A production scheduling-batch grouping-layout joint optimization method and system for plate products

Abstract

The present application relates to the technical field of panel product production, and particularly relates to a production scheduling-batch grouping-layout joint optimization method and system, which comprises the following steps: constructing a production scheduling model based on a column generation algorithm, decomposing a main problem and a sub-problem, iteratively mining a negative reduction cost solution column, and generating a production scheduling result meeting job coverage and capacity constraints; constructing an order multi-dimensional feature vector based on a time slice of the production scheduling result and normalizing the order multi-dimensional feature vector, measuring similarity by using a weighted Euclidean distance, generating a batch grouping result compatible with a layout by using multi-constraint clustering and legality screening; based on the batch grouping result, using a double iteration search mechanism and a variable field search algorithm, combining a post-processing strategy to generate a layout scheme with the smallest unplaced area; and simultaneously realizing information sharing and bidirectional adjustment among the three stages in the optimization process. The present application can solve the bottleneck of "segmented solution and difficult integration" in the prior art, and improve the execution efficiency and resource utilization level of the panel product manufacturing process.

Description

Technical Field

[0001] This invention relates to the field of panel product manufacturing technology, and in particular to a method and system for joint optimization of production scheduling, batching, and sampling of panel products. Background Technology

[0002] With the continued growth in demand for flexible manufacturing and personalized customization, the manufacturing process of panel products (which use sheet metal as the main raw material, flat processing as the main form, and are assembled from various panel components) is characterized by multiple batches, small orders, and high-frequency switching. This manufacturing process needs to complete three key stages in sequence: task scheduling, order batching, and layout. There are close information flow, resource matching, and structural control relationships between each stage: scheduling needs to take into account delivery time and capacity distribution, batching needs to balance structural rationality and layout efficiency, and layout needs to maximize material utilization and match batch structure with task launch sequence.

[0003] However, existing technologies generally employ an optimization strategy of "stage separation and sequential execution," which has the following core drawbacks:

[0004] (1) Production scheduling is disconnected from subsequent processes: The production scheduling results are used as static inputs directly for batching and sampling, without considering the impact of capacity configuration, order launch time and delivery cycle on subsequent processes in the early stages of optimization, resulting in an imbalance in production rhythm;

[0005] (2) Insufficient flexibility of batching strategy: The batching rules are fixed and cannot be adjusted according to product attributes (such as material and process path) and production dynamics, which easily leads to poor intra-batch compatibility and increased difficulty in sampling;

[0006] (3) Strong independence of layout: Layout optimization is mostly independent of the production scheduling and batching stages. It only pursues material utilization rate and ignores process feasibility and task rhythm matching, resulting in the layout scheme being unable to adapt to the actual production plan.

[0007] (4) Lack of global optimization capability: When faced with complex and heterogeneous orders, the highly coupled relationship between production scheduling, batching and sampling is difficult to model in a unified manner. Moreover, as the scale of the task increases, the computational complexity increases sharply, resulting in problems such as excessively long solution time and unstable results, which restricts the overall scheduling quality and real-time response capability. Summary of the Invention

[0008] One objective of this invention is to propose a joint optimization method for production scheduling, batching, and sampling of panel products, which can break down stage barriers and achieve multi-stage collaboration, thereby solving the bottleneck of existing technologies that are "segmented and difficult to integrate", and improving the execution efficiency and resource utilization level of panel product manufacturing processes.

[0009] Another objective of this invention is to propose a joint optimization system for production scheduling, batching, and sampling of panel products, employing the joint optimization method for production scheduling, batching, and sampling of panel products as described above.

[0010] To achieve this objective, the present invention adopts the following technical solution:

[0011] A method for joint optimization of production scheduling, batching, and sampling of panel products includes the following steps:

[0012] S1, Task-driven multi-constraint scheduling stage: Based on the column generation algorithm, a scheduling model is built. Through the decomposition of the main problem and sub-problems, the negative cost reduction scheme column is iteratively mined to generate a scheduling result that meets the job coverage and capacity constraints.

[0013] S2, Order batching optimization stage under constraint control: Based on the time slice of the production scheduling results, construct and normalize the multi-dimensional feature vector of the order, use weighted Euclidean distance to measure similarity, and generate batching results with compatible sampling through multi-constraint clustering and legality screening;

[0014] S3, Heuristic Layout Optimization Stage Driven by Layout Performance: Based on batching results, a double iterative search mechanism and a variable neighborhood search algorithm are used, combined with post-processing strategies to generate a layout scheme with the smallest unplaced area.

[0015] S4. Three-stage linkage and closed-loop feedback: Use production scheduling results to guide batch generation, then input the batch results into the layout to generate a layout plan. If the layout plan has layout abnormalities, it will be fed back to the production scheduling stage or batch optimization stage for adjustment, and finally generate a layout plan with the smallest unplaced area that meets the requirements.

[0016] Preferably, the production scheduling model based on the column generation algorithm described in S1 includes the following symbol definitions: a set J of production jobs to be scheduled j, a set S of feasible production scheduling schemes s, and a scheme selection variable x. s Job Coverage Variable a s,j The lower bound of the number of machines used is UB, and the upper bound of the number of machines used is LB.

[0017] Where, j∈J, s∈S, x s ∈{0,1}, a s,j ∈ {0, 1};

[0018] When a feasible production scheduling scheme s∈S is selected, then x s =1, otherwise 0;

[0019] When feasible production scheduling plan s covers the production operation to be scheduled j, then a s,j =1, otherwise 0.

[0020] Preferably, the objective function of the main problem described in S1 is:

[0021]

[0022] The constraints of the main problem include coverage constraints, variable value constraints, and machine usage upper and lower bound constraints:

[0023]

[0024] Preferably, the formula for calculating the cost reduction of the sub-problem described in S1 is as follows:

[0025]

[0026] Where a j Let β be the implicit cost weight of the production operation j to be scheduled, and β be the implicit cost weight of the number of machines; if r s If the value is less than 0, then the scheme is a scheme with negative cost reduction.

[0027] The objective function of the subproblem is:

[0028]

[0029] Preferably, the subproblem in S1 is solved by a dynamic programming algorithm based on label setting. The dynamic programming algorithm introduces a dominance rule and an upper bound estimate: under the same remaining capacity, the label with the lower cumulative dual value is retained; if a partial solution cannot obtain a negative reduction cost, the branch is terminated early.

[0030] Preferably, the order multidimensional feature vector in S2 includes product geometry, sheet material, color code, surface treatment category, process path label, delivery deadline, and priority.

[0031] The normalization is performed using either Min-Max normalization or Z-score normalization.

[0032] Preferably, the similarity metric in S2 uses a weighted Euclidean distance:

[0033]

[0034] Where ω k ∈[0,1] represents the weight of the k-th dimension feature, and ;

[0035] The criteria for multi-constraint clustering and legality screening include: uniform board type within the batch, number of product types within the batch ≤ set value, delivery period span within the batch ≤ threshold, process path similarity within the batch ≥ threshold, and total order area / number of pieces within the batch ≥ lower limit value.

[0036] Preferably, the variable neighborhood search algorithm in S3 includes three neighborhood structures: randomly swapping the positions of any two parts, randomly inserting a part into a random position in the sequence, and flipping a local subsequence;

[0037] The GPack algorithm selects the placement position of the part through fitness scoring. The fitness scoring rules are as follows: fitness = 3 when the part size is fully adapted to the board, fitness = 1 when it is partially adapted, fitness = 0 when it can be rotated to adapt, and fitness = -1 when it cannot adapt.

[0038] Preferably, the triggering conditions for the closed-loop feedback in S4 include: unplaced sample area ≥ set threshold, batch process incompatibility, mismatch between sheet material demand and inventory, and mismatch between task rhythm and machine load; the feedback adjustment methods include batch splitting / merging, order reallocation, job-machine allocation adjustment, and task online time adjustment.

[0039] A joint optimization system for production scheduling, batching, and sampling of panel products, employing the joint optimization method for production scheduling, batching, and sampling of panel products as described above, includes:

[0040] The production scheduling optimization module is used to build a production scheduling model based on the column generation algorithm. By decomposing the main problem and sub-problems, iteratively mining negative cost reduction schemes, and generating production scheduling results that meet the job coverage and capacity constraints.

[0041] The batch optimization module is used to construct and normalize multi-dimensional feature vectors of orders based on the time slices of the production scheduling results, use weighted Euclidean distance to measure similarity, and generate batch results with compatible scheduling through multi-constraint clustering and legality screening.

[0042] The layout optimization module is used to generate a layout scheme with the smallest unplaced area based on the batch results, using a double iterative search mechanism and a variable neighborhood search algorithm, combined with post-processing strategies.

[0043] The joint optimization module is used to guide the batch generation of batch results using the production scheduling results. The batch results are then input into the layout to generate a layout plan. If the layout plan has layout abnormalities, it is fed back to the production scheduling optimization module or the batch optimization module for adjustment. Finally, a layout plan with the smallest unplaced area that meets the requirements is generated.

[0044] One of the above technical solutions has the following beneficial effects:

[0045] (1) Improved global optimization capability: Break down stage barriers, achieve coordinated optimization of production scheduling, batching, and sampling, avoid global efficiency loss caused by local optima, and improve the overall production response speed;

[0046] (2) Improved resource utilization efficiency: The column generation algorithm in the production scheduling stage reduces machine idle rate, the multi-constraint clustering of batches improves batch compatibility, and the variable domain search of the sampling improves material utilization.

[0047] (3) Enhanced dynamic adaptability: The closed-loop feedback mechanism can adjust the plan at each stage in real time to adapt to changes in order structure and production dynamics (such as the insertion of emergency orders and equipment failures).

[0048] (4) Optimization of computational efficiency: strategies such as decomposition of main problem and subproblem, dominance rules, and upper bound estimation reduce the computational complexity of large-scale tasks, shorten the solution time, and meet the needs of real-time production. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the overall process of a combined optimization method for production scheduling, batching, and sampling of panel products according to the present invention.

[0050] Figure 2 This is a flowchart of the production scheduling optimization method in the joint optimization method of production scheduling-batch assembly-sampling of panel products of the present invention;

[0051] Figure 3 This is a flowchart of the batch optimization method in the joint optimization method of production scheduling-batch assembly-sampling for panel products of the present invention;

[0052] Figure 4 This is a flowchart of the layout optimization method in the production scheduling-batch assembly-sampling joint optimization method for panel products of the present invention. Detailed Implementation

[0053] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0054] A method for joint optimization of production scheduling, batching, and sampling of panel products includes the following steps:

[0055] S1, Task-driven multi-constraint scheduling stage: Based on the column generation algorithm, a scheduling model is built. Through the decomposition of the main problem and sub-problems, the negative cost reduction scheme column is iteratively mined to generate a scheduling result that meets the job coverage and capacity constraints.

[0056] S2, Order batching optimization stage under constraint control: Based on the time slice of the production scheduling results, construct and normalize the multi-dimensional feature vector of the order, use weighted Euclidean distance to measure similarity, and generate batching results with compatible sampling through multi-constraint clustering and legality screening;

[0057] S3, Heuristic Layout Optimization Stage Driven by Layout Performance: Based on batching results, a double iterative search mechanism and a variable neighborhood search algorithm are used, combined with post-processing strategies to generate a layout scheme with the smallest unplaced area.

[0058] S4. Three-stage linkage and closed-loop feedback: Use production scheduling results to guide batch generation, then input the batch results into the layout to generate a layout plan. If the layout plan has layout abnormalities, it will be fed back to the production scheduling stage or batch optimization stage for adjustment, and finally generate a layout plan with the smallest unplaced area that meets the requirements.

[0059] This invention proposes a joint optimization method for production scheduling, batching, and sampling of panel products. It constructs an integrated optimization framework of "three-stage collaboration + closed-loop feedback" around the three key stages of panel product production: production scheduling, batching, and sampling. The specific steps include:

[0060] Step S1 primarily addresses the scheduling needs of large-scale operations by constructing a scheduling model based on column generation. By decomposing the main problem into sub-problems, computational complexity is reduced, generating an efficient production plan that meets task coverage and capacity constraints, providing a rhythm benchmark for subsequent batching.

[0061] Step S2 primarily involves dividing time slices based on production scheduling results, extracting and normalizing order feature vectors, combining order features with production constraints to achieve intelligent batching of orders, and outputting candidate batching schemes that can be used for evaluation.

[0062] Step S3 mainly relies on batch results, with the goal of minimizing the unplaced area, to generate a high-quality layout plan, while also providing feedback on batch feasibility.

[0063] Step S4 primarily constructs a closed loop of "production scheduling → batching → sampling → feedback adjustment." If an unreasonable sampling plan is found, it is fed back to the batching optimization stage for batch structure adjustment. Simultaneously, the sampling plan can also be fed back to the production scheduling stage to adjust production rhythm and task distribution, thereby achieving information sharing and two-way adjustment between the three stages. This constructs a closed-loop optimization mechanism of task scheduling – resource allocation – material utilization, achieving global optimization.

[0064] To further explain, the production scheduling model based on the column generation algorithm described in S1 includes the following symbol definitions: the set J of production jobs to be scheduled, the set S of feasible scheduling schemes s, and the scheme selection variable x. s Job Coverage Variable a s,j The lower bound of the number of machines used is UB, and the upper bound of the number of machines used is LB.

[0065] Where, j∈J, s∈S, x s ∈{0,1}, a s,j ∈ {0, 1};

[0066] When a feasible production scheduling scheme s∈S is selected, then x s =1, otherwise 0;

[0067] When feasible production scheduling plan s covers the production operation to be scheduled j, then a s,j =1, otherwise 0.

[0068] To further explain, the objective function of the main problem described in S1 is:

[0069]

[0070] The constraints of the main problem include coverage constraints, variable value constraints, and machine usage upper and lower bound constraints:

[0071]

[0072] To further explain, the formula for calculating the cost reduction of the sub-problem described in S1 is as follows:

[0073]

[0074] Where a j Let β be the implicit cost weight of the production operation j to be scheduled, and β be the implicit cost weight of the number of machines; if r s If the value is less than 0, then the scheme is a scheme with negative cost reduction.

[0075] The objective function of the subproblem is:

[0076]

[0077] To further explain, the subproblem described in S1 is solved by a dynamic programming algorithm based on label setting. The dynamic programming algorithm introduces a dominance rule and an upper bound estimate: under the same remaining capacity, the label with the lower cumulative dual value is retained; if a partial solution cannot obtain a negative reduction cost, the branch is terminated early.

[0078] Step S1, as the first step in the joint optimization process of production scheduling, batching, and nesting, plays a crucial role in production scheduling. Traditional production scheduling methods often struggle to find the global optimum quickly and effectively when facing large-scale production tasks, especially when the workload is huge and the constraints are complex, resulting in extremely high computational costs and optimization difficulties. For panel product manufacturing tasks, this invention constructs a production scheduling method based on column generation. Taking the one-dimensional packing problem as an example, the goal is to minimize the number of machines used. By decomposing the main problem into sub-problems, the model size and computational complexity are effectively reduced. This method not only flexibly explores optimization potential and improves production scheduling efficiency but also provides a reliable foundation for subsequent batching and nesting optimization. The specific steps of S1 are as follows:

[0079] First, the production scheduling model based on the column generation algorithm includes symbol definitions:

[0080] J: The set of production jobs to be scheduled j, where j∈J;

[0081] S: The set of feasible production scheduling plans s, where each feasible production scheduling plan s corresponds to a unique machine;

[0082] x s : Variables for scheme selection, x s If x ∈ {0,1}, and a feasible production scheduling scheme s is selected, then x s =1, otherwise 0;

[0083] a s,j : Job coverage variable, a s,j ∈ {0,1}, if the feasible production scheduling scheme s covers the production operations to be scheduled, then a s,j =1, otherwise 0;

[0084] LB, UB: Lower and upper bounds of the number of machines used.

[0085] Secondly, taking one-dimensional packing as an example, each feasible solution is equivalent to a set of jobs completed on one machine. Therefore, the number of solutions selected is the number of machines used. To minimize the total number of machines used, the initial main problem is to minimize the number of machines used, and a production scheduling model is established as follows:

[0086]

[0087] The constraints of the main problem include coverage constraints, variable value constraints, and machine usage upper and lower bound constraints:

[0088]

[0089] Since the set of feasible solutions S is too large to be pre-enumerated, the main problem is optimized by iteratively discovering new solutions with "negative cost reduction". The specific process is as follows:

[0090] The first step is to solve the restricted master problem: randomly select an initial list of solutions, and use linear programming to solve the master problem to obtain the dual variable: a j The dual value of constraint formula (2) is the implicit cost weight of the production operation j to be arranged (reflecting the potential impact of the operation on the production scheduling cost); the dual value of constraint formula (4) is the implicit cost weight of the number of machines.

[0091] The second step is to calculate the cost reduction of the single-machine subproblem: For each machine, a single-machine subproblem is constructed. The core objective is to find a feasible scheduling solution *s* on that machine, such that adding this solution to the main problem effectively reduces the total scheduling cost. Therefore, the single-machine subproblem is defined as the cost reduction *r* of the feasible scheduling solution *s*. s This makes it a potential measure of the cost of optimizing the main problem:

[0092]

[0093] If r s If the value is less than 0, it indicates that the feasible scheduling plan s has the potential to optimize the cost of the main problem and should be added to the main problem. Adding it to the main problem can reduce the total scheduling cost, so it should be added as a new column to the main problem.

[0094] The third step is to solve the single-machine subproblem: Transform the subproblem into a 0-1 knapsack problem, where the production job to be scheduled j is considered the "item," the machine capacity is the "knapsack capacity," the size of the production job to be scheduled j is the "item weight," and the job coverage variable a... j Let 'r' represent the "value of the items". Since each plan is essentially a packing method, a plan is only a feasible production scheduling plan 's' if the total weight of the items does not exceed the knapsack capacity. Therefore, the goal is to find 'r'. s Feasible solutions with a value less than 0:

[0095]

[0096] To achieve efficient solution, a dynamic programming algorithm based on label setting is used:

[0097] First, an initial label is created for each machine, containing the current packing status (set of jobs placed, remaining capacity, and cumulative duality). Then, the labels are expanded sequentially according to the job order:

[0098] (1) For each label, try to add a new job. If the job can be placed under the knapsack capacity constraint, generate a new label and update the corresponding cumulative dual value.

[0099] (2) If adding this operation would cause the knapsack capacity to exceed the limit, or the corresponding dual value would not be better than the current state, then the label would be discarded;

[0100] (3) Introduce a dominance rule during the expansion process. That is, if two labels have the same remaining capacity, and the cumulative dual value of a certain label is lower, then retain the dominant label and discard the inferior label.

[0101] This process is equivalent to progressively exploring all possible bin packing combinations. Through label pruning and dominance determination, the search space is effectively reduced, and computational efficiency is improved. Simultaneously, an upper bound estimate is introduced to quickly determine whether certain partial solutions are likely to result in negative cost reduction; if the upper bound estimate indicates infeasibility, the branch is terminated early to avoid redundant computation.

[0102] Once all tasks have been processed, the labels are extended to a virtual endpoint, resulting in a complete packing scheme, and the corresponding reduction cost is calculated. If the scheme satisfies the requirements, it is determined to be a potentially valid column, and its scheme information is extracted and added to the feasible scheme set of the main problem.

[0103] The fourth step is to iteratively update the main problem: repeat the process of "solving the constrained main problem → calculating the cost reduction → solving the subproblems to find new columns → adding columns to update the main problem" until there are no new negative cost reduction scheme columns to add, and output the production scheduling results (including job-machine allocation and task launch time).

[0104] To further explain, the multidimensional feature vector of the order mentioned in S2 includes product geometry, sheet material, color code, surface treatment category, process path label, delivery deadline, and priority;

[0105] The normalization is performed using either Min-Max normalization or Z-score normalization.

[0106] To further clarify, the similarity metric described in S2 uses a weighted Euclidean distance:

[0107]

[0108] Where ω k ∈[0,1] represents the weight of the k-th dimension feature, and ;

[0109] The criteria for multi-constraint clustering and legality screening include: uniform board type within the batch, number of product types within the batch ≤ set value, delivery period span within the batch ≤ threshold, process path similarity within the batch ≥ threshold, and total order area / number of pieces within the batch ≥ lower limit value.

[0110] Step S2, as a crucial intermediate step in the joint optimization process of production scheduling, batching, and sampling, aims to improve inter-batch coordination and resource utilization during the sampling stage, exhibiting good versatility and scalability. This invention is based on the construction of multi-dimensional order feature vectors, integrating hierarchical clustering algorithms and batch validity screening mechanisms, and employing a dual strategy of "similarity-driven + rule-guided" to achieve intelligent batching. The specific steps of S2 are as follows:

[0111] First, order feature vector construction and normalization: extracting o from each order i ∈O (O={o1,o2,...,on}) represents the multidimensional features of the order set: product geometry (length, width, thickness), sheet material, color code, surface treatment category, process path label, delivery deadline, and priority;

[0112] Constructing a multidimensional feature vector x i ∈R d (d is the feature dimension), Min-Max normalization or Z-score normalization is used to standardize all feature dimensions to eliminate dimensional differences and enhance the stability of clustering results:

[0113] Min-Max normalization: , where x ik Let k be the k-th dimension feature of order i;

[0114] Z-score normalization: , where μ k σ k denoted as the mean and standard deviation of the k-th feature, respectively.

[0115] Secondly, an order similarity measurement model is constructed: weighted Euclidean distance is used to calculate the similarity between any two orders. i o j The similarity reflects the difference in importance between different features:

[0116]

[0117] Where ω k ∈[0,1] represents the weight of the k-th dimension feature, which is set by business requirements (such as priority of process compatibility, priority of delivery time), and ;

[0118] Next, initial batching is achieved using multi-constraint clustering:

[0119] Initial state: Each order is an independent cluster;

[0120] Iterative merging: Calculate the similarity of all cluster pairs (take the average of the pairwise similarities of orders within the cluster), and merge the two clusters with the highest similarity (smallest distance);

[0121] Cluster truncation: Set boundary conditions (maximum batch size, intra-batch delivery time span threshold ΔT, maximum number of product types m in the batch), prune the cluster tree, and generate the initial batch.

[0122] Simultaneous batch legality screening and structure optimization: Considering actual manufacturing constraints, design a set of batch legality criteria, including but not limited to:

[0123] Criterion 1: The type of sheet material within the batch is uniform;

[0124] Criterion 2: Number of product types within a batch ≤ m;

[0125] Criterion 3: Delivery period within the batch ≤ ΔT;

[0126] Criterion 4: Intra-batch process path similarity ≥ set threshold θ (process path label matching degree);

[0127] Criterion 5: Total order area / number of pieces in the batch ≥ lower limit requirement (to avoid wasting production line change costs on small batches).

[0128] The initial clustering results are screened for legality batch by batch. For batches that violate the criteria, the batch structure is reconstructed by "intra-batch re-clustering" (splitting the batch into sub-clusters) or "problem order stripping and redistribution" (assigning incompatible orders to other batches) to ensure that the final batches are in balance between physical executability and production coordination.

[0129] Finally, batch structure evaluation and output: A multi-index evaluation system was designed, and a linear weighted method was used for comprehensive evaluation. The evaluation indicators include intra-batch structure balance (characteristic variance), material redundancy rate prediction (based on layout experience), expected nesting efficiency (proportion of similar size orders), and changeover cost (number of batch process changes). The comprehensive score was used for evaluation. ; where λ t is the indicator weight, and Indt is the standardized indicator value; finally, the batch structure with the highest score is output as the batching result.

[0130] To further explain, the variable neighborhood search algorithm described in S3 includes three neighborhood structures: randomly swapping the positions of any two parts, randomly inserting a part into a random position in the sequence, and flipping a local subsequence;

[0131] The GPack algorithm selects the placement position of the part through fitness scoring. The fitness scoring rules are as follows: fitness = 3 when the part size is fully adapted to the board, fitness = 1 when it is partially adapted, fitness = 0 when it can be rotated to adapt, and fitness = -1 when it cannot adapt.

[0132] Step S3 mainly consists of a double-iterative search mechanism, a variable neighborhood search algorithm, and a post-processing strategy. The variable neighborhood search algorithm is used to decode the raw material sheet usage sequence, the post-processing strategy is used to further improve the current solution, and the double-iterative search mechanism is used to dynamically control the number of iterations of the variable neighborhood search and the range of search combinations. The specific steps are as follows:

[0133] The double-iteration search mechanism divides the board combinations into several groups based on the total available area of ​​the raw material boards. The objective function value (expected area of ​​unplaced area) of the combinations within each group is the same. For each group, a feasible layout scheme is searched: if a feasible scheme is found, all combinations with objective values ​​greater than or equal to that group are removed to reduce the search space; if no feasible scheme is found, the range of combinations is expanded and the search continues.

[0134] The variable neighborhood search algorithm first generates an initial sequence: sorting parts by area from largest to smallest to generate an initial part placement sequence (prioritizing the placement of larger parts to reduce the difficulty of subsequent placements). Next, it generates candidate solutions: randomly oscillating the current sequence (e.g., swapping the positions of two parts, inserting parts into random positions) to generate a new sequence of candidate solutions. Then, it optimizes the local search: calling the local search algorithm LSearch to optimize the candidate solutions. LSearch uses three neighborhood structures, executed sequentially:

[0135] Neighborhood 1: Randomly swap the positions of any two parts;

[0136] Neighborhood 2: Randomly select a part and insert it into a random position in the sequence;

[0137] Neighborhood 3: Select any local subsequence and perform a flip operation;

[0138] Search logic: If a better solution (smaller unplaced area) is found in the current neighborhood, immediately update the current solution and return to neighborhood 1 to search again; if there is no improvement in the current neighborhood, switch to the next neighborhood; if there is no improvement in all neighborhoods, terminate and return the best solution.

[0139] The pseudocode for the variable neighborhood search algorithm is as follows:

[0140]

[0141] It should be noted that the variable neighborhood search algorithm uses an iterative segmentation-based heuristic algorithm, GPack(seq, c), to convert the part sequence seq into a specific part placement scheme. This algorithm places parts sequentially according to the given sequence and dynamically updates the remaining space through spatial segmentation. During each placement, a scoring strategy is used to evaluate the fitness of candidate positions and select the optimal position to place the part. For a given placement space S (of length L)... s Width is W s ) and part i (length L) i Width is W i Fitness calculations can be divided into the following cases:

[0142] 1. If L s =L i And W s =W i If so, then the fitness is set to 3;

[0143] 2. If L s =L i ∧W s <W i or W s =W i ∧Ls <L i If so, then the fitness is set to 1;

[0144] 3. If L i <L s And W i <W s If the fitness is zero, then the fitness is set to 0.

[0145] 4. If L i >L s or W i >W s If the fitness is -1, then the fitness is set to -1.

[0146] Based on the space update method and scoring strategy described above, GPack(seq, c) adopts a sequential placement strategy, placing each part in sequence until all parts are successfully placed or there is no available space in the board.

[0147] The pseudocode for the local search algorithm is as follows:

[0148]

[0149] The final termination condition is determined by setting the parameter nonImp (the number of iterations before an improved solution is found). If nonImp reaches its upper limit, or if a feasible solution of "all parts are placed" is found, the algorithm terminates and outputs the layout scheme.

[0150] To further clarify, the triggering conditions for the closed-loop feedback described in S4 include: unplaced sample area ≥ set threshold, batch process incompatibility, mismatch between sheet material demand and inventory, and mismatch between task rhythm and machine load; the feedback adjustment methods include batch splitting / merging, order reallocation, job-machine allocation adjustment, and task online time adjustment.

[0151] Specifically, the S4 step constructs a closed loop of "production scheduling → batching → sampling → feedback adjustment" to achieve global optimization:

[0152] Production scheduling → Batch feedback: The "time slice" and "capacity constraint" in the production scheduling results serve as inputs for batching, ensuring that batch tasks are within capacity and are divided into batches according to the online time.

[0153] Batch → Layout Feedback: The batching result is input into the layout module. If the area not placed after layout is greater than or equal to the set threshold (or key parts cannot be placed), the batch is determined to be incompatible and feedback is sent to the batching module to adjust the batch structure (such as splitting / merging batches or replacing orders).

[0154] Sampling → Production Scheduling Feedback: If the sampling results show that "the demand for boards far exceeds the inventory in a certain period of time" or "the task rhythm does not match the machine load", feedback is sent to the production scheduling module to adjust the job-machine allocation or task online time to achieve dynamic matching of resources and rhythm.

[0155] A joint optimization system for production scheduling, batching, and sampling of panel products, employing the joint optimization method for production scheduling, batching, and sampling of panel products as described above, includes:

[0156] The production scheduling optimization module is used to build a production scheduling model based on the column generation algorithm. By decomposing the main problem and sub-problems, iteratively mining negative cost reduction schemes, and generating production scheduling results that meet the job coverage and capacity constraints.

[0157] The batch optimization module is used to construct and normalize multi-dimensional feature vectors of orders based on the time slices of the production scheduling results, use weighted Euclidean distance to measure similarity, and generate batch results with compatible scheduling through multi-constraint clustering and legality screening.

[0158] The layout optimization module is used to generate a layout scheme with the smallest unplaced area based on the batch results, using a double iterative search mechanism and a variable neighborhood search algorithm, combined with post-processing strategies.

[0159] The joint optimization module is used to guide the batch generation of batch results using the production scheduling results. The batch results are then input into the layout to generate a layout plan. If the layout plan has layout abnormalities, it is fed back to the production scheduling optimization module or the batch optimization module for adjustment. Finally, a layout plan with the smallest unplaced area that meets the requirements is generated.

[0160] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0161] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for joint optimization of production scheduling, batching, and sampling of panel products, characterized in that, Includes the following steps: S1, Task-driven multi-constraint scheduling stage: Based on the column generation algorithm, a scheduling model is built. Through the decomposition of the main problem and sub-problems, the negative cost reduction scheme column is iteratively mined to generate a scheduling result that meets the job coverage and capacity constraints. S2, Order batching optimization stage under constraint control: Based on the time slice of the production scheduling results, construct and normalize the multi-dimensional feature vector of the order, use weighted Euclidean distance to measure similarity, and generate batching results with compatible sampling through multi-constraint clustering and legality screening; S3, Heuristic Layout Optimization Stage Driven by Layout Performance: Based on batching results, a double iterative search mechanism and a variable neighborhood search algorithm are used, combined with post-processing strategies to generate a layout scheme with the smallest unplaced area. S4. Three-stage linkage and closed-loop feedback: Use production scheduling results to guide batch generation, then input the batch results into the layout to generate a layout plan. If the layout plan has layout abnormalities, it will be fed back to the production scheduling stage or batch optimization stage for adjustment, and finally generate a layout plan with the smallest unplaced area that meets the requirements. The production scheduling model based on the column generation algorithm described in S1 includes the following symbol definitions: the set J of production jobs to be scheduled, the set S of feasible scheduling schemes s, and the scheme selection variable x. s Job Coverage Variable a s,j The lower bound of the number of machines used is UB, and the upper bound of the number of machines used is LB. Where, j∈J, s∈S, x s ∈{0,1}, a s,j ∈ {0, 1}; When a feasible production scheduling scheme s∈S is selected, then x s =1, otherwise 0; When feasible production scheduling plan s covers the production operation to be scheduled j, then a s,j =1, otherwise 0; The objective function of the main problem described in S1 is: The constraints of the main problem include coverage constraints, variable value constraints, and machine usage upper and lower bound constraints: The formula for calculating the cost reduction of the subproblem described in S1 is as follows: Where a j Let β be the implicit cost weight of the production operation j to be scheduled, and β be the implicit cost weight of the number of machines; if r s If the value is less than 0, then the scheme is a scheme with negative cost reduction. The objective function of the subproblem is: In S3, the variable neighborhood search algorithm is used to decode the raw material sheet usage sequence, the post-processing strategy is used to further improve the current solution, and the double iterative search mechanism is used to dynamically control the number of iterations of the variable neighborhood search and the range of search combinations. The specific steps are as follows: The double-iteration search mechanism divides the board combinations into several groups based on the total usable area of ​​the raw material boards, with the objective function value of the combinations within each group being the same; for each group, it searches for feasible layout schemes: if a feasible scheme is found, all combinations with objective values ​​≥ that group are removed to reduce the search space; if no feasible scheme is found, the range of combinations is expanded and the search continues. The variable neighborhood search algorithm first generates an initial sequence: sorting the parts by area from largest to smallest to generate an initial part placement sequence; secondly, it generates candidate solutions: randomly oscillating the current sequence to generate a new candidate solution sequence; then, it optimizes the local search: calling the local search algorithm LSearch to optimize the candidate solutions. LSearch uses three neighborhood structures, executed sequentially: Neighborhood 1: Randomly swap the positions of any two parts; Neighborhood 2: Randomly select a part and insert it into a random position in the sequence; Neighborhood 3: Select any local subsequence and perform a flip operation; Search logic: If a better solution is found in the current neighborhood, immediately update the current solution and return to neighborhood 1 to search again; if there is no improvement in the current neighborhood, switch to the next neighborhood; if there is no improvement in all neighborhoods, terminate and return the best solution.

2. The method for joint optimization of production scheduling, batching, and sampling of panel products according to claim 1, characterized in that, The subproblem described in S1 is solved by a dynamic programming algorithm based on label setting. The dynamic programming algorithm introduces a dominance rule and upper bound estimation: under the same remaining capacity, the label with the lower cumulative dual value is retained; if a partial solution cannot obtain a negative reduction cost, it is terminated early.

3. The method for joint optimization of production scheduling, batching, and sampling of panel products according to claim 1, characterized in that, The multidimensional feature vector of the order mentioned in S2 includes product geometry, sheet material, color code, surface treatment category, process path label, delivery deadline, and priority; The normalization is performed using either Min-Max normalization or Z-score normalization.

4. The method for joint optimization of production scheduling, batching, and sampling of panel products according to claim 1, characterized in that, In S2, the similarity metric uses weighted Euclidean distance: Where ω k ∈[0,1] represents the weight of the k-th dimension feature, and ; The criteria for multi-constraint clustering and legality screening include: uniform board type within the batch, number of product types within the batch ≤ set value, delivery period span within the batch ≤ threshold, process path similarity within the batch ≥ threshold, and total order area / number of pieces within the batch ≥ lower limit value.

5. The method for joint optimization of production scheduling, batching, and sampling of panel products according to claim 1, characterized in that, The triggering conditions for closed-loop feedback described in S4 include: unplaced sample area ≥ set threshold, batch process incompatibility, mismatch between sheet material demand and inventory, and mismatch between task rhythm and machine load; the feedback adjustment methods include batch splitting / merging, order reallocation, job-machine allocation adjustment, and task online time adjustment.

6. A joint optimization system for production scheduling, batching, and sampling of panel products, characterized in that, The method for joint optimization of production scheduling, batching, and sampling of panel products as described in any one of claims 1-5 includes: The production scheduling optimization module is used to build a production scheduling model based on the column generation algorithm. By decomposing the main problem and sub-problems, iteratively mining negative cost reduction schemes, and generating production scheduling results that meet the job coverage and capacity constraints. The batch optimization module is used to construct and normalize multi-dimensional feature vectors of orders based on the time slices of the production scheduling results, use weighted Euclidean distance to measure similarity, and generate batch results with compatible scheduling through multi-constraint clustering and legality screening. The layout optimization module is used to generate a layout scheme with the smallest unplaced area based on the batch results, using a double iterative search mechanism and a variable neighborhood search algorithm, combined with post-processing strategies. The joint optimization module is used to guide the batch generation of batch results using the production scheduling results. The batch results are then input into the layout to generate a layout plan. If the layout plan has layout abnormalities, it is fed back to the production scheduling optimization module or the batch optimization module for adjustment. Finally, a layout plan with the smallest unplaced area that meets the requirements is generated.

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