Route optimization method for multi-vehicle circulating goods taking three-dimensional boxing, terminal and medium

Abstract

The invention relates to the technical field of path planning, and discloses a path optimization method for multi-vehicle circulating goods taking three-dimensional boxing, a terminal and a medium. The method comprises the following steps: acquiring related data, uniformly mapping part requirements of suppliers into a box body set taking a packaging box as a unit, and determining a unit residual space opportunity cost coefficient; constructing an original model according to the related data, wherein a target function of the original model comprises vehicle driving cost, vehicle starting fixed cost and compartment remaining space opportunity cost; a Dantzigzag-Wolfe decomposition method is adopted to decompose the original model into a limiting main problem and a pricing sub-problem; iteratively solving a limitation main problem and a pricing sub-problem through a column generation algorithm; and if the solution for limiting the main problem contains a non-integer, entering a branch and bound process, repeatedly executing a column generation algorithm on branch nodes until a preset termination condition is met, and outputting an optimal circulating goods taking scheme including vehicle path planning and carriage three-dimensional boxing layout. According to the invention, the transportation efficiency of circulating goods taking can be improved.

Description

Technical Field

[0001] This invention relates to the field of route planning technology, specifically to a route optimization method, terminal, and medium for multi-vehicle cyclic pickup and three-dimensional packing. Background Technology

[0002] In the inbound logistics scenario of automobile manufacturing, OEMs typically need to replenish various parts such as seats, wiring harnesses, and interior components from twenty or more parts suppliers at high frequency. To facilitate the turnover and loading / unloading of these parts, standardized packaging using uniform collapsible or palletized boxes is often adopted. Then, carrier vehicles depart from the OEM or consolidation center using a milk-run (circular pickup) method, collecting full containers of goods from multiple suppliers along a pre-designed pickup route, and finally returning to the OEM for centralized unloading. Compared to the traditional direct delivery model, the milk-run model helps reduce empty runs and waiting times caused by suppliers delivering goods individually, and also helps OEMs reduce on-site inventory and the number of loading / unloading points. Therefore, it has been widely adopted in the automotive industry.

[0003] However, in practice, whether using vehicles operated by OEMs or in cooperation with third-party logistics companies, current milk-run solutions still heavily rely on dispatcher experience or relatively crude heuristic methods. Planners typically judge "can it fit / can't fit" simply based on the total volume of the supplier's packaging boxes and the truck's cargo space, rarely simulating the three-dimensional arrangement of each box inside the truck during the planning phase. As a result, as long as the total volume does not exceed the truck's cargo space, the solution is considered "capacity feasible" in the system, but on-site loading often reveals a situation where it is feasible on paper but physically impossible to fit. Meanwhile, with continuously rising freight rates and increasingly stringent environmental constraints, empty runs and wasted space have become core pain points affecting companies' overall logistics costs and carbon emission levels. Industry surveys show that the average loading rate of highway freight vehicles has long been low, and in the milk-run scenario for automotive parts, where the size and shape of components vary greatly, the cargo space utilization rate often hovers around 60%–70%, indicating significant room for improvement.

[0004] Previous research has yielded several technical solutions for vehicle routing problems involving cyclic pickup or container-based loading. For example, when designing milk-run routes, vehicle capacity is simplified to a scalar constraint of "nominal volume or load capacity." A seemingly reasonable route and number of vehicles are initially derived using VRP (Vehicle Routing Problem) or VRPTW (Vehicle Routing with Time Window) models. Then, container loading is arranged separately within each route, sometimes even based on on-site experience. This sequential decomposition makes it difficult to fully perceive the loading difficulties of different suppliers' goods in three-dimensional space during the route decision-making stage, and also fails to recognize the space waste caused by three-dimensional container loading. Therefore, situations often arise where the paper capacity constraint is met, but the actual loading is insufficient or loose. Furthermore, existing work mostly considers only "vehicle mileage × unit price" or "vehicle trips × fixed cost" in terms of cost characterization. Even when some solutions introduce loading rate or space utilization as indicators, they are only used as auxiliary optimization directions, failing to systematically answer the question of whether "taking a longer route to pick up two more suppliers" or "taking a shorter route but with a large amount of empty space in the truck bed" is more cost-effective overall. Summary of the Invention

[0005] To address the technical problems existing in the prior art, this invention provides a path optimization method, terminal, and medium for multi-vehicle cyclic pickup and three-dimensional packing. In the Milk-run scenario with unified packaging, it can coordinate the path travel cost, vehicle activation cost, and opportunity cost of remaining space in the vehicle compartment, and reliably generate a physically loadable and cost-optimal multi-vehicle cyclic pickup solution under multi-vehicle conditions.

[0006] To achieve the above objectives, the present invention provides the following technical solution: This invention discloses a path optimization method for three-dimensional packing of goods in a multi-vehicle cyclic pickup system, comprising the following steps: S1. Obtain the OEM's production plan data, supplier distribution data, and vehicle parameter data, map the supplier's component requirements into a set of boxes in units of packaging boxes, and determine the opportunity cost coefficient of the unit remaining space. S2. Construct a multi-vehicle three-dimensional loading vehicle path original model based on the data obtained in step S1. The objective function of the original model includes vehicle driving cost, vehicle activation fixed cost, and opportunity cost of remaining cargo space. The opportunity cost of remaining cargo space is obtained by multiplying the difference between the total vehicle volume and the actual loading volume by the unit remaining space opportunity cost coefficient. S3. The original model is decomposed into a constrained master problem and a pricing subproblem using the Dantzig-Wolfe decomposition method. The constrained master problem is used to select the optimal path combination, and the pricing subproblem is used to generate new paths that satisfy the three-dimensional binning constraints. S4. Iteratively solve the constrained master problem and the pricing subproblem using a column generation algorithm; when solving the pricing subproblem, use a labeling algorithm combined with the constraints of the original model to generate a list of feasible paths with negative reduced costs and add them to the constrained master problem; S5. If the solution to the main problem is restricted to non-integers, then proceed to the branch and bound process, repeatedly execute the column generation algorithm on the branch node until the preset termination condition is met, and output the optimal cyclic pickup solution including vehicle route planning and three-dimensional packing layout of the carriage.

[0007] As a further improvement to the above scheme, the objective function of the original model is expressed as: ; In the formula, The set of vehicles; the set of nodes corresponding to the OEM and each supplier is: ,in Indicates the OEM (Original Equipment Manufacturer). Represents the set of suppliers; For the set of arcs, , For nodes and nodes The arc between; For each car in the arc On-the-ground transportation costs; Choose a 0-1 variable for the vehicle arc, when the vehicle Select Arc hour When not selected ; Fixed cost for engaging a single vehicle; Enable 0-1 variables for vehicles, when the vehicle When enabled When not enabled ; The opportunity cost coefficient per unit of remaining space; , , For vehicles The internal effective loading dimensions, namely the length, width, and height of the cargo compartment; For suppliers A collection of boxes; For suppliers The Middle The volume of each box.

[0008] As a further improvement to the above scheme, in step S3, the main constraint problem is specifically: with the goal of minimizing the total cost of the path, select several paths, the constraints of which include: each supplier is covered by exactly one path, and the number of selected paths does not exceed the maximum number of available vehicles; the total cost of the path includes the actual transportation cost of the path and the opportunity cost calculated based on the loading rate. The pricing subproblem specifically involves: based on the dual variables obtained from the linear relaxation solution of the restricted main problem, searching for paths with negative reduced costs from the set of candidate paths that satisfy the path structure and three-dimensional binning constraints; wherein the formula for calculating the reduced cost is as follows: ; In the formula, To reduce costs; and As dual variables; It is a 0-1 variable; if arc (i,j) is selected, it is 1; otherwise, it is 0.

[0009] As a further improvement to the above scheme, the original model also satisfies the following constraints: Service integrity and uniqueness constraints: These ensure that each supplier is accessed only once within the planned period. Vehicle inbound / outbound flow balance constraints: These are used to ensure that activated vehicles depart from the OEM, pass through the supplier, and finally return to the OEM, and that the inbound and outbound flows at intermediate nodes are balanced. Whole Lot Pickup Constraint: Used to ensure that all goods from a supplier are picked up in a single service. Path validity constraint: Used to eliminate all infeasible paths that do not meet the load constraint; 3D packing physical constraints: used to ensure that all packing boxes are located within the vehicle's internal boundaries and do not overlap.

[0010] As a further improvement to the above scheme, step S4, the labeling algorithm for the pricing sub-problem specifically includes the following steps: S41. Obtain a set of tags, each tag containing the current node, the set of visited suppliers, the cumulative driving cost, the dual revenue, the maximum remaining space in the carriage, and the loaded volume; S42. Select a label that has not yet been expanded from the current label set as the current label, and enumerate the candidate supplier nodes that can be expanded by this label; S43. Try to fit all the boxes of the candidate supplier node into the maximum remaining space set of the current label according to the set placement rules. If all the maximum remaining space of the vehicle cannot accommodate the batch of boxes, then prune and abandon the expansion; if the box packing is feasible, then update the box coordinates and the maximum remaining space set, and generate a new label. S44. Perform multidimensional dominance judgments between labels on the same node to determine whether the current label is dominated in order to decide whether to delete it, thereby continuously compressing the state space during the recursive expansion process.

[0011] As a further improvement to the above scheme, the specific rules for the multidimensional dominance judgment in step S44 are as follows: For two tags at the same node, if the first tag satisfies the following conditions compared to the second tag: the cumulative driving cost is not inferior to the second tag, the loaded volume is not inferior to the second tag, and the dual benefit is not inferior to the second tag, and it is superior to the second tag in at least one of the above indicators, then the second tag is determined to be dominated by the first tag and is removed from the tag set.

[0012] As a further improvement to the above scheme, in step S4, before executing the column generation algorithm, the main constraint problem is initialized, specifically including: For each supplier, construct a single-point round-trip path that starts from the OEM, visits only the supplier, and then returns directly to the OEM. Verify the loading feasibility of the single-point round-trip path using the constraints of the original model. Add the verified single-point round-trip path as an initial column to the constrained master problem to ensure that the constrained master problem has a feasible solution in the first solution.

[0013] As a further improvement to the above scheme, in step S5, the branch delimitation process adopts a binary branching strategy, specifically including: When the linear relaxation solution of the constrained main problem has fractional variables, select an arc or supplier-vehicle allocation relationship to branch, generating two child nodes with additional constraints; use the global upper bound to prune nodes whose reduced cost is lower than the set lower bound until the entire branch-bound tree meets the preset optimal gap threshold or all nodes have been processed.

[0014] The present invention also discloses a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the multi-vehicle cyclic pickup and three-dimensional packing path optimization method as described above.

[0015] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the path optimization method for multi-vehicle cyclic pickup and three-dimensional packing as described above.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention introduces a novel framework for collaborative optimization of three-dimensional packing and route costs for multiple vehicles and vehicle types. By incorporating the opportunity cost of remaining cargo space into the objective function, this invention maximizes the utilization of cargo space in each vehicle, significantly improving loading efficiency. Experimental results show that after implementing this method, vehicle space waste rate is reduced by 51.15%, total cost is reduced by 55.84%, and transportation efficiency is significantly improved.

[0017] 2. Because the route planning and 3D packing are closely integrated, this invention not only avoids the problem of "optimal route but insufficient cargo space" in traditional methods, but also achieves the practical feasibility of 3D packing while ensuring the shortest route. The optimized route not only reduces empty mileage, but also ensures that the cargo space of each vehicle can be fully utilized, thereby improving the overall supply chain operating efficiency.

[0018] 3. This invention combines Dantzig-Wolfe decomposition with branch pricing, enabling the algorithm to accurately solve real-world problems involving large-scale, multi-vehicle, and multi-supplier scenarios. Especially in scenarios with 20-50 suppliers, the algorithm can provide high-quality solutions in a short time, satisfying both accuracy requirements and providing fast and effective decision support under complex constraints. Attached Figure Description

[0019] Figure 1 This is a flowchart of the path optimization method for multi-vehicle cyclic pickup and three-dimensional packing in Embodiment 1 of the present invention.

[0020] Figure 2 This is a flowchart of column generation in Embodiment 1 of the present invention.

[0021] Figure 3 This is a flowchart of the labeling algorithm in Embodiment 1 of the present invention.

[0022] Figure 4 This is a route map of 10 vehicles in Embodiment 1 of the present invention.

[0023] Figure 5 This is a three-dimensional diagram of the stacking of boxes inside the carriage in Embodiment 1 of the present invention.

[0024] Figure 6 for Figure 5 The route map of the vehicles.

[0025] Figure 7 This is a comparison diagram of the effects of the method of the present invention and the conventional method in Embodiment 1 of the present invention.

[0026] Figure 8 This is a comparison diagram of space waste in Embodiment 1 of the present invention.

[0027] Figure 9This is a schematic diagram of the structure of the computer terminal in Embodiment 2 of the present invention. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Example 1 This invention proposes a path optimization method for multi-vehicle circular pickup in Milk-run cyclic pickup scenarios with unified packaging for automobile OEMs. Starting from the OEM's BOM data, supplier spatial distribution and packaging quantity, vehicle transportation costs and freight contracts, this method goes through a series of steps, including data preprocessing and unified packaging mapping, construction of the original model of 3D packing vehicle path, Dantzig-Wolfe decomposition and column generation, labeling algorithm for pricing subproblems and solving 3D packing with maximum remaining space (EMS), branch pricing, and result output and visualization. Finally, it generates a physically packable and cost-optimal multi-vehicle circular pickup solution.

[0030] Please see Figure 1 The path optimization method includes the following steps, namely S1 to S5.

[0031] S1. Obtain the OEM's production plan data, supplier distribution data, and vehicle parameter data, map the supplier's component requirements into a set of boxes in units of packaging boxes, and determine the opportunity cost coefficient of the unit remaining space.

[0032] Specifically, the system can read the OEM's BOM and production plan for a future planning cycle, summarize the component requirements of each supplier for that cycle, and then, based on the loading relationship of uniform packaging boxes, convert different types of components into a set of boxes. Simultaneously, it can obtain the planar coordinates of the OEM and each supplier from GIS or the company's existing geographic database and calculate the distance matrix between each node. Then, combined with the pricing rules of different vehicle models (such as segmented pricing or linear pricing), the distance matrix can be converted into the transportation cost of each vehicle model on each arc. Furthermore, it can read the internal effective dimensions, total cargo volume, and corresponding fixed activation costs of all vehicle models in the vehicle set. Finally, the user or strategy module provides the opportunity cost coefficient of the unit remaining space, thereby completing the unified mapping of all raw business data to model parameters.

[0033] S2. Construct a three-dimensional original model of the multi-vehicle loading route. The objective function of the original model includes vehicle driving cost, vehicle activation fixed cost, and opportunity cost of remaining cargo space. The opportunity cost of remaining cargo space is obtained by multiplying the difference between the total vehicle volume and the actual loading volume by the opportunity cost coefficient per unit of remaining space.

[0034] This invention constructs a multi-vehicle 3D packing vehicle path original model P based on the parameters obtained in step S1, and the set of nodes considered is as follows: ,in Indicates the OEM (Original Equipment Manufacturer). Represents the set of suppliers; set of arcs , For nodes and nodes The arc between; the available vehicle set is For each supplier The A box, given its dimensions. and volume Based on this, we introduce 0-1 variables for vehicle arc selection and vehicle activation, and construct a unified objective function that includes the opportunity cost of remaining space, as shown in the following expression: (1) In the formula, Represents the set of suppliers; For each car in the arc On-the-ground transportation costs; Choose a 0-1 variable for the vehicle arc, when the vehicle Select Arc hour When not selected ; Fixed cost for engaging a single vehicle; Enable 0-1 variables for vehicles, when the vehicle When enabled When not enabled ; The opportunity cost coefficient per unit of remaining space; , , For vehicles The internal effective loading dimensions, namely the length, width, and height of the cargo compartment; For suppliers A collection of boxes; For suppliers The Middle The volume of each box.

[0035] In the objective function, the first term is the driving cost of all vehicles on the road network, the second term is the fixed cost of vehicle activation, and the third term is the difference between the total volume of each vehicle's cargo compartment and its actual loaded volume multiplied by a coefficient. The formation of the opportunity cost of surplus space, thereby depicting the economic trade-off between "more detours, more loading" and "less detours, more surplus", is one of the key innovations of this invention in cost modeling.

[0036] This invention proposes an overall framework of "route and 3D packing collaborative optimization". By combining route travel cost, vehicle activation cost, and opportunity cost of remaining space in the carriage in the objective function (1), a new integrated optimization model of "route-packing-cost" is formed. This model explicitly transforms the waste of remaining carriage space into economic loss for the first time and fully considers this loss in the route planning process. This makes the optimization process no longer just pursue short mileage or fewer vehicles, but actively seek the comprehensive optimal point of "mileage, vehicle use, and space utilization".

[0037] To ensure the feasibility of business rules and 3D geometry, a series of constraints are imposed on model P: One is the constraint of service integrity and uniqueness, used to ensure that each supplier It must be accessed within the planned period and only once, expressed as: (2) The second is the vehicle return-to-factory constraint, used to ensure that only activated vehicles depart from the OEM and ultimately return to the factory. The expression is: (3) In the formula, Choose a 0-1 variable for the vehicle arc, when the vehicle Select Arc hour, Conversely, it is 0. Among them... This represents the arc from OEM 0 to supplier j.

[0038] Thirdly, there is the flow balance constraint, which ensures that the inflow and outflow at each intermediate node remain balanced, thus forming a continuous closed loop. Its expression is: (4) Fourthly, there is the bulk pickup constraint, which ensures that all goods awaiting shipment must be picked up in a single service. The expression is: (5) In the formula, For the set of suppliers that have been visited; Let be the quantity of goods supplied by supplier i.

[0039] Fifthly, there is the path validity constraint, used to eliminate all infeasible paths that do not meet the loading constraint. The expression is: (6) In the formula, Let γ be the set of all arcs contained in the route γ; This is a set of routes that only satisfy the basic constraints of vehicle routing; A set of routes that satisfy the basic constraints of two-dimensional loading and vehicle routing; The set of routes that do not satisfy the two-dimensional loading constraints; For routes that do not meet the two-dimensional loading constraints.

[0040] The sixth is the three-dimensional packing boundary constraint, used to ensure that each packing box loaded into the vehicle is located within the vehicle's internal boundary. The expression is: (7) (8) (9) Let the x-axis coordinate of box b of supplier j be the x-axis coordinate of the kth vehicle. Let the y-axis coordinate of box b of supplier j be the coordinate of the kth vehicle. Let the z-axis coordinate of box b of supplier j be the coordinate of the kth vehicle. This refers to the width of the packaging box; The height of the packaging box; The length of the packaging box; This refers to the interior width of the carriage; The height of the interior of the carriage; This refers to the depth of the interior of the carriage. For the supplier group.

[0041] The seventh constraint is the geometric non-overlap constraint, which ensures that no two goods occupy the same volume in three-dimensional space (i.e., no collision occurs), guaranteeing that the loading scheme is executable in physical reality. Its expression is: (10) In the formula, For the remaining space set; It indicates "or".

[0042] By using the objective function (1) and constraints (2)-(10), the original model P fully characterizes the multi-vehicle three-dimensional packing and cyclic picking problem.

[0043] The objective function and constraints of this invention can incorporate a variety of adaptive modules, which can flexibly adjust the pricing method (such as segmented pricing, linear pricing, etc.) and cope with the loading requirements of different vehicle types and different suppliers, providing logistics companies with a more flexible and efficient route planning solution.

[0044] S3. The original model is decomposed into a constrained master problem and a pricing subproblem using the Dantzig-Wolfe decomposition method. The constrained master problem is used to select the optimal path combination, and the pricing subproblem is used to generate new paths that satisfy the three-dimensional binning constraints.

[0045] To overcome the combinatorial explosion of model P, this invention employs Dantzig-Wolfe decomposition to break it down into a restricted master problem (RMP) with the entire route as the column, plus a pricing subproblem (PP). RMP and PP are described in detail below.

[0046] RMP: A complete, physically feasible, three-dimensional pickup route that starts from the OEM, visits several suppliers, and finally returns to the OEM is defined as... Its total cost is Introducing 0-1 decision variables To indicate whether to choose this route, a 0-1 decision variable is introduced. Indicate whether route r covers supplier i, thus obtaining the following RMP: (11) The constraints are: (12) (13) (14) Among them, constraint (12) ensures that each supplier is covered by exactly one route; constraint (13) limits the number of route selections to no more than the maximum number of vehicles. .

[0047] PP: Linear relaxation of RMP is performed and solved to obtain the dual variables of constraints (12) and (13). and Based on this, PP is constructed, with the goal of finding a set of candidate routes that satisfy path structure and 3D binning constraints. In the given condition, find the path r with a negative reduced cost (RC). The expression for the reduced cost is as follows: ; In the formula, Let (i,j) be the travel cost of arc (i,j). It is a 0-1 variable; if arc (i,j) is selected, it will be 1. and It is the dual variable; otherwise, it is 0.

[0048] The objective function of the pricing subproblem is: (15) Its constraints are constraints (2)-(10).

[0049] S4. Iteratively solve the constrained master problem and the pricing subproblem using a column generation algorithm; when solving the pricing subproblem, use a labeling algorithm combined with the constraints of the original model to generate a list of feasible paths with negative reduced costs and add them to the constrained master problem.

[0050] The branch-pricing algorithm employed in this invention is the core of achieving collaborative optimization of multi-vehicle 3D bin packing and path cost. Through the organic integration of column generation and branch-bound, it solves the combinatorial explosion problem of the original model while ensuring the accuracy and physical feasibility of the solution results, fully covering the entire chain from path iterative generation to integer solution output. The specific processes of column generation and branch-bound are described below.

[0051] The specific details of column generation (i.e., step S4) are as follows: like Figure 2 As shown, firstly, the RMP is solved and the dual variables are obtained. and These dual variables are used to guide further optimization of path generation. Secondly, a labeling algorithm is used to generate new path columns and calculate their reduced costs. Finally, it is determined whether the current node no longer has any new columns with negative reduced costs. If they still exist, these new columns are added to the column pool, and the solution to the RMP problem is returned for further iteration. If they do not exist, the optimal value for the current node's RMP linear relaxation problem has been found, and this value can be used as the lower bound for that node.

[0052] Because the solution process for the labeling algorithm is quite complex, therefore... Figure 3 The document specifically outlines its processing flow. For example... Figure 3 As shown, the detailed solution process of the label algorithm of the present invention can be summarized as steps (i)-(vii).

[0053] (i) Input a set of labels, each label containing status information such as the current node, the set of suppliers visited, the cumulative driving cost, the dual revenue, the EMS set space in the carriage, and the loaded volume.

[0054] (ii) Select a label i that has not yet been expanded from the current label set as the "current label".

[0055] (iii) Enumerate the candidate supplier nodes j that can be expanded by this label (e.g., all suppliers that have not yet been visited in this label and that meet the basic path structure constraints after being added).

[0056] (iv) Call the EMS algorithm and combine it with the constraints of the original model to try to put all the boxes of supplier j into the EMS set of the current label according to the established placement rules. If the boxing is not feasible (i.e. all EMS cannot accommodate the batch of boxes), then prune and abandon this extension directly; if the boxing is feasible, then continue to step (v).

[0057] (v) Generate a new label, update the current node to j, record the placement coordinates of each box in 3D space and update the EMS set and loaded volume accordingly, while also adjusting the dual variables. and and path cost Update cumulative costs and dual benefits.

[0058] (vi) Perform multidimensional dominance judgment between labels at the same node. When there is another label that is better than the current label in at least one of the states of "cumulative path cost, loaded volume, dual revenue, and unvisited supplier set" and is not inferior in other states, the current label is considered to be dominated and deleted, thereby continuously compressing the state space during the recursive expansion process.

[0059] The explanations for "superior" and "not inferior" above are as follows: Let the two labels at the same node be... Each label has three metrics: cumulative driving cost C ( L (The smaller the better; the already loaded volume) V ( L (, the larger the better; dual benefit) R ( L (), the bigger the better. "If the first tag Compared to the second tag The mathematical expression for "simultaneously satisfying: cumulative driving cost not higher than the second label, loaded volume not lower than the second label, and dual benefit not lower than the second label, and exceeding the second label in at least one of the above indicators" is: ; In other words, the first label must be "completely good" and at least one of them must be "significantly better" in order to dominate the second label.

[0060] (vii) The labels that are checked by dominance will be extended from the current node back to the starting point (such as the OEM) to form a complete closed path, thus completing the label construction of a feasible path.

[0061] By coupling label expansion with EMS real-time bin packing, this invention achieves synchronous linkage between path generation and 3D bin packing in the pricing subproblem, ensuring that each expansion step strictly respects 3D geometric constraints and opportunity cost information. This label algorithm with 3D bin packing status is another important innovation of this invention at the solution strategy level.

[0062] Branch delimitation is step S5.

[0063] S5. If the solution to the main problem is restricted to non-integers, then proceed to the branch and bound process, repeatedly execute the column generation algorithm on the branch node until the preset termination condition is met, and output the optimal cyclic pickup solution including vehicle route planning and three-dimensional packing layout of the carriage.

[0064] Specifically, after obtaining the optimal RMP linear relaxation value for the current node, this value is used as the lower bound for that node. Simultaneously, it is checked whether the RMP solution is an integer. If it is an integer, it is compared with the current global best solution, and the upper bound is updated. If a fractional variable exists, an arc or supplier-vehicle allocation relationship is selected at this node to branch, generating two child nodes with additional constraints. The column generation and pricing sub-problem solving is then performed again at each child node. Nodes with poor lower bounds are pruned using the global upper bound value until the entire branch-bound tree meets the preset optimal gap threshold or all nodes have been processed.

[0065] Through the branch pricing process, the final output includes each vehicle's cyclic pickup route, the number of vehicles used, the three-dimensional packing scheme of the cargo compartment, and key indicators such as the corresponding total cost, average loading rate, and remaining space.

[0066] This invention employs a precise solution method combining branch pricing and labeling algorithms. By using Dantzig-Wolfe decomposition and column generation techniques, it combines path planning and 3D bin packing, ensuring that each path has been validated in 3D bin packing before being selected. This guarantees the feasibility and efficiency of the loading scheme and solves the problem of path and bin packing being separated in existing methods.

[0067] Next, this embodiment selects an experimental example of "A logistics company's segmented pricing + 20 suppliers + 9.6m large truck + national standard palletized box" to illustrate the path optimization method of the present invention. The specific steps are as follows.

[0068] S101: Read the basic data of the simulation example and complete the instantiation, including the OEM node is recorded as 0 and the supplier node set is recorded as N={1,…,20}. At the same time, read the coordinate information of each node and the unified packaging box set corresponding to the supplier requirements (the supplier scale in this embodiment is 20).

[0069] S102: Read vehicle parameters and construct vehicle set K. In this embodiment, a 9.6-meter wing-opening van is selected as the transport vehicle. Its cargo box dimensions are 9.6×2.45×2.6 (unit: m). The vehicle's internal effective loading dimensions (length, width, height) and vehicle activation fixed cost f are written into the vehicle parameter table to support the subsequent "few vehicles / more vehicles" trade-off solution.

[0070] S103: Read the uniform packaging box specifications and construct a supplier box set In this embodiment, standard pallet boxes are used, and the outer dimensions of a single box are 1.2×1.0×0.8 (unit: m). Based on this, the volume of a single box is calculated as v=1.2×1.0×0.8, and the needs of each supplier are mapped to several boxes.

[0071] S104: Load the transportation pricing contract of this embodiment and construct the cost function. (Where x is the route mileage / km), this example adopts the segmented pricing rules of a certain logistics company: ; Use the contract parameters as input to the "Route Cost" module to ensure that the output plan is consistent with the actual freight rate.

[0072] S105: Construct a distance matrix based on node coordinates / distance data And generate an arc set accordingly. The distance matrix is ​​then mapped to arc cost or segment cost using a pricing function. (If the price is calculated based on the entire route, then the total mileage will be calculated after the route is closed.) Substitution (Get the transportation cost for this route).

[0073] S106: The opportunity cost coefficient for remaining space is generated by the read strategy module or set by the user. And simultaneously record the total vehicle volume in the loading decision for each vehicle. Compared with actual loading volume ,Will This serves as the "opportunity cost of remaining space" for the vehicle, allowing for a calculable economic trade-off between "taking a detour to load more cargo" and "taking a less detour but having more empty space."

[0074] S107: Construct the original 3D packing vehicle path model P for multiple vehicles, and introduce vehicle arc selection variables. Vehicle activation variables The unified objective is "route cost + vehicle usage cost + opportunity cost of remaining space"; the route cost is calculated by a logistics company's segmented pricing contract, the vehicle usage cost is included by f, and the opportunity cost is included by the unused space of each vehicle.

[0075] S108: Apply service integrity and uniqueness constraints, vehicle entry and exit and flow balance constraints to model P, and clarify that this embodiment is a "non-split transportation" whole batch pickup scenario, that is, each supplier's container must be loaded into the same vehicle and brought back to the OEM in one trip when it is visited, so as to ensure business feasibility.

[0076] S109: Write the 3D packing physical constraints into the feasibility judgment module, including boundary constraints: the placement coordinates of any box plus its 3D dimensions must not exceed the boundary of the carriage; geometric non-overlap constraints: any two boxes must not overlap in volume in 3D space; and use these constraints as real-time verification conditions for pricing sub-problems to ensure that each generated candidate route is "physically packable" before output.

[0077] S110: To overcome combinatorial explosion in the original model, Dantzig-Wolfe decomposition is performed on model P, using "complete feasible routes" as columns to construct a restricted master problem (RMP): Select several routes on a finite set of columns such that each supplier is covered exactly once and the number of vehicles used does not exceed the upper limit. And with the goal of minimizing the total path cost; where This represents the route cost under segmented pricing by logistics company A. This represents the actual volume loaded within the route.

[0078] S201: Initialize the column pool, generate a "single-point round-trip route" (i.e., 0→i→0) covering each supplier, and verify its installability before adding it to RMP as an initial column to ensure that RMP is feasible in the first solution.

[0079] S202: Solve for the linear relaxation of RMP and obtain the dual variables. (Corresponding to "Supplier Coverage Constraints") and (Corresponding to "vehicle number constraint / vehicle resource constraint"), and pass it as a "price signal" to the pricing subproblem (PP) to guide the generation direction of the next improvement route.

[0080] S203: Construct a pricing subproblem PP with the goal of reducing cost: For any candidate route r, calculate the reduced cost. When a route with a negative reduced cost is found, add that route as a new column to RMP.

[0081] S204: The tag algorithm is used to solve the pricing sub-problem, and the "path expansion" and "3D packing feasibility" are coupled synchronously: each tag contains the current node, visited set, cumulative travel cost, dual revenue, the maximum remaining space set (EMS) of the current carriage, and the loaded volume, etc. After taking the tag to be expanded from the queue, the expandable suppliers are enumerated and the EMS packing module is called to try to pack all the cofferdam boxes of the supplier into the current EMS set. If the packing fails, the expansion is pruned immediately. If the packing is successful, the 3D coordinates of the box and the EMS splitting result are updated and a new tag is formed.

[0082] S205: Perform domination pruning during label expansion: When there is another label at the same node that is superior to the current label in at least one of the following conditions: cumulative cost not greater than, loaded volume not less than, and dual benefit not inferior, the current label is determined to be dominated and deleted. This significantly compresses the state space and improves the pricing solution efficiency, and finally returns the feasible closed path with the minimum (most negative) reduction cost to the column generation main loop.

[0083] S206: Repeat the column generation iteration of "solving RMP—finding dual—solving PP—adding columns" until no new path with negative reduced cost exists. At this point, the current RMP linear relaxation solution serves as the lower bound of this branch node. If the solution is already an integer, update the global optimal upper bound; otherwise, proceed to the branch pricing process. Perform binary branching on the fractional arc and continue column generation on the child nodes, while using a node pruning strategy of "lower bound ≥ current optimal upper bound" to reduce the search.

[0084] S207: When the branch tree meets the termination condition (the entire tree has been processed or the preset optimal gap threshold has been reached), output the optimal multi-vehicle solution of this embodiment: such as Figure 4 As shown, the 20 suppliers ultimately needed 10 vehicles for pickup, covering a total distance of 636 km, with a remaining volume of 38.8 cubic meters and a total cost of 8186.7 yuan; the average loading rate was approximately 70.7%. Figure 4 In this context, Veh1~10 represent vehicle serial numbers, Type represents vehicle model, and Depot represents the manufacturer. Figure 4 The horizontal and vertical coordinates represent two-dimensional geographic locations.

[0085] Taking one of the 10 cars as an example, Figure 5 This is a 3D diagram showing the stacking of containers inside the carriage; different colored containers represent goods from different suppliers. Figure 6 This is the route map for the vehicle. The horizontal and vertical axes represent two-dimensional geographical locations. The numbers on the blue lines are supplier numbers, and the red squares represent the OEMs.

[0086] This embodiment also provides the following experiments: Experiment 1: Accuracy and Scalability Verification To verify the accuracy and scalability of the method of this invention, benchmark comparison experiments were conducted using computational examples of different scales (10, 20, 30, and 50 suppliers respectively). The comparison method included: a general-purpose MIP solver (CPLEX / Gurobi) and the method of this invention. Evaluation indicators included: solution time and consistency of objective function values ​​(when the general-purpose MIP solver can obtain the optimal solution within a given time, its optimal objective value was used as the benchmark).

[0087] (1) Accuracy Verification: In a small-scale test case (10–20 suppliers), the objective function value obtained by the algorithm of this invention is completely consistent with the optimal objective value of the general MIP solver, thus verifying the correctness and accuracy of the solution results of this invention. Wherein: Ten suppliers: The MIP solution time is 10 minutes, while the method of this invention takes 0.5 minutes, and the target values ​​are completely consistent; 20 suppliers: MIP solution time is 75 minutes, the method of this invention takes 9.5 minutes, and the target values ​​are completely consistent.

[0088] Scalability verification: When the scale of the simulation increased to 30 and 50 suppliers, the general MIP solver failed due to timeout under the preset time limit and could not provide a comparable optimal target value; while the method of this invention could still remain feasible and continue to iterate, and obtained the solution results in 10 hours (30 suppliers) and 27 hours (50 suppliers) respectively, demonstrating the scalability advantage of the general solver in large-scale scenarios.

[0089] Experiment 2: Comparison of effects with traditional methods To verify the improvement effect of this invention on actual business indicators, under the same service constraints, the method of this invention was compared with two traditional solutions for 50 suppliers. The direct delivery method refers to each supplier independently delivering directly to the OEM; while the geographic clustering method refers to organizing transportation after clustering suppliers according to their geographic locations.

[0090] The comparative indicators in this experiment included: total cost, number of trips, and space waste rate (the space waste rate is the proportion of unused space in the vehicle's cargo compartment, used to measure loading utilization). The experimental results are as follows: Figure 7 and Figure 8 As shown, compared to direct delivery, the total cost of this invention is reduced by 55.84%, the number of trips is reduced from 50 to 19, and the space wastage rate is reduced by 51.15%. Compared to geographical clustering, the total cost of this invention is reduced by 42.66%, the number of trips is reduced from 38 to 19, and the space wastage rate is reduced by 48.64%. This indicates that this invention can achieve significant cost reduction when comprehensively considering mileage, vehicle usage, and space opportunity costs.

[0091] Example 2 This embodiment provides a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the multi-vehicle cyclic pickup and three-dimensional packing path optimization method as described in Embodiment 1.

[0092] like Figure 9 As shown, the computer terminal provided in this embodiment includes: at least one processor 101, and a memory 102 connected to at least one processor 101. This embodiment does not limit the specific connection medium between the processor 101 and the memory 102. Figure 9 The example shown is the connection between processor 101 and memory 102 via bus 100. Bus 100 is... Figure 9 The connections between other components are shown in bold lines and are for illustrative purposes only, not as limiting information. Bus 100 can be divided into address bus, data bus, control bus, etc., for ease of representation. Figure 9 The bus is represented by a single thick line, but this does not indicate that there is only one bus or one type of bus. Alternatively, the processor 101 may also be called a controller; there is no restriction on the name.

[0093] In this embodiment, the memory 102 stores instructions that can be executed by at least one processor 101. The at least one processor 101 can execute the aforementioned method by executing the instructions stored in the memory 102.

[0094] The processor 101 is the control center of the device. It can connect to various parts of the control device through various interfaces and lines. By running or executing instructions stored in memory 102 and calling data stored in memory 102, the processor can perform various functions and process data, thereby monitoring the device as a whole.

[0095] In one possible design, processor 101 may include one or more processing units. Processor 101 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, user interface, and applications, and the modem processor mainly handles wireless communication. It is understood that the modem processor may also not be integrated into processor 101. In some embodiments, processor 101 and memory 102 may be implemented on the same chip; in some embodiments, they may also be implemented on separate chips.

[0096] Processor 101 can be a general-purpose processor, such as a central processing unit (CPU), digital signal processor, application-specific integrated circuit, field-programmable gate array or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the multi-vehicle cyclic pickup three-dimensional packing path optimization method disclosed in Embodiment 1 can be directly implemented by the hardware processor, or implemented by a combination of hardware and software modules in processor 101.

[0097] Memory 102, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory 102 may include at least one type of storage medium, such as flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic storage, magnetic disk, optical disk, etc. Memory 102 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures that can be accessed by a computer, but is not limited thereto. In this embodiment, memory 102 can also be a circuit or any other device capable of implementing storage functions for storing program instructions and / or data.

[0098] By designing and programming the processor 101, the code corresponding to the multi-vehicle cyclic pickup and three-dimensional packing path optimization method described in the foregoing embodiments can be embedded into the chip, thereby enabling the chip to execute the code during runtime. Figure 1 The steps of the multi-vehicle cyclic pickup and three-dimensional packing path optimization method are shown. How to design and program the processor 101 is a technique well-known to those skilled in the art and will not be described further here.

[0099] Example 3 This embodiment provides a computer-readable storage medium storing a computer program thereon. When the program is executed by a processor, it implements the steps of the multi-vehicle cyclic pickup and three-dimensional packing path optimization method as described in Embodiment 1.

[0100] The computer-readable storage medium may include flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the storage medium may be an internal storage unit of a computer device, such as the hard disk or memory of the computer device. In other embodiments, the storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc., provided on the computer device. Of course, the storage medium may include both internal storage units and external storage devices of the computer device. In this embodiment, the memory is typically used to store the operating system and various application software installed on the computer device. In addition, the memory can also be used to temporarily store various types of data that have been output or will be output.

[0101] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A path optimization method for three-dimensional packing of goods in a multi-vehicle cyclic pickup system, characterized in that, Includes the following steps: S1. Obtain the OEM's production plan data, supplier distribution data, and vehicle parameter data, map the supplier's component requirements into a set of boxes in units of packaging boxes, and determine the opportunity cost coefficient of the unit remaining space. S2. Construct a multi-vehicle three-dimensional loading vehicle path original model based on the data obtained in step S1. The objective function of the original model includes vehicle driving cost, vehicle activation fixed cost, and opportunity cost of remaining cargo space. The opportunity cost of remaining cargo space is obtained by multiplying the difference between the total vehicle volume and the actual loading volume by the unit remaining space opportunity cost coefficient. S3. The original model is decomposed into a constrained master problem and a pricing subproblem using the Dantzig-Wolfe decomposition method. The constrained master problem is used to select the optimal path combination, and the pricing subproblem is used to generate new paths that satisfy the three-dimensional binning constraints. S4. Iteratively solve the constrained master problem and the pricing subproblem using a column generation algorithm; when solving the pricing subproblem, use a labeling algorithm combined with the constraints of the original model to generate a list of feasible paths with negative reduced costs and add them to the constrained master problem; S5. If the solution to the main problem is restricted to non-integers, then proceed to the branch and bound process, repeatedly execute the column generation algorithm on the branch node until the preset termination condition is met, and output the optimal cyclic pickup solution including vehicle route planning and three-dimensional packing layout of the carriage.

2. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 1, characterized in that, The objective function of the original model is expressed as: In the formula, The set of vehicles; the set of nodes corresponding to the OEM and each supplier is: ,in Indicates the OEM (Original Equipment Manufacturer). Represents the set of suppliers; For the set of arcs, , For nodes and nodes The arc between; For vehicles in arc On-the-ground transportation costs; Choose a 0-1 variable for the vehicle arc, when the vehicle Select Arc hour, When not selected ; Fixed cost for engaging a single vehicle; Enable 0-1 variables for vehicles, when the vehicle When enabled When not enabled ; The opportunity cost coefficient per unit of remaining space; , , For vehicles The internal effective loading dimensions, namely the length, width, and height of the cargo compartment; For suppliers A collection of boxes; For suppliers The Middle The volume of each box.

3. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 2, characterized in that, In step S3, the main constraint problem is as follows: with the goal of minimizing the total cost of the route, select several routes, with constraints including: each supplier is covered by exactly one route, and the number of selected routes does not exceed the maximum number of available vehicles; the total cost of the route includes the actual transportation cost of the route and the opportunity cost calculated based on the loading rate. The pricing subproblem specifically involves: based on the dual variables obtained from the linear relaxation solution of the restricted main problem, searching for paths with negative reduced costs from the set of candidate paths that satisfy the path structure and three-dimensional binning constraints; wherein the formula for calculating the reduced cost is as follows: In the formula, To reduce costs; and As dual variables; It is a 0-1 variable; if arc (i,j) is selected, it is 1; otherwise, it is 0.

4. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 2, characterized in that, The original model also satisfies the following constraints: Service integrity and uniqueness constraints: These ensure that each supplier is accessed only once within the planned period. Vehicle inbound / outbound flow balance constraints: These are used to ensure that activated vehicles depart from the OEM, pass through the supplier, and finally return to the OEM, and that the inbound and outbound flows at intermediate nodes are balanced. Whole Lot Pickup Constraint: Used to ensure that all goods from a supplier are picked up in a single service. Path validity constraint: Used to eliminate all infeasible paths that do not meet the load constraint; 3D packing physical constraints: used to ensure that all packing boxes are located within the vehicle's internal boundaries and do not overlap.

5. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 4, characterized in that, In step S4, the labeling algorithm for the pricing subproblem specifically includes the following steps: S41. Obtain a set of tags, each tag containing the current node, the set of visited suppliers, the cumulative driving cost, the dual revenue, the maximum remaining space in the carriage, and the loaded volume; S42. Select a label that has not yet been expanded from the current label set as the current label, and enumerate the candidate supplier nodes that can be expanded by this label; S43. Try to fit all the boxes of the candidate supplier node into the maximum remaining space set of the current label according to the set placement rules. If all the maximum remaining space of the vehicle cannot accommodate the batch of boxes, then prune and abandon the expansion; if the box packing is feasible, then update the box coordinates and the maximum remaining space set, and generate a new label. S44. Perform multidimensional dominance judgments between labels on the same node to determine whether the current label is dominated in order to decide whether to delete it, thereby continuously compressing the state space during the recursive expansion process.

6. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 5, characterized in that, In step S44, the specific rules for the multidimensional dominance judgment are as follows: For two tags at the same node, if the first tag satisfies the following conditions compared to the second tag: the cumulative driving cost is not inferior to the second tag, the loaded volume is not inferior to the second tag, and the dual benefit is not inferior to the second tag, and it is superior to the second tag in at least one of the above indicators, then the second tag is determined to be dominated by the first tag and is removed from the tag set.

7. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 5, characterized in that, In step S4, before executing the column generation algorithm, the main constraint problem is initialized, specifically including: For each supplier, construct a single-point round-trip path that starts from the OEM, visits only the supplier, and then returns directly to the OEM. Verify the loading feasibility of the single-point round-trip path using the constraints of the original model. Add the verified single-point round-trip path as an initial column to the constrained master problem to ensure that the constrained master problem has a feasible solution in the first solution.

8. The path optimization method for multi-vehicle cyclic pickup and three-dimensional packing according to claim 2, characterized in that, In step S5, the branch delimitation process adopts a binary branching strategy, specifically including: When the linear relaxation solution of the constrained main problem has fractional variables, select an arc or supplier-vehicle allocation relationship to branch, generating two child nodes with additional constraints; use the global upper bound to prune nodes whose reduced cost is lower than the set lower bound until the entire branch-bound tree meets the preset optimal gap threshold or all nodes have been processed.

9. A computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the path optimization method for multi-vehicle cyclic pickup and three-dimensional packing as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the multi-vehicle cyclic pickup and three-dimensional packing path optimization method as described in any one of claims 1 to 8.

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