Dry bulk cargo fleet scheduling and fuel supply strategy collaborative optimization method under uncertain fuel price

Abstract

The invention provides a dry bulk cargo fleet scheduling and fuel supply strategy collaborative optimization method under an uncertain fuel price, and the method comprises the steps: constructing a virtual shipping space-time network, and describing the transportation paths and fuel consumption conditions of a dry bulk cargo fleet and cargoes; calculating a fuel price mean value and a covariance coefficient based on historical port fuel price information; according to the shipping space-time network and the fuel price mean value, establishing a dry bulk fleet operation scheduling and fuel supply strategy collaborative optimization model under the fuel price determination condition; and according to the fuel price mean value and covariance, constructing an oil price ellipsoid uncertainty set and a robust optimization model under the condition of oil price uncertainty, deducing a closed solution form of an objective function, and obtaining a fleet scheduling and fuel supply scheme. According to the method, the space-time volatility of the fuel price is considered, the fleet scheduling and fuel supply decision is made under the condition that the fuel price is uncertain, the fuel supply cost of the dry bulk cargo fleet is reduced, and the competitiveness of a shipping company under the condition that the fuel price fluctuates is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of dry bulk cargo fleet scheduling and fuel supply strategy, and in particular to a method for collaborative optimization of dry bulk cargo fleet scheduling and fuel supply strategy under uncertain fuel prices. Background Art

[0002] As an important part of the global transportation system, the shipping industry carries more than 90% of the world's freight volume and plays an indispensable role in the world's economic and trade activities. Among them, dry bulk shipping accounts for about 1 / 3 of the entire shipping industry. It is mainly responsible for the ocean transportation of bulk commodities such as coal, ore, and grain. It is an important pillar industry supporting the development of the national economy. However, affected by multiple factors such as inflation and changes in supply and demand, the global shipping industry has continued to be sluggish in recent years. The median of the Baltic Dry Index (BDI) in 2023 was only 1296.50 points, a decrease of 33.34% compared with 2022. Faced with a difficult market environment, how to wisely organize cargo transportation, improve operational efficiency, maximize profits and effectively control operating cost expenditures has become a major issue that dry bulk shipping companies urgently need to solve.

[0003] Compared with liner shipping, dry bulk shipping has unique characteristics such as unfixed routes and unfixed sailing schedules. Therefore, the operation process of dry bulk fleets is more complicated, which brings great challenges to fleet managers in ship scheduling and cost control. On the one hand, fleet managers need to comprehensively consider multiple factors such as the deadweight tonnage, speed range and cargo loading period of each ship in the fleet, and reasonably match ships and cargoes to formulate the optimal fleet scheduling plan. This is directly related to the freight revenue level of the entire fleet. On the other hand, fleet managers also need to focus on controlling the fleet's operating costs. Among them, fuel costs account for the largest proportion of voyage costs, up to 45% of total operating costs. In practice, fleet managers usually control fuel costs by adjusting the speed. However, although reducing the speed can save fuel consumption and indirectly control fuel costs, it may also cause some cargoes to fail to arrive at the loading and unloading port on time, resulting in freight revenue losses. In addition, fuel prices are not static, and fuel prices not only fluctuate greatly over time, but also vary greatly between different ports, which further brings difficulties to fleet fuel cost control. Therefore, developing a collaborative optimization method for dry bulk fleet scheduling and fuel replenishment strategy based on uncertain oil prices not only has important theoretical significance for shipping companies, but also has very broad application prospects, which can inject new impetus into the company's benefit maximization and sustainable development. Summary of the invention

[0004] According to the technical problems raised above, a method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices is provided. The present invention has the characteristics of considering the volatility of fuel prices, constructing an uncertain set of fuel price ellipsoids, and designing robust fleet scheduling and fuel supply strategies under fuel price uncertainty. The method of the present invention can be used to optimize the scheduling and fuel supply decisions of dry bulk fleets, reduce the operating and fuel supply costs of dry bulk fleets, and improve the competitiveness of shipping companies under fuel price fluctuations.

[0005] The technical means adopted by the present invention are as follows:

[0006] A collaborative optimization method for dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices, including:

[0007] S1. Construct a virtual shipping space-time network to describe the transportation routes of dry bulk fleets and cargoes, and represent the fuel consumption of bulk fleets during navigation based on the transportation routes;

[0008] S2. Based on the historical port fuel price information in the shipping space-time network, the mean and covariance coefficient of the fuel price are calculated;

[0009] S3. Based on the virtual shipping space-time network and the average fuel price, a collaborative optimization model for dry bulk fleet operation scheduling and fuel supply strategy under the condition of determined fuel price is established;

[0010] S4. According to the mean and covariance of fuel prices, an uncertainty set of fuel price ellipsoids is constructed, and a robust optimization model under fuel price uncertainty is constructed. The Lagrangian duality theory is used to derive the closed solution form of the objective function, and a robust fleet scheduling and fuel supply plan is obtained.

[0011] Furthermore, step S1 specifically includes:

[0012] S11. Assume that the scenario under consideration is that a dry bulk fleet transports goods, and the fleet signs K cargo transportation contracts with the shipper within a given planning period of T days;

[0013] S12. The fleet manager arranges a fleet of V dry bulk carriers to carry out dry bulk cargo transportation tasks between P ports;

[0014] S13. Introduce the space-time network model and abstract the actual transportation process into a directed graph In the spatiotemporal network model, each node Represents a unique combination of a specific time and place; arc (i, j) represents the displacement process of the ship and cargo from node i to node j;

[0015] S14. During the voyage of a dry bulk carrier, the fuel consumption of ship v moving from node i to node j is The operating cost is

[0016] S15. To ensure the safe navigation of dry bulk carriers, the minimum fuel supply at node i is set to q i .

[0017] Further, step S2 specifically includes:

[0018] Based on the constructed virtual shipping space-time network model, according to the historical fuel price data of the nodes, Calculate the mean fuel price μ for each node i and the covariance matrix Σ of the node’s historical fuel prices.

[0019] Furthermore, step S3 specifically includes:

[0020] S31. Setting model variables, including ship navigation variables Freight transport variables Fuel supply variables and and fuel transfer variables

[0021] S32. Design the objective function of the coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination, as follows:

[0022]

[0023] In the above formula, represents the total freight revenue generated by the fleet during the planning period; represents the operating cost of ship voyages during the planning period; represents the fuel supply cost incurred by the ship during the planning period;

[0024] S33. The constraints of the coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination are as follows:

[0025] The first set of constraints:

[0026] The second set of constraints:

[0027] The third set of constraints:

[0028] The fourth set of constraints:

[0029] The fifth set of constraints:

[0030] The sixth set of constraints:

[0031] The seventh set of constraints:

[0032] The eighth set of constraints:

[0033] The ninth set of constraints: In the above formula, M represents a large positive real number; the first set of constraints ensures that ship v executes the flow conservation rule and travels a complete path within the planning period; where node O and node D are the starting node and the ending node of all ships respectively; the second set of constraints ensures that only ship v passes through the cargo transportation arc The cargo k can be transported by ship v when v Exceeding cargo weight Q k The fourth group of constraints ensures that cargo k can be transported by at most one ship and will not be divided; the fifth group of constraints stipulates the initial fuel volume of ship v; the sixth group of constraints dynamically tracks the changes in the remaining fuel volume of ship v on the tth day during the planning period, including fuel replenishment and fuel consumption; the seventh group of constraints ensures that the remaining fuel volume of ship v during the entire planning period will not be lower than the minimum safety requirement of the oil tank. The maximum capacity of the oil tank will not be exceeded. The eighth set of constraints ensures that ship v can only refuel when it passes through node i. The ninth set of constraints stipulates the minimum amount of fuel for ship v when refueling at node i, ensuring that the ship has enough fuel to reach the next refueling point safely even in an emergency.

[0034] Furthermore, in the model variables set in step S31:

[0035] Said ship navigation variables Indicates whether the ship v passes through the arc (i, j), if so, it is 1; otherwise, it is 0;

[0036] The cargo transport variables Indicates whether cargo k is transported by ship v, if so, it is 1; otherwise, it is 0;

[0037] The refueling variable Indicates whether the ship v is refueling at node i. If so, it is 1; otherwise, it is 0. Fuel refueling variable represents the fuel supply of ship v at node i;

[0038] The fuel transfer variable represents the remaining fuel of ship v at time t.

[0039] Further, step S4 specifically includes:

[0040] S41. According to the fuel price mean and covariance matrix, a fuel price uncertainty ellipsoid set is constructed as follows:

[0041]

[0042] In the above formula, the oil price mean vector μ is the ellipsoid uncertainty set The center of the covariance matrix is ​​∑ -1 Used to "normalize" this deviation, ensuring that the ellipsoid shape correctly reflects the uncertainty in all directions; (p-μ) T ∑ -1 (p-μ) is the square of the standardized deviation, which is used as a distance metric to measure the distance between each possible oil price observation and the mean oil price. When this distance is less than the parameter δ, the actual oil price observation belongs to the ellipsoid.

[0043] S42. Introducing the uncertain fuel price into the objective function, the robust optimization model is obtained and converted into a closed solution form, including:

[0044] S421. After introducing the uncertain fuel price, in order to ensure that the objective function is still optimized under the worst fuel cost condition, it is transformed into the following:

[0045]

[0046] S422. In order to deal with the uncertain fuel supply cost part of the objective function, the uncertain fuel supply cost part is treated as a sub-problem separately, as follows:

[0047]

[0048] S423, introduce the Lagrange multiplier λ≥0, and transform the uncertainty set The constraints are embedded into the objective function to form an unconstrained Lagrangian function L(p,λ):

[0049] L(p,λ)=p T We+λ(δ-(p-μ) T ∑-1(p-μ))

[0050] Among them, W is the matrix form of the refueling decision variable, and the elements represents the refueling volume of ship v at node i;

[0051] S424, in order to solve the optimal fuel price vector p * and Lagrangian multiplier λ, thereby minimizing the Lagrangian function L(p,λ), taking the partial derivative of L(p,λ) with respect to p, and solving the optimal fuel price vector p that makes the partial derivative zero * :

[0052]

[0053] S425, the optimal fuel supply price p * Bringing back the Lagrangian function L(p,λ), we get an expression only for the Lagrangian multiplier λ:

[0054]

[0055] S426. According to the duality theory, is the dual problem of the subproblem, namely:

[0056]

[0057] S427. In order to find a closed form solution, we need to find an optimal Lagrange multiplier λ. Therefore, we first separate the constant term μ that is independent of λ. T We then take the partial derivative of the function of λ and set the derivative to zero to find the extreme point:

[0058]

[0059] Rearranging the above equation, we get λ * The value is as follows:

[0060]

[0061] S428, the obtained λ * Substitute the value back into the formula of step S426 to calculate the minimum value:

[0062]

[0063] S429. Bring the minimum value of the dual problem back to the objective function to obtain the final form of the distributed robust optimization objective function:

[0064]

[0065] Combining a series of constraints of dry bulk fleet scheduling and fuel refueling methods, robust fleet scheduling and fuel refueling decisions under fuel price uncertainty are obtained.

[0066] Compared with the prior art, the present invention has the following advantages:

[0067] 1. The collaborative optimization method of dry bulk fleet scheduling and fuel supply strategy based on uncertain fuel prices provided by the present invention reduces the operating costs and fuel supply costs of shipping companies by optimizing fleet scheduling plans and fuel supply strategies, thereby improving the competitiveness of shipping companies under fuel price fluctuations.

[0068] 2. The collaborative optimization method of dry bulk cargo fleet scheduling and fuel supply strategy based on uncertain fuel prices provided by the present invention, its collaborative optimization model of dry bulk cargo fleet scheduling and fuel supply strategy takes into account the ship-cargo matching constraints and fuel supply restriction constraints, and the model has strong practicality.

[0069] 3. The collaborative optimization method of dry bulk fleet scheduling and fuel supply strategy based on uncertain fuel prices provided by the present invention constructs an ellipsoidal uncertainty set and develops a robust optimization model using the fuel price mean and covariance matrix, and then uses the Lagrangian duality theory to obtain a closed solution form, which has high computational efficiency.

[0070] Based on the above reasons, the present invention can be widely promoted in the fields of dry bulk fleet scheduling and fuel supply strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0072] Figure 1 The figure is a flow chart of the method of the present invention.

[0073] Figure 2 A schematic diagram of a virtual shipping space-time network model provided by an embodiment of the present invention.

[0074] Figure 3 A schematic diagram of shipping network ports and cargoes provided in an embodiment of the present invention.

[0075] Figure 4 Actual fuel supply cost trends of different strategies under different fuel price fluctuation ranges provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0076] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0077] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0078] like Figure 1 As shown, the present invention provides a method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices, including:

[0079] S1. Construct a virtual shipping space-time network to describe the transportation routes of dry bulk fleets and cargoes, and represent the fuel consumption of bulk fleets during navigation based on the transportation routes;

[0080] S2. Based on the historical port fuel price information in the shipping space-time network, the mean and covariance coefficient of the fuel price are calculated;

[0081] S3. Based on the virtual shipping space-time network and the average fuel price, a collaborative optimization model for dry bulk fleet operation scheduling and fuel supply strategy under the condition of determined fuel price is established;

[0082] S4. According to the mean and covariance of fuel prices, an uncertainty set of fuel price ellipsoids is constructed, and a robust optimization model under fuel price uncertainty is constructed. The Lagrangian duality theory is used to derive the closed solution form of the objective function, and a robust fleet scheduling and fuel supply plan is obtained.

[0083] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0084] S11. Assume that the scenario under consideration is that a dry bulk fleet transports goods, and the fleet signs K cargo transportation contracts with the shipper within a given planning period of T days;

[0085] S12. The fleet manager arranges a fleet of V dry bulk carriers to carry out dry bulk cargo transportation tasks between P ports;

[0086] S13. Introducing the spatiotemporal network model to effectively abstract the actual transportation process into a directed graph In the spatiotemporal network model, each node Represents a unique combination of a specific time and place; arc (i, j) represents the displacement process of the ship and cargo from node i to node j;

[0087] S14. During the voyage of a dry bulk carrier, the fuel consumption of ship v moving from node i to node j is The operating cost is

[0088] S15. To ensure the safe navigation of dry bulk carriers, the minimum fuel supply at node i is set to q i .

[0089] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0090] Based on the constructed virtual shipping space-time network model, according to the historical fuel price data of the nodes, Calculate the mean fuel price μ for each node i and the covariance matrix Σ of the node’s historical fuel prices.

[0091] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0092] S31. Setting model variables, including ship navigation variables Freight transport variables Fuel supply variables and and fuel transfer variables

[0093] S32. Design the objective function of the coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination, as follows:

[0094]

[0095] In the above formula, represents the total freight revenue generated by the fleet during the planning period; represents the operating cost of ship voyages during the planning period; represents the fuel supply cost incurred by the ship during the planning period;

[0096] S33. The constraints of the coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination are as follows:

[0097] The first set of constraints:

[0098] The second set of constraints:

[0099] The third set of constraints:

[0100] The fourth set of constraints:

[0101] The fifth set of constraints:

[0102] The sixth set of constraints:

[0103] The seventh set of constraints:

[0104] The eighth set of constraints:

[0105] The ninth set of constraints: In the above formula, M represents a large positive real number; the first set of constraints ensures that ship v executes the flow conservation rule and travels a complete path within the planning period; where node O and node D are the starting node and the ending node of all ships respectively; the second set of constraints ensures that only ship v passes through the cargo transportation arc The cargo k can be transported by ship v when v Exceeding cargo weight Q k The fourth group of constraints ensures that cargo k can be transported by at most one ship and will not be divided; the fifth group of constraints stipulates the initial fuel volume of ship v; the sixth group of constraints dynamically tracks the changes in the remaining fuel volume of ship v on the tth day during the planning period, including fuel replenishment and fuel consumption; the seventh group of constraints ensures that the remaining fuel volume of ship v during the entire planning period will not be lower than the minimum safety requirement of the oil tank. The maximum capacity of the oil tank will not be exceeded. The eighth set of constraints ensures that ship v can only refuel when it passes through node i. The ninth set of constraints stipulates the minimum amount of fuel for ship v when refueling at node i, ensuring that the ship has enough fuel to reach the next refueling point safely even in an emergency.

[0106] In specific implementation, as a preferred embodiment of the present invention, the model variables set in step S31 are:

[0107] Said ship navigation variables Indicates whether the ship v passes through the arc (i, j), if so, it is 1; otherwise, it is 0;

[0108] The cargo transport variables Indicates whether cargo k is transported by ship v, if so, it is 1; otherwise, it is 0;

[0109] The refueling variable Indicates whether the ship v is refueling at node i. If so, it is 1; otherwise, it is 0. Fuel refueling variable represents the fuel supply of ship v at node i;

[0110] The fuel transfer variable represents the remaining fuel of ship v at time t.

[0111] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0112] S41. According to the fuel price mean and covariance matrix, a fuel price uncertainty ellipsoid set is constructed as follows:

[0113]

[0114] In the above formula, the oil price mean vector μ is the ellipsoid uncertainty set The center of the covariance matrix is ​​∑ -1 Used to "normalize" this deviation, ensuring that the ellipsoid shape correctly reflects the uncertainty in all directions; (p-μ) T ∑ -1 (p-μ) is the square of the standardized deviation, which is used as a distance metric to measure the distance between each possible oil price observation and the mean oil price. When this distance is less than the parameter δ, the actual oil price observation belongs to the ellipsoid.

[0115] S42. Introducing the uncertain fuel price into the objective function, the robust optimization model is obtained and converted into a closed solution form, including:

[0116] S421. After introducing the uncertain fuel price, in order to ensure that the objective function is still optimized under the worst fuel cost condition, it is transformed into the following:

[0117]

[0118] S422. In order to deal with the uncertain fuel supply cost part of the objective function, the uncertain fuel supply cost part is treated as a sub-problem separately, as follows:

[0119]

[0120] S423, introduce the Lagrange multiplier λ≥0, and transform the uncertainty set The constraints are embedded into the objective function to form an unconstrained Lagrangian function L(p,λ):

[0121] L(p,λ)=p T We + λ(δ-(p-μ) T ∑- 1 (p-μ)

[0122] Among them, W is the matrix form of the refueling decision variable, and the elements represents the refueling amount of ship v at node i;

[0123] S424, in order to solve the optimal fuel price vector p * and Lagrangian multiplier λ, thereby minimizing the Lagrangian function L(p,λ), taking the partial derivative of L(p,λ) with respect to p, and solving the optimal fuel price vector p that makes the partial derivative zero * :

[0124]

[0125]

[0126] S425, the optimal fuel supply price p * Bringing back the Lagrangian function L(p,λ), we get an expression only for the Lagrangian multiplier λ:

[0127]

[0128] S426. According to the duality theory, is the dual problem of the subproblem, namely:

[0129]

[0130] S427. In order to find a closed form solution, we need to find an optimal Lagrange multiplier λ. Therefore, we first separate the constant term μ that is independent of λ. T We then take the partial derivative of the function of λ and set the derivative to zero to find the extreme point:

[0131]

[0132] Rearranging the above equation, we get λ* The value is as follows:

[0133]

[0134] S428, the obtained λ * Substitute the value back into the formula of step S426 to calculate the minimum value:

[0135]

[0136] S429. Bring the minimum value of the dual problem back to the objective function to obtain the final form of the distributed robust optimization objective function:

[0137]

[0138] Combining a series of constraints of dry bulk fleet scheduling and fuel refueling methods, robust fleet scheduling and fuel refueling decisions under fuel price uncertainty are obtained.

[0139] Example

[0140] The data used in this example comes from the actual shipping world. Ports and freight demand are mainly concentrated in Northwestern Europe, the Mediterranean and the Black Sea. Figure 3 Considering that a dry bulk carrier performs dry bulk cargo transportation tasks and refuels in this shipping space-time network, the main parameters can be set as follows: the number of ports N = 6, the planning period length T = 10, the average fuel price μ of node i i The covariance matrix of the node historical fuel prices is obtained through historical data. The fuel consumption of dry bulk ship v from node i to port j and sailing costs It is calculated by the ship's deadweight tonnage and sailing speed. The specific information of dry bulk ships and cargoes is shown in Tables 1 and 2.

[0141] Table 1 Ship information

[0142]

[0143] Table 2 Cargo information

[0144]

[0145] In order to ensure the safe navigation of dry bulk ships, a minimum refueling volume is set at the port. i , whose value is obtained by converting with the oil tank capacity. According to the fuel price determination dry bulk fleet scheduling and fuel supply strategy optimization model established by the present invention and the robust optimization model considering fuel price uncertainty, the navigation decision, cargo transportation decision and fuel supply decision of dry bulk ships are calculated.

[0146] Step 1: Establish a virtual shipping space-time network based on the geographical location of the port, the length of the planning period, the information of dry bulk vessels and cargo, as follows: Figure 2 As shown, including:

[0147] Combine geographic location and time into space-time nodes to obtain the space-time node set of the shipping network Determine the deadweight tonnage C of a dry bulk carrier according to its model v and oil tank capacity Use the fuel consumption calculation formula to calculate the fuel consumption between two nodes based on the deadweight tonnage and sailing speed of the dry bulk carrier and the cost of sailing Minimum refueling quantity i Through the oil tank capacity Converted.

[0148] Step 2: Based on the virtual shipping space-time network, the mean and covariance coefficient of the fuel price of the space-time node are calculated, including:

[0149] According to the historical fuel price data of the shipping space-time network involved, combined with the aforementioned virtual shipping space-time network model, the mean fuel price μ of each node i is obtained i According to the historical fuel price information and combined with mathematical statistics methods, the fuel price covariance Σ of all nodes is obtained.

[0150] Step 3: Establish a collaborative optimization model for dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination, including:

[0151] According to the virtual shipping spatiotemporal network model and the average fuel price, a coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy determined by fuel price is established. First, write out the navigation decision variables, cargo transportation decision variables and fuel supply decision variables of the model, as well as the maximization objective function of total freight revenue minus ship navigation cost and fuel supply cost. Secondly, write out the constraints of the model, including network flow equilibrium constraints, ship-cargo matching constraints, fuel supply constraints and tank capacity constraints.

[0152] Step 4: Use a robust optimization model to solve the collaborative optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of fuel price uncertainty.

[0153] The present invention uses the fuel price mean and covariance matrix to construct a fuel price uncertainty ellipsoid set Then the objective function is reformulated as

[0154]

[0155] The worst-case fuel supply cost of the third item is derived into a closed-form solution using Lagrangian relaxation theory, and the final form of the objective function of the robust optimization model is obtained:

[0156]

[0157] Combining a series of constraints of dry bulk fleet scheduling and fuel refueling methods, robust fleet scheduling and fuel refueling decisions under fuel price uncertainty are obtained.

[0158] According to the method proposed in the present invention, a robust dry bulk ship scheduling and fuel supply decision is obtained under the condition of fuel price uncertainty. The present invention generates 1000 sets of simulated fuel price data based on the constructed ellipsoid uncertainty set and calculates the actual fuel supply cost in combination with the actual decision variables to evaluate the actual performance of the method. For comparison, the present invention uses the dry bulk ship scheduling and fuel supply decision method based on the mean fuel price as a benchmark method: the mean fuel price method. This method does not take into account the volatility of fuel prices, so when the fuel price fluctuates greatly, it will cause the fuel supply cost to deteriorate significantly.

[0159] Therefore, the robust optimization model proposed in the present invention can make a robust fuel supply decision based on the historical fuel price mean and covariance matrix when the fuel price fluctuates. By comparing with the benchmark method, it can be found that the method proposed in the present invention can achieve better results under various fuel price fluctuation ranges and has better practical application value. Considering the fuel price fluctuation range δ of 60, 80 and 100 respectively, the final results are shown in Table 3 below.

[0160] Table 3. Simulation of fuel supply costs under different strategies

[0161]

[0162] According to the calculation results, the present invention concludes that the robust refueling method designed by the present invention can significantly reduce the standard deviation of the refueling cost and the worst-case refueling cost under a given tank capacity condition compared to the refueling method based on the mean value of the fuel price, thereby reducing the operating cost risk caused by fuel price fluctuations. In addition, the proportion of the improvement of the refueling cost fluctuation by the robust optimization method designed by the present invention is proportional to the range of fuel price fluctuations, which indicates that it performs better when the fuel price fluctuates greatly.

[0163] The present invention also considers the actual fuel supply cost trend of the robust fuel supply optimization method and the fuel price mean fuel supply optimization method under the fuel prices generated 1000 times. As shown in Figure 4, it can be seen that the actual fuel supply costs of the two methods show a larger variation range as the fluctuation range increases. In addition, as the fluctuation range increases, the robust effect of the robust fuel supply optimization method gradually increases.

[0164] In summary, the coordinated optimization strategy for dry bulk fleet scheduling and fuel supply strategy provided by the present invention takes into account the randomness and volatility of fuel prices, establishes a robust optimization model with uncertain fuel prices, and uses the Lagrange relaxation theorem to derive the closed solution form of the objective function of the robust optimization model. The strategy makes decisions on dry bulk fleet scheduling and fuel supply based on the constructed ellipsoid fuel price uncertainty set, thereby reducing the risk of fuel supply cost fluctuations of shipping companies and improving the competitiveness of liner companies under fuel price fluctuations.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A collaborative optimization method for dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices, characterized in that: include: S1. Construct a virtual shipping space-time network to describe the transportation routes of dry bulk fleets and cargoes, and represent the fuel consumption of bulk fleets during navigation based on the transportation routes; S2. Based on the historical port fuel price information in the shipping space-time network, the mean and covariance coefficient of the fuel price are calculated; S3. Based on the virtual shipping space-time network and the average fuel price, a collaborative optimization model for dry bulk fleet operation scheduling and fuel supply strategy under the condition of determined fuel price is established; S4. According to the mean and covariance of fuel prices, an uncertainty set of fuel price ellipsoids is constructed, and a robust optimization model under fuel price uncertainty is constructed. The Lagrangian duality theory is used to derive the closed solution form of the objective function, and a robust fleet scheduling and fuel supply plan is obtained.

2. The method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices according to claim 1 is characterized in that: Step S1 specifically includes: S11. Assume that the scenario under consideration is that a dry bulk fleet transports goods, and the fleet signs K cargo transportation contracts with the shipper within a given planning period of T days; S12. The fleet manager arranges a fleet of V dry bulk carriers to carry out dry bulk cargo transportation tasks between P ports; S13. Introduce the space-time network model and abstract the actual transportation process into a directed graph In the spatiotemporal network model, each node Represents a unique combination of a specific time and place; arc (i, j) represents the displacement process of the ship and cargo from node i to node j; S14. During the voyage of a dry bulk carrier, the fuel consumption of ship v moving from node i to node j is The operating cost is S15. To ensure the safe navigation of dry bulk carriers, the minimum fuel supply at node i is set to q i .

3. The method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices according to claim 1 is characterized in that: Step S2 specifically includes: Based on the constructed virtual shipping space-time network model, according to the historical fuel price data of the nodes, Calculate the mean fuel price μ for each node i and the covariance matrix Σ of the node’s historical fuel prices.

4. The method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices according to claim 1 is characterized in that: Step S3 specifically includes: S31. Setting model variables, including ship navigation variables Freight transport variables Fuel supply variables and and fuel transfer variables S32. Design the objective function of the coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination, as follows: In the above formula, represents the total freight revenue generated by the fleet during the planning period; represents the operating cost of ship voyages during the planning period; represents the fuel supply cost incurred by the ship during the planning period; S33. The constraints of the coordinated optimization model of dry bulk fleet operation scheduling and fuel supply strategy under the condition of oil price determination are as follows: The first set of constraints: The second set of constraints: The third set of constraints: The fourth set of constraints: The fifth set of constraints: The sixth set of constraints: The seventh set of constraints: The eighth set of constraints: The ninth set of constraints: In the above formula, M represents a large positive real number; the first set of constraints ensures that ship v executes the flow conservation rule and travels a complete path within the planning period; where node O and node D are the starting node and the ending node of all ships respectively; the second set of constraints ensures that only ship v passes through the cargo transportation arc The cargo k can be transported by ship v when v Exceeding cargo weight Q k The fourth group of constraints ensures that cargo k can be transported by at most one ship and will not be divided; the fifth group of constraints stipulates the initial fuel volume of ship v; the sixth group of constraints dynamically tracks the changes in the remaining fuel volume of ship v on the tth day during the planning period, including fuel replenishment and fuel consumption; the seventh group of constraints ensures that the remaining fuel volume of ship v during the entire planning period will not be lower than the minimum safety requirement of the oil tank. The maximum capacity of the oil tank will not be exceeded. The eighth set of constraints ensures that ship v can only refuel when it passes through node i. The ninth set of constraints stipulates the minimum amount of fuel for ship v when refueling at node i, ensuring that the ship has enough fuel to reach the next refueling point safely even in an emergency.

5. The method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices according to claim 4 is characterized in that: Among the model variables set in step S31: Said ship navigation variables Indicates whether the ship v passes through the arc (i, j), if so, it is 1; otherwise, it is 0; The cargo transport variables Indicates whether cargo k is transported by ship v, if so, it is 1; otherwise, it is 0; The refueling variable Indicates whether the ship v is refueling at node i. If so, it is 1; otherwise, it is 0. Fuel refueling variable represents the fuel supply of ship v at node i; The fuel transfer variable represents the remaining fuel of ship v at time t.

6. The method for collaborative optimization of dry bulk fleet scheduling and fuel supply strategy under uncertain fuel prices according to claim 1, characterized in that: Step S4 specifically includes: S41. According to the fuel price mean and covariance matrix, a fuel price uncertainty ellipsoid set is constructed as follows: In the above formula, the oil price mean vector μ is the ellipsoid uncertainty set The center of the covariance matrix is ​​∑ -1 Used to "normalize" this deviation, ensuring that the ellipsoid shape correctly reflects the uncertainty in all directions; (p-μ) T ∑ -1 (p-μ) is the square of the standardized deviation, which is used as a distance metric to measure the distance between each possible oil price observation and the mean oil price. When this distance is less than the parameter δ, the actual oil price observation belongs to the ellipsoid. S42. Introducing the uncertain fuel price into the objective function, the robust optimization model is obtained and converted into a closed solution form, including: S421. After introducing the uncertain fuel price, in order to ensure that the objective function is still optimized under the worst fuel cost condition, it is transformed into the following: S422. In order to deal with the uncertain fuel supply cost part of the objective function, the uncertain fuel supply cost part is treated as a sub-problem separately, as follows: S423, introduce the Lagrange multiplier λ≥0, and transform the uncertainty set The constraints are embedded into the objective function to form an unconstrained Lagrangian function L(p,λ): L(p,λ)=p T We+λ(δ-(p-μ) T ∑ -1 (p-μ)) Among them, W is the matrix form of the refueling decision variable, and the elements represents the refueling amount of ship v at node i; S424, in order to solve the optimal fuel price vector p * and Lagrangian multiplier λ, thereby minimizing the Lagrangian function L(p,λ), taking the partial derivative of L(p,λ) with respect to p, and solving the optimal fuel price vector p that makes the partial derivative zero * : S425, the optimal fuel supply price p * Bringing back the Lagrangian function L(p,λ), we get an expression only for the Lagrangian multiplier λ: S426. According to the duality theory, is the dual problem of the subproblem, namely: S427. In order to find a closed form solution, we need to find an optimal Lagrange multiplier λ. Therefore, we first separate the constant term μ that is independent of λ. T We then take the partial derivative of the function of λ and set the derivative to zero to find the extreme point: Rearranging the above equation, we get λ * The value is as follows: S428, the obtained λ * Substitute the value back into the formula of step S426 to calculate the minimum value: S429. Bring the minimum value of the dual problem back to the objective function to obtain the final form of the distributed robust optimization objective function: Combining a series of constraints of dry bulk fleet scheduling and fuel refueling methods, robust fleet scheduling and fuel refueling decisions under fuel price uncertainty are obtained.

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