Bi-objective Recoverable Berth Allocation and Quay Crane Assignment Planning under Environmental Uncertainty

This study discusses the development of tactical-level integrated planning at seaport container terminals in an uncertain environment. The suggested approach seeks to strike a balance between the cost-effectiveness of a robust baseline schedule and recovery plan and the required quality of customer service in order to enhance the competitive edge of container ports. Integrated planning for a tactical level at the container terminal synchronizes the decisions of berth allocation and quay crane assignment planning by taking into account the unpredictability of the vessel's arrival time and handling time caused by a variety of unforeseen factors such as unfavorable weather conditions, instability in the productivity rate of the quay cranes, the uncertainty of the quantity of loading and discharging containers, and other unpredictable events. The proposed optimization model produces a robust and proactive baseline schedule with a recoverable reactive plan for each scenario that occurs by utilizing buffer times and quay cranes that anticipate fluctuations in uncertain parameters. The proposed bi-objective recoverable robustness optimization model is solved by applying a hybrid method, namely the Rolling Horizon-based Optimization Algorithm (RHOA) and the Preemptive Goal Programming approach, using Gurobi-Python Optimization. The proposed bi-objective recoverable robust optimization model demonstrates superior solution quality in terms of service level and total costs, as well as a more efficient computational time when compared to an optimization model that minimizes total costs for tactical level planning decisions in seaside container terminals.

Bi-objective optimization model; Container terminal; Environmental uncertainty; Recoverable robustness; Rolling horizon-based optimization algorithm

The tactical level planning decisions in resources planning that have the most influence on container terminal performance are the berth and quay cranes as the primary resources at seaport container terminals (Carlo et al., 2015). The Tactical Berth Allocation Problem (TBAP) dictates the timetable and placement of each incoming vessel's berth. This decision is heavily influenced by the Quay Crane Assignment Problem (QCAP) decision, which determines the number of quay cranes assigned to each vessel, and vice versa. Since TBAP and QCAP decisions are intertwined, these two issues should be considered as a whole (Prayogo et al., 2018).

    The essential factor in getting ahead of the intense competition in container terminals is to improve service quality through a well-balanced combination of robust resource planning, recoverable planning in an uncertain environment, and operational cost-efficiency (Iris & Lam, 2019). Maximization of the service level is required to increase the competitive advantage of container terminals. However, maximizing the service level will increase the expected total operating and recovery costs. Therefore, this study offers a bi-objective recoverable robust optimization model for integrated tactical planning that considers two objectives, i.e., maximization of minimum service levels for all vessels served and minimization of total operational and recovery costs at a seaside container terminal. To obtain a compromise solution between these two conditions. Non-Polynomial/NP-hard problem characterizes the integrated model (Li et al. 2015; He 2016; Gutierrez et al. 2018; Homayouni & Fontes 2018; Yu et al. 2019), that becomes more complex when considering the uncertain environment. When there is uncertainty, it is extremely challenging to compute the global optimal solution of the TBAP and QCAP integration models using the exact method, and if it is even feasible, it takes an extremely long time. Therefore, in this study, we apply a hybrid solution methodology using the Rolling Horizon-based Optimization Algorithm (RHOA) of Xiang et al. (2018), adapted with Pre-emptive Goal programming to solve the proposed bi-objective recoverable robust optimization model to get good quality solution with efficient computation time. In the case of complex problems, RHOA's solution methodology provides various advantages. The computation time can be reduced by subdividing the problem into multiple subproblems. We shall obtain the optimal solutions while tackling sub-problems utilizing the exact method. In addition, the rolling horizon-based optimization will let the subproblems be linked together, which will make for a smooth transition and the best solution overall. The following are the main contributions of this study:

• The proposed model of bi-objective recoverable robust optimization for integrated tactical planning decisions at a seaside container terminal in an uncertain environment aims to increase the competitive advantage of the container terminal by maximizing the service level and balancing total cost efficiency, robustness, and recoverable planning. This is different from a single-objective optimization model, which only tries to minimize expected total costs.
• We describe a hybrid method that combines the RHOA and Preemptive Goal Programming approaches to get a high-quality solution in a reasonable amount of computing time. This method is used to solve the proposed bi-objective recoverable robust optimization model.
• Moreover, by maximizing the minimum service level of all vessels served as the first objective function, which is solved by the Preemptive Goal Programming approach, and then using the solution result as a goal constraint to minimize the total cost, this is in addition to being able to produce a better quality solution as well as more efficient computational time compared to the single-objective model, which has a greater computational burden to achieve the same result.

This paper will henceforth be arranged as described below. In Section 2, there is a review of the research on the deterministic and probabilistic TBAP and QCAP integrated planning models. In Section 3, the construction of a bi-objective optimization model is discussed. The Rolling Horizon-based Optimization approach is proposed as a solution method for this study in Section 4. The proposed model and solution approach are evaluated in Section 5 through numerical experiments and analysis of the findings. Finally, Section 6 concludes with conclusion thoughts and some research directions. 

This paper presents a proposed bi-objective recoverable robust optimization model for integrated tactical planning in seaside container terminals with uncertain vessel arrival and handling times. We consider two objectives: maximizing the minimum service level of all vessels served and minimizing the total costs of the baseline schedule, recovery plan, and expected total costs for all scenarios such that the container terminal has a competitive advantage. The rolling horizon-based optimization algorithm and Pre-emptive Goal Programming approaches are proposed as a solution method to solve the bi-objective recoverable robust BACAP model, resulting in good quality solution for a large-scale problem in reasonable computation time. For further research development, recoverable robust optimization can be considered for integrated planning with storage container yards under uncertainty and effective solution methods for real-time disruption recovery.

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