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Vessel Schedule Recovery in Liner Shipping: Modeling Alternative Recovery Options
Abstract and Figures
Disruption occurrences in liner shipping operations affect schedule reliability and may increase the total cost of delivering cargoes at ports. If a vessel experiences disruption occurrences either at ports of call or in sea, the liner shipping company is required to decide on the schedule recovery action to execute in order to recover the resulting delays. This study formulates a novel mathematical model for the vessel schedule recovery problem (VSRP) in liner shipping. The objective aims to minimize the total profit loss, suffered by the liner shipping company due to disruption occurrences at a given liner shipping route. A total of four recovery strategies are considered in the model, which include: (1) vessel sailing speed adjustment; (2) vessel handling rate adjustment; (3) port skipping without container diversion; and (4) port skipping with container diversion. The proposed mathematical formulation for the nonlinear VSRP model is solved to the global optimality using BARON. A set of computational experiments are further performed for the Middle East/Pakistan/India-West Mediterranean (WM3) route, which is served by the OOCL liner shipping company, for various scenarios of disruption occurrences in sea and at ports. The results from the performed analyses demonstrate potential benefits for liner shipping companies from using the proposed methodology for various realistic scenarios of disruptions.
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... Extreme value prediction problems in engineering being frequent and challenging, especially when data is scarce (ISSC 2009;Wang and Wang 2021;Dulebenets 2022;Drummen et al. 2006;Abioye et al. 2021;Elmi et al. 2022;Chen et al. 2021;Jovanović et al. 2022;Parunov et al. 2015; European Maritime Safety Agency (EMSA) 2021). Hence, from a practical standpoint, it is essential to develop new, effective, and precise extrapolation approaches. ...
... The study's research object is a 245-m long 4400 TEU Panamax container ship (ISSC 2009). Motion sensors were installed on the 4400 TEU Panamax container ship during its trans-Atlantic journeys in 2010s years (Dulebenets 2022;Drummen et al. 2006;Abioye et al. 2021;Elmi et al. 2022). Captain made special measures to avoid the worst storms. ...
... Estimating structural system safety using traditional engineering reliability methods is often challenging Dulebenets 2022;Drummen et al. 2006;Abioye et al. 2021;Elmi et al. 2022;Chen et al. 2021;Jovanović et al. 2022;Parunov et al. 2015; European Maritime Safety Agency (EMSA) 2021; Gafero Priapalla Rahim 2019; Falzarano et al. 2012). The reliability of a complex structural system may be directly assessed by doing direct numerical Monte Carlo simulations, or by having sufficiently large measured dataset. ...
Modern cargo vessel transport constitutes an important part of global economy; hence it is of paramount importance to develop novel, more efficient reliability methods for cargo ships, especially if onboard recorded data is available. Classic reliability methods, dealing with timeseries, do not have the advantage of dealing efficiently with system high dimensionality and cross-correlation between different dimensions. This study validates novel structural reliability method suitable for multi-dimensional structural systems versus a well-established bivariate statistical method. An example of this reliability study was a chosen container ship subjected to large deck panel stresses during sailing. Risk of losing containers, due to extreme motions is the primary concern for ship cargo transport. Due to non-stationarity and complicated nonlinearities of both waves and ship motions, it is challenging to model such a phenomenon. In the case of extreme motions, the role of nonlinearities dramatically increases, activating effects of second and higher order. Moreover, laboratory tests may also be questioned. Therefore, data measured on actual ships during their voyages in harsh weather provides a unique insight into statistics of ship motions. This study aimed at benchmarking and validation of the state-of-the-art method, which enables extraction of the necessary information about the extreme system dynamics from onboard measured time histories. The method proposed in this study opens up broad possibilities of predicting simply, yet efficiently potential failure or structural damage risks for the nonlinear multi-dimensional cargo vessel dynamic systems as a whole. Note that advocated novel reliability method can be used for a wide range of complex engineering systems, thus not limited to cargo ship only.
... Different heuristics were used to find a solution to the problem because of the commercial solver's runtime restrictions and the dimensionality curse that could arise for larger problems. Abioye et al. (2021) developed a new non-linear optimization model for ship schedule recovery with different recovery options, including the adjustment of sailing speed, adjustment of port handling rates, skipping of ports, and skipping of ports with the diversion of containers. The original mathematical model was partially linearized and then solved using the BARON optimization solver. ...
... Considering the dummy nodes, the final port rotation, along with the corresponding distances in nautical miles, can be presented as follows (Searoutes, Table 2 presents the input data utilized in the computational experiments conducted for this study. The primary source for the values of the input data was the previous research related to liner shipping scheduling and ship schedule recovery (Pasha et al., 2020;Zhuge et al., 2020;Abioye et al., 2021;Liu et al., 2022;Wen et al., 2022;OOCL, 2023;PBT International, 2023;Port of Los Angeles, 2023;Searoutes, 2023). Since the SEAP shipping route traverses the North American coast, which is one of the ECAs established by the IMO, it was assumed that the shipping line would use ultra-low sulfur fuel oil (ULSFO) and very-low sulfur fuel oil (VLSFO) within and outside the ECAs, respectively, to ensure compliance with the environmental regulations. ...
Liner shipping networks often experience disruptions, and shipping lines must implement certain recovery measures. However, environmental concerns have to be considered as well. The implementation of vessel speed reduction incentive programs (VSRIPs) provides monetary incentives to shipping lines for sailing speed compliance in the vicinity of certain ports but, in the meantime, increases delays, since the speed-up option could not be used to the same extent. There is a scarcity of research that focuses on effectively addressing the competing objectives that arise during ship schedule recovery and incorporates emission reduction policies at ports. This study introduces a new multi-objective approach for ship schedule recovery, considering the presence of VSRIPs, emission control regulations, and a variety of recovery options. A customized algorithm inspired by the principles of dynamic secant approximation and the ε-constraint algorithm is developed and validated through extensive computational experiments. Detailed sensitivity analyses provide thorough managerial insights as well.
... Sea transportation, in particular, a critical factor in facilitating the movement of goods and services across the globe. Now, about 90% of world trade is transported by the international shipping industry [1][2][3][4][5]. With the surge in demand for container shipping, global maritime trade rebounded in 2021. ...
Uncertainties, such as road restrictions at shipyards and the irregular shape of blocks, pose challenges for transporter scheduling. Efficient scheduling of multiple transporters is critical to improving transportation efficiency. The digital twin (DT) technology offers numerous benefits, enabling interactions between the virtual and real worlds, real-time mapping, and dynamic performance evaluation. Based on DT technology, this study proposes a dynamic scheduling approach for cooperative transportation utilizing multiple transporters. The scheduling problem for multiple transporters is addressed and modeled in this study, considering factors such as block size and transporter loading. To solve this problem, a framework of DT-based multiple transporters system is established in a virtual environment. By inputting block information into this system, a solution is generated using transporter scheduling rules and interference detection methods. Experimental comparisons are conducted in this paper, exploring various scenarios with different number of tasks and the application of DT. The results demonstrate that the proposed approach effectively enhances transportation efficiency and improves ship construction efficiency. Hence, this study expands the application of DT technology in dynamic scheduling of transportation in shipyards and provides new ideas for shipbuilding company managers.
... Most papers published on disruption management focus on post-disruption recovery, with some immediate measures including port skipping or swapping (Abioye et al., 2020), rescheduling based on weather with the overall objective to minimize losses (De et al., 2019). Adjustments of buffer times between port calls with speed adjustments are also a recurring subject (Mulder et al., 2019). ...
Purpose
This paper focusses on the aftermath of disruptions and the importance of the two largest canals (Suez and Panama), commenting on how during the pandemic the canal fees were lowered. Considering the ongoing efforts to decarbonize shipping, some of the ongoing disruptions will help reach these objectives faster.
Design/methodology/approach
Following a literature review of route choice in shipping, and a presentation of significant disruptions in recent years, the author deploys a simplified fuel consumption model and conduct case study analyses to compare different routes environmentally and economically.
Findings
The results explain why at times of low fuel prices as in 2020, canals provided discounts to entice ship operators to keep transiting these, instead of opting for longer routes. Considering the ongoing repercussions of the pandemic in supply chains, as well as the potential introduction of market-based measures in shipping, the value of transiting canals will be much higher in the coming years.
Research limitations/implications
The main limitation in this work is that the author used the publicly available information on canal tolls, for the different ship types examined.
Practical implications
The envisioned model is simple, and it can be readily used for any ship and route (port to port) combination available, if ship data are available to researchers.
Social implications
It is possible that canal tolls will increase, to account for the additional environmental benefits brought to ship operators.
Originality/value
The methodology is simple and transferable, and the author proposes several interesting research questions for follow-up work.
... One crucial aspect of maritime transportation's significance lies in its unmatched ability to efficiently and affordably move a wide range of goods internationally, making it a pivotal mode for conveying diverse commodities (Dulebenets, 2022;Elmi et al., 2022). The intricate dynamics of the maritime supply chain hold immense importance within the global economy, underscored by its indispensable role in facilitating over 80 % of the world's trade (Abioye et al., 2021;UNCTAD, 2022;Wang and Wang, 2021). The substantial cargo capacity of maritime transport facilitates the transportation of large quantities of goods, including raw materials, intermediates, and finished products, across vast distances (Chen et al., 2023). ...
Purpose
Disruptions at ports may destroy the planned ship schedules profoundly, which is an imperative operation problem that shipping companies need to overcome. This paper attempts to help shipping companies cope with port disruptions through recovery scheduling.
Design/methodology/approach
This paper studies the ship coping strategies for the port disruptions caused by severe weather. A novel mixed-integer nonlinear programming model is proposed to solve the ship schedule recovery problem (SSRP). A distributionally robust mean conditional value-at-risk (CVaR) optimization model was constructed to handle the SSRP with port disruption uncertainties, for which we derive tractable counterparts under the polyhedral ambiguity sets.
Findings
The results show that the size of ambiguity set, confidence level and risk-aversion parameter can significantly affect the optimal values, decision-makers should choose a reasonable parameter combination. Besides, sailing speed adjustment and handling rate adjustment are effective strategies in SSRP but may not be sufficient to recover the schedule; therefore, port skipping and swapping are necessary when multiple or longer disruptions occur at ports.
Originality/value
Since the port disruption is difficult to forecast, we attempt to take the uncertainties into account to achieve more meaningful results. To the best of our knowledge, there is barely a research study focusing on the uncertain port disruptions in the SSRP. Moreover, this is the first paper that applies distributionally robust optimization (DRO) to deal with uncertain port disruptions through the equivalent counterpart of DRO with polyhedral ambiguity set, in which a robust mean-CVaR optimization formulation is adopted as the objective function for a trade-off between the expected total costs and the risk.
Container vessel dynamics
Liner shipping plays a major role for freight transportation and international seaborne trade. The economic development of different countries is significantly dependent on the movement of a containerized cargo. One of the most challenging decision problems, tackled by liner shipping companies, is the design of vessel schedules. At the vessel scheduling stage, the liner shipping company aims to determine vessel sailing speeds at voyage legs of a given liner shipping route, port times, vessel handling rates at ports, the minimum number of vessels required in order to provide the agreed service frequency at ports, and other factors. Considering the existing pollution levels, the environmental impacts of liner shipping have to be captured in the vessel scheduling models as well. This study conducts a comprehensive survey of the existing research on vessel scheduling in liner shipping. The collected vessel scheduling studies are classified into different categories, including general vessel scheduling, uncertainty in liner shipping operations, collaborative agreements, vessel schedule recovery, and green liner shipping. Based on a detailed analysis of the collected literature, findings are discussed, and limitations in the state-of-the-art are identified for each category of studies. The study concludes with a number of future research opportunities, taking into account the recent developments and trends in liner shipping.
Liner shipping is a vital component of the world trade. Liner shipping companies usually operate fixed routes and announce their schedules. However, disruptions in sea and/or at ports affect the planned vessel schedules. Moreover, some liner shipping routes pass through the areas, designated by the International Maritime Organization (IMO) as emission control areas (ECAs). IMO imposes restrictions on the type of fuel that can be used by vessels within ECAs. The vessel schedule recovery problem becomes more complex when disruptions occur at such liner shipping routes, as liner shipping companies must comply with the IMO regulations. This study presents a novel mixed-integer nonlinear mathematical model for the green vessel schedule recovery problem, which considers two recovery strategies, including vessel sailing speed adjustment and port skipping. The objective aims to minimize the total profit loss, endured by a given liner shipping company due to disruptions in the planned operations. The nonlinear model is linearized and solved using CPLEX. A number of computational experiments are conducted for the liner shipping route, passing through ECAs. Important managerial insights reveal that the proposed methodology can assist liner shipping companies with efficient vessel schedule recovery, minimize the monetary losses due to disruptions in vessel schedules, and improve energy efficiency as well as environmental sustainability.
We deal with a schedule design problem for a heterogeneous fleet liner shipping service under uncertain waiting and handling times at ports. In a liner shipping service, longer than expected waiting and handling times at a port may cause a delay from scheduled departure time. We consider the problem to find the departure times at ports and sailing times of ships between ports so that the total fuel burn is minimized while targeted overall service level (a performance measure based on on-time departure probabilities) is achieved. We consider two new aspects of the problem. The first one is the heterogeneous fleet where each ship type may have different fuel efficiency, i.e. a different fuel burn function. The second one is considering critical ports on the route, i.e. considering the fact that on-time performance at some critical ports might be more important for the shipping company. We propose a model which finds different service levels for different ship type-port pairs by considering importance of ports and fuel efficiencies of ships. We also give a new overall service level measure for the entire route by combining service levels for different ship type-ports pairs. We propose a chance constrained nonlinear mixed integer programming formulation for the problem. Finally, we give computational results that show the effects of several experimental factors on fuel consumption, speed and service level.
Liner shipping is vulnerable to many disruptive factors such as port congestion or harsh weather, which could result to delay in arriving at the ports. It could result in both financial and reputation losses. The vessel schedule recovery problem (VSRP) is concerned with different possible actions to reduce the effect of disruption. In this work, we are concerned with speeding up strategy in VSRP, which is called the Speed-based Vessel Schedule Recovery Problem (S-VSRP). We model S-VSRP as a multiobjective optimization (MOO) problem and resort to several multiobjective evolutionary algorithms (MOEAs) to approximate the optimal Pareto set, which provides vessel route-based speed profiles. It gives the stakeholders the ability to tradeoff between two conflictive
objectives: total delay and financial loss. We evaluate the problem in three scenarios (i.e., scalability analysis, vessel steaming policies, and voyage distance analysis) and statistically validate their performance significance. According to experiments, the problem complexity varies in different scenarios, and NSGA-II performs better than other MOEAs in all scenarios.
The international seaborne trade volumes have been continuously increasing over the last years. Many liner shipping companies started consolidation to form stronger alliances and attract new customers. In order to remain competitive and avoid potential monetary losses liner shipping companies have to improve efficiency of their vessel schedules. Some of the decisions that have to be made by liner shipping companies are conflicting in their nature. However, the existing vessel scheduling models generally combine the conflicting objectives into one objective function, which aims to minimize the total route service cost. Such approach imposes limitations for liner shipping companies in the analysis of tradeoffs between the conflicting objectives. To avoid the latter drawback this study proposes a multi-objective mixed integer nonlinear optimization model for the vessel scheduling problem, which accounts for all major route service cost components reported in the literature and separates them in two conflicting groups. The original mixed integer nonlinear model is linearized by discretizing the vessel sailing speed reciprocal, and the Global Multi-Objective Optimization Algorithm is developed to solve the linearized model. A set of numerical experiments are conducted for the Asia-Mediterranean Express Service liner shipping route. Results demonstrate that negotiation of both vessel service time windows and handling rates between liner shipping companies and marine container terminal operators may significantly reduce the total route service cost components. Furthermore, vessel schedules are found to be more sensitive to the unit fuel cost as compared to the unit carbon dioxide emission cost.
Increasing volumes of the international seaborne trade and new regulations on vessel emissions require liner shipping companies to enhance efficiency of their operations to remain competitive and in the meantime comply with the established restrictions on emissions that are produced by vessels. This paper presents a novel mixed integer nonlinear mathematical programming model for the green vessel scheduling problem with transit time requirements in a liner shipping route with “Emission Control Areas”, which not only enforces constraints on the quantity of emissions that are produced by vessels within “Emission Control Areas”, but also captures the cargo transit time requirements. The model’s objective aims to minimize the overall route service cost. A number of linearization techniques are proposed for linearizing the original nonlinear problem. The dynamic secant approximation procedure is used to solve the linearized problem. A set of numerical experiments are performed to evaluate the efficiency of the proposed solution approach and assess the effect of introducing both emission constraints and cargo transit time requirements on design of vessel schedules.
Purpose
Emissions produced by oceangoing vessels not only negatively affect the environment but also may deteriorate health of living organisms. Several regulations were released by the International Maritime Organization (IMO) to alleviate negative externalities from maritime transportation. Certain polluted areas were designated as “Emission Control Areas” (ECAs). However, IMO did not enforce any restrictions on the actual quantity of emissions that could be produced within ECAs. This paper aims to perform a comprehensive assessment of advantages and disadvantages from introducing restrictions on the emissions produced within ECAs. Two mixed-integer non-linear mathematical programs are presented to model the existing IMO regulations and an alternative policy, which along with the established IMO requirements also enforces restrictions on the quantity of emissions produced within ECAs. A set of linearization techniques are applied to linearize both models, which are further solved using the dynamic secant approximation procedure. Numerical experiments demonstrate that introduction of emission restrictions within ECAs can significantly reduce pollution levels but may incur increasing route service cost for the liner shipping company.
Design/methodology/approach
Two mixed-integer non-linear mathematical programs are presented to model the existing IMO regulations and an alternative policy, which along with the established IMO requirements also enforces restrictions on the quantity of emissions produced within ECAs. A set of linearization techniques are applied to linearize both models, which are further solved using the dynamic secant approximation procedure.
Findings
Numerical experiments were conducted for the French Asia Line 3 route, served by CMA CGM liner shipping company and passing through ECAs with sulfur oxide control. It was found that introduction of emission restrictions reduced the quantity of sulfur dioxide emissions produced by 40.4 per cent. In the meantime, emission restrictions required the liner shipping company to decrease the vessel sailing speed not only at voyage legs within ECAs but also at the adjacent voyage legs, which increased the total vessel turnaround time and in turn increased the total route service cost by 7.8 per cent.
Research limitations/implications
This study does not capture uncertainty in liner shipping operations.
Practical implications
The developed mathematical model can serve as an efficient practical tool for liner shipping companies in developing green vessel schedules, enhancing energy efficiency and improving environmental sustainability.
Originality/value
Researchers and practitioners seek for new mathematical models and environmental policies that may alleviate pollution from oceangoing vessels and improve energy efficiency. This study proposes two novel mathematical models for the green vessel scheduling problem in a liner shipping route with ECAs. The first model is based on the existing IMO regulations, whereas the second one along with the established IMO requirements enforces emission restrictions within ECAs. Extensive numerical experiments are performed to assess advantages and disadvantages from introducing emission restrictions within ECAs.
Increasing size of vessels and formation of alliances are the common strategies, which have been widely used by liner shipping companies over the last years, aiming to serve the growing demand for the international seaborne trade efficiently. However, without a proper design of vessel schedules liner shipping companies may incur substantial monetary losses. This paper proposes a novel collaborative agreement, according to which multiple vessel arrival time windows, start and end times for each time window, and multiple handling rates during each time window are offered by the marine container terminal operator to the liner shipping company at each port of the given liner shipping route. The vessel scheduling problem is formulated as a mixed integer nonlinear programming model, where the total liner shipping route service cost is minimized. A set of linearization techniques are applied to the original model, and the linearized model is solved using CPLEX. A number of computational experiments are performed for the Pacific Atlantic 1 liner shipping route, served by the NYK liner shipping company. Results showcase effectiveness of the adopted solution methodology. Moreover, the proposed collaborative agreement outperforms the existing collaborative agreements, where either vessel arrival time windows or handling rates are offered to the liner shipping company at ports, in terms of the total route service cost on average by 10.9% and 6.6%, respectively. Therefore, the proposed collaborative agreement can be considered as an efficient alternative for improving the liner shipping operations.
Considering a substantial increase in the international seaborne containerized trade volumes, marine container terminal operators have to improve efficiency of the processes inside their terminals in order to meet the growing demand. An efficient berth scheduling is of a high importance for the terminal's performance, as it significantly influences the turnaround time of vessels. This paper proposes a novel Evolutionary Algorithm to assist with berth scheduling at marine container terminals that, unlike published to date studies on berth scheduling, applies a parameter control strategy. Specifically, an adaptive mechanism is developed for the mutation operator, in which the mutation rate is altered based on feedback from the search. The objective of the proposed mixed integer model aims to minimize the total weighted vessel service cost. A set of numerical experiments are conducted to assess performance of the developed algorithm based on a comparison against a typical Evolutionary Algorithm that applies a constant mutation rate value, determined from the parameter tuning analysis. Results indicate that the optimality gap does not exceed 0.80% for both algorithms. Furthermore, deployment of the adaptive mechanism for the mutation operator yields an average of 5.4% and 8.5% savings in terms of the total weighted vessel service cost for medium and large size problem instances, respectively, without a significant increase in the computational time.
Increasing volumes of the international seaborne trade force liner shipping companies to improve efficiency of their operations to remain competitive. Many of liner shipping companies continue increasing size of their vessels, as larger vessels provide lower voyage costs per container due to their economies of scale. Larger vessels also allow liner shipping companies more efficiently share the demand with the alliance partners. Nowadays, many of liner shipping routes are served by vessels of different types (e.g., small, medium, large). However, the key assumption of studies on vessel scheduling, conducted to date, is homogeneous nature of the vessel fleet (i.e., all vessels in the fleet, serving a given liner shipping route, have the same technical characteristics). This study proposes a novel mathematical model for the vessel scheduling problem with heterogeneous fleet. The objective of a mixed integer non-linear model is to minimize the total vessel turnaround cost. Due to high non-linearity of the proposed mathematical model a non-linear optimization solver is used to solve it. Numerical experiments are performed to evaluate efficiency of the proposed solution approach and the novel methodology. Results demonstrate a computational efficiency of the adopted solution approach. Furthermore, vessel schedules are found to be more sensitive to introduction of larger vessels in the fleet as compared to increase in the unit bunker cost.