Container liner shipping period interference recovery method and system based on improved space-time network, and medium

Abstract

The invention discloses a container liner shipping period interference recovery method and system based on an improved space-time network, and a medium, and belongs to the field of interference management of ship navigation. Firstly, liner operation and interference delay data are acquired; an improved space-time network is constructed, the ship navigation process is simulated by generating space-time nodes and connecting arcs, and the network scale is optimized by adopting a redundancy deletion strategy; on the basis, a mathematical optimization model considering the laws and regulations of the emission control area is constructed with the minimum total cost as the target, and the total cost comprises the fuel cost, the capital operation cost, the delay cost and the port jumping cost; and finally, an optimization solver is adopted to solve the model, and an optimal shipping date recovery scheme is generated. According to the method, the economic benefits of compliance navigation and shipping schedule interference recovery of the emission control area of the container liner are comprehensively considered, decision reference is provided for improving the transportation efficiency of a container liner company, and green shipping development is promoted from the operation level.

Description

Technical Field

[0001] This invention belongs to the field of interference management for ship navigation, and specifically relates to a method, system and medium for restoring container liner schedule interference based on an improved spatiotemporal network. Background Technology

[0002] In the field of international trade, maritime transport has become an indispensable and economically efficient form of logistics due to its significant advantages of large cargo capacity and low cost. In my country, the maritime transport industry occupies a core position in the foreign trade landscape, undertaking approximately 95% of import and export cargo transportation tasks. Among them, liner shipping, with its reliability, efficiency, and extensive service network, has become one of the most important forms of maritime transport.

[0003] However, due to the highly uncertain environment of maritime transport, especially the numerous unforeseen disruptive events, liner shipping often experiences delays, making it difficult to arrive at the destination port on schedule. This severely impacts the stability of the supply chain. According to the global trunk route comprehensive on-time performance index released by the Shanghai Shipping Exchange in December 2024, the current comprehensive on-time performance index is only 36.68%. The delays and unpredictability of cargo transportation directly hinder the smooth operation of the supply chain and the normal growth of business. Therefore, strengthening liner disruption management is urgently needed.

[0004] With the continuous development of global maritime transport, air pollutants emitted by ships have gradually attracted attention, especially in ports, straits, and sea areas with dense shipping traffic. To reduce ship emissions and promote green shipping, the International Maritime Organization (IMO) has established and implemented a strict Emission Control Area (ECA) system. Since January 1, 2020, the global upper limit for sulfur content in marine fuel oil has been significantly reduced from 3.50% m / m to 0.50% m / m. This regulation applies to all ships operating outside designated ECAs, while the upper limit within ECAs is strictly limited to 0.10% m / m. Currently, four ECAs have been designated: the Baltic Sea, the North Sea, North America and the Caribbean, and the Mediterranean Sea, which will come into effect on May 1, 2025. Ships at sea must strictly comply with existing international conventions and laws and regulations concerning ECAs. Low-sulfur fuel oil is often much more expensive than high-sulfur fuel oil; therefore, liner ships typically reduce speed within ECAs to reduce the consumption of expensive fuel oil. However, when uncertainties arise, liner services need to accelerate to reduce schedule delays, especially when considering compliant navigation within and outside emission control areas. Choosing the appropriate speed to minimize delays and balancing economic and environmental benefits has become an urgent issue.

[0005] In the field of research on ship schedule disruption management, although numerous academic journal articles and a small number of patents can be found through publicly available information, such as Chai Jieqiong's "Research on Cruise Ship Schedule Recovery Based on Disruption Management" published in *Logistics Technology*, 2015, Issue 16; Xing Jiangbo et al.'s "Linerary Shipping Schedule Recovery Model Considering Container Flow Recovery" published in *Transportation Systems Engineering and Information*, 2017, Issue 02; Zhao Xu et al.'s "Research on Multi-Objective Model for Liner Shipping Container Flow Disruption Recovery" published in *China Water Transport (Second Half Month)*, 2019, Issue 11; and Lin... The following papers are cited: "Bilingual Objective Optimization of Liner Schedule Recovery Based on Improved NSGA-II Algorithm" published by Jin et al. in the Journal of Dalian Maritime University, 2020, No. 2; "Liner Schedule Interference Recovery Model Based on Hierarchical Recovery Strategy" published by Zhuang Huimin et al. in China Water Transport, 2020, No. 6; "Research on Container Liner Interference Recovery Based on Redundancy Elimination Time Period Network" published by Hu Yuzhen et al. in China Management Science, 2024 (first published online); and the invention patent "A Joint Optimization Method and System for Container Liner Route Speed" with publication number CN117910366A.

[0006] These published journal articles mainly concern the management of shipping schedule disruptions, but none of them fully consider the policy constraints of compliant navigation in emission control areas. Although the invention patent "A Joint Optimization Method and System for Container Liner Route Speed" considers emission control areas in speed optimization, it mainly focuses on the optimization of container liner navigation in the planning stage, rather than on disruption management in the operational stage. It is evident that the existing technology has obvious limitations and shortcomings in dealing with the problem of restoring container liner shipping schedule disruptions under emission control area regulations. An effective solution is urgently needed to ensure that container liner transportation can efficiently respond to disruption events and achieve rapid restoration of shipping schedules and stable operation while meeting environmental protection requirements. Summary of the Invention

[0007] The purpose of this invention is to provide a method, system, and medium for restoring container liner schedules after disruptions based on an improved spatiotemporal network. This method restores schedules after disruptions while meeting emission control zone navigation requirements, thereby balancing the economic and environmental benefits of liner companies, improving the ability of container liner shipping to cope with uncertainties, and promoting the development of green shipping.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] A method for recovering container liner shipping schedule disruptions based on an improved spatiotemporal network, specifically including:

[0010] Based on acquired delay data caused by liner company operations and interference, an improved spatiotemporal network with redundancy reduction strategies was constructed. The construction process includes: generating a network structure comprising spatiotemporal nodes and arcs based on operational and delay data; the spatiotemporal nodes include initial nodes, intermediate nodes, and sink nodes, and the arcs include navigation arcs representing inter-port navigation and stationary arcs representing berthing in ports; wherein, the node time information, speed changes, and navigation arc cost information in the network structure are determined by simulating the navigation process of ships at different speeds, and redundancy is reduced in the generated spatiotemporal network structure to optimize the network size;

[0011] Based on the improved spatiotemporal network, a mathematical model for liner schedule disruption recovery with the objective of minimizing total cost is constructed, and the model complies with emission control area regulations;

[0012] The container liner schedule disruption recovery model is solved using an optimization solver, and a container liner schedule disruption recovery scheme is output.

[0013] Furthermore, the acquired delay data caused by liner company operations and disruptions includes: container liner size M; planned port of call P for the route; and planned arrival time bte for port P. p and planned departure time dte p Port P's service time in port t p Low-sulfur fuel price Pi, high-sulfur fuel price Po, minimum speed V min Maximum speed V max Number of containers loaded at port P and the number of containers unloaded Liner unit delay cost dl, container unit delay cost dc, distance between two adjacent ports (p, p') within the emission control area. Distance to navigation outside emission control areas The delay time Dt caused by the interference.

[0014] Furthermore, the generated spatiotemporal nodes are: a set of initial nodes OnS, intermediate nodes MnS, and sink nodes SnS generated based on the original planned node set OsS, Dt, speed discrete interval Δv, network interval Δs, and interference recovery end time Tt; the generated arcs are: a set of navigation arcs SarcS and dwell arcs TarcS.

[0015] Furthermore, the computational network structure includes node time information, restrictions on speed changes, and navigation arc costs:

[0016] According to the formula Calculate the fuel costs of container liners included in the navigation arc within the emission control area;

[0017] According to the formula Calculate the fuel costs of container liners included in the navigation arc outside the emission control area;

[0018] According to the formula Calculate the capital and operating costs of container liners included in the navigation arc within the emission control area;

[0019] According to the formula Calculate the capital and operating costs of container liners included in the navigation arc outside the emission control area;

[0020] According to the formula Calculate the delay costs included in the flight arc;

[0021] Where λ is fuel efficiency; γ is the capital cost coefficient; and These represent the speeds of container liners inside and outside emission control areas, respectively; V min V is the lower limit of speed. max As the upper limit of speed, the speed satisfies bta p' bte represents the actual arrival time of the navigation arc. p' Here, dl represents the planned arrival time of the navigation arc, dc represents the unit delay cost for liner shipping, and dc represents the unit delay cost for container shipping. The number of containers unloaded at port P.

[0022] Furthermore, the actual arrival time at the port of the navigation arc. According to the formula dta p =max(bta) p +t p ,dte p ) Calculate the actual departure time of the navigation arc from the port, where t p dta represents the service time of a liner at port p. p dte represents the actual time the container liner leaves the port (p). p This indicates the time when the container liner is scheduled to leave port p.

[0023] Furthermore, the spatiotemporal network structure undergoes redundancy reduction, specifically including:

[0024] (1) Among all nodes belonging to the port of origin, delete the intermediate nodes other than the initial node;

[0025] (2) Traverse all nodes and calculate the in-degree of each node according to the number of arcs emanating from the node and the number of arcs reaching the node.

[0026] (3) Delete nodes with an out-degree or in-degree of 0, and delete the arcs connected to those nodes;

[0027] (4) Repeat steps (2) to (3) until there are no nodes in the network structure that can be deleted.

[0028] Furthermore, the total cost includes fuel costs, capital and operating costs, delay costs, and port-skipping costs; the port-skipping costs... The number of containers loaded at port P. denoted as , where is the number of containers unloaded at port P, and ctc is the unit charter cost for a container.

[0029] The objective function of the mathematical model for liner schedule disruption recovery is:

[0030]

[0031] Where Z represents the total cost, L represents the set of initial and intermediate nodes, i and j are the indices of the nodes, K(i) represents the set of nodes originating from node i, and y ij Indicates whether to take the navigation arc from node i to node j, Fc ij and Fo ij Divided into representing the fuel costs of container liners inside and outside emission control areas, Oc ij and Oo ij The breakdown represents the capital and operating costs of container liners both inside and outside emission control areas, Dc ij q represents the delay cost of container liner shipping. p Indicate whether to skip ports p and C. p The port skipping cost for container liners to skip port P.

[0032] Furthermore, the optimization solver is CPLEX.

[0033] A computer device / apparatus / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a container liner schedule disruption recovery method based on an improved spatiotemporal network.

[0034] A computer-readable storage medium having a computer program / instructions thereon that, when executed by a processor, implements the steps of a method for recovering container liner shipping schedule interference based on an improved spatiotemporal network.

[0035] The beneficial effects of this invention are as follows:

[0036] This invention focuses on the problem of schedule disruption recovery for container liner ships under emission control area (ECA) compliance. By combining traditional spatiotemporal network structures with the operational characteristics of individual container liners, redundant arcs and nodes are removed to improve the spatiotemporal network, reduce its size, and increase the efficiency of network model solving. Simultaneously, this invention explores how container liners can cope with the challenges of ECA compliance after encountering disruptions. Through a targeted spatiotemporal network model, it comprehensively considers the economic benefits of ECA compliance and schedule disruption recovery for container liners, providing decision-making references for improving the transportation efficiency of container liner companies and promoting green shipping development from an operational perspective. Attached Figure Description

[0037] Figure 1 This is a flowchart of the container liner shipping schedule interference recovery method based on an improved spatiotemporal network according to the present invention.

[0038] Figure 2 This is a comparison chart of the model solving performance measured by the present invention. Detailed Implementation

[0039] The present invention will now be further described with reference to the accompanying drawings.

[0040] This invention addresses the problem of container liner schedule interference management in existing technologies that do not fully consider emission control area regulations. It proposes a method, system, and medium for container liner schedule interference recovery based on an improved spatiotemporal network. Figure 1 The method includes the following steps:

[0041] Step S1: Obtain data related to liner company operations and disruptions. Based on the operational situation, set the values ​​for the following parameters accordingly:

[0042] Container liner size M, planned port set P for the route, and planned arrival time at the port bte p Port planned departure time dte p Port service hours t p Fuel price Pi with sulfur content not exceeding 0.10% m / m, fuel price Po with sulfur content not exceeding 0.50% m / m, and minimum speed limit V. min Speed ​​limit V max Number of containers loaded at the port Number of containers unloaded at the port Liner unit delay cost dl, container unit delay cost dc, distance between ports within emission control areas Distance between ports navigating outside emission control areas The delay time Dt caused by the interference.

[0043] Step S2: Based on the improved spatiotemporal network, characterize the liner schedule interference recovery problem, and generate the set of initial nodes, intermediate nodes, sink nodes, navigation arcs and dwell arcs of the improved spatiotemporal network.

[0044] Step S21: Define and initialize the node and arc sets of the improved spatiotemporal network. All nodes contain spatial port information and time information. The arc and node sets contain the original planned node set OsS, the initial node OnS, the intermediate node MnS, and the sink node SnS, as well as the navigation arc SarcS and the dwell arc TarcS.

[0045] Step S22: Generate an initial node set OnS, an intermediate node set MnS, and a sink node set SnS, as well as a navigation arc set SarcS and a dwell arc set TarcS, based on the original planned nodes (according to the planned arrival times at each port in the shipping schedule), the delay time Dt caused by the interference, the speed discrete interval Δv, the network interval Δs, and the time Tt after the interference recovery ends. The time information of the initial nodes and intermediate nodes, and the cost information included in the navigation arcs, are calculated using the following formula:

[0046] pass Calculate the actual arrival time of the flight arc to form intermediate nodes;

[0047] via DTA p =max(bta) p +t p ,dte p (2) Calculate the actual departure time of the liner at each port to form intermediate nodes;

[0048] And according to the constraints of (3) and formula (4) and the speed interval, the speed inside and outside the emission control area is continuously generated, and all possible speed combinations are traversed between any two ports;

[0049]

[0050] Through formula Calculate the fuel costs of container liners included in the navigation arc within the emission control area;

[0051] Through formula Calculate the fuel costs of container liners included in the navigation arc outside the emission control area;

[0052] Through formula Calculate the capital and operating costs of container liners included in the navigation arc within the emission control area;

[0053] Through formula Calculate the capital and operating costs of container liners included in the navigation arc outside the emission control area;

[0054] Through formula Calculate the delay costs included in the flight arc;

[0055] Where λ is the fuel efficiency and γ is the capital cost coefficient; and These represent the speeds of container liners inside and outside emission control areas, respectively; V min V is the lower limit of speed. max For the maximum speed, bte p' Here, dl represents the planned arrival time of the navigation arc, dc represents the unit delay cost for liner shipping, and dc represents the unit delay cost for container shipping. The number of containers unloaded at port P.

[0056] Step S23: Redundancy reduction of sink nodes, navigation arcs, and dwell arcs in the generated spatiotemporal network;

[0057] Step S231: Among all nodes belonging to the port of origin, delete the intermediate nodes other than the initial node;

[0058] Step S232: Traverse all nodes and calculate the in-degree and out-degree of each node according to the number of arcs emanating from the node and the number of arcs reaching the node.

[0059] Step S233: Delete nodes with an out-degree or in-degree of 0, and delete the arcs connected to those nodes;

[0060] Step S234: Repeat steps S232-S233 until there are no more nodes to delete.

[0061] Step S24: Output the set of initial nodes OnS, intermediate nodes MnS and sink nodes SnS, as well as the set of navigation arcs SarcS and dwell arcs TarcS of the improved spatiotemporal network.

[0062] Step S3: Construct a liner schedule disruption recovery model that complies with emission control area regulations.

[0063] First, based on the number of containers loaded and unloaded at each port, the cost of skipping that port is calculated using formula (10).

[0064]

[0065] Then, combining the set of nodes and arcs from step S2 with the port skipping cost, a liner schedule disruption recovery model that complies with emission control area regulations is constructed using formula (11).

[0066]

[0067] Step S4: Solve the model to obtain a solution for container liner schedule disruptions that comply with emission control area regulations.

[0068] By solving the constructed model using CPLEX, a solution for container liner schedule disruptions considering emission control area regulations is obtained.

[0069] To further illustrate the specific implementation process of this invention, a test case is provided using a container liner sailing on a route calling at 12 ports. This case tests a scenario where interference occurs at the port of origin, causing a 24-hour delay. The improved spatiotemporal network modeling method of this invention is used to provide a recovery scheme for container liner schedule interference. The speed discrete interval of the improved spatiotemporal network is set to 1 knot, and the network interval is set to 3 hours. Figure 2 This test case demonstrates the application of the target value of the container liner interference recovery scheme based on the present invention. After adopting the interference recovery scheme of the present invention, the target value changed from 15,027,578 to 14,327,290, that is, the total cost was significantly reduced, proving the effectiveness of the present invention.

[0070] Through the detailed implementation methods described above, this invention effectively solves the problem of restoring container liner shipping schedules amidst emission control zones, providing liner companies with a scientific, reasonable, and practical solution. This improves the efficiency and reliability of liner operations and reduces economic losses and environmental impacts caused by disruptions. In practical applications, relevant parameters and data can be adjusted and improved according to the specific operating conditions and needs of different liner companies, further enhancing the applicability and effectiveness of this invention.

[0071] In particular, in some preferred embodiments of the present invention, a computer device is also provided, including a memory and a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the container liner schedule interference recovery method based on an improved spatiotemporal network described in any of the above embodiments.

[0072] In some other preferred embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program / instruction is stored, wherein when the computer program is executed by a processor, the steps of the container liner schedule interference recovery method based on an improved spatiotemporal network described in any of the above embodiments are implemented.

[0073] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above embodiments of the container liner schedule interference recovery method based on improved spatiotemporal networks, which will not be repeated here.

[0074] Computer-readable storage media encompass a variety of types, including persistent and non-persistent, portable and fixed. These media store information using different technologies, and the content can be machine instructions, data structures, program modules, or other types of data. Some typical examples of computer storage media include: phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), various types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory and other storage technologies, optical storage media such as CD-ROM and digital video disc (DVD), magnetic storage devices such as magnetic tape and disks, and other non-transferable media used to store information accessible to computing devices. It is important to note that the computer-readable media described herein do not include temporary storage media, such as modulated data signals and carrier waves.

[0075] Those skilled in the art will further recognize that the operation of the module can be achieved using existing technical protocols or programs, without relying on new computer programs themselves. The units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0076] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented in hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0077] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for recovering container liner shipping schedule interference based on an improved spatiotemporal network, characterized in that, Specifically, it includes: Based on the acquired delay data caused by liner company operations and disruptions, an improved spatiotemporal network was constructed, incorporating a redundancy reduction strategy. The construction process includes: generating a network structure including spatiotemporal nodes and arcs based on operational data and delay data; the spatiotemporal nodes include initial nodes, intermediate nodes, and sink nodes, and the arcs include navigation arcs representing navigation between ports and dwell arcs representing berthing in ports; wherein, the node time information, speed changes, and navigation arc cost information in the network structure are determined by simulating the navigation process of ships at different speeds, and redundancy is removed from the generated spatiotemporal network structure to optimize the network size; Based on the improved spatiotemporal network, a mathematical model for liner schedule disruption recovery with the objective of minimizing total cost is constructed, and the model complies with emission control area regulations; The container liner schedule disruption recovery model is solved using an optimization solver, and a container liner schedule disruption recovery scheme is output.

2. The method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 1, characterized in that, The acquired delay data due to liner company operations and disruptions includes: container liner size M; planned port of call P for the route; and planned arrival time bte for port P. p and planned departure time dte p Port P's service time in port t p Low-sulfur fuel price Pi, high-sulfur fuel price Po, minimum speed V min Maximum speed V max Number of containers loaded at port P and the number of containers unloaded Liner unit delay cost dl, container unit delay cost dc, distance between two adjacent ports (p, p') within the emission control area. Distance to navigation outside emission control areas The delay time Dt caused by the interference.

3. The method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 2, characterized in that, The generated spatiotemporal nodes are: a set of initial nodes OnS, intermediate nodes MnS, and sink nodes SnS generated based on the original planned node set OsS, Dt, speed discrete interval Δv, network interval Δs, and interference recovery end time Tt; the generated arcs are: a set of navigation arcs SarcS and dwell arcs TarcS.

4. The method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 3, characterized in that, The computational network structure includes node time information, speed limit variations, and navigation arc costs. According to the formula Calculate the fuel costs of container liners included in the navigation arc within the emission control area; According to the formula Calculate the fuel costs of container liners included in the navigation arc outside the emission control area; According to the formula Calculate the capital and operating costs of container liners included in the navigation arc within the emission control area; According to the formula Calculate the capital and operating costs of container liners included in the navigation arc outside the emission control area; According to the formula Calculate the delay costs included in the flight arc; Where λ is fuel efficiency; γ is the capital cost coefficient; and These represent the speeds of container liners inside and outside emission control areas, respectively; V min V is the lower limit of speed. max As the upper limit of speed, the speed satisfies bta p' bte represents the actual arrival time of the navigation arc. p' Here, dl represents the planned arrival time of the navigation arc, dc represents the unit delay cost for liner shipping, and dc represents the unit delay cost for container shipping. The number of containers unloaded at port P.

5. The method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 4, characterized in that, The actual arrival time of the navigation arc at the port According to the formula dta p =max(bta) p +t p ,dte p ) Calculate the actual departure time of the navigation arc from the port, where t p dta represents the service time of a liner at port p. p dte represents the actual time the container liner leaves the port (p). p This indicates the time when the container liner is scheduled to leave port p.

6. The method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 3, characterized in that, The spatiotemporal network structure undergoes redundancy reduction, specifically including: (1) Among all nodes belonging to the port of origin, delete the intermediate nodes other than the initial node; (2) Traverse all nodes and calculate the in-degree of each node according to the number of arcs emanating from the node and the number of arcs reaching the node. (3) Delete nodes with an out-degree or in-degree of 0, and delete the arcs connected to those nodes; (4) Repeat steps (2) to (3) until there are no nodes in the network structure that can be deleted.

7. A method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 1 or 4, characterized in that, The total cost includes fuel costs, capital and operating costs, delay costs, and port-skipping costs; the cost of skipping a port... The number of containers loaded at port P. denoted as , where is the number of containers unloaded at port P, and ctc is the unit charter cost for a container. The objective function of the mathematical model for liner schedule disruption recovery is: Where Z represents the total cost, L represents the set of initial and intermediate nodes, i and j are the indices of the nodes, K(i) represents the set of nodes originating from node i, and y ij Indicates whether to take the navigation arc from node i to node j, Fc ij and Fo ij Divided into representing the fuel costs of container liners inside and outside emission control areas, Oc ij and Oo ij The breakdown represents the capital and operating costs of container liners both inside and outside emission control areas, Dc ij q represents the delay cost of container liner shipping. p Indicate whether to skip ports p and C. p The port skipping cost for container liners to skip port P.

8. The method for recovering container liner shipping schedule interference based on an improved spatiotemporal network according to claim 1, characterized in that, The optimization solver is CPLEX.

9. A computer device / equipment / system, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 8.

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