A ship deployment and refueling joint optimization method considering multiple uncertainties

Abstract

The application discloses a ship deployment and refueling joint optimization method considering multiple uncertainties. The method firstly constructs a nonlinear mixed integer programming deterministic model with the minimum total cost as the target, then introduces random oil prices and berthing times, constructs a robust optimization model containing an uncertainty set, and integrates the two to form a two-stage robust optimization model. The robust optimal ship deployment scheme and fuel injection strategy are obtained by iteratively solving the model through a Benders decomposition algorithm embedded with a branch and bound algorithm. The application constructs an integrated joint decision framework, simultaneously optimizes the ship deployment and fuel management in a unified mathematical model, captures and utilizes the internal relationship between different decisions, avoids the potential huge cost caused by separate decisions, fully considers the influence of the uncertainty of oil prices and port berthing times, makes the decisions have good risk hedging characteristics, fundamentally improves the scientificity and economy of the decisions, and effectively reduces the comprehensive cost of operation.

Description

Technical Field

[0001] This invention relates to ship deployment and refueling methods, belonging to the field of ship shipping planning, and particularly to a joint optimization method for ship deployment and refueling that takes into account multiple uncertainties. Background Technology

[0002] Against the backdrop of global energy demand growth and the development of the petrochemical industry, the refined oil transportation market is showing strong growth. Maritime transportation dominates the refined oil transportation market because it can achieve high-efficiency long-distance and large-volume transportation. However, factors such as port price fluctuations and crude oil price volatility have made the market dynamics more complex, requiring more refined operations.

[0003] Current maritime logistics frequently faces significant uncertainties such as port congestion, weather disruptions, and fuel price fluctuations. Uncertainty regarding port berthing times causes variations in vessel waiting times, impacting fuel consumption and delivery schedules, increasing decision-making complexity, and consequently leading to increased operating costs, disrupted schedules, and adjustments to refueling plans. Fuel price fluctuations, on the other hand, drive up voyage costs, forcing operators to reassess routes, port selections, and refueling strategies. While lower fuel prices can alleviate expenses, they also introduce long-term uncertainty. Current technologies typically treat tanker deployment and refueling strategies separately, optimizing them independently. However, ignoring their inherent connection can lead to suboptimal results. For example, inefficient deployment plans may force tankers to refuel at ports with high fuel prices or under unfavorable conditions, increasing total operating costs. The lack of a comprehensive decision-making framework to effectively address the dual uncertainties of fuel price fluctuations and port berthing delays makes it difficult to guarantee operational economy and reliability. Therefore, there is an urgent need for a means to effectively improve the resilience and cost-effectiveness of maritime logistics in unpredictable environments, addressing the aforementioned shortcomings of existing technologies. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings and problems of insufficient consideration of uncertainties in the existing technology, which leads to high operating costs, and to provide a joint optimization method for ship deployment and refueling that fully considers uncertainties and effectively reduces operating costs by taking into account multiple uncertainties.

[0005] To achieve the above objectives, the technical solution of the present invention is: a joint optimization method for ship deployment and refueling considering multiple uncertainties, comprising:

[0006] Define variables and parameters, aim to minimize the total cost of fleet operating costs, fuel refueling costs, and port charges, and define constraints to construct a deterministic basic model of nonlinear mixed integer programming;

[0007] Using random oil prices and random berthing times as uncertainty variables, and determining the set of uncertainties used to capture constraints, a robust optimization model for uncertainty factors is constructed.

[0008] A two-stage robust optimization model is constructed by integrating a deterministic basic model and a robust optimization model. The main problem in the first stage is the ship deployment scheme with a robust objective. The sub-problem in the second stage is to solve the optimal fuel refueling strategy for a given ship deployment scheme, considering uncertain variables, evaluate the worst-case cost, and generate the Benders cut plane.

[0009] The Benders decomposition algorithm with embedded branch and bound is used to iteratively solve the first-stage main problem and the second-stage subproblem until convergence, thus obtaining the robust optimal ship deployment scheme and the corresponding fuel refueling strategy.

[0010] Preferably, the variables and parameters include route and vessel parameters, fuel consumption rate parameters, fuel selection parameters, decision variables, and a set of vessel route segments;

[0011] Preferably, the route and vessel parameters include: the transport demand of the route, the sailing distance of the segment, the vessel's carrying capacity, the vessel's heavy fuel oil tank capacity, the vessel's light fuel oil tank capacity, the vessel's economic cruising speed on the coastal route, the time required for the vessel to load and unload a unit of cargo, the total amount of cargo loaded and unloaded at the starting port of the segment, and the vessel's speed on the route. The price of high-quality fuel oil at several ports, and the status of ships on their routes. The price of refueling with light fuel oil at each port, and the vessel's position on the route. Port fees at each port, and the minimum safe levels of heavy and light fuel oil that ships must maintain;

[0012] Preferably, the fuel consumption rate parameters include: the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship on the coastal route, the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship in the restricted area, the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship while anchored in the port, and the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship while carrying out cargo loading and unloading operations in the port.

[0013] Preferably, the fuel selection parameters include: a binary parameter for whether the vessel uses heavy or light fuel oil during the voyage, and a binary parameter for whether the vessel uses heavy or light fuel oil during anchoring and operations at the port of origin of the voyage.

[0014] Preferably, the decision variables include: a binary decision variable of the ship being deployed to the route, a binary decision variable of whether the ship refuels with heavy fuel oil or light fuel oil at a port on the route, a non-negative decision variable of the amount of heavy fuel oil and light fuel oil refueled at a port on the route, and a state variable of the amount of heavy fuel oil and light fuel oil remaining in the ship's fuel tank after completing the voyage.

[0015] Preferably, the set of vessel routes and segments includes: a set of vessels owned by the company, a set of routes used for coastal transportation, and a set of routes and segments.

[0016] Preferably, the objective function for minimizing the total cost of fleet operation, fuel refueling, and port charges is as follows:

[0017] ;

[0018] in: Total cost; For fleet operating costs, For fuel refueling costs, Port fees and costs;

[0019] The fleet operating cost is expressed as follows:

[0020] ;

[0021] in: For ships Deployed to the flight path Binary decision variables on The distance traveled in a segment of the voyage. The economic cruising speed for ships on coastal routes. This refers to the total time a ship spends in port. This refers to the transportation demand of the air route. The time required for loading and unloading cargo from a ship;

[0022] The total time the vessel spent in the port This includes the ship's anchoring time and refueling time, and its expression is as follows:

[0023] ;

[0024] in: For the route No. The time required for loading and unloading fuel oil at each port , These are the non-negative decision variables for the amount of heavy fuel oil and light fuel oil added by the ship at the port of origin of the voyage, respectively. , These refer to the speeds of adding heavy fuel oil and light fuel oil, respectively.

[0025] The fuel refueling cost includes the total cost of refueling the ship with both bulk fuel oil and light fuel oil, expressed as follows:

[0026] ;

[0027] in: , The ship is on the route of the first Prices of heavy fuel oil and light fuel oil at several ports have increased.

[0028] The port charges are expressed as follows:

[0029] ;

[0030] in: For ships Deployed to the flight path Binary decision variables on For the ship on the route Port fees for each port.

[0031] Preferably, the constraints include the following:

[0032] Ensure that the refined oil transportation needs of each shipping route are met: ;

[0033] in: For ships Deployed to the flight path Binary decision variables on For ships The capacity, For the route The demand for transportation;

[0034] Ensure that each ship serves a maximum of one route: ;

[0035] Continuity constraints on marine fuel oil consumption:

[0036] ;

[0037] ;

[0038] in: , They represent ships After completing the flight segment The amount of heavy fuel oil and light fuel oil remaining in the rear fuel tank; , Ships In the flight segment The quantity of heavy fuel oil and light fuel oil loaded at the port of origin; This refers to the consumption of heavy fuel oil in ships. This refers to the consumption of light fuel oil in ships;

[0039] The quantity of heavy and light fuel oil in a ship's fuel tanks must not fall below a minimum level during navigation:

[0040] ;

[0041] ;

[0042] in: , These are the minimum safe fuel oil levels that ships must maintain for heavy fuel oil and light fuel oil, respectively.

[0043] Ensure that the amount of fuel in the fuel tank does not exceed the maximum capacity during refueling:

[0044] ;

[0045] ;

[0046] in: , Ships The tank capacity for heavy fuel oil and light fuel oil;

[0047] The amount of fuel purchased must exceed the minimum purchase amount.

[0048] ;

[0049] ;

[0050] in: , These are the minimum purchase quantities for heavy fuel oil and light fuel oil, respectively.

[0051] Logical constraints of the deterministic basic model:

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] in: , They represent ships On the route The The decision variable for whether a port should refuel with heavy or light fuel oil;

[0057] Boundaries of decision variables in deterministic basic models:

[0058] ;

[0059] ;

[0060] ;

[0061] .

[0062] Preferably, the consumption of heavy fuel oil and the consumption of light fuel oil are expressed as follows:

[0063] ;

[0064] ;

[0065] in: , These represent the consumption of heavy fuel oil and light fuel oil by the ship during the voyage. , These represent the consumption of heavy fuel oil and light fuel oil by ships during anchoring and loading / unloading in port, respectively.

[0066] The expressions for the consumption of heavy fuel oil and light fuel oil by the ship during the voyage are as follows:

[0067] ;

[0068] ;

[0069] in: The binary parameters for determining whether a ship uses heavy or light fuel oil during a voyage. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time for ships on coastal routes, respectively. The distance traveled in a segment of the voyage. The economic cruising speed for ships on coastal routes. For the company's collection of ships, A collection of shipping routes used for coastal transportation. For flight routes;

[0070] The consumption of heavy fuel oil and light fuel oil by the vessel during anchorage and operations in port are expressed as follows:

[0071] ;

[0072] ;

[0073] in: The binary parameters for the use of heavy or light fuel oil by the vessel during anchorage and operations at the port of origin of the voyage. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time within the restricted area, respectively. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time during ship operations in port. This refers to the total amount of cargo loaded and unloaded at the port of origin of the shipping segment. The time required for loading and unloading cargo from a ship; This refers to the total time a ship spends in port.

[0074] Preferably, the uncertain variables include random oil prices and random berthing times;

[0075] The random oil price is represented as follows: This indicates that oil prices are within a range. The upper part follows any distribution;

[0076] The random berthing time is represented as: This indicates that the berthing time is distributed in Inside;

[0077] The set of uncertainties used to capture constraints is expressed as follows:

[0078] ;

[0079] in: Let this be the set of uncertainties surrounding oil prices. For the set of uncertainties in berthing time, This represents the fluctuation vector of oil prices; This represents the fluctuation vector of berthing time; Budgeting for the uncertainty of oil prices; Budgeting for the uncertainty of berthing time;

[0080] The expression for the robust optimization model is as follows:

[0081] .

[0082] Preferably, the main problem in the first stage specifically refers to:

[0083] With cost minimization as the primary objective of the first phase of decision-making, a ship deployment plan is constructed. Meanwhile, ship deployment plans were also considered. The impact of the worst-case cost on the second-stage decision subproblem is expressed through auxiliary variables. To approximate the objective of the primary decision problem in the first stage, the expression is as follows:

[0084] ;

[0085] The constraints are as follows:

[0086] ; ;

[0087] ; ;

[0088] in: For ships Deployed to the flight path Binary decision variables on For the ship on the route Port fees for each port, For ships The capacity, For the route The demand for transportation;

[0089] The second-stage decision sub-problem specifically refers to:

[0090] The current ship deployment plan is based on the main decision-making problem in the first phase. The second-stage decision subproblems all calculate the worst-case cost of the solution under the set of uncertainties. Its expression is as follows:

[0091] ;

[0092] in: For fleet operating costs, For fuel refueling costs, This represents the fluctuation vector of berthing time. For fuel refueling time, The set of decision variables for the refueling strategy in the second-stage decision sub-problem. Let be the vector of oil price fluctuations. This represents the amount of fuel remaining in the fuel tank.

[0093] Based on the strong duality theorem, the second-stage decision subproblem is transformed into a single max problem, the expression of which is as follows:

[0094] ;

[0095] in: Let this be the set of uncertainties surrounding oil prices. For the set of uncertainties in berthing time, As dual variables, For dual feasible region, This is a transpose.

[0096] Preferably, the Benders decomposition algorithm with embedded branch and bound is used to iteratively solve the first-stage main problem and the second-stage subproblems until convergence, obtaining a robust and optimal ship deployment scheme and corresponding fuel refueling strategy, specifically including:

[0097] Initialize the global upper bound of the global optimal solution to the primary decision problem in the first stage. Global lower bound Iteration counter for Benders decomposition Convergence tolerance And determine the decision variables for the main decision problem in the first stage. Auxiliary variables and constraints;

[0098] In the In the next Benders decomposition iteration, the first-stage decision master problem is solved based on the branch and bound algorithm to obtain the optimal integer solution, i.e., the ship deployment scheme;

[0099] Substitute the optimal integer solution into the second-stage decision subproblem to solve for the optimal value and the corresponding worst-case cost, and determine the state of the optimal value.

[0100] If the optimal value is a finite value, then calculate the robust total cost. and update the global upper bound. It also stores the current complete solution corresponding to the updated global upper bound; at the same time, it constructs a robust optimality cutting plane and adds it to the constraints of the first-stage decision master problem;

[0101] If the optimal value is infinite, then construct a robust feasibility cutting plane and add it to the constraints of the first-stage decision problem.

[0102] Determine if the difference between the global upper bound and the global lower bound converges; if If the algorithm converges, the current complete solution corresponding to the global upper bound is taken as the optimal robust solution, and the robust optimal ship deployment scheme and corresponding fuel refueling strategy are obtained.

[0103] like Then set the Benders iteration counter. The algorithm continues to solve the first-stage decision problem based on the branch and bound algorithm until the algorithm converges.

[0104] Preferably, generating the Benders cut plane specifically includes:

[0105] If the optimal value of the second-stage decision subproblem is a finite value, then the solution corresponds to the worst-case uncertainty realization. and optimal dual variables The expression for the robust optimal cutting plane is as follows:

[0106] ;

[0107] If the optimal value of the second-stage decision subproblem is infinite, then the current ship deployment plan... If the constraints of the uncertainty set are infeasible, then all non-robust feasible ship deployment schemes are removed from the main decision problem of the first stage; the expression for the robust feasibility cutting plane is as follows:

[0108] ;

[0109] in: For extreme rays in the dual feasible region.

[0110] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0111] 1. This invention provides a joint optimization method for ship deployment and refueling considering multiple uncertainties. The method first constructs a nonlinear mixed-integer programming deterministic model with the objective of minimizing total cost. Then, it introduces stochastic oil prices and berthing time to construct a robust optimization model containing a set of uncertainties. These two are then integrated to form a two-stage robust optimization model. The model is iteratively solved using a Benders decomposition algorithm with embedded branch and bound to obtain the robust optimal ship deployment scheme and refueling strategy. In application, this design constructs an integrated joint decision-making framework, simultaneously optimizing ship deployment and fuel management within a unified mathematical model. This captures and utilizes the inherent connections between different decisions, avoiding the potentially huge costs associated with separate decision-making. Furthermore, it fully considers the uncertainties of oil prices and port berthing time, giving the decision-making a good risk-hedging characteristic, fundamentally improving the scientific and economic efficiency of the decision-making process, and effectively reducing the overall operating cost.

[0112] 2. In the joint optimization method for ship deployment and refueling that considers multiple uncertainties, the present invention lays a reliable foundation for the goal of minimizing costs by focusing on core elements such as fleet operation, fuel refueling, and port fees. At the same time, it fully considers uncertain variables such as random oil prices and berthing time. By constructing a reasonable set of uncertainties, it enhances the model's adaptability to complex real-world scenarios, making the final robust optimal solution more in line with actual operational needs.

[0113] 3. In the joint optimization method for ship deployment and refueling considering multiple uncertainties, this invention constructs a two-stage robust optimization model, decomposes the optimization problem into a main problem and sub-problems, and processes ship deployment and refueling strategies in layers, reducing the difficulty of solving complex problems. Furthermore, by continuously shrinking the feasible solution space through the cutting plane technique, invalid searches are avoided, significantly improving the solution efficiency. At the same time, the worst-case cost situation is evaluated through sub-problems, and accurate feedback is provided to the main ship deployment problem, so that the final ship deployment decision can not only adapt to uncertain scenarios, but also efficiently obtain robust optimal solutions, taking into account both the efficiency of handling complex problems and the robustness of the final decision. Attached Figure Description

[0114] Figure 1 This is a flowchart of the method of the present invention.

[0115] Figure 2 This is a schematic diagram comparing cost results under the fluctuation of heavy fuel oil prices in Embodiment 1 of the present invention.

[0116] Figure 3 This is a schematic diagram comparing cost results under the fluctuation of light fuel oil prices in Embodiment 1 of the present invention.

[0117] Figure 4 This is a schematic diagram comparing cost results under anchoring time fluctuations in Embodiment 1 of the present invention.

[0118] Figure 5 This is a system structure diagram of the present invention.

[0119] Figure 6 This is a structural diagram of the device of the present invention.

[0120] In the diagram: Deterministic basic model building unit 1, Robust optimization model building unit 2, Two-stage robust optimization model building unit 3, Ship deployment and refueling strategy acquisition unit 4, Processor 5, Memory 6, Computer program code 61. Detailed Implementation

[0121] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0122] Example 1:

[0123] See Figure 1 A joint optimization method for ship deployment and refueling that considers multiple uncertainties includes:

[0124] Determine the variables and parameters used to build the model, including route and ship parameters, fuel consumption rate parameters, fuel selection parameters, decision variables, and the set of ship route segments;

[0125] The route and vessel parameters include: route Transportation demand Flight segment sailing distance Ships transport capacity (Deadweight Tonnage), Ship Heavy fuel oil (HFO) tank capacity Ships Light fuel oil (LFO) tank capacity Ships Economic cruising speed on coastal routes Ships Time required for loading and unloading of goods Flight segment Total volume of cargo loaded and unloaded at the port of origin Vessels on the route No. The price of high-quality fuel oil at various ports has increased. Vessels on the route No. The price of light fuel oil refueling at each port Ships On the route No. Port fees for each port (Due to berth size limitations, some ports cannot accommodate large vessels. In such cases, port charges for these vessels should be set to a maximum value to reflect actual constraints.) Minimum safe levels of heavy and light fuel oil that vessels must maintain. ;

[0126] Product tankers are typically equipped with separate heavy fuel oil (HFO) and light fuel oil (LFO) tanks; HFO is mainly consumed during coastal voyages, while LFO is required in restricted areas such as ports and anchorages, as well as during cargo handling; the fuel consumption values ​​in this embodiment can be obtained from historical data statistics of shipping companies.

[0127] Furthermore, the fuel consumption rate parameter includes: ship Consumption rate of heavy fuel oil and light fuel oil per unit time on coastal shipping routes Ships Consumption rate of heavy fuel oil and light fuel oil per unit time within the restricted area Ships Consumption rate of heavy fuel oil and light fuel oil per unit time during anchorage at port Ships Consumption rate of heavy fuel oil and light fuel oil per unit time during cargo loading and unloading operations at the port. ;

[0128] The fuel selection parameters include: a binary parameter indicating whether the vessel uses heavy or light fuel oil during the voyage. When its value is 1, it indicates that the ship... In the flight segment During navigation, HFO is used; when its value is 0, it indicates that LFO is used.

[0129] Binary parameters for the use of heavy or light fuel oil by the vessel during anchorage and operations at the port of origin of the voyage. When its value is 1, it indicates that the ship... In the flight segment HFO is used during anchorage and operations at the port of origin; when its value is 0, LFO is used.

[0130] , These are externally input binary parameters, determined by the shipping company based on the characteristics of the ship's fuel tanks and historical data, in order to achieve the most economical choice.

[0131] Furthermore, the decision variables include: ship Deployed to the flight path Binary decision variables on If deployed, the value is 1; otherwise, it is 0.

[0132] Ships On the route The Middle The nonnegative decision variable for the quantity of high-quality fuel oil added to each port. The non-negative decision variable of the amount of light fuel oil added. ;

[0133] Ships On the route The Middle of the Whether or not a port should refuel with heavy fuel oil is a binary decision variable. The binary decision variable is whether or not to refuel with light fuel oil. ;

[0134] Ships After completing the flight segment The state variables of the remaining heavy fuel oil and light fuel oil in the rear fuel tank ;

[0135] Furthermore, the set of vessel routes and segments includes: the set of vessels owned by the company. The index is A collection of shipping routes used for coastal transportation. The index is ;route Flight segment collection , Indicates flight route The first Each flight segment.

[0136] Based on the above variables and parameters, a deterministic basic model of nonlinear mixed-integer programming is constructed with the objective of minimizing the total cost of fleet operating costs, fuel refueling costs, and port charges, and constraints are defined. Its objective function is as follows:

[0137] (1);

[0138] in: Total cost; For fleet operating costs, For fuel refueling costs, Port fees and costs;

[0139] The ship operating cost is expressed as follows:

[0140] ;

[0141] in: For ships Deployed to the flight path Binary decision variables on The distance traveled in a segment of the voyage. The economic cruising speed for ships on coastal routes. This refers to the total time a ship spends in port. This refers to the transportation demand of the air route. The time required for loading and unloading cargo from a ship;

[0142] The total time the vessel spent in the port This includes the ship's anchoring time and refueling time, and its expression is as follows:

[0143] ;

[0144] in: For the route No. The time required for loading and unloading fuel oil at each port , These are the non-negative decision variables for the amount of heavy fuel oil and light fuel oil added by the ship at the port of origin of the voyage, respectively. , These refer to the speeds of adding heavy fuel oil and light fuel oil, respectively.

[0145] The fuel refueling cost includes the total cost of refueling the ship with both bulk fuel oil and light fuel oil, expressed as follows:

[0146] ;

[0147] in: , The ship is on the route of the first Prices of heavy fuel oil and light fuel oil at several ports have increased.

[0148] The port charges are expressed as follows:

[0149] ;

[0150] in: For ships Deployed to the flight path Binary decision variables on For the ship on the route Port fees for each port.

[0151] The constraints involve cargo volume constraints on the route, constraints on HFO and LFO meeting navigation conditions, and fuel tank status constraints, specifically including the following:

[0152] (2);

[0153] (3);

[0154] (4);

[0155] (5);

[0156] in: This refers to the amount of fuel oil consumed by a ship during a leg of its voyage. This refers to the amount of fuel oil consumed by a ship while it is anchored and operating in port.

[0157] (6);

[0158] (7);

[0159] (8);

[0160] (9);

[0161] (10);

[0162] (11);

[0163] (12);

[0164] (13);

[0165] (14);

[0166] (15);

[0167] (16);

[0168] (17);

[0169] (18);

[0170] (19);

[0171] The above expressions (1)-(19) are used to represent the deterministic basic model of nonlinear mixed integer programming, where all parameters are determined. The objective function (1) represents minimizing the sum of fleet operating costs, fuel costs and port charges; constraint (2) is used to ensure that the refined oil transportation demand of each route is met; constraint (3) is used to ensure that each ship serves at most one route; constraints (4)-(5) are the continuity constraints of ship fuel consumption; constraints (6)-(7) are to limit the amount of heavy fuel oil and light fuel oil in the fuel tank during the ship's voyage to not be lower than the minimum level; constraints (8)-(9) are used to ensure that the amount of fuel in the fuel tank during the ship's refueling does not exceed the maximum capacity; constraints (10)-(11) are used to stipulate that the refueling amount must be greater than the minimum purchase amount; constraints (12)-(15) are the logical constraints of the deterministic basic model; constraints (16)-(19) are used to define the limits of decision variables.

[0172] Furthermore, the expressions for the consumption of heavy fuel oil and light fuel oil in the ship are as follows:

[0173] ;

[0174] ;

[0175] in: , These represent the consumption of heavy fuel oil and light fuel oil by the ship during the voyage. , These represent the consumption of heavy fuel oil and light fuel oil by ships during anchoring and loading / unloading in port, respectively.

[0176] The expressions for the consumption of heavy fuel oil and light fuel oil by the ship during the voyage are as follows:

[0177] ;

[0178] ;

[0179] in: The binary parameters for determining whether a ship uses heavy or light fuel oil during a voyage. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time for ships on coastal routes, respectively. The distance traveled in a segment of the voyage. The economic cruising speed for ships on coastal routes. For the company's collection of ships, A collection of shipping routes used for coastal transportation. For flight routes.

[0180] The consumption of heavy fuel oil and light fuel oil by the vessel during anchorage and operations in port are expressed as follows:

[0181] ;

[0182] ;

[0183] in: The binary parameters for the use of heavy or light fuel oil by the vessel during anchorage and operations at the port of origin of the voyage. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time within the restricted area, respectively. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time during ship operations in port. This refers to the total amount of cargo loaded and unloaded at the port of origin of the shipping segment. The time required for loading and unloading cargo from a ship; This refers to the total time a ship spends in port.

[0184] Furthermore, in the actual operation of refined oil transportation, various uncertainties significantly impact vessel scheduling and refueling strategies. Among these, the unpredictability of oil price fluctuations and berth availability is particularly prominent. Oil price fluctuations directly affect operating costs, making it difficult for shipping companies to optimize refueling plans and effectively manage fuel reserves. Sudden price increases may force companies to adjust routes or postpone refueling, thereby increasing the overall complexity of voyage planning. In addition to fuel price fluctuations, the uncertainty of port berth times also leads to a decline in operational efficiency. Berthing delays caused by port congestion, severe weather, or logistical bottlenecks extend waiting times, thus affecting shipping plans and fuel consumption. This unpredictability makes the coordination of vessel arrivals and departures more complex, leading to further disruptions to the supply chain.

[0185] To address these challenges, this solution explicitly considers two key uncertainties: the unpredictability of stochastic fuel prices and stochastic berthing times; it incorporates these uncertainties into a deterministic base model to capture changes in fuel costs and port conditions, thereby enabling more resilient decision-making in vessel deployment and refueling strategies; and by integrating these uncertainties, it improves operational flexibility, ensuring that shipping companies can minimize disruptions and maintain efficiency under different conditions.

[0186] Using random oil prices and random berthing times as uncertainty variables, and determining the set of uncertainties used to capture constraints, a robust optimization model for uncertainty factors is constructed.

[0187] Furthermore, the specific operation involves transforming the two external input parameters, namely the oil price and berth time at each port, into uncertain variables; the random oil price is represented as:

[0188] (20);

[0189] This indicates that oil prices are within a range. The upper part follows any distribution;

[0190] The random berthing time is represented as:

[0191] (twenty one);

[0192] Indicates the distribution of berthing time in Inside;

[0193] The set of uncertainties used to capture constraints is defined as follows:

[0194] (twenty two);

[0195] in: Let this be the set of uncertainties surrounding oil prices. For the set of uncertainties in berthing time, This represents the fluctuation vector of oil prices; This represents the fluctuation vector of berthing time; Budgeting for the uncertainty of oil prices; Budgeting for the uncertainty of berthing time;

[0196] The robust optimization model is represented as follows:

[0197] ;

[0198] A two-stage robust optimization model is constructed by integrating a deterministic basic model and a robust optimization model. The main problem in the first stage is the ship deployment scheme with a robust objective. The sub-problem in the second stage is to solve the optimal fuel refueling strategy for a given ship deployment scheme, considering uncertain variables, evaluate the worst-case cost, and generate the Benders cut plane.

[0199] Furthermore, the optimization model proposed in this scheme is a two-stage robust optimization model, and a Benders decomposition algorithm with embedded branch and bound is customized according to its structure for solving it.

[0200] The first stage of decision-making is the main issue. It is necessary to determine the ship deployment plan before uncertainties (fuel prices, anchoring time) occur. This type of decision is strategic and long-term.

[0201] The second stage of decision-making is a sub-problem. After the ship deployment plan is determined, a fuel refueling strategy needs to be formulated to cope with all possible scenarios within the set of uncertainties. This type of decision-making needs to be robust.

[0202] This solution employs a Benders decomposition algorithm combined with branch and bound to solve this problem. The outer layer of this algorithm is a Benders decomposition loop used to generate the cutting plane; the inner layer uses a branch and bound algorithm to solve the main problem containing integer variables, as detailed below:

[0203] For the primary decision-making problem in the first phase, with cost minimization as the objective, a ship deployment plan is constructed. Meanwhile, ship deployment plans were also considered. The impact of the worst-case cost on the second-stage decision subproblem is expressed through auxiliary variables. To approximate the objective of the primary decision problem in the first stage, the expression is as follows:

[0204] ;

[0205] The constraints are as follows:

[0206] ;

[0207] ;

[0208] ;

[0209] ;

[0210] in: For ships Deployed to the flight path Binary decision variables on For the ship on the route Port fees for each port, For ships The capacity, For the route The demand for transportation;

[0211] For the second-stage decision subproblem, the goal is to evaluate the "worst-case cost," which means first considering all possible values ​​of the uncertain parameters (oil price, anchoring time), then calculating the corresponding optimal adjustment cost (such as fuel refueling cost) for each value, and finally taking the maximum cost as the evaluation result.

[0212] The current ship deployment plan is based on the main decision-making problem in the first phase. The second-stage decision subproblems all calculate the worst-case cost of the solution under the set of uncertainties. Its expression is as follows:

[0213] ;

[0214] in: For fleet operating costs, For fuel refueling costs, This represents the fluctuation vector of berthing time. For fuel refueling time, The set of decision variables for the refueling strategy in the second-stage decision sub-problem. Let be the vector of oil price fluctuations. This represents the amount of fuel remaining in the fuel tank.

[0215] Furthermore, the second-stage sub-problem is a max-min optimization problem. The inner "min" requires finding the optimal adjustment decision (such as fuel refueling amount) to minimize costs given the uncertain parameters and the main problem's deployment scheme. The outer "max" iterates through all possible values ​​of the uncertain parameters to find the "worst-case" scenario that maximizes the minimum cost, serving as a robustness evaluation metric for the deployment scheme. To solve this max-min problem, this scheme utilizes the strong duality theorem to transform the inner min linear programming problem into its dual form.

[0216] make Let V be the vector of dual variables constrained by all constraints of the internal problem, and let V be the vector of dual feasible variables constrained by the dual feasible region. Its dual problem is expressed as follows:

[0217] ;

[0218] in: The right-hand side of the internal problem constraint depends on the ship deployment scheme of the main problem. and uncertain variables ;

[0219] Substituting the dual form back into the original expression, the second-stage decision subproblem is transformed into a single max problem, expressed as follows:

[0220] ;

[0221] in: Let this be the set of uncertainties surrounding oil prices. For the set of uncertainties in berthing time, As dual variables, For dual feasible region, This is the transpose. Although this optimization problem has many variables, its objective function and constraints are... , , The above is linear (or linearizable), so it can be reconstructed into a large-scale mixed integer programming (MIP) problem and solved.

[0222] Furthermore, the cutting plane serves as a bridge connecting the main problem and subproblems. The generation of the Benders cutting plane specifically includes:

[0223] If the optimal value of the second-stage decision subproblem is a finite value, that is, a finite optimal solution to the robust subproblem. If the solution is generated at a specific time, then the solution corresponds to the worst-case uncertainty realization. and optimal dual variables The expression for the robust optimal cutting plane is as follows:

[0224] ;

[0225] This cut-off plane ensures compatibility with all ship deployment schemes. Its estimated cost It must be greater than or equal to in the worst-case scenario The actual cost of refueling.

[0226] If the optimal value of the second-stage decision subproblem is infinite, then the robust subproblem has no solution. If generated in real time, it indicates the current ship deployment plan. If the constraints of the uncertain set are infeasible, then find an extreme ray of the dual problem. This inequality must apply to all uncertain variables. Once established, it will remove all non-robust feasible ship deployment options from the primary decision-making problem of the first stage; the expression for the robust feasibility cut plane is as follows:

[0227] ;

[0228] in: For extreme rays in the dual feasible region.

[0229] The Benders decomposition algorithm with embedded branch and bound is used to iteratively solve the first-stage main problem and the second-stage subproblems until convergence, obtaining the robust and optimal ship deployment scheme and corresponding fuel refueling strategy; the specific process is as follows:

[0230] Initialize the global upper bound of the global optimal solution to the primary decision problem in the first stage. Global lower bound Iteration counter for Benders decomposition Convergence tolerance And determine the decision variables for the main decision problem in the first stage. Auxiliary variables and constraints, which only include... Related primitive constraints, such as demand satisfaction constraints and single-ship single-line constraints;

[0231] In the In each iteration of the Benders decomposition, the branch and bound algorithm is called to solve the current first-stage decision problem; the first-stage decision problem includes all the previous... The Benders cut plane generated in the next iteration; the steps of the branch and bound algorithm are as follows:

[0232] S1. Create a list of active nodes (subproblems) or a priority queue, initially containing only the root node;

[0233] S2, the root node represents the linear programming relaxation (LP Relaxation) problem of the first-stage decision-making main problem, that is, the problem with integer variables. relaxation ;

[0234] S3. Solve the linear programming relaxation problem to obtain an initial relaxed solution; use the objective function value of the initial relaxed solution as the global lower bound of the linear programming relaxation problem, and set the initial global upper bound of the linear programming relaxation problem to infinity. ;

[0235] S4. Select a node from the list of active nodes to explore, and solve the linear programming relaxation problem of that node to obtain its relaxed solution;

[0236] If the objective function value of the current node's relaxation solution is inferior to (greater than or equal to) the global upper bound. If the node is not found to be a better solution, then pruning should be performed on that node, since neither the node nor any of its subsequent branches can produce a better solution.

[0237] If there is no solution for the relaxation of the current node, then prune the node.

[0238] If the relaxed solution of the current node satisfies all integer constraints, then its objective function value is compared with the global upper bound. Compare; if superior Then update Set the target value for the current solution and save the current solution. As the current optimal solution to the primary decision problem in the first stage; if inferior to If so, then perform a pruning operation on that node;

[0239] If the relaxed solution of the current node contains an integer variable with a decimal value, then execute the branch operation in step S5.

[0240] S5. Select an integer variable with a decimal value from the relaxed solutions of the current node, for example... Based on this integer variable, create two new child nodes and add constraints to each; add constraints to one of the child nodes. Add constraints to another child node Add both new child nodes to the active node list; and repeat steps S4-S5.

[0241] When the list of active nodes is empty, the branch and bound algorithm ends. At this point, the solution saved in step S4 is the optimal integer solution to the primary decision problem in the first stage. This solution is returned, and the global lower bound LB is updated with its objective function value.

[0242] S6. Substitute the optimal integer solution into the second-stage decision subproblem to solve for the optimal value. And the corresponding worst-case cost, and determine the optimal state;

[0243] If the optimal value is a finite value, then calculate the robust total cost. and update the global upper bound. It also stores the current complete solution corresponding to the updated global upper bound; at the same time, it constructs a robust optimality cutting plane and adds it to the constraints of the first-stage decision master problem;

[0244] If the optimal value is infinite. Then construct a robust feasibility cutting plane and add it to the constraints of the first-stage decision problem;

[0245] Determine if the difference between the global upper bound and the global lower bound converges; if If the algorithm converges, the current complete solution corresponding to the global upper bound is taken as the optimal robust solution, and the robust optimal ship deployment scheme and corresponding fuel refueling strategy are obtained.

[0246] like Then set the Benders iteration counter. Continue with step S4 until the algorithm converges. When the algorithm converges, the solution corresponding to the updated global upper bound is the optimal robust solution. This solution not only has a lower cost in the nominal scenario, but more importantly, it can ensure that the total cost will not exceed the controllable range when there are any adverse fluctuations in fuel prices, berthing time, etc. within a preset range. It exhibits extremely high stability and reliability, providing strong decision support for the actual operation of shipping companies.

[0247] In this embodiment, a computer is used to perform a practical operation on the joint optimization of ship deployment and refueling considering uncertainties.

[0248] (1) Requirements gathering and data input, see Table 1 and Table 2:

[0249]

[0250] Table 1

[0251] Table 1 provides operational and fuel-related parameters for vessel input parameters (LY-121 to KLY-206), offering crucial insights for cost optimization and fuel management across different vessel classes. The table details key metrics such as deadweight tonnage (DWT), consumption rates of high-sulfur fuel oil (HFO) and low-sulfur fuel oil (LFO) in three operating modes—navigation (SC), port (PC), and anchoring (AC), as well as fuel tank capacity (HFO-Cap and LFO-Cap), daily operating costs (in RMB, OC), and cruising speed (kont). Notably, smaller vessels like those in the LY series (e.g., LY-121, LY-123) rely on LFO for port and anchoring operations but use HFO for navigation, while larger vessels in the KLY series (e.g., KLY-201, KLY-205) prioritize HFO for navigation due to its cost-effectiveness, despite higher daily operating costs (e.g., KLY-205 costs RMB 62,100 per day). Fuel tank capacity increases with ship size, with the KLY series vessels accommodating up to 590 tons of HFO, while the LY series vessels can only accommodate 343 tons, reflecting a strategic trade-off between fuel storage and cargo hold capacity. The data also reveals changes in speed and DWT, such as the KLY-205's higher cruising speed (12.80 knots) and the LY-121's three times greater cargo capacity, highlighting the need for operators to balance fuel selection, route planning, and compliance with environmental regulations (such as the use of LFO in emission control areas). Ship data is stored in local Excel format and read using Python, converted into input variables for the program.

[0252]

[0253] Table 2

[0254] Table 2 presents specific parameters for 26 ports (such as CNTJN and CNZPU), focusing on fuel cost dynamics and operational constraints crucial for optimizing maritime logistics. Key indicators include the price per tonne of high-sulfur fuel oil (HFO) and low-sulfur fuel oil (LFO), as well as average anchorage time (in hours). Notably, significant price differences exist between ports: HFO costs range from RMB 4,524.24 / tonne in CNYPG to RMB 7,391.11 / tonne in CNWGQ, while LFO prices vary from RMB 5,958.87 / tonne in CNGLA to RMB 7,381.07 / tonne in CNNHUI. For example, CNFUZ offers the lowest LFO price (RMB 5,961.23 / tonne), contrasting with the high premium LFO price in CNNHUI, which in some ports (such as CNGLA where LFO is cheaper than HFO) even exceeds HFO prices. Anchorage times also vary significantly, ranging from a minimum of 4.0 hours in CNDAL and CNXIA to 23.7 hours in CNJIJ, directly impacting vessel operating time and related costs. These differences highlight the strategic importance of route planning—operators may prioritize ports like CNFUZ or CNGLA for low-cost LFO procurement, while shorter anchorage times (such as in CNDAL) reduce downtime. Conversely, high fuel prices or long anchorage times (such as in CNWGQ and CNJIJ) may reduce port attractiveness unless freight demand or regulatory requirements offset the impact. This dataset underscores the necessity of meticulous cost-benefit analysis when selecting ports, balancing fuel costs, time sensitivity, and compliance with emission control regulations (e.g., the tendency to use LFOs despite higher prices in sulfur emission control areas). This information serves as a foundational input for optimizing fuel procurement strategies, voyage scheduling, and overall fleet efficiency across diverse port networks. Route input parameters include the shipping distance between ports and the transport demand for each route.

[0255] (2) Calculation process:

[0256] This solution establishes a systematic joint decision-making process to guide refined oil transportation companies in optimizing both fleet deployment and refueling along the route—two core aspects—to minimize overall operating costs. This process is executed via a computer system, and its core steps are as follows:

[0257] Step 1: Basic data input and parameter preparation;

[0258] Before the process begins, a series of basic data and operational parameters need to be input into the system. This data serves as the basis for all subsequent decision-making and analysis, and mainly includes the following categories:

[0259] 1. Flight route and mission data;

[0260] Transportation task list: Defines the set of all transportation routes that need to be executed, as well as the specific transportation demand for each route (e.g., how many tons of refined oil).

[0261] Route structure: Clearly define the segments (i.e., the route from one port to the next) that are included in each route and arranged in sequence.

[0262] Segment attributes: The sailing distance of each segment, and the amount of cargo to be loaded or unloaded at the starting and ending ports of the segment.

[0263] 2. Fleet and vessel attribute data;

[0264] Available vessel list: The collection of all vessels that the company can currently schedule.

[0265] Detailed vessel specifications: Performance parameters for each vessel, including its maximum deadweight (carrying capacity), economical cruising speed, heavy fuel oil (HFO) and light fuel oil (LFO) tank capacity, and cargo handling efficiency (tonnes handled per hour).

[0266] Fuel consumption characteristics: The hourly consumption rate of two types of fuel (HFO / LFO) for each ship under different operating conditions (such as ocean voyage, port voyage, anchorage waiting, loading and unloading operations) determined based on historical data.

[0267] Initial ship condition: The initial fuel stock of each ship at the start of the mission.

[0268] 3. Market and cost data;

[0269] Fuel price information: Current market prices of HFO and LFO at all alternative refueling ports along the route.

[0270] Port fee standards: Fees charged by each port for berthing, pilotage, etc., for vessels of different tonnages.

[0271] Vessel operating cost rate: The unit time operating cost of a vessel, such as daily fixed costs (converted to hours).

[0272] 4. Definition of uncertainty range;

[0273] Price fluctuation range: Based on historical data or market forecasts, enter the maximum range within which fuel prices at each port may fluctuate.

[0274] Time fluctuation range: Enter the average and estimated maximum delay range for each port, which may be caused by congestion, weather, etc.

[0275] Step 2: Define the decision problem and the order of task execution;

[0276] Once the data preparation is complete, the core of the process is to solve a highly correlated joint decision-making problem. This process requires simultaneously defining two things:

[0277] 1) Fleet deployment decision: From the list of available vessels, assign the most suitable vessels or combinations of vessels to each transport route.

[0278] 2) Refueling strategy decision-making: For each assigned vessel, plan which port to refuel at, what type of fuel to refuel at, and how much fuel to refuel at throughout the voyage.

[0279] The "task priority" in this process is reflected in the route structure, where a route is defined as a series of segments arranged in geographical order. For example, a route from "Port A -> Port B -> Port C" has a fixed task order. The brilliance of this decision-making process lies in its approach: it doesn't make decisions for each segment in isolation and sequentially, but rather considers and optimizes all segments of the entire route as a whole. When formulating a refueling strategy for a vessel, the system weighs the pros and cons of refueling at ports A, B, and C simultaneously. For instance, refueling at port A with cheaper fuel might increase fuel consumption, but it avoids refueling at port C, where fuel prices are high. This global optimization approach ensures optimal cost for the entire voyage, fully demonstrating a deep understanding of task priority and the interrelationships between decisions.

[0280] Step 3: Construct and execute joint optimization logic;

[0281] This step is the "brain" of the decision-making process; it seeks the optimal solution based on the input parameters and the defined decision problem. Optimization objective: The sole objective of the process is to find a deployment and refueling plan that minimizes the total cost (ship operating costs + fuel refueling costs + port charges).

[0282] Core trade-off logic:

[0283] When deploying vessels, the system weighs the trade-off between the high capacity of large vessels but also their high fuel consumption and port fees, and the high flexibility of small vessels but their unit cost may not be as competitive.

[0284] When formulating a refueling strategy, the system calculates and compares combinations of different refueling points and refueling volumes, taking into account factors such as fuel price differences, ship fuel tank capacity, safety stock requirements, and the time costs that may be incurred due to refueling operations.

[0285] Logic for handling uncertainty:

[0286] Once the uncertainty range is input, the process will activate robust optimization logic. At this point, it will not only consider the current price but also evaluate the performance of the decision-making scheme under the most unfavorable conditions of future price or waiting time fluctuations. The goal is to find a "robust" solution with high stability and resilience, where total costs will not spiral out of control even during periods of severe market volatility or port congestion.

[0287] Step 4: Output a comprehensive decision-making solution;

[0288] Once the process is complete, it will output a clear and directly executable comprehensive decision-making solution, specifically including:

[0289] Fleet deployment instruction sheet: clearly lists which ship is assigned to which specific route.

[0290] Detailed refueling plan: Provide each vessel on a mission with a detailed refueling instruction for the voyage, clearly specifying which port on the route, how many tons of HFO and how many tons of LFO should be refueled.

[0291] Expected Cost Analysis: Provides a detailed budget of all costs (operation, fuel, port) under this optimal solution.

[0292] The final output of this invention is a complete, clear, and directly executable set of operational instructions, clearly defining the route allocation for each ship and providing detailed, port-specific refueling plans. Furthermore, this framework is highly adaptable, capable of being adjusted to different fleet compositions (such as vessels of different tonnages and fuel consumption characteristics) and changing external regulatory environments (such as fuel usage regulations in different emission control areas). Its broad applicability makes it not merely a theoretical model, but a practical tool that helps maritime logistics companies improve decision-making and enhance competitiveness in a complex and ever-changing market.

[0293] In this embodiment, a company is used as an example for analysis. The company owns 16 vessels with a total deadweight tonnage of over 420,000 DWT, an annual transport volume of 20 million tons, and more than 2,400 voyages. In addition, it has access to 238 vessels in the charter market with a total deadweight tonnage of over 2 million DWT. These vessels range in size from 2,000 tons to 40,000 tons. The shipping routes served by the company connect 27 ports on the coast and inland waterways. The company also owns 10 product tankers.

[0294] See Figure 2 and Figure 3 , Figure 2 and Figure 3The cost comparison between the robust optimization model and the deterministic model is shown separately under the price fluctuation range of heavy fuel oil (HFO) and light fuel oil (LFO). The figure shows that under the condition of HFO and LFO price fluctuation, when the price fluctuation exceeds the critical threshold, the robust optimization model (RO) shows superior performance compared with the deterministic basic model (D), and the robust optimization model has a more stable cost advantage.

[0295] For the HFO refueling strategy, when the HFO price fluctuates by more than 300 units (e.g., 300 and 400 units), the robust optimization model consistently outperforms the deterministic method through stable cost. Under a 300-unit HFO fluctuation, the deterministic cost rises to 117,437,000, while the robust model reduces the cost to 115,071,000 (a decrease of 2.0%). Under a 400-unit fluctuation, the deterministic cost further increases to 119,076,000, while the robust optimization model maintains a lower cost of 117,607,000 (a decrease of 1.2%).

[0296] For LFO refueling strategies, the advantage of robust optimization models is particularly evident when LFO price fluctuations exceed 250 units (e.g., 350, 400, and 450 units). With an LFO fluctuation of 350 units, the deterministic cost reaches 116,390,000, while the robust optimization model reduces the cost to 112,517,000 (a reduction of 3.3%). With a fluctuation of 400 units, the deterministic cost soars to 122,407,000, but the robust optimization model demonstrates its resilience by controlling the cost to 115,242,000 (a reduction of 6.0%). This resilience stems from the robust optimization model's ability to hedge against HFO price shocks through diversified fuel procurement and alternative port selection, thereby minimizing exposure to the risks of volatile markets.

[0297] By dynamically adjusting fuel ratios and optimizing route flexibility, robust optimization models can mitigate the risks of extreme price volatility, especially at higher volatility levels. Even at lower volatility levels (such as 250 units), deterministic costs temporarily outperform. The long-term stability and ability to handle extreme scenarios make robust optimization models the preferred choice in unpredictable markets. These results highlight the value of robust optimization in dealing with price instability, especially when volatility exceeds predefined thresholds.

[0298] Figure 4This paper compares the costs of the Robust Optimization (RO) model and the Deterministic (D) model under varying berthing time fluctuations. When berthing time fluctuations exceed 12 hours, the Robust Optimization (RO) model demonstrates a significant cost advantage over the Deterministic (D) model in high-fluctuation scenarios. For fluctuations exceeding 12 hours (e.g., 13-19 hours), the RO model consistently achieves lower or more stable costs. Notably, with a 16-hour fluctuation, the Deterministic cost spikes to 121.773 million, while the RO model reduces the cost to 111.4 million (an 8.5% reduction) through optimized scheduling and contingency planning. With a 17-hour fluctuation, the Deterministic cost reaches 122.646 million, while the RO model further reduces it to 120.57 million (a 1.7% reduction). In extreme scenarios, such as a 19-hour fluctuation, the RO model reduces the cost to 113.582 million, while the Deterministic model's cost is 115.064 million (a 1.3% reduction). These results highlight the ability of robust optimization models to dynamically adjust vessel scheduling and fuel reserves to offset berthing time uncertainties, ensuring cost stability in volatile operating environments where the rigidity of parameter assumptions causes deterministic models to fail.

[0299] Example 2:

[0300] See Figure 5 A joint optimization system for ship deployment and refueling that considers multiple uncertainties includes:

[0301] The deterministic basic model building unit 1 is used to define variables and parameters, with the goal of minimizing the total cost of fleet operating costs, fuel refueling costs and port charges, and to define constraints to build a deterministic basic model of nonlinear mixed integer programming.

[0302] Robust optimization model building unit 2 is used to construct a robust optimization model for uncertainty factors by using random oil price and random berthing time as uncertainty variables and determining the set of uncertainties used to capture the constraints.

[0303] Two-stage robust optimization model building unit 3 is used to build a two-stage robust optimization model based on the integration of a deterministic basic model and a robust optimization model. The main problem in the first stage is a ship deployment scheme with a robust objective. The sub-problem in the second stage is to solve the optimal fuel refueling strategy for a given ship deployment scheme, considering uncertain variables, evaluate the worst-case cost, and generate the Benders cut plane.

[0304] The ship deployment and refueling strategy acquisition unit 4 is used to iteratively solve the first-stage main problem and the second-stage subproblem using the Benders decomposition algorithm with embedded branch and bound until convergence, so as to obtain the robust optimal ship deployment scheme and the corresponding fuel refueling strategy.

[0305] Furthermore, the specific functions implemented by the deterministic basic model construction unit 1, the robust optimization model construction unit 2, the two-stage robust optimization model construction unit 3, and the ship deployment and refueling strategy acquisition unit 4 are described in the corresponding description in Embodiment 1, and will not be repeated here.

[0306] Example 3:

[0307] See Figure 6 A joint optimization device for ship deployment and refueling that takes into account multiple uncertainties, the device including a processor 5 and a memory 6;

[0308] The memory 6 is used to store computer program code 61 and transmit the computer program code 61 to the processor 5;

[0309] The processor 5 is used to execute the ship deployment and refueling joint optimization method considering multiple uncertainties as described in Embodiment 1 according to the instructions in the computer program code 61.

[0310] This embodiment also includes a computer-readable storage medium storing computer-executable instructions. When the computer-executable instructions are executed on a computer, the ship deployment and refueling joint optimization method considering multiple uncertainties described in Embodiment 1 is implemented.

[0311] The aforementioned equipment and non-transitory computer-readable storage media can be found in the detailed description of a joint optimization method for ship deployment and refueling that takes into account multiple uncertainties and its beneficial effects, which will not be repeated here.

[0312] Although embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A joint optimization method for ship deployment and refueling considering multiple uncertainties, characterized in that, include: Define variables and parameters, aim to minimize the total cost of fleet operating costs, fuel refueling costs, and port charges, and define constraints to construct a deterministic basic model of nonlinear mixed integer programming; The constraints include the following: Ensure that the refined oil transportation needs of each shipping route are met: ; in: For ships Deployed to the flight path Binary decision variables on For ships The capacity, For the route The demand for transportation; Ensure that each ship serves a maximum of one route: ; Continuity constraints on marine fuel oil consumption: ； ； in: , They represent ships After completing the flight segment The amount of heavy fuel oil and light fuel oil remaining in the rear fuel tank; , Ships In the flight segment The quantity of heavy fuel oil and light fuel oil loaded at the port of origin; This refers to the consumption of heavy fuel oil in ships. This refers to the consumption of light fuel oil in ships; The quantity of heavy and light fuel oil in a ship's fuel tanks must not fall below a minimum level during navigation: ； ； in: , These are the minimum safe fuel oil levels that ships must maintain for heavy fuel oil and light fuel oil, respectively. Ensure that the amount of fuel in the fuel tank does not exceed the maximum capacity during refueling: ； ； in: , Ships The tank capacity for heavy fuel oil and light fuel oil; The amount of fuel purchased must exceed the minimum purchase amount. ； ； in: , These are the minimum purchase quantities for heavy fuel oil and light fuel oil, respectively. Logical constraints of the deterministic basic model: ； ； ； ； in: , They represent ships On the route The The decision variable for whether a port should refuel with heavy or light fuel oil; Boundaries of decision variables in deterministic basic models: ； ； ； ； Using random oil prices and random berthing times as uncertainty variables, and determining the set of uncertainties used to capture constraints, a robust optimization model for uncertainty factors is constructed. The random oil price is represented as follows: This indicates that oil prices are within a range. The upper part follows any distribution; The random berthing time is represented as: This indicates that the berthing time is distributed in Inside; The set of uncertainties used to capture constraints is expressed as follows: ； in: Let this be the set of uncertainties surrounding oil prices. For the set of uncertainties in berthing time, This represents the fluctuation vector of oil prices; This represents the fluctuation vector of berthing time; Budgeting for the uncertainty of oil prices; Budgeting for the uncertainty of berthing time; The expression for the robust optimization model is as follows: ； A two-stage robust optimization model is constructed by integrating a deterministic basic model and a robust optimization model. The main problem in the first stage is the ship deployment scheme with a robust objective. The sub-problem in the second stage is to solve the optimal fuel refueling strategy for a given ship deployment scheme, considering uncertain variables, evaluate the worst-case cost, and generate the Benders cut plane. The Benders decomposition algorithm with embedded branch and bound is adopted. Before the uncertainty variables, the first stage main problem is solved iteratively to obtain the robust optimal ship deployment scheme. After the ship deployment scheme is determined, the uncertainty variables are considered and the second stage sub-problem is solved iteratively until convergence, and the optimal fuel refueling strategy is obtained.

2. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 1, characterized in that: The variables and parameters include route and vessel parameters, fuel consumption rate parameters, fuel selection parameters, decision variables, and the set of vessel route segments; The route and vessel parameters include: the transport demand of the route, the sailing distance of the segment, the vessel's carrying capacity, the vessel's heavy fuel oil tank capacity, the vessel's light fuel oil tank capacity, the vessel's economic cruising speed on the coastal route, the time required for the vessel to load and unload a unit of cargo, the total amount of cargo loaded and unloaded at the port of origin of the segment, and the vessel's speed on the route. The price of high-quality fuel oil at several ports, and the status of ships on their routes. The price of refueling with light fuel oil at each port, and the vessel's position on the route. Port fees at each port, and the minimum safe levels of heavy and light fuel oil that ships must maintain; The fuel consumption rate parameters include: the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship on the coastal route, the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship in the restricted area, the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship while anchored in the port, and the consumption rate of heavy fuel oil and light fuel oil per unit time of the ship while loading and unloading cargo in the port. The fuel selection parameters include: a binary parameter for whether the vessel uses heavy or light fuel oil during the voyage, and a binary parameter for whether the vessel uses heavy or light fuel oil during anchorage and operations at the port of origin of the voyage.

3. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 1, characterized in that: The decision variables include: a binary decision variable on the deployment of the ship to the route; a binary decision variable on whether the ship refuels with heavy or light fuel oil at a port on the route; a non-negative decision variable on the amount of heavy and light fuel oil refueled at a port on the route; and a state variable on the amount of heavy and light fuel oil remaining in the ship's fuel tank after the completion of the voyage. The set of vessel routes and segments includes: the set of vessels owned by the company, the set of routes used for coastal transportation, and the set of routes and segments.

4. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 1, characterized in that: The objective function for minimizing the total cost of fleet operation, fuel refueling, and port charges is as follows: ； in: Total cost; For fleet operating costs, For fuel refueling costs, Port fees and costs; The fleet operating cost is expressed as follows: ； in: For ships Deployed to the flight path Binary decision variables on The distance traveled in a segment of the voyage. The economic cruising speed for ships on coastal routes. This refers to the total time a ship spends in port. This refers to the transportation demand of the air route. The time required for loading and unloading cargo from a ship; The total time the vessel spent in the port This includes the ship's anchoring time and refueling time, and its expression is as follows: ； in: For the route No. The time required for loading and unloading fuel oil at each port , These are the non-negative decision variables for the amount of heavy fuel oil and light fuel oil added by the ship at the port of origin of the voyage, respectively. , These refer to the speeds of adding heavy fuel oil and light fuel oil, respectively. The fuel refueling cost includes the total cost of refueling the ship with both bulk fuel oil and light fuel oil, expressed as follows: ； in: , The ship is on the route of the first Prices of heavy fuel oil and light fuel oil at several ports have increased. The port charges are expressed as follows: ； in: For ships Deployed to the flight path Binary decision variables on For the ship on the route Port fees for each port.

5. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 4, characterized in that: The expressions for the consumption of heavy fuel oil and light fuel oil in ships are as follows: ； ； in: , These represent the consumption of heavy fuel oil and light fuel oil by the ship during the voyage. , These represent the consumption of heavy fuel oil and light fuel oil by ships during anchoring and loading / unloading in port, respectively. The expressions for the consumption of heavy fuel oil and light fuel oil by the ship during the voyage are as follows: ； ； in: The binary parameters for determining whether a ship uses heavy or light fuel oil during a voyage. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time for ships on coastal routes, respectively. The distance traveled in a segment of the voyage. The economic cruising speed for ships on coastal routes. For the company's collection of ships, A collection of shipping routes used for coastal transportation. For flight routes; The consumption of heavy fuel oil and light fuel oil by the vessel during anchorage and operations in port are expressed as follows: ； ； in: The binary parameters for the use of heavy or light fuel oil by the vessel during anchorage and operations at the port of origin of the voyage. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time within the restricted area, respectively. , These represent the consumption rates of heavy fuel oil and light fuel oil per unit time during ship operations in port. This refers to the total amount of cargo loaded and unloaded at the port of origin of the shipping segment. The time required for loading and unloading cargo from a ship; This refers to the total time a ship spends in port.

6. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 1, characterized in that: The main problem in the first stage specifically refers to: With cost minimization as the primary objective of the first phase of decision-making, a ship deployment plan is constructed. Meanwhile, ship deployment plans were also considered. The impact of the worst-case cost on the second-stage decision subproblem is expressed through auxiliary variables. To approximate the objective of the primary decision problem in the first stage, the expression is as follows: ； The constraints are as follows: ； ； ； ； in: For ships Deployed to the flight path Binary decision variables on For the ship on the route Port fees for each port, For ships The capacity, For the route The demand for transportation; The second-stage decision sub-problem specifically refers to: The current ship deployment plan is based on the main decision-making problem in the first phase. The second-stage decision subproblems all calculate the worst-case cost of the solution under the set of uncertainties. Its expression is as follows: ； in: For fleet operating costs, For fuel refueling costs, This represents the fluctuation vector of berthing time. For fuel refueling time, The set of decision variables for the refueling strategy in the second-stage decision sub-problem. Let be the vector of oil price fluctuations. This represents the amount of fuel remaining in the fuel tank. Based on the strong duality theorem, the second-stage decision subproblem is transformed into a single max problem, the expression of which is as follows: ； in: Let this be the set of uncertainties surrounding oil prices. For the set of uncertainties in berthing time, As dual variables, For dual feasible region, This is a transpose.

7. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 6, characterized in that: The Benders decomposition algorithm with embedded branch and bound is used to iteratively solve the first-stage main problem and the second-stage subproblems until convergence, obtaining a robust and optimal ship deployment scheme and corresponding fuel refueling strategy, specifically including: Initialize the global upper bound of the global optimal solution to the primary decision problem in the first stage. Global lower bound Iteration counter for Benders decomposition Convergence tolerance And determine the decision variables for the main decision problem in the first stage. Auxiliary variables and constraints; In the In the next Benders decomposition iteration, the first-stage decision master problem is solved based on the branch and bound algorithm to obtain the optimal integer solution, i.e., the ship deployment scheme; Substitute the optimal integer solution into the second-stage decision subproblem to solve for the optimal value and the corresponding worst-case cost, and determine the state of the optimal value. If the optimal value is a finite value, then calculate the robust total cost. and update the global upper bound. It also stores the current complete solution corresponding to the updated global upper bound; at the same time, it constructs a robust optimality cutting plane and adds it to the constraints of the first-stage decision master problem; If the optimal value is infinite, then construct a robust feasibility cutting plane and add it to the constraints of the first-stage decision problem. Determine if the difference between the global upper bound and the global lower bound converges; if If the algorithm converges, the current complete solution corresponding to the global upper bound is taken as the optimal robust solution, and the robust optimal ship deployment scheme and corresponding fuel refueling strategy are obtained. like Then set the Benders iteration counter. The algorithm continues to solve the first-stage decision problem based on the branch and bound algorithm until the algorithm converges.

8. The joint optimization method for ship deployment and refueling considering multiple uncertainties according to claim 7, characterized in that: The generation of the Benders cut plane specifically includes: If the optimal value of the second-stage decision subproblem is a finite value, then the solution corresponds to the worst-case uncertainty realization. and optimal dual variables The expression for the robust optimal cutting plane is as follows: ； If the optimal value of the second-stage decision subproblem is infinite, then the current ship deployment plan... If the constraints of the uncertainty set are infeasible, then all non-robust feasible ship deployment schemes are removed from the main decision problem of the first stage; the expression for the robust feasibility cutting plane is as follows: ； in: For extreme rays in the dual feasible region.

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