Oil supply ship dispatching optimization method considering order selection

Abstract

The invention provides a fuel supply ship scheduling optimization method considering order selection, and belongs to the technical field of marine transportation, and the method comprises the following steps: S1, building a fuel supply ship scheduling problem based on actual demands, the fuel supply ship scheduling problem comprising an order selection mechanism, client ship distribution and sequence, and fuel supply scheduling; s2, modeling the scheduling problem of the fuel supply ship into a mixed integer linear programming model; and S3, solving the mixed integer linear programming model by adopting a logic-based Benders decomposition algorithm to obtain a scheduling scheme. According to the method, order selection, distribution and sequence of customer ships and fuel oil refilling scheduling are brought into an optimization range by considering a more practical FSVSP-OS, introducing an order selection mechanism, adopting a flexible oil refilling time model, considering travel time between the customer ships, introducing a heterogeneity supply ship model and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of maritime transportation, and more particularly, to an optimization method for fuel supply vessel scheduling considering order selection. Background Art

[0002] The maritime industry is the main mode of transportation for global trade, undertaking approximately 80% of the global trade volume. As the core transportation tool in the maritime industry, ships need to be refueled regularly to maintain operation. With the development of the maritime industry, the offshore refueling service industry has also developed rapidly. Major ports such as Singapore Port, Rotterdam Port in the Netherlands, and Zhoushan Port in China provide fuel supply services, bringing significant profits to the ports. Fuel supply vessels are the main executors of offshore refueling services, responsible for transporting fuel from onshore oil depots to customer vessels. However, the scheduling problem of fuel supply services is very complex, involving multiple decision-making levels, including order selection, vessel allocation, service sequence, and fuel supply plan, etc.

[0003] With limited supply vessel resources, it is necessary to decide whether to accept the fuel demand orders submitted by customers, and to arrange supply vessels to execute the selected order tasks, including vessel allocation and sequence arrangement. In addition, supply vessels also need to refuel at the onshore fuel storage tanks, which poses an additional decision for the refueling scheduling of supply vessels.

[0004] The first study on the Fuel Supply Vessel Scheduling Problem (FSVSP) was in Christiansen et al. (2015). For this problem, the authors proposed a mixed integer programming model and verified it through examples. The goal was to optimize the routes and schedules of supply vessels to maximize the company's profitability. Then, in Christiansen et al. (2017), they contributed to FSVSP by considering a new path flow model and designing a path generation algorithm. However, the above studies ignored order selection, which is a key decision in supply vessel services. In addition, they considered a fixed fuel refueling time and ignored the travel time between different customer vessels. Subsequently, Rachaniotis and Masvoula (2020) considered order selection in FSVSP. They developed a decision-making tool that can help managers decide whether to accept orders. With the goal of minimizing the total fuel transportation cost, order selection, allocation, and sequence were jointly optimized within the time range. However, in their study, the fuel reloading operation was ignored, so their model was simplified to a single-trip VRP vehicle routing problem, rather than the traditional multi-trip VRP. In addition, the sailing distances between different customer vessels could also be ignored in their study.

[0005] The current research on the fuel ship scheduling problem with order selection (FSVSP-OS) is still relatively limited. Existing research usually does not consider order selection, or only focuses on the allocation of customer ships while ignoring the service order. In addition, the refueling time is usually assumed to be fixed, ignoring the travel time between different customer ships. At the same time, existing technologies usually assume that supply ships are homogeneous, without considering differences in the capacity and pumping speed of different supply ships. This assumption limits the flexibility of the scheduling plan and cannot adapt to the diverse needs in actual operations, making it inapplicable to the actual situation. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to propose an optimized fuel supply ship scheduling method considering order selection. By considering a more realistic FSVSP-OS, introducing an order selection mechanism, adopting a flexible refueling time model, considering the travel time between customer ships, and introducing a model of heterogeneous supply ships, etc., the order selection, the allocation and sequence of customer ships, and the fuel refueling scheduling are incorporated into the optimization scope.

[0007] The technical means adopted by the present invention are as follows:

[0008] An optimized fuel supply ship scheduling method considering order selection, comprising the following steps:

[0009] S1. Construct a fuel supply ship scheduling problem based on actual demands;

[0010] S2. Model the fuel supply ship scheduling problem as a mixed-integer linear programming model;

[0011] S3. Use a logic-based Benders decomposition algorithm to solve the mixed-integer linear programming model to obtain a scheduling plan.

[0012] Further, in S2, when establishing the mixed-integer linear programming model, first consider a single optimization objective, and then consider other constraint conditions;

[0013] The single optimization objective is as follows: The mixed-integer linear programming model sets the goal to maximize the total profit;

[0014] Profit is defined as the total revenue minus the total cost, where the total revenue comes from the product of the fuel quantity sold to customer ships and the unit fuel price, and the total cost includes the rental cost of supply ships;

[0015] The objective function of the single optimization objective is as follows:

[0016]

[0017] where: maxz represents the objective function to be maximized, i.e., the total profit z, J is the set of all customer vessels, f is the selling price per unit of fuel, and c j is the cost of serving customer vessel j, and d j represents the fuel demand of customer vessel j, and y j is a decision variable. If customer vessel j is served, then y j = 1; otherwise, y j = 0.

[0018] Furthermore, in S2, the other constraint conditions include order selection constraints, refueling completion time constraints, travel time constraints between customer vessels, heterogeneous supply vessel constraints, and realistic complex constraints;

[0019] The order selection mechanism constraints include the first constraint, the second constraint, and the third constraint, which are specifically as follows:

[0020] Define the decision variable y j , where the decision variable indicates whether to serve a certain customer vessel, 1 for serving and 0 for not serving; whether to accept a specific service request is determined by the decision variable;

[0021] The first constraint:

[0022] where: K represents the set of supply vessels, R represents the set of refueling operations, v jkr is a decision variable. If customer vessel j is served by the r-th trip of supply vessel k, it is 1; otherwise, it is 0, and y j is a decision variable. If customer vessel j is served, it is 1; otherwise, it is 0;

[0023] The first constraint ensures that each customer vessel j is assigned to a certain trip v of the supply vessel jkr , which only occurs when y j = 1, that is, when it is decided to serve this customer vessel;

[0024] The second constraint:

[0025] The second constraint is the service order constraint for the fuel supply vessel. For each customer vessel j, there must be a pre-service point and a post-service point connected to it. The service points are the oil depot 0 or service vessels. k is the fuel supply vessel and r is the number of trips;

[0026] The third constraint:

[0027] where: J is the set of all customer vessels, d j represents the fuel demand of customer vessel j, and y jis a decision variable. If customer vessel j is served, then y j = 1; otherwise y j = 0, O max represents the maximum amount of oil that can be supplied by the onshore fuel tank within the planning time range;

[0028] The third constraint limits the total amount of fuel replenished for the supply vessels within the planning range not to exceed the maximum supply of the onshore oil depot O max ; Only for the selected orders, that is, customer vessels with y j = 1, will their demand d j be calculated;

[0029] The fuel replenishment completion time constraint includes a fourth constraint, which is as follows:

[0030] Considering the correlation between the fuel replenishment time and the replenishment quantity, that is, the replenishment time is linearly related to the replenishment oil quantity. The replenishment time is calculated by the ratio of the replenishment quantity δ kr and the replenishment speed β k ;

[0031] β k represents the replenishment speed of supply vessel k at the oil depot, that is, δ kr / β k represents the time required to complete a specific replenishment quantity δ kr ;

[0032] Fourth constraint:

[0033] where: C kr represents the time when supply vessel k completes the r-th refueling operation, S j represents the service completion time of customer vessel j, t j0 represents the travel time from customer vessel j to the starting point (dock) of supply vessel, α is the fixed setup time for refueling, δ kr represents the refueling quantity during the r-th refueling of supply vessel k, β k represents the refueling speed of supply vessel k at the dock, M1 is a large constant used to ensure that the constraint does not take effect in the absence of refueling operations, v jk,r-1 is a decision variable. If customer vessel j is served by the itinerary after the (r - 1)-th refueling of supply vessel k, it is 1; otherwise it is 0;

[0034] The travel time constraint between customer vessels includes a fifth constraint and a sixth constraint, which are as follows:

[0035] Fifth constraint:

[0036] where: S jis the service completion time of customer vessel j, S i is the service completion time of customer vessel i, t ij is the travel time from customer vessel i to customer vessel j, p jk is the time required for supply vessel k to serve customer vessel j, M3 is a large constant used to ensure that the constraint does not take effect when x ijkr = 0, x ijkr is a decision variable, which is 1 if supply vessel k travels from customer vessel i to customer vessel j during its r-th trip, and 0 otherwise;

[0037] The fifth constraint ensures that the time S when supply vessel k travels to customer vessel j and starts service after completing the service for customer vessel i j must take into account the travel time t from i to j ij ; where, x ijkr is a binary decision variable, which is 1 if supply vessel k travels directly from customer vessel i to customer vessel j during its r-th trip; otherwise 0; a constant set by M3 is used to ensure that when x ijkr = 0, this fifth constraint does not take effect;

[0038] Sixth constraint:

[0039] The sixth constraint ensures that the time S when supply vessel k travels to customer vessel j and starts service after completing the r-th replenishment operation j must take into account the travel time t from the oil depot 0 to customer vessel j j0 ;

[0040] The heterogeneous supply vessel constraints include the seventh constraint, the eighth constraint, the ninth constraint and the tenth constraint:

[0041] Seventh constraint:

[0042] Where: I kr represents the fuel quantity of supply vessel k before the r-th replenishment operation, δ kr represents the fuel quantity replenished by supply vessel k during the r-th replenishment, Q k represents the capacity of supply vessel k, that is, the maximum fuel quantity that the vessel can carry, K is the set of supply vessels, and R ∪ {0} represents the set of all replenishment operations including the initial state;

[0043] The seventh constraint ensures that the fuel quantity of the supply vessel after any replenishment operation does not exceed its capacity;

[0044] Eighth constraint:

[0045] Where: δ kr represents the fuel quantity replenished by supply vessel k during the r-th replenishment, Qk denotes the capacity of supply vessel \(k\), i.e., the maximum amount of oil that the vessel can carry, \(w\) kr is a binary decision variable indicating whether supply vessel \(k\) performs the \(r\)-th refueling operation;

[0046] The eighth constraint ensures that the refueling amount matches the capacity of the supply vessel and whether the refueling operation is performed;

[0047] The ninth constraint: \(I\) k0 = \(Q\) k

[0048] The ninth constraint means that at the start of the planning period, different oil supply vessels are in an initial full-oil state;

[0049] The described realistic complex constraints include customer time window constraints, refueling amount constraints, and other realistic constraints. The customer time window constraints include the tenth constraint and the eleventh constraint;

[0050] The tenth constraint:

[0051] The eleventh constraint:

[0052] where \(e\) j denotes the start time of the time window of customer vessel \(j\), i.e., the earliest time when the customer vessel can receive service;

[0053] where \(l\) j denotes the end time of the time window of customer vessel \(j\), i.e., the latest time when the customer vessel can receive service. The tenth constraint and the eleventh constraint ensure that the supply vessel completes the service within the time window of the customer vessel;

[0054] The refueling amount constraints include the twelfth constraint;

[0055] The twelfth constraint:

[0056] The twelfth constraint ensures the conservation of refueling amount. The remaining oil amount \(I\) of supply vessel \(k\) before the \(r\)-th refueling kr , is equal to the remaining oil amount \(I\) after the \((r - 1)\)-th refueling k,r-1 plus the refueling amount \(\delta\) of the \((r - 1)\)-th refueling k,r-1 minus the total oil consumption for serving customer vessels during the \((r - 1)\)-th journey;

[0057] The other realistic constraints include the thirteenth constraint, the fourteenth constraint, and the fifteenth constraint:

[0058] The thirteenth constraint:

[0059] The thirteenth constraint states that the r-th refueling operation can be performed if and only if the (r - 1)-th refueling operation has been completed.

[0060] The fourteenth constraint:

[0061] The fourteenth constraint indicates that if there are no customer vessels to be served in the r-th trip, the r-th refueling operation does not need to be performed.

[0062] The fifteenth constraint:

[0063] The fifteenth constraint means that a refueling operation is performed at the planned start time to fill the tank to full.

[0064] Furthermore, S3 specifically includes the following steps:

[0065] S31. Problem decomposition:

[0066] Decompose the complex fuel supply vessel scheduling problem of the mixed-integer linear programming model into a master problem and multiple sub-problems;

[0067] The master problem is responsible for order selection and supply vessel allocation decisions.

[0068] The sub-problems focus on the specific supply vessel route planning and scheduling, including service order and fuel replenishment plan;

[0069] S32. Construct the master problem:

[0070] The objective of the master problem is to maximize the total profit while considering order selection and supply vessel allocation; the master problem formula is as follows:

[0071]

[0072] Where: maxz represents the objective function to be maximized, i.e., the total profit z, J is the set of all customer vessels, f is the selling price per unit of fuel, c j is the cost of serving customer vessel j, d j represents the fuel demand of customer vessel j, y j is a decision variable, if customer vessel j is served, then y j = 1, otherwise y j = 0;

[0073] Introduce decision variables, including whether to serve a certain customer vessel, supply vessel allocation and order;

[0074] The constraints of the master problem are as follows:

[0075]

[0076]

[0077] Where: K represents the set of supply vessels, R represents the set of refueling operations, z represents the total profit, f represents the unit price of fuel, c j represents the unit cost of serving customer vessel j, d j is the fuel demand of customer vessel j, y j is a binary decision variable, which is 1 if customer vessel j is served; otherwise 0, v jkr is a decision variable, which is 1 if customer vessel j is served by the r-th trip of supply vessel k; otherwise 0, w kr represents a binary decision variable indicating whether supply vessel k performs the r-th refueling operation, I kr represents the fuel quantity of supply vessel k before the r-th refueling operation, δ k,r-1 represents the fuel quantity refueled by supply vessel k in the (r - 1)-th refueling, Q k represents the capacity of supply vessel k, that is, the maximum fuel quantity that the vessel can carry, C kr represents the time when supply vessel k completes the r-th refueling operation, S j represents the service completion time of customer vessel j, t j0 represents the travel time from the oil depot to customer vessel j, α represents the fixed refueling setup time, β k represents the refueling speed of supply vessel k at the oil depot, p jk represents the time required for supply vessel k to serve customer vessel j, e j represents the earliest service time of customer vessel j, l j represents the latest service time of customer vessel j, O max represents the maximum supply fuel quantity of the onshore oil depot;

[0078] S33. Construct the sub-problem:

[0079] For each supply vessel k, based on the solution of the master problem, construct a sub-problem to verify the feasibility of the solution. The objective of the sub-problem is to minimize the completion time and ensure that all allocated customer vessels are served within the time window;

[0080] The formula of the sub-problem is as follows:

[0081] min z = C max

[0082] The constraint conditions of the sub-problem are:

[0083]

[0084] I0 = Q k

[0085] w0 = 1

[0086]

[0087]

[0088] Where: C max represents the final completion time after all customer vessel services are completed, v jr is a decision variable, which is 1 if customer vessel j is served in the r-th trip and 0 otherwise, w r represents the binary decision variable indicating whether the supply vessel refuels before the r-th trip, I r represents the remaining fuel of the fuel supply vessel after the r-th voyage, δ r-1 represents the amount of fuel replenished by the supply vessel during the (r - 1)-th trip, Q k represents the capacity of supply vessel k, that is, the maximum amount of fuel that the vessel can carry, C r represents the completion time of the replenishment vessel after the r-th voyage, S j is the service completion time of customer vessel j, t j0 is the travel time from the oil depot to customer vessel j, α represents the fixed refueling setup time, β represents the refueling speed of the supply vessel, p j represents the service time of customer vessel j, x ij is the binary decision variable indicating whether customer vessel i is served before customer vessel j, e j represents the earliest service time of customer vessel j, l j represents the latest service time of customer vessel j;

[0089] S34. Benders Cuts:

[0090] When the sub-problem is infeasible, Benders cuts are generated and added to the main problem to exclude the current infeasible solution; that is, when the sub-problem is infeasible, it means that according to the current solution of the main problem, it is impossible to arrange for the supply vessel to complete the service within the time window of the customer vessel. To solve this problem, we use Benders cut technology to modify the main problem to exclude the current infeasible solution.

[0091] The Benders cut formula is as follows:

[0092]

[0093] Where: J k represents the set of customer vessels assigned to supply vessel k, |J k | represents the number of customer vessels in set J k , v jkr is a decision variable, which is 1 if customer vessel j is served by the r-th trip of supply vessel k and 0 otherwise, K represents the set of supply vessels, R represents the set of refueling operations, S kDenote the minimum infeasible set of supply ship \(k\), that is, the minimum set of customer ships that causes the sub - problem to be infeasible;

[0094] S35. Repeat S32 - S34 to iteratively optimize the master problem and the sub - problem until one of the first condition or the second condition is satisfied:

[0095] First condition, time limit: A preset time limit. When the time limit is reached, if a feasible solution cannot be found, or the optimization gap between the found solution and the historical best value is less than the rated value, the iteration will stop;

[0096] Second condition, Gap equals 0: During the iteration, calculate the Gap between the upper bound and the lower bound of the optimal solution. The upper bound is given by the solution of the master problem, and the lower bound is given by the solution of the sub - problem. If the Gap becomes zero, or shrinks to the preset range, the iteration stops;

[0097] Through the iterative process, alternately optimize the master problem and the sub - problem, and gradually approach the optimal solution;

[0098] In each iteration, generate a sub - problem based on the current master - problem solution, check the feasibility of the sub - problem, and update the master problem according to the result;

[0099] Furthermore, the solution process of the optimal solution is as follows:

[0100] Alternately solve the master problem and the sub - problem through the commercial solver CPLEX. The master problem provides the lower bound of the original problem, and the sub - problem provides the upper bound of the original problem. During the iteration, continuously remove the infeasible solutions or sub - optimal solutions, so that the gap between the upper bound and the lower bound gradually decreases. When the upper bound is equal to the lower bound, the iteration stops, indicating that the optimal solution scheme has been obtained.

[0101] Furthermore, the steps to generate a sub - problem based on the current master - problem solution are as follows:

[0102] S351. Obtain the solution of the master problem from the master problem in the current iteration. The solution includes the following:

[0103] The decision variable \(y\) of whether each customer ship is selected by the order;

[0104] The decision variable \(v\) of which supply ship's which trip each customer ship is assigned to jkr ;

[0105] S352. Construct the set of customer - ship service orders;

[0106] S353. For each supply ship, judge whether the solution is feasible by solving the sub - problem;

[0107] The main problem transmits the set of orders that each supply ship has to serve to the sub - problem. The objective of the sub - problem is to verify whether the solution of the current main problem is feasible, that is, whether all the customer ships assigned to the supply ship can be served within their respective time windows. The objective function of the sub - problem is to minimize the completion time.

[0108] S354. The constraints of the sub - problem include:

[0109] Itinerary assignment constraint: Ensure that each customer ship is assigned to one itinerary of the supply ship.

[0110] Fuel replenishment and itinerary link constraint: Ensure that the supply ship has enough fuel before serving the customer ship and replenish fuel when necessary.

[0111] Capacity constraint: Ensure that the total demand of the customer ships assigned to the supply ship does not exceed the capacity of the supply ship.

[0112] Time window constraint: Ensure that each customer ship is served within its time window.

[0113] Sequence constraint: Ensure that the sequence of serving customer ships meets the requirements of time windows and fuel replenishment.

[0114] S355. Solving the sub - problem;

[0115] Use a solver to solve the sub - problem. If the sub - problem is feasible, it means that the solution of the current main problem is feasible. If the sub - problem is infeasible, it means that the solution of the current main problem is infeasible, and Benders cuts need to be generated and the main problem needs to be updated.

[0116] S356. Adjust the main problem based on the results of the sub - problem;

[0117] If the sub - problem is feasible: Continue to explore whether there is a better solution;

[0118] If the sub - problem is infeasible: Generate Benders cuts, add them to the main problem, exclude the current infeasible solution, and update the main problem to find a new feasible solution.

[0119] Furthermore, in S33, the steps to construct the sub - problem to verify the feasibility of the solution are as follows:

[0120] Construct the set J k : According to the value of v obtained from the main problem jkr form a set J k to store the customer ships assigned to the supply ship k.

[0121] The objective and constraints of the sub - problem: The objective of the sub - problem is to minimize the time after all the customer ships assigned to the supply ship k are served, that is, to minimize C max; The constraints include ensuring that each customer ship is assigned to exactly one itinerary, the relationship between the fuel replenishment variable and the customer ship assignment variable, the fuel flow balance constraint, the supply ship capacity constraint, the initial full load constraint, the itinerary sequence constraint, and the time window constraint;

[0122] Feasibility check of the sub - problem: Using an optimization solver, input the sub - problem into the solver as an optimization problem. By setting the objective function to zero, the solver gives priority to satisfying all constraint conditions. Check the time window constraint. If the solution of the sub - problem satisfies the time window constraints of all customer ships, the solution is feasible; if not, the solution is infeasible.

[0123] Adding Benders Cut: If the sub - problem is infeasible, that is, there is at least one customer ship that cannot be served within its time window, add a Benders Cut to the master problem. The Benders Cut removes at least one customer ship from J in future iterations to make the solution feasible; k in future iterations to make the solution feasible;

[0124] Iterative process: The master problem and the sub - problem are solved alternately. Each time a new integer solution is obtained from the master problem, a sub - problem is constructed to verify the feasibility of this solution. If the sub - problem is infeasible, add a Benders Cut and update the master problem, and then solve the master problem again until a feasible solution that satisfies all constraint conditions is found or the iteration count limit is reached.

[0125] Furthermore, when solving the master problem, use an optimization solver to solve it, taking advantage of the built - in optimization and cut generation functions of the optimization solver.

[0126] The present invention also provides a storage medium, which includes a stored program. When the program runs, it executes any one of the above - mentioned fuel supply ship scheduling optimization methods considering order selection.

[0127] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor runs the computer program to execute any one of the above - mentioned fuel supply ship scheduling optimization methods considering order selection.

[0128] Compared with the prior art, the present invention has the following advantages:

[0129] The prior art usually does not consider the importance of order selection, resulting in service providers being unable to effectively manage customer demands when resources are limited. The present invention introduces an order selection mechanism to help service providers make more informed decisions when accepting orders, thereby reducing order cancellations and fines.

[0130] Existing studies often assume that the fuel replenishment time is fixed and do not consider the relationship between the replenishment time and the fuel quantity in actual operations. The present invention introduces a flexible fuel replenishment time model, making the scheduling more in line with the actual situation and improving the feasibility and efficiency of scheduling.

[0131] Many existing technologies do not consider the travel time between customer ships, resulting in the infeasibility of the scheduling scheme in actual operations. The present invention ensures that the supply ship can complete the service within the specified time window by considering the travel time.

[0132] Existing technologies mostly focus on cost minimization while ignoring the goal of profit maximization. The present invention clearly sets the goal as maximizing profit, reflecting the comprehensive consideration of revenue and cost in actual operations.

[0133] Existing studies usually assume that supply ships are homogeneous and do not consider differences such as the capacity and pumping speed of different supply ships. The present invention introduces a model of heterogeneous supply ships, enabling the scheduling scheme to better adapt to different types of supply ships and improving the flexibility and efficiency of scheduling.

[0134] Existing technologies often fail to fully consider various constraints, such as the distance of customer ships and service setup time. The present invention comprehensively considers these constraints and provides a more comprehensive and practical scheduling scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0135] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0136] Figure 1 It is a flowchart of the decomposition algorithm of the present invention.

[0137] Figure 2 It is a schematic diagram of the supply ship route of the present invention.

[0138] Figure 3 It is a Gantt chart of the supply ship scheduling of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0139] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0140] It should be noted that the terms "first", "second", etc. in the description, claims and above-mentioned drawings of the present invention are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0141] The present invention introduces a fuel supply ship scheduling problem and proposes a mixed integer linear programming (MILP) model to solve this problem. The model takes into account order selection, the allocation and sequence of customer ships, and fuel replenishment scheduling. The model aims to help fuel supply companies optimize their fuel replenishment services to maximize profits.

[0142] Specifically, the model is applied to the fuel replenishment service industry, where fuel supply companies need to arrange fuel supply ships to provide fuel replenishment services for customer ships. Each customer ship has a specific location and time window and must receive service within the specified time. Due to the limitations of fuel supply ship resources, the company must first decide whether to accept the order of the customer ship. Then, the company needs to arrange a team of fuel supply ships to execute the selected order tasks, including ship allocation and sequence. In addition, the fuel supply ships also need to replenish fuel at the onshore oil depot, which adds another decision to the fuel replenishment scheduling.

[0143] Therefore, the model and algorithm proposed by the present invention can be used as a decision support tool for fuel supply companies to help them accept or reject orders and arrange the service tasks of fuel supply ships, thereby improving the efficiency and profits of the entire fuel replenishment service.

[0144] Parameter description:

[0145] Set definitions: J: The set of customer ships. K: The set of supply ships. N: The set of nodes including the starting point (oil depot) and all customer ships. R: The set of replenishment operations.

[0146] Parameter: t ij : The travel time from customer ship i to customer ship j. d j : The fuel demand of customer ship j. c j : The rental cost of serving customer ship j. h j: The acceptable service pump speed of customer ship j. a: Service setup time, representing the pipeline connection time. b k : The service pump speed of supply ship k. p jk : The service time required for supply ship k to serve customer ship j, calculated as p jk = a + d j / min{b k , h j}. Q k : The capacity of supply ship k. O max : The maximum supply oil volume of the onshore oil depot. f: The revenue per unit fuel volume. α: Fixed replenishment setup time. β k : The replenishment speed of supply ship k at the oil depot.

[0147] Decision variable: y j : 1 if customer ship j is served; 0 otherwise. w kr : 1 if supply ship k performs the r-th replenishment operation; 0 otherwise. δ kr : The replenishment oil volume of supply ship k in the r-th replenishment. v jkr : 1 if customer ship j is served by the r-th trip of supply ship k; 0 otherwise. x ijkr : 1 if the r-th trip of supply ship k passes through the path from customer ship i to customer ship j; 0 otherwise. S j : The service completion time of customer ship j. C kr : The completion time of the r-th replenishment operation of supply ship k. I kr : The oil volume of supply ship k before the r-th replenishment operation.

[0148] The present invention provides an optimized method for fuel supply ship scheduling considering order selection, including the following steps:

[0149] S1. Construct a fuel supply ship scheduling problem based on actual demands;

[0150] Background introduction: Describes the proportion of maritime trade in global trade and the development of the ship fuel replenishment industry.

[0151] Current situation research: Analyzes existing research, including FSVSP research without considering order selection and research considering order selection. Points out the aspects not considered in existing research, such as order selection, service sequence, fuel replenishment plan, etc.

[0152] Introduction of this research description: Defines the problem as a fuel supply ship scheduling problem, with the goal of maximizing profit, that is, while meeting the service demands of customer ships, obtaining the maximum revenue through reasonable scheduling, and considering constraints such as customer ship service time window constraints, supply ship capacity constraints, fuel replenishment time constraints, etc.

[0153] Identify key decisions: Determine the decisions of accepting orders, the task allocation and sequence of supply vessels, and the fuel replenishment plan for supply vessels.

[0154] Finally, systematically sort out and introduce the research problem of this study as the fuel supply vessel scheduling problem considering order selection.

[0155] S2. Model the fuel supply vessel scheduling problem as a mixed-integer linear programming model;

[0156] In S2, when establishing the mixed-integer linear programming model, first consider a single optimization objective, and then consider other constraint conditions;

[0157] Traditional studies on FSVSP (Fuel Supply Vessel Scheduling Problem) usually focus on minimizing the fixed costs and variable costs of supply vessels, such as fuel consumption, labor costs, etc. The model proposed in this invention sets the objective as maximizing the total profit, which is more in line with the principle of enterprises pursuing economic benefits in actual operations.

[0158] Profit is defined as total revenue minus total cost. The total revenue comes from the product of the fuel quantity sold to customer vessels and the unit fuel price. The total cost includes the cost of purchasing fuel from the onshore oil depot and the rental cost of supply vessels, etc. This calculation method reflects the comprehensive consideration of revenue and cost in actual operations, rather than just minimizing costs.

[0159] Objective function:

[0160] Among them: maxz represents the objective function we want to maximize, that is, the total profit z, J is the set of all customer vessels, f is the selling price per unit of fuel, c j is the cost of serving customer vessel j, d j represents the fuel demand of customer vessel j, y j is a decision variable. If customer vessel j is served, then y j = 1, otherwise y j = 0.

[0161] The profit maximization objective takes into account fuel price differences, service costs, and the specific demands of customer vessels. By maximizing profit, this invention supports fuel supply companies to consider not only cost control but also revenue acquisition in decision-making, making the scheduling plan more in line with actual operating conditions.

[0162] The other constraint conditions include order selection constraints, refueling completion time constraints, travel time constraints between customer vessels, heterogeneous supply vessel constraints, and realistic complex constraints;

[0163] Order selection constraints:

[0164] In the mathematical model part, the decision variable y is defined j , indicating whether to serve a certain customer ship (1 for service, 0 for non-service). Whether to accept a specific service request is determined by this variable.

[0165] The following are the relevant explanations for this:

[0166] The first constraint:

[0167] Where: K represents the set of supply ships, R represents the set of refueling operations, v jkr is a decision variable, which is 1 if customer ship j is served by the r-th trip of supply ship k, and 0 otherwise, and y j is a decision variable, which is 1 if customer ship j is served, and 0 otherwise

[0168] This constraint ensures that each customer ship j is assigned to a certain trip v of the supply ship jkr , and it will only occur when y j = 1, that is, when it is decided to serve this customer ship.

[0169] The second constraint:

[0170] The second constraint is the service order constraint for the refueling ships. For each customer ship j, there must be a pre-service point and a post-service point connected to it. The service points are the oil depot 0 or the service ships. Only in this way can the complete path of the r-th trip of each refueling ship k be formed. That is, each trip must start from the oil depot, serve a series of ships, and then return to the oil depot. At the same time, it is ensured that when and only when v jkr = 1, that is, customer ship j is assigned to the r-th trip, can he have the corresponding path order x ijkr .

[0171]

[0172]

[0173] These two constraints state that when and only when there is an r-th refueling operation, can customer ships be assigned after the r-th refueling operation. If there is no r-th refueling operation, no customers are served after the r-th refueling operation. w kr is a decision variable, indicating whether to perform the r-th refueling operation. Moreover, since w kr can only take 1 or 0, ∑x 0jkr = w kr This constraint also implies that each trip can only go out of the oil depot once.

[0174] The third constraint:

[0175] This constraint limits the total amount of fuel replenishment for supply vessels within the planning scope such that it cannot exceed the maximum supply of the onshore oil depot O. max . This indirectly reflects the order selection mechanism because only the selected orders (i.e., the customer vessels with y j = 1) will have their demand d j .

[0176] Fuel replenishment completion time constraint:

[0177] The model proposed in the present invention takes into account the correlation between fuel replenishment time and replenishment quantity, that is, the replenishment time is linearly related to the replenishment fuel quantity, which is different from the assumption of a fixed fuel replenishment time. In the model, the replenishment time is calculated through the ratio of the variable δ kr (replenishment quantity) and β k (replenishment speed), reflecting the flexibility of the replenishment time.

[0178] In the parameter definition of the model, β k represents the replenishment speed of supply vessel k at the oil depot. This parameter directly affects the calculation of the time for the replenishment operation, that is, δ kr / β k represents the time required to complete a specific replenishment quantity δ kr .

[0179] Fourth constraint: Calculation of time

[0180]

[0181] Ensures that the completion time of the replenishment operation takes into account the service completion time S j , the travel time t j0 to the oil depot, the fixed setup time α, and the dynamic replenishment time related to the replenishment quantity δ kr and the replenishment speed β k .

[0182] Traditional models may assume a fixed replenishment time without considering the impact of the replenishment quantity on time. The model of the present invention provides a more practical solution by linking the replenishment time with the replenishment quantity and replenishment speed, making the replenishment scheduling more flexible and efficient.

[0183] Travel time constraint between customer vessels:

[0184] Fifth constraint:

[0185] This constraint ensures that after supply vessel k completes the service for customer vessel i and travels to customer vessel j to start the service, the time S j must take into account the travel time t from i to jij where \(x\) ijkr is a binary decision variable, which is 1 if supply vessel \(k\) travels directly from customer vessel \(i\) to customer vessel \(j\) during its \(r\)-th trip; otherwise it is 0. \(M3\) is a large constant used to ensure that when \(x\) ijkr = 0, this constraint does not take effect.

[0186] Sixth constraint:

[0187] Similarly, this constraint ensures that the time \(S\) when supply vessel \(k\) arrives at customer vessel \(j\) and starts serving after completing the \(r\)-th refueling operation j must take into account the travel time \(t\) from the oil depot to customer vessel \(j\) j0 .

[0188] By considering the travel time between customer vessels, the model can more accurately calculate the time when the supply vessel arrives at each customer vessel, thus ensuring that the service requirements of each customer vessel are met within the predetermined time window. At the same time, the consideration of travel time enables the model to more effectively plan the route and itinerary of the supply vessel, reduce unnecessary waiting and delays, and improve the efficiency and effectiveness of the overall scheduling.

[0189] Heterogeneous supply vessel constraint:

[0190] Capacity constraint (Seventh constraint):

[0191] Ensures that the fuel level of the supply vessel does not exceed its capacity after any refueling operation.

[0192] Refueling quantity constraint (Eighth constraint):

[0193] Ensures that the refueling quantity matches the capacity of the supply vessel and whether the refueling operation is performed

[0194] Ninth constraint: \(I\) k0 = \(Q\) k

[0195] The ninth constraint means that at the start of the planning period, different fuel supply vessels are in the initial full-fuel state;

[0196] The said realistic complex constraints include customer time window constraints, refueling quantity constraints and other realistic constraints. The customer time window constraints include the tenth constraint and the eleventh constraint;

[0197] Tenth constraint:

[0198] Eleventh constraint:

[0199] where \(e\) jdenotes the start time of the time window of customer vessel j, i.e., the earliest time when the customer vessel can receive service;

[0200] where l j denotes the end time of the time window of customer vessel j, i.e., the latest time when the customer vessel can receive service. The tenth constraint and the eleventh constraint ensure that the supply vessel completes the service within the time window of the customer vessel;

[0201] The supplementary fuel quantity constraint includes the twelfth constraint;

[0202] Twelfth constraint:

[0203] The twelfth constraint ensures the conservation constraint of the supplementary fuel quantity. The remaining fuel quantity I kr before the r-th refueling of the supply vessel k is equal to the remaining fuel quantity I k.r-1 after the (r - 1)-th refueling plus the refueling quantity δ k,r-1 at the (r - 1)-th refueling minus the total fuel consumption for serving customer vessels during the (r - 1)-th journey;

[0204] The other realistic constraints include the thirteenth constraint, the fourteenth constraint, and the fifteenth constraint:

[0205] Thirteenth constraint: w kr ≤w k,r-1

[0206] The thirteenth constraint means that the r-th refueling operation can be performed if and only if the (r - 1)-th refueling operation is completed;

[0207] Fourteenth constraint:

[0208] The fourteenth constraint means that if there are no customer vessels to be served in the r-th journey, the r-th refueling operation does not need to be performed;

[0209] Fifteenth constraint: w k0 =1

[0210] The fifteenth constraint means that a refueling operation is performed at the planned start time to make it full of fuel.

[0211] By introducing realistic complex constraints into the model, the model of the present invention can more comprehensively reflect the actual operation environment of the fuel supply service and provide a more accurate and practical scheduling scheme.

[0212] S3. Use the logic-based Benders decomposition algorithm to solve the mixed-integer linear programming model to obtain a scheduling scheme, as Figure 3 shown.

[0213] S31. Problem decomposition:

[0214] Decompose the complex Fuel Supply Vessel Scheduling Problem (FSVSP-OS) into a Master Problem (MP) and multiple Sub-Problems (SPs).

[0215] The MP is responsible for order selection and the allocation decision of fuel supply vessels.

[0216] The SPs focus on the specific route planning and scheduling of fuel supply vessels, including the service sequence and fuel replenishment plan.

[0217] S32. Construction of the Master Problem (MP):

[0218] The objective of the master problem is to maximize the total profit while considering order selection and the allocation of fuel supply vessels. The formula is as follows:

[0219] maxz = ∑(f - c j )d j y j

[0220] Introduce decision variables, including whether to serve a certain customer vessel, the allocation and sequence of fuel supply vessels, etc.

[0221] Include a series of constraints, such as the capacity of the fuel supply vessel, the service time window, the fuel replenishment requirement, etc. The constraints are as follows:

[0222]

[0223]

[0224] The master problem is used to determine order selection and the task allocation of fuel supply vessels. The following is an explanation of each constraint mentioned in the master problem: The first constraint above ensures that each customer vessel j is assigned to a trip of a fuel supply vessel. If the customer vessel j is served (y j = 1), then it must be assigned to a certain trip r of a certain fuel supply vessel k.; The second constraint ensures that the customer vessel j cannot be assigned to an unexecuted trip r; The third constraint ensures that the fuel supply vessel k cannot start the r-th trip until it has completed the (r - 1)-th trip; The fourth constraint ensures that the fuel quantity I kr at the start of the r-th trip of the fuel supply vessel k is the fuel quantity I k,r-1 at the end of the previous trip plus the replenished fuel quantity δ k,r-1 minus the fuel quantity consumed for serving the customer vessel; The fifth constraint ensures that the fuel quantity at the end of the r-th trip of the fuel supply vessel k plus the replenished fuel quantity does not exceed the capacity Q k of the vessel; The sixth constraint ensures that the replenished fuel quantity δ kr is non-zero only when a replenishment operation is carried out (W kr = 1), and does not exceed the capacity Q k; The seventh constraint ensures that if supply vessel k makes the r-th trip, then at least one customer vessel is assigned to that trip; the eighth and ninth constraints ensure that each supply vessel k is initially fully loaded with fuel quantity Q k and ready to depart. Tenth, eleventh, twelfth, and thirteenth constraints are time window constraints, which involve calculating the completion time of each replenishment operation and customer vessel service to ensure they meet the time window requirements of the customer vessels. The fourteenth constraint ensures that the total demand of all accepted orders does not exceed the maximum supply fuel quantity O of the onshore oil depot max .

[0225] S33. Construction of sub-problems (SPs):

[0226] For each supply vessel k, based on the solution of the MP, sub-problems are constructed to verify the feasibility of the solution. The objective of the sub-problem is to minimize the completion time to ensure that all assigned customer vessels are served within the time window

[0227] minz = C max

[0228] The constraints are as follows:

[0229]

[0230] I0 = Q k

[0231] w0 = 1

[0232]

[0233] The sub-problem is a problem of further optimizing the service sequence and fuel replenishment plan of each supply vessel k based on the order selection and allocation determined by the main problem. The following are the explanations of each constraint mentioned in the sub-problem: The first constraint ensures that for each customer vessel j in the set J k , it is assigned to one trip of supply vessel k; the second constraint and the third constraint relate the fuel reloading variable w r and the customer vessel allocation variable v jr . The second constraint ensures that a customer vessel cannot be assigned to the r-th trip before the r-th fuel reloading operation is performed. The third constraint ensures that if no customer vessel is served during the r-th voyage, the supply vessel cannot perform the r-th fuel reloading operation; the fourth constraint ensures that supply vessel k cannot perform the fuel replenishment for the r-th trip unless it has completed the fuel replenishment for the (r - 1)-th trip; the fifth constraint ensures that the fuel quantity I r of supply vessel k at the start of the r-th trip is equal to the fuel quantity I r-1 at the end of the previous trip plus the fuel quantity δ replenished during the (r - 1)-th replenishment r-1Subtract the fuel consumed by serving the customer ships to achieve a flow balance in terms of fuel quantity; the sixth constraint is the supply ship capacity constraint, ensuring that the fuel quantity of supply ship k at the end of the r-th trip plus the replenished fuel does not exceed the ship's capacity Q k ; the seventh and eighth constraints ensure that supply ship k is initially fully loaded with fuel Q k and ready to depart; the ninth constraint ensures that the replenished fuel δ r is non-zero only when a replenishment operation is being carried out (w r = 1), and does not exceed the ship's capacity Q; the tenth and eleventh constraints calculate the completion time C r of the r-th replenishment operation and the service completion time S j of customer ship j, ensuring that they meet the time window requirements of the customer ship; the twelfth and thirteenth constraints define the order of customer ship services, ensuring that the service order conforms to the time window and itinerary arrangements; the fourteenth and fifteenth constraints ensure that each customer ship j is served within its time window [e j , l j ; the sixteenth constraint ensures that the time C max after all customer ship services are completed is greater than or equal to the service completion time C j of the last customer ship.

[0234] S34, Benders Cut:

[0235] If the sub-problem is infeasible, generate a Benders cut and add it to the master problem to exclude the current infeasible solution.

[0236]

[0237] S35. Repeat S32 - S34 to iteratively optimize the master problem and the sub-problem until one of the first condition or the second condition is met:

[0238] The first condition, time limit: a preset time limit. When the time limit is reached and no feasible solution is found, or the found solution has not been significantly improved, the iteration will stop;

[0239] The second condition, Gap equals 0: During the iteration process, calculate the Gap between the upper bound and the lower bound of the optimal solution. The upper bound is given by the solution of the master problem, and the lower bound is given by the solution of the sub-problem. If the Gap becomes zero, or shrinks to the preset range, the iteration stops;

[0240] Through the iteration process, alternately optimize the master problem and the sub-problem to gradually approach the optimal solution;

[0241] The master problem and the sub-problem are alternately solved by the commercial solver CPLEX. The master problem provides a lower bound for the original problem, and the sub-problem provides an upper bound for the original problem. During the iteration process, infeasible solutions or sub-optimal solutions are continuously removed, so that the gap between the upper bound and the lower bound gradually decreases. When the upper bound is equal to the lower bound, the iteration stops, indicating that the optimal solution has been obtained;

[0242] In each iteration, a sub-problem is generated based on the current solution of the master problem, the feasibility of the sub-problem is checked, and the master problem is updated according to the result;

[0243] The steps of generating the sub-problem based on the current solution of the master problem are as follows in S351~S356:

[0244] S351. Obtain the solution of the master problem

[0245] First, obtain the solution from the master problem of the current iteration. This solution includes the following content:

[0246] The decision variable of whether each customer ship is served (order selection y).

[0247] The decision variable of which trip of which supply ship each customer ship is assigned to (v jkr ).

[0248] S352. Construct the set of customer ship service orders

[0249] For each supply ship, we can know which orders are assigned to it and construct the order set

[0250] S353. For each supply ship, judge whether the solution is feasible by solving the sub-problem

[0251] Specifically, the master problem transmits to the sub-problem the set of orders to be served by each supply ship. However, the travel time constraint between serving customer ships is not considered in the master problem, resulting in the supply ship being unable to complete all the assigned orders within the time window required by the customer ship.

[0252] The goal of the sub-problem is to verify whether the current solution of the master problem is feasible, that is, whether all the customer ships assigned to the supply ship can be served within their respective time windows. Therefore, the objective function of the sub-problem is usually to minimize the completion time:

[0253] S354. The constraint conditions of the sub-problem

[0254] The constraint conditions of the sub-problem include:

[0255] Trip assignment constraint: Ensure that each customer ship is assigned to one trip of the supply ship.

[0256] Fuel replenishment and trip link constraint: Ensure that the supply ship has enough fuel before serving the customer ship and perform fuel replenishment when necessary.

[0257] Capacity constraint: Ensure that the total demand of the customer ships assigned to the supply ship does not exceed the capacity of the supply ship.

[0258] Time window constraint: Ensure that each customer ship is served within its time window.

[0259] Sequence constraint: Ensure that the sequence of customer ship services meets the requirements of the time window and fuel replenishment.

[0260] S355, Solving sub-problems

[0261] Use a solver to solve the sub-problem. If the sub-problem is feasible, it means that the solution of the current master problem is feasible; if the sub-problem is infeasible, it means that the solution of the current master problem is infeasible and Benders cuts need to be generated and the master problem updated.

[0262] S356, Adjusting the master problem based on the results of the sub-problem

[0263] If the sub-problem is feasible: The solution of the current master problem is feasible and it is possible to continue exploring for a better solution.

[0264] If the sub-problem is infeasible: Generate Benders cuts, add them to the master problem, exclude the current infeasible solution, and update the master problem to find a new feasible solution.

[0265] Through the above steps, in each iteration, a sub-problem is generated based on the solution of the current master problem and the master problem is adjusted according to the solution of the sub-problem, thereby gradually approaching the optimal solution. This process is iterative until the optimal solution is found or the stopping condition is met.

[0266] S36, Algorithm implementation:

[0267] Use the branch and bound method to solve the MP, which is an effective integer programming solution method.

[0268] Utilize a commercial solver to implement the algorithm, taking advantage of its built-in optimization and cut generation capabilities.

[0269] As Figure 2 and 3 shown, in Figure 2In this example, the present invention presents an example including two supply vessels and ten customer vessels. This scenario simulates the offshore fuel supply service environment in the Bohai Bay area of China. The Bohai Bay is one of the important shipping hubs in China, with busy maritime traffic and numerous port facilities. In this area, the fuel supply demand for vessels is strong, and it is restricted by strict port operation hours and relevant regulations. Therefore, efficient scheduling of fuel supply vessels is crucial for ensuring the normal operation of vessels and the efficient operation of ports. In this example, the simulated scenario reflects the actual characteristics of the fuel supply service in the Bohai Bay area. Five customer vessels are received, including J1, J3, J4, J5, and J6. These customer vessels represent vessels of different types and requirements. They may come from different shipping routes and have different time windows and service requirements. Two supply vessels are arranged to perform refueling services for the received customer vessels. Vessel No. 1 makes two trips, and Vessel No. 2 makes one trip, as Figure 2 shown. This scheduling arrangement fully considers the heterogeneity of supply vessels, the time windows of customer vessels, and dynamic factors during the supply process, such as the relationship between supply time and supply volume, and the travel time between customer vessels. Figure 3 The Gantt chart of the two vessels is given. The symbol "J1 / p1" indicates that customer vessel J1 enters Port p1, and "TW" indicates the time window of each customer vessel.

[0270] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An optimization method for the scheduling of oil supply ships considering order selection, characterized in that, It includes the following steps: S1. Construct a fuel supply ship scheduling problem based on actual requirements; S2. Model the fuel supply ship scheduling problem as a mixed-integer linear programming model; S3. Use a logic-based Benders decomposition algorithm to solve the mixed-integer linear programming model to obtain a scheduling plan.

2. The optimized fuel supply ship scheduling method considering order selection according to claim 1, characterized in that In S2, when establishing the mixed-integer linear programming model, first consider a single optimization objective, and then consider other constraint conditions; The single optimization objective is as follows: The mixed-integer linear programming model sets the goal to maximize the total profit; Profit is defined as total revenue minus total cost, where total revenue comes from the product of the fuel quantity sold to customer ships and the unit fuel price, and the total cost includes the rental cost of supply ships; The objective function of the single optimization objective is as follows: where: maxz represents the objective function to be maximized, i.e., the total profit z, J is the set of all customer vessels, f is the selling price per unit of fuel, and c j is the cost of serving customer vessel j, and d j represents the fuel demand of customer vessel j, and y j is a decision variable. If customer vessel j is served, then y j = 1; otherwise, y j = 0.

3. The optimized fuel supply ship scheduling method considering order selection according to claim 1, characterized in that In S2, the other constraint conditions include order selection constraints, refueling completion time constraints, travel time constraints between customer ships, heterogeneous supply ship constraints, and realistic complex constraints; The order selection mechanism constraints include the first constraint, the second constraint, and the third constraint, which are specifically as follows: Define the decision variable y j , where the decision variable indicates whether to serve a certain customer vessel, with 1 for serving and 0 for not serving; determine whether to accept a specific service request through the decision variable; First constraint: where: K represents the set of supply vessels, R represents the set of refueling operations, v jkr is a decision variable that is 1 if customer vessel j is served by the r-th trip of supply vessel k and 0 otherwise, y j is a decision variable that is 1 if customer vessel j is served and 0 otherwise; The first constraint ensures that each customer vessel j is assigned to a trip v of a supply vessel only if y jkr = 1, i.e., when it is decided to serve that customer vessel; j this occurs only when y Second Constraint: The second constraint is the service sequence constraint of the oil supply ship. For each customer ship j, there must be a pre-service point and a post-service point connected to it. The service point is the oil depot 0 or the service ship. k is the oil supply ship, and r is the number of trips; Third constraint: Where: J is the set of all customer vessels, d j represents the fuel demand of customer vessel j, y j is a decision variable, if customer vessel j is served, then y j = 1, otherwise y j = 0, O max represents the maximum amount of fuel that can be supplied by the onshore fuel tank within the planning time horizon; The third constraint limits the total amount of fuel replenishment for supply vessels within the planning scope such that it cannot exceed the maximum supply O of the onshore oil depot. max ; Only for selected orders, i.e., customer vessels where y j = 1, will their demand d be calculated. j ; The refueling completion time constraint includes the fourth constraint, which is specifically as follows: Consider the correlation between the fuel replenishment time and the replenishment quantity, that is, the replenishment fuel quantity has a linear relationship with the replenishment time, and the replenishment time is calculated by the ratio of the replenishment quantity δ kr and the replenishment speed β k ; β k represents the replenishment speed of supply ship k at the oil depot, i.e., δ kr / β k represents the time required to complete a specific replenishment volume δ kr required; Fourth constraint: Where: C kr represents the time when supply vessel k completes the r-th refueling operation, S j represents the service completion time of customer vessel j, t j0 represents the travel time from customer vessel j to the starting point (dock) of the supply vessel, α is the fixed setup time for refueling, δ kr represents the refueling volume during the r-th refueling of supply vessel k, β k represents the refueling speed of supply vessel k at the dock, M1 is a large constant used to ensure that the constraint does not take effect in the absence of refueling operations, v jk,r-1 is a decision variable that is 1 if customer vessel j is served by the itinerary after the (r - 1)-th refueling of supply vessel k, and 0 otherwise; The travel time constraints between customer ships include the fifth constraint and the sixth constraint, which are specifically as follows: Fifth Constraint: Where: S j is the service completion time of customer vessel j, S i is the service completion time of customer vessel i, t ij is the travel time from customer vessel i to customer vessel j, p jk is the time required for supply vessel k to serve customer vessel j, M3 is a large constant used to ensure that the constraint does not take effect when x ijkr = 0, x ijkr is a decision variable, which is 1 if supply vessel k travels from customer vessel i to customer vessel j in its r-th trip, and 0 otherwise; The fifth constraint ensures the time S when the supply ship k departs for the customer ship j and starts service after completing the service for the customer ship i j The travel time t from i to j must be considered ij ; where x ijkr is a binary decision variable, which is 1 if the supply ship k travels directly from the customer ship i to the customer ship j during its r-th trip; otherwise it is 0; a constant set by M3 to ensure that when x ijkr = 0, this fifth constraint is not in effect; Sixth Constraint: The sixth constraint ensures the time S at which the supply ship k departs for the customer ship j and starts service after completing the rth replenishment operation j The travel time t from the oil depot 0 to the customer ship j must be considered j0 ; The heterogeneous supply ship constraints include the seventh constraint, the eighth constraint, the ninth constraint, and the tenth constraint: Seventh Constraint: Where: I kr represents the fuel quantity of supply ship k before the r-th replenishment operation, δ kr represents the fuel quantity replenished by supply ship k during the r-th replenishment, Q k represents the capacity of supply ship k, that is, the maximum fuel quantity that the ship can carry. K is the set of supply ships, and R ∪ {0} represents the set of all replenishment operations including the initial state; The seventh constraint ensures that the oil quantity of the supply ship after any refueling operation does not exceed its capacity; Eighth Constraint: Where: δ kr represents the amount of fuel replenished by supply ship k in the r-th replenishment, Q k represents the capacity of supply ship k, that is, the maximum amount of fuel that the ship can carry, w kr represents a binary decision variable indicating whether supply ship k performs the r-th replenishment operation; The eighth constraint ensures that the refueling quantity matches the capacity of the supply ship and whether the refueling operation is performed; Ninth Constraint: I k0 = Q k The ninth constraint means that at the start time of the planning period, different oil supply ships are in the initial full oil state; The realistic complex constraints include customer time window constraints, refueling quantity constraints, and other realistic constraints. The customer time window constraints include the tenth constraint and the eleventh constraint; Tenth Constraint: Eleventh Constraint: where e j represents the start time of the time window of customer vessel j, i.e., the earliest time when the customer vessel can receive service; where l j represents the end time of the time window of customer vessel j, that is, the latest time when the customer vessel can receive service. The tenth constraint and the eleventh constraint ensure that the supply vessel completes the service within the time window of the customer vessel; The refueling quantity constraint includes the twelfth constraint; Twelfth Constraint: The twelfth constraint ensures the conservation constraint of the supplementary oil quantity. The remaining oil quantity I of the oil supply ship k before the r-th supplementary oil is kr , equal to the remaining oil quantity I k,r-1 after the (r - 1)-th supplementary oil plus the supplementary oil quantity δ k,r-1 in the (r - 1)-th trip minus the total oil consumption of the serviced customer ships; The other realistic constraints include the thirteenth constraint, the fourteenth constraint, and the fifteenth constraint: The thirteenth constraint: The thirteenth constraint means that the r-th refueling operation can be performed if and only if the (r - 1)-th refueling operation is completed; The Fourteenth Constraint: The fourteenth constraint means that if there are no customer ships to be served in the r-th trip, the r-th refueling operation does not need to be performed; Fifteenth Constraint: The fifteenth constraint means that a refueling operation is performed at the start time of the plan to make it full of oil.

4. The optimized fuel supply ship scheduling method considering order selection according to claim 1, characterized in that S3 specifically includes the following steps: S31. Problem decomposition: Decompose the complex fuel supply ship scheduling problem of the mixed-integer linear programming model into a master problem and multiple sub-problems; The master problem is responsible for order selection and supply ship allocation decisions. The sub-problems focus on the specific supply ship route planning and scheduling, including service sequence and fuel replenishment plan; S32. Construct the master problem: The goal of the master problem is to maximize the total profit while considering order selection and supply ship allocation. The master problem formula is as follows: where: max z represents the objective function to be maximized, i.e., the total profit z, J is the set of all customer vessels, f is the selling price per unit of fuel, c j is the cost of serving customer vessel j, d j represents the fuel demand of customer vessel j, y j is a decision variable, if customer vessel j is served, then y j = 1, otherwise y j = 0; Introduce decision variables, including whether to serve a certain customer ship, supply ship allocation, and sequence; The constraints of the master problem are as follows: Where: K represents the set of supply vessels, R represents the set of refueling operations, z represents the total profit, f represents the selling price per unit of fuel, c j represents the unit cost of serving customer vessel j, d j is the fuel demand of customer vessel j, y j is a binary decision variable, which is 1 if customer vessel j is served; otherwise it is 0, v jkr is a decision variable, which is 1 if customer vessel j is served by the r-th trip of supply vessel k, otherwise it is 0, w kr represents the binary decision variable indicating whether supply vessel k performs the r-th refueling operation, I kr represents the fuel quantity of supply vessel k before the r-th refueling operation, δ k,r-1 represents the fuel quantity refueled by supply vessel k in the (r - 1)-th refueling, Q k represents the capacity of supply vessel k, that is, the maximum fuel quantity that the vessel can carry, C kr represents the time when supply vessel k completes the r-th refueling operation, S j represents the service completion time of customer vessel j, t j0 represents the travel time from the oil depot to customer vessel j, α represents the fixed refueling setup time, β k represents the refueling speed of supply vessel k at the oil depot, p jk represents the time required for supply vessel k to serve customer vessel j, e j represents the earliest service time of customer vessel j, l j represents the latest service time of customer vessel j, O max represents the maximum supply oil quantity of the onshore oil depot; S33. Construct the sub-problems: For each supply ship \(k\), based on the solution of the master problem, a sub-problem is constructed to verify the feasibility of the solution. The objective of the sub-problem is to minimize the completion time and ensure that all assigned customer ships are served within their time windows; The formula of the sub-problem is as follows: min z = C max The constraints of the sub-problem are: Among them: C max represents the final completion time after all customer vessel services are completed, v jr is a decision variable, which is 1 if customer vessel j is served in the r-th trip, and 0 otherwise, w r represents the binary decision variable indicating whether the supply vessel conducts a refueling operation before the r-th trip, I r represents the remaining fuel quantity after the supply vessel executes the r-th voyage, δ r-1 represents the fuel quantity refueled by the supply vessel in the (r - 1)-th trip, Q k represents the capacity of supply vessel k, that is, the maximum fuel quantity that the vessel can carry, C r represents the completion time after the replenishment vessel finishes the r-th voyage, S j is the service completion time of customer vessel j, t j0 is the travel time from the oil depot to customer vessel j. α represents the fixed refueling setup time, β represents the refueling speed of the supply vessel, p j represents the service time of customer vessel j, x ij represents the binary decision variable indicating whether customer vessel i is served before customer vessel j, e j represents the earliest service time of customer vessel j, l j represents the latest service time of customer vessel j; S34, Benders cut: When the sub-problem is infeasible, a Benders cut is generated and added to the master problem to exclude the current infeasible solution; that is, when the sub-problem is infeasible, it means that according to the current solution of the master problem, it is impossible to arrange the supply ship to complete the service within the time window of the customer ship. To solve this problem, we use the Benders cut technique to modify the master problem to exclude the current infeasible solution. The Benders cut formula is as follows: Where: J k represents the set of customer vessels assigned to supply vessel k, and |J k | represents the number of customer vessels in the set J k , v jkr is a decision variable that is 1 if customer vessel j is served by the r-th trip of supply vessel k and 0 otherwise. K represents the set of supply vessels, R represents the set of refueling operations, and S k represents the minimum infeasible set of supply vessel k, i.e., the smallest set of customer vessels that causes the subproblem to be infeasible; S35. Repeat S32 - S34 to iteratively optimize the master problem and the sub-problem until one of the first condition or the second condition is satisfied: The first condition, time limit: A preset time limit. When the time limit is reached, if a feasible solution is not found, or the optimization gap between the found solution and the historical best value is less than the rated value, the iteration will stop; The second condition, Gap equals 0: During the iteration process, calculate the Gap between the upper bound and the lower bound of the optimal solution. The upper bound is given by the solution of the master problem, and the lower bound is given by the solution of the sub-problem. If the Gap becomes zero, or shrinks to the preset range, the iteration stops; Through the iteration process, alternately optimize the master problem and the sub-problem, and gradually approach the optimal solution; In each iteration, generate a sub-problem based on the current solution of the master problem, check the feasibility of the sub-problem, and update the master problem according to the result.

5. The optimized fuel supply ship scheduling method considering order selection according to claim 4, characterized in that The solution process of the optimal solution is as follows: Alternately solve the master problem and the sub-problem through the commercial solver CPLEX. The master problem provides the lower bound of the original problem, and the sub-problem provides the upper bound of the original problem. During the iteration process, continuously remove the infeasible solutions or sub-optimal solutions, so that the gap between the upper bound and the lower bound gradually decreases. When the upper bound is equal to the lower bound, the iteration stops, indicating that the optimal solution is obtained.

6. The optimized fuel oil tanker scheduling method considering order selection according to claim 4, characterized in that The steps to generate a sub-problem based on the current solution of the master problem are as follows: S351. Obtain the solution of the master problem from the master problem of the current iteration. The solution includes the following: The decision variable \(y\) of whether each customer ship is selected by the order; Decision variable v for which trip of which supply ship each customer ship is assigned to jkr ; S352. Construct the set of customer ship service orders; S353. For each supply ship, judge whether the solution is feasible by solving the sub-problem; The master problem transmits the set of orders to be served by each supply ship to the sub-problem. The objective of the sub-problem is to verify whether the current solution of the master problem is feasible, that is, whether all customer ships assigned to the supply ship can be served within their respective time windows; The objective function of the sub-problem is to minimize the completion time; S354. The constraints of the sub-problem include: Itinerary assignment constraint: Ensure that each customer ship is assigned to one itinerary of the supply ship; Fuel replenishment and itinerary link constraint: Ensure that the supply ship has enough fuel before serving the customer ship and replenish fuel when necessary; Capacity constraint: Ensure that the total demand of the customer ships assigned to the supply ship does not exceed the capacity of the supply ship; Time window constraint: Ensure that each customer ship is served within its time window; Sequence constraint: Ensure that the sequence of customer ship services meets the requirements of time windows and fuel replenishment; S355, Solving sub-problems; Use a solver to solve the sub-problem. If the sub-problem is feasible, it indicates that the solution of the current master problem is feasible; if the sub-problem is infeasible, it indicates that the solution of the current master problem is infeasible, and a Benders cut needs to be generated and the master problem updated; S356, Adjusting the master problem based on the results of the sub-problem; If the sub-problem is feasible: Continue to explore whether there is a better solution; If the sub-problem is infeasible: Generate a Benders cut, add it to the master problem, exclude the current infeasible solution, and update the master problem to find a new feasible solution.

7. The optimized fuel supply ship scheduling method considering order selection according to claim 4, characterized in that In S33, the steps to construct a sub-problem to verify the feasibility of the solution are as follows: Construct set J k : Based on the value of v obtained from the main problem jkr , form a set J k to store the customer ships assigned to supply ship k; Objectives and Constraints of Sub - problems: The objective of the sub - problem is to minimize the time after the service of all customer ships assigned to supply ship k is completed, that is, to minimize C max ; The constraints include ensuring that each customer ship is assigned to exactly one trip, the relationship between the fuel replenishment variable and the customer ship assignment variable, the fuel flow balance constraint, the supply ship capacity constraint, the initial full - load constraint, the trip sequence constraint, and the time - window constraint; Feasibility check of the sub-problem: Use an optimization solver, input the sub-problem as an optimization problem into the solver, and by setting the objective function to zero, make the solver prioritize satisfying all constraint conditions; Check the time window constraint. If the solution of the sub-problem satisfies the time window constraints of all customer ships, then the solution is feasible; if not, the solution is infeasible; Adding a Benders Cut: If the sub-problem is infeasible, that is, there is at least one customer ship that cannot be served within its time window, add a Benders Cut to the master problem; The Benders Cut removes at least one customer ship from J in future iterations to make the solution feasible; k ​ Iterative process: The master problem and the sub-problem are solved alternately. Each time a new integer solution is obtained from the master problem, a sub-problem is constructed to verify the feasibility of this solution; if the sub-problem is infeasible, then a Benders Cut is added and the master problem is updated, and then the master problem is solved again; until a feasible solution that satisfies all constraint conditions is found or the iteration count limit is reached.

8. The optimized fuel supply ship scheduling method considering order selection according to claim 4, characterized in that, When solving the master problem, use an optimization solver for solving, leveraging the built-in optimization and cut generation capabilities of the optimization solver.

9. A storage medium, characterized in that, The storage medium includes a stored program, wherein when the program runs, it executes the fuel supply ship scheduling optimization method considering order selection according to any one of claims 1 to 8.

10. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor runs through the computer program to execute the fuel supply ship scheduling optimization method considering order selection according to any one of claims 1 to 8.

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