig. 1) and container handling equipment such as quay cranes (QCs, [2] in Fig. 1) and yard cranes (YCs, [3] in Fig. 1). A container terminal generally performs operations for inbound and outbound container flows. In an inbound container flow, containers are unloaded from vessels using QCs, transported to the designated blocks in the yard using internal trucks (ITs), unloaded from ITs for temporary storage using YCs, and finally loaded onto the external trucks (ETs) using YCs. Outbound flows are carried out in the opposite direction. As container operations are tightly correlated, they must be jointly planned to achieve overall efficiency (Qin et al., 2020). The literature sees an increasing trend in investigating integrated planning problems of container terminals. Examples include integrated berth allocation and quay crane scheduling problems (Malekahmadi et al., 2020), integrated berth allocation and channel path scheduling problems (Corry and Bierwirth, 2019), among others. As QCs and YCs are both electricity consumers and scarce resources of a container terminal, current research mainly focuses on the integrated scheduling of QCs and YCs to improve container terminal turnover and reduce electricity costs simultaneously (He et al., 2015b, Kizilay et al., 2020).

Recently, the release of the TOU pricing policy has significantly impacted the electricity costs of container terminals (Kusakana, 2021). Exploring operations planning under TOU tariffs provides a massive opportunity to reduce electricity costs (Chatterjee et al., 2015, Wang et al., 2019). In particular, most major ports in China have not been equipped with port microgrids or energy storage systems. Since these ports are completely dependent on the utility grid for power supply, they are more sensitive to electricity prices and rely more on operations planning in response to TOU tariffs. In practice, many container terminals have already managed their operational activities under TOU tariffs. For example, container terminals in the ports of Los Angeles, Long Beach, and Qingdao have adopted the truck appointment system to arrange for ETs to arrive during non-peak periods (Li et al., 2018). However, related studies to support the operations planning of terminals under TOU tariffs are limited. Moreover, current studies focus on simple strategies or mechanisms to address the challenge brought by the TOU policy (Parise et al., 2017, Duin et al., 2018). Although it is essential to reduce cost and improve operational efficiency through optimal operations planning methods, limited attention has been paid to this interesting problem.

The integrated operations planning under TOU tariffs shows a significant difference compared with flat tariffs. In a traditional planning problem of container terminal operations, the objective maximizes operations efficiency. However, the electricity price varies a lot during the day under TOU tariffs, forcing decision-makers to consider electricity costs and reoptimize all electricity-intensive operations planning. Furthermore, as hourly electricity demand mainly depends on the hourly assignment of tasks, operations planning considering TOU tariffs focus on assigning tasks to different types of handling equipment. In contrast, most previous modeling paradigms for classical operations planning focus on the exact starting (or stopping) times of task processing to improve operational efficiency. Therefore, they may not apply to the studied problem.

As mentioned above, the TOU tariffs should be fully considered when making an integrated plan of all operations in a container terminal. To this end, we investigate an integrated operations planning problem considering TOU tariffs for a container terminal. The objective is to minimize the electricity costs and efficiency-related costs measured by the delay costs of vessels and ETs. The decisions to be made include the berthing plan of vessels at berths, the deployment of QCs among vessels and YCs among yard blocks, and the assignment of containers to the QCs and YCs. We first formulate this new problem as a mixed-integer linear programming (MILP) model. Generally, integrated operations planning problems are challenging to solve due to high complexity (Kizilay et al., 2020). We then propose a novel logic-based Benders decomposition (LBBD) method to obtain optimal solutions for small- to medium-sized instances. However, it loses efficiency in solving practical-sized instances. To this end, we further propose a tailored genetic algorithm (GA) with problem-specific features to tackle practical-sized instances. The excellent performance of the proposed algorithms is demonstrated in numerical experiments.

In summary, we make the following contributions. (1) We investigate the integrated operations planning problem under TOU tariffs and formulate it as an MILP model. (2) We design an effective LBBD method to solve the problem to optimality. Specifically, we exploit the properties of the problem and propose valid inequalities to accelerate the solving process. (3) We design a tailored genetic algorithm (GA) to solve practical-sized instances. The GA uses mathematical models and several efficient strategies to generate the initial population. It is improved by tailored genetic operators to reduce the generation of infeasible offspring. (4) We perform extensive numerical experiments to validate the performance of the proposed models and algorithms and provide managerial implications for port operators.

The rest of this work is organized as follows. In Section 2, relevant literature is briefly reviewed. Our problem is described in detail and formulated as an MILP model in Section 3. Section 4 develops a logic-based Benders decomposition to solve the problem. The tailored genetic algorithm for practical-sized instances is presented in Section 5. Section 6 conducts extensive numerical experiments, analyzes the results, and performs sensitivity analysis. Managerial implications are discussed in Section 7. Finally, conclusions and future research are given in the last section.

Section snippets

Literature review

Our research falls in the scope of integrated operations planning of container terminals. We first review studies on integrated operations planning problems at container terminals. Then, we briefly review recent studies that consider TOU tariffs.

Problem description

In this section, we introduce the MILP model for the studied problem, which extends the models of Iris and Lam (2021). Our model generalizes the model of Iris and Lam (2021) by jointly planning and optimizing the tasks from vessels and ETs. Since berth positions do not directly influence the electricity consumption of the container terminal, they are taken as input data in the integrated operations planning problems considering electricity consumption (He et al., 2015a, Iris and Lam, 2021).

Framework of the logic-based Benders decomposition method

The LBBD method is widely implemented to address the challenging combinatorial optimization problems (Hooker and Ottosson, 2003). Its basic idea is to decompose the initial problem into a master problem and a subproblem, solved iteratively until an optimal solution is obtained. The studied problem has a good decomposition structure since it involves two types of variables. One is associated with vessels’ tasks, while the other is associated with ETs’ tasks. The two types of variables are only

Framework of the tailored genetic algorithm

The studied problem is very complicated and hard to be solved by commercial solvers. The developed LBBD method manages to solve small- and medium-sized instances to optimality. However, it loses efficiency when solving practical-sized instances. To this end, we design a tailored genetic algorithm (GA). GA is widely used to approximately solve large-sized optimization problems in the field of container terminal operations (Fu et al., 2014, He et al., 2015a, Guo et al., 2022). However, classical

Numerical experiments

In order to solve the integrated operations planning problem under TOU tariffs, numerical experiments are conducted on a computer with Intel Core TM i5-8265U @ 1.60 GHz processors and 8 GB RAM and a 64-bit operation system. The described solution method is coded in Java, and the BMP and BSP are solved by IBM ILOG CPLEX 12.10. All experiments are performed by imposing a time limit of 3600 s. The solution procedure terminates with the best solution found so far when it consumes the time limit.

Managerial implications

The paper addresses the integrated operations planning problem under TOU tariffs to minimize the total costs, consisting of electricity and vessel ET delay costs. A systematic solution is provided for the studied problem. Considering TOU tariffs, the integrated operations planning problem is a complicated combinatorial optimization problem. The developed LBBD finds optimal or near-optimal solutions for instances with up to ten vessels and 600 ETs’ tasks in acceptable computation time. The

Conclusion

This paper addresses a significant integrated operations planning problem considering TOU tariffs at container terminals. We formally describe the problem and formulate it as an MILP. As CPLEX has difficulties in efficiently handling practical-sized instances, we develop an effective LBBD method and a tailored GA based on the problem structure. In addition, multiple acceleration techniques are developed to speed up the solution process of the proposed algorithms.

We conduct numerical experiments

CRediT authorship contribution statement

Sumin Chen: Conceptualization, Methodology, Investigation, Software, Validation, Writing – original draft, Writing – review & editing, Formal analysis, Data curation. Qingcheng Zeng: Conceptualization, Methodology, Investigation, Writing – original draft, Writing – review & editing, Funding acquisition, Supervision. Yantong Li: Conceptualization, Methodology, Software, Writing – original draft, Writing – review & editing, Supervision.

Acknowledgments

This work was partly supported by: (1) the National Natural Science Foundation of China under Grants 71671021 and 72201044; (2) the Key R and D project of Liaoning Provincial Department of Science and Technology, PR China under Grant 2020JH2/10100042; (3) the Humanities and Social Science Foundation of the Chinese Ministry of Education, PR China under Grant 22YJC630071; (4) the China Postdoctoral Science Foundation, PR China under Grant 2022M710018. These supports are greatly acknowledged.

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