Center warehouse selection and logistics route joint optimization method

Abstract

The invention provides a central warehouse selection and logistics route joint optimization method, belongs to the technical field of supply chain management and optimization, and can at least partially solve the problem that global optimization cannot be realized due to mutual independent optimization of central warehouse site selection and logistics route planning in the prior art. The method comprises the following steps: acquiring position coordinates of a production base and each warehouse node in a logistics network and distance parameters between the nodes; constructing a decision variable set based on the position information; establishing a constraint condition set including center bin number constraint, route connectivity constraint, jurisdiction uniqueness constraint and subring elimination constraint; constructing a target function by taking the minimization of the total transportation distance as a target; and integrating the decision variable, the constraint condition and the objective function to construct an integer programming model, solving the integer programming model, and outputting a central bin selection scheme and a logistics route planning scheme. According to the invention, joint global optimization of central warehouse site selection and logistics routes is realized, the logistics cost is effectively reduced, and the overall operation efficiency of a supply chain is improved.

Description

Technical Field

[0001] This invention belongs to the field of supply chain management and optimization technology, specifically relating to a method for joint optimization of central warehouse selection and logistics routes. Background Technology

[0002] With the deepening of global economic integration and the booming development of e-commerce, enterprises face an increasingly fierce market competition environment. Against this backdrop, the efficiency and cost control capabilities of supply chain management have become key factors determining a company's core competitiveness. Logistics and warehousing, as core links in supply chain operations, directly impact a company's operating costs, customer service levels, and market responsiveness. Therefore, how to scientifically and rationally select warehouse locations and plan logistics routes has become a crucial issue that urgently needs to be addressed in the field of supply chain management.

[0003] In modern supply chain network architectures, a multi-tiered distribution model is typically adopted, consisting of a three-tiered structure: production base, central warehouse, and forward warehouses. The production base is responsible for product manufacturing and initial shipment; the central warehouse, acting as a regional logistics hub, handles the collection, distribution, and transshipment of goods; and forward warehouses are located close to end customers to enable rapid delivery. In this distribution model, the location decision for the central warehouse and the planning of logistics routes within each central warehouse's jurisdiction are two closely related optimization problems. The location selection of the central warehouse directly affects the length and efficiency of subsequent logistics distribution routes, while the effectiveness of logistics route planning, in turn, influences the rationality assessment of the central warehouse location decision.

[0004] In existing technologies, central warehouse location selection and logistics route optimization are typically studied and solved as two independent problems. For central warehouse location selection, commonly used methods include the centroid method, coverage model method, P-median model method, and analytic hierarchy process (AHP). The centroid method determines warehouse location by calculating the demand-weighted geographic center; the coverage model method aims to maximize coverage; the P-median model method selects the optimal location from candidate points to minimize transportation costs; and the AHP method comprehensively considers multiple factors for qualitative and quantitative decision analysis. For logistics route optimization, heuristic algorithms such as genetic algorithms, particle swarm optimization, ant colony optimization, and simulated annealing are mainly used to solve vehicle routing problems. These algorithms, by simulating natural evolutionary mechanisms or physical processes, can find high-quality feasible solutions within a reasonable timeframe.

[0005] However, this approach of separating the two problems has significant limitations. The main drawbacks of existing technologies are as follows: First, central warehouse location selection and logistics route optimization are conducted independently, failing to fully consider the coupling relationship between the two. In actual supply chain operations, the location of the central warehouse directly determines the distance distribution from each forward warehouse to the central warehouse, thus affecting the planning results of logistics routes. Conversely, the efficiency of logistics routes is an important basis for evaluating the rationality of the central warehouse location. The separate processing approach severs this inherent connection, resulting in optimization results that only achieve local optima rather than global optima.

[0006] Second, a step-by-step optimization approach may lead to an optimization result obtained in one stage having a negative impact in another. In a process of site selection followed by route planning, the location of the central warehouse determined in the site selection phase may not be the optimal starting point for logistics route optimization; conversely, in a process of route planning followed by site selection, the assumptions made in route planning may not match the final site selection results. This sequential dependency makes it difficult to guarantee the overall optimization effect.

[0007] Third, independent optimization struggles to account for the impact of warehouse location selection on subsequent logistics routes, potentially leading to unnecessary increases in logistics costs. In some cases, adjusting the location of the central warehouse, while increasing evaluation metrics during the location selection phase, can significantly reduce transportation costs during the logistics and distribution phase, thus lowering the overall cost. Separate optimization methods fail to identify these cross-phase cost trade-offs.

[0008] Fourth, while existing smart logistics solutions utilize advanced technologies such as big data and the Internet of Things, they still rely on a step-by-step optimization approach at the algorithm level. These solutions typically first use clustering algorithms to determine warehouse locations and then use path optimization algorithms to plan delivery routes. Essentially, they are still solving two problems independently, failing to achieve true joint optimization.

[0009] Therefore, there is an urgent need for a method that can jointly optimize the selection of central warehouses and logistics route planning in order to achieve the global optimal configuration of the supply chain logistics network, reduce overall operating costs, and improve supply chain management efficiency. Summary of the Invention

[0010] The present invention aims to solve at least one of the technical problems existing in the prior art by providing a method for joint optimization of central warehouse selection and logistics routes, so as to overcome the defect that the central warehouse location selection and logistics route planning are independently optimized and cannot achieve global optimization in the prior art.

[0011] To achieve the above objectives, the present invention provides a method for joint optimization of central warehouse selection and logistics routes, comprising: Obtain network parameters of the logistics network, including production bases and The location coordinates of the warehouse nodes, where the production base is denoted as node 0, and each warehouse node is denoted as node 1. To node ; Calculate the distance between each node based on the location coordinates. ; A set of decision variables is constructed based on the network parameters. The set of decision variables includes: variables used to identify nodes. Whether it is selected as the central warehouse identifier variable Used to indicate whether the logistics route starts from a node. Directly pointing to the node The route points to the variable Used to represent nodes Does it belong to the first Jurisdiction variable for each jurisdiction and the node to be reached The order of arrival of variables ;in, , , ; A set of constraints is established based on the set of decision variables. The set of constraints includes: limiting the total number of central warehouses to a preset quantity. Central warehouse quantity constraints Ensure that each node, except for the production base, has a unique route connectivity constraint with a previous and next station within its jurisdiction; ensure that each node belongs to a unique jurisdiction constraint; and ensure that there are sub-loop elimination constraints to eliminate independent sub-loops within each jurisdiction. With the goal of minimizing the total transportation distance, based on the distance... and the route pointing variable Construct the objective function: ; By integrating the set of decision variables, the set of constraints, and the objective function, an integer programming model is constructed for jointly optimizing the selection of central warehouses and logistics route planning. Solve the integer programming model to obtain the values ​​of each decision variable in the decision variable set, and output the central warehouse selection scheme and logistics route planning scheme based on the values.

[0012] Furthermore, the distance The calculation is performed using Euclidean distance, and the formula is as follows: ,in, and They are nodes and nodes The location coordinates.

[0013] Furthermore, the central warehouse identifier variable Time represents node Selected as the central warehouse Time represents node Selected as a forward warehouse; The route points to a variable Time indicates the logistics route from node Directly pointing to the node , This indicates that the logistics route does not start from the node. Directly pointing to the node .

[0014] Furthermore, the route connectivity constraints include: For each non-production base node ,satisfy ,and ,at the same time ; in, Indicates whether the logistics route starts from a node. Directly pointing to the node , Represents a node Is the next stop for itself?

[0015] Furthermore, the uniqueness constraint of the jurisdiction is as follows: For each non-production base node ,satisfy .

[0016] Furthermore, the set of constraints also includes a jurisdictional central warehouse constraint, which is used to ensure that each jurisdiction has one and only one central warehouse, expressed as: For each jurisdiction ,satisfy ,in, arrive .

[0017] Furthermore, the set of constraints also includes jurisdictional consistency constraints, which are used to ensure that when... Time node With nodes Those belonging to the same jurisdiction are indicated as: ; in, Represents a node Does it belong to the first Each jurisdiction.

[0018] Furthermore, the sub-loop elimination constraint is achieved by introducing the arrival order variable. Achieve, when When, satisfy ,in, , Indicates arrival at node The order of priority.

[0019] Furthermore, the integer programming model is solved precisely using the branch and bound method and the cutting plane method, and approximately using the simulated annealing algorithm and the genetic algorithm.

[0020] Furthermore, in the logistics route planning scheme, the logistics route in each jurisdiction starts from the central warehouse of that jurisdiction, passes through all the forward warehouses in that jurisdiction in sequence, and each forward warehouse is passed through only once, and finally returns to the central warehouse of that jurisdiction to form a closed loop.

[0021] The beneficial effects of this invention are as follows: This invention constructs a unified integer programming model to jointly optimize two traditionally separate problems: central warehouse selection and logistics route planning. This model defines a central warehouse identifier variable. , route pointing variable Jurisdiction Variable and arrival order variables Four types of decision variables were used, and a complete constraint system was established, including constraints on the number of central warehouses, route connectivity, uniqueness of jurisdiction, central warehouses in the jurisdiction, consistency of jurisdiction, and elimination of sub-loops. With the goal of minimizing the total transportation distance, the global optimal solution for central warehouse location and logistics route was achieved.

[0022] Compared to existing technologies that independently optimize central warehouse location and logistics routes, this invention fully considers the coupling relationship between the two, avoiding local optima problems that may arise from step-by-step optimization. Through joint optimization, this invention can optimize logistics routes within each jurisdiction while determining the location of the central warehouse, minimizing the overall transportation cost of the logistics network, thereby effectively reducing the enterprise's logistics costs and improving the overall operational efficiency of the supply chain.

[0023] Furthermore, the integer programming model constructed in this invention has good scalability and versatility, and the number of central warehouses can be flexibly adjusted according to actual business needs. By adding new constraints or modifying optimization objectives, a scientific and effective decision support framework is provided for supply chain optimization in different scenarios. Attached Figure Description

[0024] Figure 1 A flowchart illustrating the method for joint optimization of central warehouse selection and logistics routes provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the logistics network structure provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the integer programming model structure provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the optimization results provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and beneficial effects of this application clearer, the following detailed description, in conjunction with the accompanying drawings and specific embodiments, further illustrates this application. It should be understood that the specific embodiments described in this specification are merely for explaining this application and are not intended to limit it.

[0026] Example 1 This embodiment provides a method for jointly optimizing central warehouse selection and logistics routes, which is used to solve the logistics network optimization problem in supply chain management. In modern supply chain networks, production bases need to transport the components they produce to central warehouses for distribution and storage. The central warehouses then distribute the components to various forward warehouses within their jurisdiction based on the needs of end customers. These forward warehouses are responsible for providing delivery services to end customers. The goal of this method is to scientifically select several central warehouses from all candidate warehouses, rationally determine the jurisdiction of each central warehouse, and optimize the logistics distribution routes within each jurisdiction, so as to minimize the total transportation distance of the entire logistics network, thereby reducing logistics operating costs.

[0027] like Figure 1 As shown, the central warehouse selection and logistics route joint optimization method in this embodiment includes the following steps: Step S1: Obtain the network parameters of the logistics network.

[0028] Before selecting a central warehouse and jointly optimizing logistics routes, it is necessary to first obtain basic data about the logistics network as input parameters for model construction. These network parameters include the location coordinates of all nodes in the logistics network and the distance parameters between each node.

[0029] In this embodiment, the logistics network is assumed to include a total of There are several nodes. The production base, as the source of the entire supply chain, is denoted as node 1. The production base is where products are manufactured and initially shipped; all components awaiting delivery originate from the production base. The rest... Each node is a candidate warehouse node, numbered sequentially as node. To node Of these candidate warehouse nodes, some will be selected as central warehouses, responsible for the collection, distribution, and transshipment of regional logistics; the rest will serve as forward warehouses, located close to end customers to enable rapid delivery.

[0030] Each node The location information is represented in the form of two-dimensional plane coordinates, denoted as . .in, Represents a node The coordinate values ​​in the horizontal direction, Represents a node The coordinates are located in the vertical direction. Location coordinates can be obtained by acquiring the latitude and longitude data of each node through a Geographic Information System (GIS), and then converting the latitude and longitude coordinates into Cartesian coordinates. In practical applications, the origin of the coordinates can be set as the geometric center of the logistics network coverage area or the location of the production base. The coordinate unit can be kilometers or hundreds of kilometers to facilitate subsequent distance calculations and result interpretation.

[0031] Calculate the distance parameter between any two nodes based on the position coordinates of each node. For a node... and nodes Its distance The Euclidean distance is used for calculation. Euclidean distance is the straight-line distance between two points in a plane, and its formula is: ; In the above formula, Let be the position coordinates of node i. For nodes The location coordinates. This formula can be used to calculate the distance between any two nodes in the logistics network, forming a... The distance matrix. This distance matrix is ​​a symmetric matrix, i.e. And diagonal elements .

[0032] In practical applications, distance parameters can be replaced by other metrics depending on business needs. When the logistics network is distributed within an urban road network, Manhattan distance can be used to more accurately reflect the actual distance traveled by vehicles. The formula for calculating Manhattan distance is... When considering factors such as traffic congestion and road grade, actual road distance or estimated transportation time can be used as distance parameters. This data can be obtained through electronic map application programming interfaces (APIs). Regardless of the distance metric used, this distance parameter will serve as the foundational data for constructing the objective function, directly impacting the accuracy and practicality of the optimization results.

[0033] Step S2: Construct a set of decision variables based on network parameters.

[0034] Decision variables are a core component of integer programming models, representing the unknowns that need to be determined during the optimization process. The values ​​of decision variables directly reflect the solution to the optimization problem; therefore, designing decision variables appropriately is crucial for accurately describing the problem and efficiently solving the model. In this embodiment, the set of decision variables includes four categories, used to describe decision-making at different levels, such as central warehouse selection, logistics route planning, jurisdictional division, and delivery sequence.

[0035] The first type of decision variable is the central warehouse identifier variable, denoted as... This variable is a binary variable, and its value range is... For each warehouse node ,when When, it indicates that the warehouse node has been selected as the central warehouse; when When this occurs, it indicates that the warehouse node has been selected as a forward warehouse. There are a total of [number] central warehouse identifier variables. Each corresponds to a node. To node Production base node No central warehouse identifier variable is set because the role of the production base is fixed. As a hub node in regional logistics, the central warehouse plays a crucial role in the distribution and transshipment functions of the supply chain network. The central warehouse receives component goods from the production base, stores and sorts them, and then distributes them to various forward warehouses within its jurisdiction according to the distribution plan. Forward warehouses are warehousing nodes located close to end customers, and their main function is to provide rapid response and delivery services for end customer order demands.

[0036] The second type of decision variable is the route direction variable, denoted as... This variable is also a binary variable, and its value range is... For any two nodes and nodes ,when When, it indicates that there exists a path from node in the optimal logistics route plan. Directly reach the node The delivery route, i.e., the route from which delivery vehicles depart from the node. After departure, drive directly to the node It does not pass through any other nodes in between; when When, it means that there is no node in the optimal logistics route plan. Directly reach the node The delivery route segment. The number of route-pointing variables is [number missing]. This is because it's necessary to consider the possible route connections between all candidate warehouse nodes. The route direction variable is a key variable in determining the logistics route planning scheme; its value can fully describe the delivery route direction within each jurisdiction.

[0037] The third type of decision variable is the jurisdictional affiliation variable, denoted as... This variable is also a binary variable, and its value range is... For warehouse nodes and jurisdiction number ,when When, it indicates a warehouse node. Belonging to the Each jurisdiction; when When, it indicates a warehouse node. Not belonging to the first There are 10 jurisdictions. The number of jurisdictional variables is 10. One, of which The number of central warehouses is preset, which is also the number of jurisdictions. The jurisdictional variable is used to determine the jurisdictional affiliation of each warehouse node. In the optimization result, each node selected as a central warehouse becomes the core of its jurisdiction. All forward warehouses within that jurisdiction are under the jurisdiction of this central warehouse, which is responsible for distributing components to these forward warehouses. Reasonable division of jurisdictions is crucial for reducing logistics costs; adjacent and closely spaced warehouse nodes should ideally belong to the same jurisdiction to minimize additional transportation costs associated with cross-regional deliveries.

[0038] The fourth type of decision variable is the arrival order variable, denoted as... This variable is a non-negative integer, and its value range is... For warehouse nodes , This indicates the order in which delivery vehicles arrive at this node during the logistics delivery process. A smaller order value indicates that the node is earlier in the delivery route, and a larger order value indicates that the node is later in the delivery route. There are a total of [number] arrival order variables. Each corresponds to a node. To node The introduction of arrival order variables is primarily to eliminate sub-loop constraints in the model, ensuring that delivery routes within each jurisdiction form a complete loop originating from and returning to the central warehouse, without any independent sub-loops disconnected from the central warehouse. The existence of sub-loops can prevent some forward warehouses from being reached by delivery vehicles, causing delivery tasks to fail. Through the constraints of arrival order variables, the possibility of sub-loops can be eliminated at the mathematical model level, guaranteeing the feasibility of the optimization results.

[0039] Step S3: Establish a set of constraints based on the set of decision variables.

[0040] Constraints are mathematical expressions used in integer programming models to limit the range of values ​​and relationships between decision variables. Constraints ensure that the optimized solution meets the requirements of actual business operations and are crucial for guaranteeing the feasibility of the optimization result. In this embodiment, the set of constraints includes the following seven categories: The first type of constraint is a binary constraint. This constraint specifies the central warehouse identifier variable. , route pointing variable and jurisdictional affiliation variables All are binary variables, and their values ​​can only be 1 / 2. or This can be expressed mathematically as: Binary constraints ensure the discreteness of these decision variables, giving the optimization results a clear physical meaning.

[0041] The second type of constraint is the central warehouse quantity constraint. This constraint requires that the number of warehouse nodes selected as central warehouses equals the preset number of central warehouses. This can be expressed mathematically as: ; Number of central warehouses It is a pre-set parameter, and its value needs to be determined comprehensively based on business factors such as the scale of the logistics network, service coverage, and delivery frequency.

[0042] The third type of constraint is the route connectivity constraint. This constraint requires that each warehouse node, excluding production bases, has exactly one next-stop node and one previous-stop node in the delivery routes within its jurisdiction. Mathematically, this can be expressed as: for each non-production base node... ,satisfy: ; The first equation represents the expression from the node The sum of the variables pointing to the starting route equals , i.e., node There is one and only one next stop. The second equation indicates the node to which the node is located. The sum of the variables pointed to by the routes equals , i.e., node There is one and only one previous station. Furthermore, this constraint requires that each warehouse node itself cannot be its next or previous station. For all nodes Established.

[0043] The fourth type of constraint is the jurisdiction uniqueness constraint. This constraint requires that each warehouse node, excluding production bases, belongs to exactly one jurisdiction. Mathematically, this can be expressed as: for each non-production base node... ,satisfy: ; The fifth type of constraint is the regional central warehouse constraint. This constraint requires that each region has one and only one central warehouse as the origin and destination of logistics distribution within that region. Mathematically, this can be expressed as: For each region... ,satisfy: ; In the above formula, Represents a node It must simultaneously meet the criteria of being a central warehouse and belonging to a jurisdiction. Two conditions. The sum equals Indicates within the jurisdiction There happens to be such a node in the middle.

[0044] The sixth type of constraint is the jurisdiction consistency constraint. This constraint requires that when a node... The next stop is the node At that time, node With nodes They must belong to the same jurisdiction. This can be expressed mathematically as: For all jurisdictions This constraint means that only when node and nodes At the same time belong to the jurisdiction Time (i.e.) and ), Only then can it take the value .

[0045] The seventh type of constraint is the sub-loop elimination constraint. This constraint is used to eliminate possible independent sub-loops within each jurisdiction. The sub-loop elimination constraint introduces an arrival order variable. To achieve this. When At that time, the following conditions are met: ; in, This constraint can be addressed by introducing an auxiliary constant. Transform into linear constraint form: ; in, For a pre-set, sufficiently large positive number, when When, the above formula simplifies to The constraint takes effect; when At that time, due to If it is large enough, the constraint will be satisfied automatically and will not have a restrictive effect.

[0046] Step S4: Construct the objective function.

[0047] The objective function is the optimization objective of an integer programming model, used to measure the merits of an optimized solution. This embodiment constructs the objective function with the goal of minimizing the total transportation distance, because transportation distance is a core factor affecting logistics costs. A shorter total transportation distance means less fuel consumption, shorter transportation time, and less vehicle wear and tear, thus lower logistics operating costs. The mathematical expression of the objective function is: ; In the above formula, Indicates the total transportation distance. Represents a node With nodes The distance between them The path points to the variable, and the double summation symbol indicates summing over all possible node pairs. When At that time, the distance of that road segment This will be included in the total transport distance; when At that time, the distance of this route segment is not included in the total transportation distance. This is achieved by minimizing the objective function. This can minimize the total transportation distance of the entire logistics network.

[0048] Step S5: Construct an integer programming model.

[0049] By integrating the set of decision variables, constraints, and objective function defined in the above steps, a complete integer programming model is constructed. This model is a mixed-integer linear programming model, containing binary integer variables and non-negative integer variables, and is a classic problem form in operations research and optimization theory.

[0050] like Figure 3 The diagram shows the structure of the integer programming model. This model unifies the central warehouse selection problem and the logistics route planning problem under the same mathematical framework, fully considering the coupling relationship between the two and avoiding the local optima problem that may occur in traditional step-by-step optimization methods.

[0051] Step S6: Solve the integer programming model and output the optimization results.

[0052] The constructed integer programming model is solved to obtain the optimal values ​​of each decision variable, and based on these values, the central warehouse selection scheme and logistics route planning scheme are output. The integer programming model can be solved using exact or approximate methods. Exact methods include branch and bound and cutting plane methods, which can find the global optimum within a finite number of steps. The branch and bound method decomposes the original problem into several subproblems and prunes them using upper and lower bounds, gradually narrowing the search space until the optimum is found. The cutting plane method approximates the integer optimum by continuously adding effective inequalities to cut the feasible region.

[0053] For large-scale problems, heuristic methods can be used for approximate solutions, including simulated annealing, genetic algorithms, and tabu search. Simulated annealing simulates the cooling mechanism in the metal annealing process, gradually approximating the optimal solution by randomly searching the solution space. Genetic algorithms simulate the evolutionary mechanism in nature, iteratively optimizing the solution population through operations such as selection, crossover, and mutation.

[0054] After the model is solved, the optimization results are output based on the optimal values ​​of the decision variables. The central warehouse selection scheme is determined by the central warehouse identifier variable. The value of is determined: all nodes It was selected as the central warehouse. The jurisdiction division scheme is determined by the jurisdictional affiliation variable. The value of is determined as follows: Represents a node Belonging to the jurisdiction Logistics route planning schemes are determined by route-oriented variables. The value of is determined: all node pairs The optimal delivery route is constructed. In the optimal logistics route planning scheme, the logistics route in each jurisdiction starts from the central warehouse of that jurisdiction, passes through all the forward warehouses in that jurisdiction in sequence, and each forward warehouse is passed only once, and finally returns to the central warehouse of that jurisdiction to form a closed loop.

[0055] Example 2 This embodiment provides a specific application scenario to further illustrate the practical application effect of the technical solution of the present invention. An electrical appliance manufacturing company owns a production base located in an urban industrial park and has 10 candidate warehouses distributed in different geographical locations within its business coverage area. The company plans to select 2 of these 10 candidate warehouses as central warehouses and the remaining 8 as forward warehouses. The production base is denoted as node 0, and the 10 candidate warehouses are numbered as nodes 1 to 10 according to their geographical locations.

[0056] like Figure 2 The diagram shows the structure of this logistics network. According to the method of this invention, the location coordinates of each node are first obtained, and the distance between any two nodes is calculated using the Euclidean distance formula. Then, a set of decision variables is constructed, including 10 central warehouse identification variables, 100 route direction variables, 20 jurisdictional variables, and 10 arrival order variables. A set of constraints is established, where the number of central warehouses is constrained as follows: ; An integer programming model is constructed with the goal of minimizing the total transportation distance, and the branch and bound method is used to solve it.

[0057] like Figure 4 The diagram shows the optimization results. The solution results indicate that nodes 3 and 7 were selected as central warehouses. Region 1, where node 3 is located, includes four forward warehouses: node 1, node 2, node 4, and node 5. The delivery route starts from central warehouse node 3, passes through nodes 1, 2, 5, and 4 in sequence, and finally returns to node 3. Region 2, where node 7 is located, includes four forward warehouses: node 6, node 8, node 9, and node 10. The delivery route starts from central warehouse node 7, passes through nodes 10, 8, 6, and 9 in sequence, and finally returns to node 7.

[0058] The optimized total transportation distance was reduced by approximately 17% compared to the traditional step-by-step optimization method, verifying the effectiveness of the joint optimization method of this invention.

[0059] Example 3 This embodiment provides a system for implementing the aforementioned method for joint optimization of central warehouse selection and logistics routes. The system adopts a modular design architecture, including four functional modules: a data acquisition module, a model building module, a solution calculation module, and a result output module.

[0060] The data acquisition module is responsible for obtaining network parameters of the logistics network. This module interfaces with the enterprise's existing geographic information system and logistics management system to automatically acquire the location coordinates of production bases and warehouse nodes, and calculate the distance parameters between each node. The system supports multiple distance calculation methods, including Euclidean distance, Manhattan distance, and actual road distance.

[0061] The model building module is responsible for automatically constructing an integer programming model based on the collected network parameters. This module automatically generates a set of decision variables, a set of constraints, and an objective function based on the number of warehouse nodes (n) and the preset number of central warehouses (K). Users can set parameters such as the number of central warehouses and the required solution accuracy through the parameter configuration interface.

[0062] The solution computation module is responsible for solving the constructed integer programming model. This module integrates various solution algorithms, including branch and bound, cutting plane method, genetic algorithm, and simulated annealing algorithm. Users can choose the appropriate solution algorithm according to the problem size and required solution accuracy.

[0063] The results output module is responsible for converting the decision variable values ​​obtained from the solution calculation module into intuitive and easy-to-understand optimization solutions. The output includes key performance indicators such as the central warehouse selection scheme, jurisdiction division scheme, logistics route planning scheme, and total transportation distance. Output formats support multiple methods, including text reports, visual maps, and data export.

[0064] In summary, this invention establishes an integer programming model for the joint optimization of central warehouse selection and logistics routes, unifying two traditionally separate optimization problems under a single mathematical framework for solution, thus achieving globally optimal configuration of the supply chain logistics network. Compared with existing technologies, this invention fully considers the coupling relationship between central warehouse location and logistics routes, effectively reducing logistics costs, improving overall supply chain operational efficiency, and providing enterprises with a scientific and effective decision support tool for supply chain management.

[0065] In summary, the embodiments disclosed herein have at least the following technical effects: This invention constructs a unified integer programming model to jointly optimize two traditionally separate problems: central warehouse selection and logistics route planning. This model defines a central warehouse identifier variable. , route pointing variable Jurisdiction Variable and arrival order variables Four types of decision variables were used, and a complete constraint system was established, including constraints on the number of central warehouses, route connectivity, uniqueness of jurisdiction, central warehouses in the jurisdiction, consistency of jurisdiction, and elimination of sub-loops. With the goal of minimizing the total transportation distance, the global optimal solution for central warehouse location and logistics route was achieved.

[0066] Compared to existing technologies that independently optimize central warehouse location and logistics routes, this invention fully considers the coupling relationship between the two, avoiding local optima problems that may arise from step-by-step optimization. Through joint optimization, this invention can optimize logistics routes within each jurisdiction while determining the location of the central warehouse, minimizing the overall transportation cost of the logistics network, thereby effectively reducing the enterprise's logistics costs and improving the overall operational efficiency of the supply chain.

[0067] Furthermore, the integer programming model constructed in this invention has good scalability and versatility, and the number of central warehouses can be flexibly adjusted according to actual business needs. By adding new constraints or modifying optimization objectives, a scientific and effective decision support framework is provided for supply chain optimization in different scenarios.

[0068] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A method for joint optimization of central warehouse selection and logistics routes, characterized in that, include: Obtain network parameters of the logistics network, including production bases and The location coordinates of the warehouse nodes, where the production base is denoted as node 0, and each warehouse node is denoted as node 1. To node ; Calculate the distance between each node based on the location coordinates. ; A set of decision variables is constructed based on the network parameters. The set of decision variables includes: variables used to identify nodes. Whether it is selected as the central warehouse identifier variable Used to indicate whether the logistics route starts from a node. Directly pointing to the node The route points to the variable Used to represent nodes Does it belong to the first Jurisdiction variable for each jurisdiction and the node to be reached The order of arrival of variables ;in, , , ; A set of constraints is established based on the set of decision variables. The set of constraints includes: limiting the total number of central warehouses to a preset quantity. Central warehouse quantity constraints Ensure that each node, except for the production base, has a unique route connectivity constraint with a previous and next station within its jurisdiction; ensure that each node belongs to a unique jurisdiction constraint; and ensure that there are sub-loop elimination constraints to eliminate independent sub-loops within each jurisdiction. With the goal of minimizing the total transportation distance, based on the distance... and the route pointing variable Construct the objective function: ; By integrating the set of decision variables, the set of constraints, and the objective function, an integer programming model is constructed for jointly optimizing the selection of central warehouses and logistics route planning. Solve the integer programming model to obtain the values ​​of each decision variable in the decision variable set, and output the central warehouse selection scheme and logistics route planning scheme based on the values.

2. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The distance The calculation is performed using Euclidean distance, and the formula is as follows: ,in, and They are nodes and nodes The location coordinates.

3. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The central warehouse identifier variable Time represents node Selected as the central warehouse Time represents node Selected as a forward warehouse; The route points to a variable Time indicates the logistics route from node Directly pointing to the node , This indicates that the logistics route does not start from the node. Directly pointing to the node .

4. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The route connectivity constraints include: For each non-production base node ,satisfy ,and ,at the same time ; in, Indicates whether the logistics route starts from a node. Directly pointing to the node , Represents a node Is the next stop for itself? 5. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The uniqueness constraint of the jurisdiction is: For each non-production base node ,satisfy .

6. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The set of constraints also includes a jurisdictional central warehouse constraint, which is used to ensure that each jurisdiction has one and only one central warehouse, and is expressed as follows: For each jurisdiction ,satisfy ,in, arrive .

7. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The set of constraints also includes jurisdictional consistency constraints, which are used to ensure that when Time node With nodes Those belonging to the same jurisdiction are indicated as: ; in, Represents a node Does it belong to the first Each jurisdiction.

8. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The sub-loop elimination constraint is achieved by introducing the arrival order variable. Achieve, when When, satisfy ,in, , Indicates arrival at node The order of priority.

9. The method for joint optimization of central warehouse selection and logistics routes according to claim 1, characterized in that, The integer programming model is solved using the branch and bound method and the cutting plane method for exact solution, and the simulated annealing algorithm and the genetic algorithm for approximate solution.

10. The method for joint optimization of central warehouse selection and logistics routes according to any one of claims 1 to 9, characterized in that, In the logistics route planning scheme, the logistics route in each jurisdiction starts from the central warehouse of that jurisdiction, passes through all the forward warehouses in that jurisdiction in sequence, and each forward warehouse is passed through only once, and finally returns to the central warehouse of that jurisdiction to form a closed loop.

Images