A tire production double-line collaborative batch scheduling method and system oriented to tire preform packaging

Abstract

This invention discloses a collaborative batch scheduling method and system for dual production lines in tire production, specifically for pre-fabricated rubber packs. Relating to the fields of intelligent manufacturing and production scheduling, the technical solution involves: acquiring basic tire production data; converting tire demand into rubber pack demand based on the mapping relationship between tire type and rubber pack type; generating predicted demand for each rubber pack type within a scheduling time window; establishing a collaborative batch scheduling model for both the rubber pack and tire production lines based on the predicted demand and the basic data; constructing a set of candidate scheduling schemes; and performing joint decoding, evaluation, and feedback correction on a unified time axis to output the optimal scheduling scheme. The beneficial effects of this invention are: achieving collaborative optimization between pre-fabricated rubber packs and tire production; reducing inventory and material shortages; improving equipment utilization and on-time order delivery capabilities; and enhancing the system's adaptability to demand fluctuations and resource changes.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and production scheduling technology, and in particular to a collaborative batch scheduling method for dual production lines in tire production for pre-fabricated rubber packs. Background Technology

[0002] As the tire manufacturing industry evolves towards multi-variety, small-batch, multi-batch, and rapid delivery, traditional production organization methods relying on experience and finished goods inventory buffers are no longer adequate to meet current manufacturing demands. The tire production process typically includes raw material preparation, mixing, cooling, extrusion, calendering, cutting, molding, and vulcanization. Upstream rubber pack prefabrication lines are responsible for the preparation and supply of rubber packs with different formulations, while downstream tire production lines handle the continuous processing and assembly of tire batches. Because there is usually a many-to-many consumption mapping relationship between tire types and rubber pack types, the production rhythms of upstream and downstream processes are difficult to match naturally, easily leading to problems such as insufficient rubber pack supply or excessive prefabrication, tire batch waiting times, frequent equipment changeovers, and increased inventory fluctuations.

[0003] In actual production, fluctuations in market demand, changes in order structure, and urgent orders are common occurrences. Enterprises not only need to ensure on-time order delivery but also need to consider equipment utilization, changeover costs, and inventory costs. Especially in the prefabrication of tire packs, if upstream tire pack production passively follows downstream tire order changes, it can easily lead to frequent adjustments to the prefabrication schedule, congestion in certain processes, and incomplete material sets. On the other hand, relying solely on advance inventory buildup will result in increased tire pack and finished product inventory, increasing capital tied up and management costs. Therefore, how to coordinate the prefabrication of tire packs with tire processing schedules while meeting the complete tire forming requirements has become a key issue in tire manufacturing production organization.

[0004] Existing production scheduling methods mostly focus on production optimization in single workshops, single production lines, or static environments, primarily revolving around maximum completion time, equipment utilization, local process sequencing, or dynamic rescheduling. They rarely consider factors such as rubber pack demand forecasting, dual-production-line collaboration, inventory roll-forwarding, material availability, and order delivery simultaneously. For scenarios like tire manufacturing, which have significant upstream and downstream coupling, high material availability requirements, and substantial inventory costs, existing technologies often struggle to comprehensively address rubber pack prefabrication decisions, tire batch scheduling, inventory control, and execution feedback within a unified framework. This results in insufficient executability of scheduling results, unsatisfactory inventory control, and weak adaptability to demand fluctuations.

[0005] Therefore, it is necessary to propose a collaborative batch scheduling method and system for dual production lines of tire production oriented towards pre-molded rubber packs, so as to achieve collaborative optimization between the rubber pack production line and the tire production line, reduce inventory occupation and material shortage waiting time, and improve equipment utilization and order delivery stability. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a collaborative batch scheduling method for dual production lines in tire production oriented towards pre-fabricated rubber packs.

[0007] The technical solution includes the following steps: S1. Obtain basic tire production data, convert tire demand into rubber pack demand based on the mapping relationship between tire type and rubber pack type, and generate predicted demand for each rubber pack type within the scheduling time window. S2. Based on the predicted demand and the basic data, establish a dual-line collaborative batch scheduling model for the rubber packaging production line and the tire production line. The model takes completion time, inventory cost and equipment operating cost as optimization objectives, and sets order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, rubber packaging inventory recursion constraints and pre-forming kitting constraints. S3. Construct a set of candidate scheduling schemes, which are used to characterize the rubber pack pre-production strategy and the tire batch scheduling strategy; S4. Jointly decode each candidate scheduling scheme on a unified time axis, synchronously promote rubber pack production, inventory update and tire batch processing, dynamically update the inventory of each rubber pack type according to the rubber pack inventory recursion constraint, and determine whether the tire batch enters the molding process according to the pre-molding kitting constraint, determine the start time, completion time and equipment allocation of each batch in each process, and evaluate according to the optimization target. S5. Based on the evaluation results, and according to the actual consumption of rubber bales, the current inventory status and the prediction deviation, the production of rubber bales is corrected by feedback, the candidate scheduling scheme is updated and iteratively solved, and the optimal scheduling scheme is output.

[0008] Preferably, the tire production basic data in step S1 includes a set of customer orders, historical demand data, a consumption mapping relationship between tire type and rubber pack type, workshop process information, and equipment operating parameters; The workshop process flow information includes at least the raw material preparation, mixing and cooling processes in the rubber packaging production line, as well as the processing sequence and corresponding process parameters of the extrusion, calendering, cutting, molding and vulcanization processes in the tire production line. The equipment operating parameters include at least the equipment's executable processes, planned available time, processing capacity parameters, mold change time parameters, and parallel processing capacity parameters of the vulcanization equipment.

[0009] The tire type, quantity required, and delivery deadline of each order in the customer order set correspond one-to-one with the product process route in the process flow information. The consumption mapping relationship between tire type and rubber pack type is used to convert tire demand into rubber pack demand, and is used for subsequent inventory roll-out and kitting determination.

[0010] The scheduling model, under the aforementioned objectives, includes at least order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, recursive packaging inventory constraints, and pre-molding kitting constraints.

[0011] In a preferred embodiment, the rubber pack inventory recursion is described using a discrete-time progression method. For any discrete moment, the rubber pack inventory is determined by the inventory at the previous moment, the current rubber pack production volume, and the current tire batch consumption volume. To ensure consistency between the inventory recursion relationship and the pre-forming kitting determination, the moment a tire batch enters the forming process is defined as the consumption moment of the corresponding rubber pack material during the time progression. The batch is allowed to enter the forming process only if the corresponding rubber pack inventory at that moment meets the batch requirements. Through this setting, rubber pack production, inventory updates, and tire kitting determination can be kept consistent along a unified time axis, thereby ensuring the executability of the joint decoding results.

[0012] In a preferred embodiment, in addition to the rubber pack inventory, the status of the finished tire inventory is also updated. The finished tire inventory is determined by the finished tire inventory at the previous time step, the quantity of completed and put into storage at the current time step, and the quantity of delivered orders. By synchronously updating the status of the finished tire inventory and the order delivery status, the finished tire inventory holding cost and the penalty for delayed delivery can be uniformly incorporated into the inventory cost evaluation process, thereby forming a closed-loop relationship between inventory cost and scheduling results.

[0013] Preferably, the optimization objective of the dual-production-line collaborative batch scheduling model in step S2 includes completion time, inventory cost, and equipment operating cost; The inventory costs include the cost of rubber pack inventory, the cost of finished tire inventory, and the cost of delayed delivery. The equipment operating costs include the cost of equipment processing and operation, and the cost of equipment switching.

[0014] Preferably, the equipment capability constraints in step S2 specifically include: Ordinary equipment is only allowed to process one batch of one process at a time; The vulcanizing equipment allows multiple batches of the same process to be processed in parallel at the same time, and its parallel capacity is a preset value; The cooling process in the rubber packaging production line corresponds to an open buffer zone, which allows multiple batches to enter the cooling process at the same time without setting a limit on the number of batches in parallel.

[0015] The recursive constraint on rubber pack inventory is used to describe the dynamic change process of rubber pack inventory over discrete time, and the pre-molding kitting constraint is used to ensure that the required rubber pack materials for each tire batch meet the inventory conditions before entering the molding process.

[0016] Preferably, the collaborative scheduling data structure in step S3 includes a rubber packaging production line substructure and a tire production line substructure, wherein: The packaging production line substructure is used to record packaging type priority, predict demand scaling, and pre-production intentions. The tire production line substructure is used to record the batch division results organized by tire type, batch priority, and process sequence. Candidate scheduling schemes are generated by instantiating and combining the rubber packaging production line substructure and the tire production line substructure to form a set of candidate scheduling schemes.

[0017] Preferably, when generating the candidate scheduling scheme set in step S3, a collaborative hybrid initialization strategy is adopted, specifically including: Based on order demand, predicted packaging demand, and basic process data, a partial heuristic candidate scheduling scheme is constructed to make the initial candidate solution have good feasibility and scheduling compactness. Other candidate scheduling schemes are constructed through random perturbation and random generation to improve the diversity of the candidate solution set and enhance the optimization capability in a large-scale search space.

[0018] Preferably, the joint decoding of candidate scheduling schemes in step S4 specifically includes: Simultaneously advance the production process of the rubber packaging production line, the inventory update process, and the batch processing process of the tire production line on a unified timeline; Establish a scheduling record structure for dual production lines to record the processing equipment, start time, and finish time of each batch in each process. When there is a time conflict on the same equipment, the start time of the later-assigned process is postponed to ensure that the equipment capacity constraints are not violated. Based on inventory status and process route constraints, a completeness determination is made to determine whether a tire batch is allowed to enter the molding process.

[0019] Preferably, the joint decoding in step S4 further includes a process overlap strategy, specifically: Under the premise of meeting the constraints of the process route and the availability of subsequent resources, the batch is divided into several sub-batches, and sub-batches that have completed the preceding process are allowed to enter the subsequent process in advance before the current batch is completed as a whole, thereby realizing parallel processing between different processes. For the vulcanization process in the tire production line, the vulcanization preparation process may be triggered in advance when the equipment has available parallel capacity and the preceding molding batch has reached the transferable condition. For the cooling process in the rubber packaging production line, batches of rubber packages that have completed internal mixing can be directly sent to the cooling buffer zone when they meet the conditions for entering the cooling process, so as to improve the continuity of rubber package supply.

[0020] Preferably, in step S4, when determining the specific processing equipment for each process in each batch, a dynamic machine selection strategy is adopted, specifically including: Determine the set of available devices based on the current decoding status; Prioritize equipment with the shortest estimated completion time; When there are multiple candidate devices with the same expected completion time, select the device with the smallest processing time among the multiple candidate devices with the same expected completion time; When multiple candidate devices still exist, the device is selected according to the preset device priority.

[0021] Among them, a single-station allocation rule is adopted for ordinary equipment, equipment selection is carried out for vulcanizing equipment under the condition of meeting the parallel capacity constraint, and the rubber pack cooling process is handled by the buffer acceptance method.

[0022] Preferably, the iterative update process in step S5 includes selecting, perturbing, and reorganizing the candidate scheduling scheme set, and updating the collaborative scheduling scheme in combination with the evaluation results; the feedback correction mechanism constructs an error feedback term based on the predicted demand for rubber packs, actual tire consumption, and current inventory status, and dynamically corrects the rubber pack production, thereby reducing the impact of the accumulation of prediction errors and improving the executability and stability of the scheduling results.

[0023] A collaborative batch scheduling system for dual production lines in tire production for pre-fabricated rubber packs, characterized in that it includes: The demand forecasting module is used to acquire basic tire production data, convert tire demand into rubber pack demand based on the mapping relationship between tire type and rubber pack type, and generate forecasted demand for each rubber pack type within the scheduling time window. The scheduling model construction module is used to establish a dual-line collaborative batch scheduling model for the rubber packaging production line and the tire production line based on the predicted demand and the basic data. The model takes completion time, inventory cost and equipment operation cost as optimization objectives, and sets order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, rubber packaging inventory recursion constraints and pre-forming kitting constraints. The candidate scheme generation module is used to construct a set of candidate scheduling schemes, which are used to characterize the pre-production strategy of rubber packs and the batch scheduling strategy of tires; The joint decoding module is used to jointly decode each candidate scheduling scheme on a unified time axis, simultaneously promote the production of rubber packs, inventory updates and tire batch processing, dynamically update the inventory of each type of rubber pack according to the recursive constraint of rubber pack inventory, determine whether the tire batch enters the molding process according to the pre-molding kitting constraint, determine the start time, completion time and equipment allocation of each batch in each process, and evaluate according to the optimization objectives. The feedback correction module is used to correct the production of rubber bales based on the evaluation results, actual consumption of rubber bales, current inventory status and prediction deviation, update candidate scheduling schemes and solve them iteratively. The results output module is used to output the optimal scheduling scheme.

[0024] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows: 1. This invention integrates the prefabrication line for rubber packaging and the tire processing line into a unified collaborative modeling framework, thereby achieving collaborative optimization of upstream material preparation and downstream batch processing and improving the overall coordination of production organization.

[0025] 2. By introducing a roll-forward inventory system for rubber packs and a pre-molding fitting constraint, this invention can effectively control inventory size while ensuring batch feasibility, reducing material shortages and inventory fluctuations.

[0026] 3. By setting process overlap strategies and dynamic machine selection strategies, this invention can shorten process waiting time, improve equipment utilization, and enhance scheduling flexibility in complex production scenarios.

[0027] 4. By combining demand forecasting results with an execution layer feedback correction mechanism, this invention improves the system's adaptability to changes in order structure, demand fluctuations, and resource load changes, and enhances the robustness and executability of scheduling results. Attached Figure Description

[0028] Figure 1 This is a diagram illustrating the comparison of production models.

[0029] Figure 2 The framework diagram for the hybrid initialization genetic algorithm HIGA.

[0030] Figure 3 This is a diagram illustrating joint decoding and inventory recursion.

[0031] Figure 4 The graph shows the results of the sensitivity analysis of key parameters.

[0032] Figure 5 Gantt chart for M-ALL's packaging production line.

[0033] Figure 6 Gantt chart for the M-ALL tire production line.

[0034] Figure 7 This is a No-Pred global Gantt chart.

[0035] Figure 8 This is a cost-inventory comparison chart. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0038] Example 1 This invention provides a method for collaborative batch scheduling of dual production lines in tire production for pre-molded tires, specifically including the following steps: S1. Obtain basic tire production data, convert tire demand into rubber pack demand based on the mapping relationship between tire type and rubber pack type, and generate predicted demand for each rubber pack type within the scheduling time window. The basic data includes customer order sets, historical demand data, mapping relationships between tire types and rubber pack types, workshop process flow information, and equipment operating parameters. Process flow information includes raw material preparation, mixing, and cooling processes in the rubber pack production line, as well as extrusion, calendering, cutting, molding, and vulcanization processes in the tire production line. Equipment operating parameters include at least the number of processes the equipment can perform, processing capacity, planned available time, mold changeover time, and the parallel processing capacity of the vulcanization equipment.

[0039] The rubber bag demand forecasting model employs a combination of trend and cyclical terms to establish a baseline forecasting model. A rolling correction term is introduced based on the deviation between actual and forecasted demand at the current moment to generate forecasted demand for each type of rubber bag within future time windows. This forecasting result serves as the foundational input for subsequent rubber bag pre-production decisions and the coordinated scheduling of dual production lines.

[0040] S2. Based on the predicted demand and the basic data, establish a dual-line collaborative batch scheduling model for the rubber packaging production line and the tire production line. The model takes completion time, inventory cost and equipment operating cost as optimization objectives, and sets order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, rubber packaging inventory recursion constraints and pre-forming kitting constraints. The model optimizes for maximum completion time, inventory costs, and equipment operating costs. Maximum completion time describes the latest time all tire batches can be produced; inventory costs describe the combined costs of rubber pack inventory, finished tire inventory, and delayed delivery; and equipment operating costs describe the costs incurred during equipment processing and type switching.

[0041] Under the above objectives, constraints are set for order batching, process sequence, equipment capacity, rollover of packaging inventory, and pre-molding kitting.

[0042] Among them, ordinary equipment is only allowed to process one batch of one process at a time, vulcanizing equipment is allowed to process multiple batches of the same process in parallel at the same time, and the cooling process in the rubber packaging production line corresponds to an open buffer zone with no upper limit on the number of parallel processes.

[0043] The recursive constraint on rubber pack inventory is used to describe the dynamic update process of the inventory of each type of rubber pack over discrete time steps, while the pre-molding kitting constraint is used to ensure that the required rubber pack inventory of a tire batch meets the demand conditions before entering the molding process.

[0044] S3. Construct a set of candidate scheduling schemes, which characterize the rubber pack pre-production strategy and the tire batch scheduling strategy. The collaborative scheduling data structure includes a rubber pack production line substructure and a tire production line substructure. The rubber pack production line substructure records the rubber pack pre-production priority and pre-production intensity information, while the tire production line substructure records the batch division results, batch priority, and process sequence. Candidate scheduling schemes are generated by instantiating and combining the two types of substructures.

[0045] When generating a set of candidate scheduling schemes, a collaborative hybrid initialization strategy can be adopted. Some of the candidate schemes are constructed based on heuristic rules to enhance the feasibility and compactness of the initial solution, while the remaining candidate schemes are generated through random perturbation to improve the diversity of the solution set.

[0046] S4. Jointly decode each candidate scheduling scheme on a unified time axis, synchronously promote rubber pack production, inventory update and tire batch processing, dynamically update the inventory of each rubber pack type according to the rubber pack inventory recursion constraint, and determine whether the tire batch enters the molding process according to the pre-molding kitting constraint, determine the start time, completion time and equipment allocation of each batch in each process, and evaluate according to the optimization objective.

[0047] Joint decoding synchronously advances the production of rubber packs, inventory updates, and tire batch processing on a unified timeline, determining the start time, completion time, and specific equipment allocated to each batch at each process stage.

[0048] In the joint decoding process, a process overlap strategy and a dynamic machine selection strategy are introduced.

[0049] The process overlap strategy allows sub-batches that have completed the preceding process to enter the next process in advance when the availability of subsequent resources and process sequence constraints are met, thereby reducing process waiting time. In the tire production line, the vulcanization process can be triggered in advance when the parallel capacity and transferability conditions are met, while the cooling process in the rubber pack production line serves as an open buffer to receive rubber pack sub-batches that have completed mixing.

[0050] The dynamic machine selection strategy is used to determine the optimal processing equipment from the candidate equipment set, prioritizing the equipment with the shortest expected completion time, and further determining the equipment based on processing time and equipment priority when there are tied candidates.

[0051] After joint decoding is completed, the candidate scheduling schemes are evaluated based on the maximum completion time, inventory costs, and equipment operating costs.

[0052] S5. Based on the evaluation results, and according to the actual consumption of rubber bales, the current inventory status and the prediction deviation, the production of rubber bales is corrected by feedback, the candidate scheduling scheme is updated and iteratively solved, and the optimal scheduling scheme is output.

[0053] The feedback correction mechanism constructs error feedback items based on predicted demand, actual consumption, and inventory status, and dynamically adjusts the prefabrication quantity of rubber bales to mitigate the impact of accumulated prediction errors.

[0054] After the preset termination conditions are met, the candidate scheduling scheme with the best evaluation result is selected as the final scheduling output. The final output includes information such as the prefabrication plan for rubber packs, tire batch scheduling scheme, inventory change trajectory, and order completion time.

[0055] Example 2 To facilitate understanding of the mathematical relationships in the demand forecasting, dual-production-line collaborative modeling, and joint decoding processes of this invention, a unified explanation of the main symbols and their meanings is provided. These symbols include time index, rubber pack type set, tire type set, order set, batch set, equipment set, predicted demand, actual output, inventory status, mapping coefficient, equipment capacity parameters, and completion time. The symbols in Table 1 are used to describe the mapping relationship from tire demand to rubber pack demand, rubber pack production constraints, inventory recursion, and the processing status of batches at each stage.

[0056] Table 1. Explanation of Symbols and Their Meanings

[0057] This invention provides a method for collaborative batch scheduling of dual production lines in tire production for pre-fabricated rubber packs, such as... Figure 2 As shown, the method includes the following steps: 1. Obtain basic data from the tire production workshop, establish a rubber pack demand forecasting model, and generate forecasted demand for each type of rubber pack within the future scheduling window.

[0058] Specifically, the process begins by collecting customer order sets, historical order data, historical tire pack demand data, the consumption mapping relationship between tire types and tire pack types, and basic workshop process parameters. The forecast output at the planning level is then defined as the tire pack type. At any moment demand .

[0059] Based on the above data, the demand for different tire types in the orders is converted into a demand sequence for the corresponding rubber pack types. Then, the demand sequence is decomposed into trends and cycles to obtain the baseline forecast results for rubber pack demand. A rolling correction term is further introduced to dynamically adjust the forecast results for future periods based on the deviation between the current actual demand and the forecast demand, thereby obtaining the forecast demand data for each type of rubber pack within the scheduling window.

[0060] In a preferred embodiment, the type of adhesive packaging The baseline demand curve is:

[0061] in, The coefficients of the constant term; The coefficient for the trend term; For the first First harmonic coefficient; The harmonic cutoff order; For demand cycles; For the first The first harmonic angular frequency. This formula can simultaneously characterize the long-term trend and periodic fluctuation characteristics of the demand sequence.

[0062] A rolling correction term is introduced based on the baseline demand curve to generate the forecast demand for rubber packs within future time windows.

[0063] In a preferred embodiment, the rolling correction term is:

[0064] Then the type of packaging In the future The predicted demand is:

[0065] Furthermore, the predicted demand vector for rubber packs at future time steps can be obtained:

[0066] The forecast results will serve as the basic input for pre-production decisions of the rubber packaging production line, and will work together with inventory status and tire production line completion information in the subsequent joint decoding stage to generate an executable rubber packaging production plan and inventory trajectory.

[0067] II. Establish a collaborative batch scheduling model for dual production lines based on predicted demand.

[0068] This model uses batches as the basic scheduling object and constructs a multi-objective collaborative scheduling model around maximum completion time, inventory cost, and equipment operation cost. The optimization objectives include at least maximum completion time, comprehensive inventory cost, and switching and processing operation cost.

[0069] When scheduling is done in batches, the maximum completion time is defined as:

[0070] in, Indicates batch Completion time of the final process.

[0071] The total inventory cost consists of the holding cost of rubber pack inventory, the holding cost of finished tire inventory, and the penalty cost for stockouts or delayed delivery. Its expression is as follows:

[0072] The first item represents the cost of holding rubber pack inventory, the second item represents the cost of holding finished tire inventory, and the third item represents the cost of penalties for stockouts or delayed delivery.

[0073] Considering that the equipment typically remains continuously available within the scheduling window, the switching and processing operation cost can be expressed as:

[0074] The first item represents the switching cost caused by equipment type switching or mold changing process, and the second item represents the operating cost generated by the equipment when performing each batch of processing operations.

[0075] Therefore, the optimization objective of the dual-production-line collaborative batch scheduling model can be expressed as:

[0076] By setting the above objectives, we can ensure the performance of tire order delivery while reducing the inventory of rubber packs and finished products, and also take into account the costs of equipment changeover and processing operations.

[0077] Regarding model constraints, at least the following should be included: (1) Establish order batching and quantity conservation constraints.

[0078] To adapt to the characteristics of multiple orders, multiple types, and multiple batches in tire production, order requirements are discretized at the batch level. Let the order... medium tire type The number of requirements is The number of batches is The relationship between order batching and quantity conservation can be expressed as:

[0079]

[0080] in, Indicates whether the sub-order is assigned to a batch. 0-1 variables, Indicates that the sub-order is in the batch The allocation quantity is determined by the constraints mentioned above. This ensures that the demand for each sub-order is fully allocated to the selected batch, while maintaining the conservation of the total demand quantity.

[0081] (2) Establish equipment allocation, process sequence and equipment mutual exclusion constraints.

[0082] To ensure that each batch of equipment is selected as exactly one available device in each process step, and to satisfy the sequential relationship between processes, the following is set: This indicates that the batch uses variables. Indicates batch Is it in the machine? Previous execution process Then we have:

[0083] Batch in process The processing time is defined as follows:

[0084] Batch in process The completion time meets the following requirements:

[0085] Adjacent processes must satisfy a sequential connection relationship:

[0086] in, and Each represents a batch In the process The start and completion times are specified. These constraints ensure that each batch selects exactly one available machine for processing at each stage, and that the next stage can only begin after the previous stage is completed.

[0087] To standardize the description of capacity rules for different types of equipment, define the equipment. At any moment The number of batches processed simultaneously is:

[0088] The equipment capacity constraint can then be expressed as:

[0089] in, Indicates equipment Parallel processing capacity. For ordinary equipment, For vulcanizing equipment, For the rubber packaging cooling process, the corresponding equipment capacity is set to a sufficiently large constant or has no upper limit, representing the open cooling buffer capacity. This constraint can simultaneously cover three types of resource rules: single-station processing of ordinary equipment, parallel processing of vulcanizing equipment, and open capacity of the cooling process.

[0090] Furthermore, for different batches of the same process on the same ordinary equipment, mutually exclusive processing and changeover connections must also be met. Let... To represent the order of batches, the following mutual exclusion relationship can be used:

[0091]

[0092] in, This indicates the time required for mold changing or switching when adjacent batches switch types on the same device. It is a sufficiently large positive number. The above constraint is used to prevent overlapping processing times on the same general-purpose equipment and to incorporate type switching time into the time progression process.

[0093] (3) Establish inventory roll-up and material matching constraints.

[0094] In this invention, a preset mapping coefficient is used to connect tire type and rubber sheath type. Establish consumption relationships, and retain the mapping relationship table as a basic process table.

[0095] Based on the batch allocation results at the tire end, tire demand can be converted into total rubber pack demand:

[0096] The packaging production line meets the total capacity constraint in each discrete time period:

[0097] in, Indicates time Packaging type The actual output, Indicates time Capacity ceiling of the rubber packaging production line Let represent the set of batches entering the molding process within a discrete time period. Then, the recursive relationship for the rubber pack inventory is:

[0098] in, This indicates the amount of rubber packs consumed by a tire batch during that period.

[0099] And satisfy the nonnegativity constraint:

[0100] Furthermore, before any batch of tires enters the molding process, it must also meet the following kitting criteria:

[0101] The above constraints ensure that the required rubber packaging materials are readily available before the tire batch enters the molding process.

[0102] 3. Construct a collaborative scheduling data structure for dual production lines and generate a set of candidate scheduling schemes.

[0103] The collaborative scheduling data structure includes a rubber pack production line substructure and a tire production line substructure. To adapt to the pre-production decisions of the rubber pack production line, in a preferred embodiment, the individual rubber pack production line adopts a two-layer coding structure. The upper layer is a priority sequence of rubber pack types. , The lower layer is a vector of production scaling factors that corresponds one-to-one with the type of rubber package. The scaling factor satisfies:

[0104] Based on predicted demand This allows us to obtain the baseline for continuous planned production:

[0105] Therefore, the decoding output of the rubber-coated terminal can be expressed as:

[0106] The tire production line subpopulation is used to generate aggregated actual demand, batch division, and processing sequence information by tire type. Its initialization uses the demand summarized by type within a scrolling window as input. Let the types within the window be... The total number of requirements is:

[0107] Randomly select the number of batches allowed for each type. and will Divided into A number of positive integer sub-batches are used to ensure that the sum of the sub-batches equals the total demand within the window, thus forming an initial batch structure that satisfies the batching constraints.

[0108] Based on the aforementioned twin structure, a collaborative hybrid initialization strategy is adopted to generate a set of candidate scheduling schemes. Some of the candidate schemes are constructed based on heuristic rules to make the initial solution more feasible, while the other part of the candidate schemes are generated randomly to improve the diversity of the candidate solution set.

[0109] In this invention, the complete scheduling scheme is composed of sub-solutions from the rubber sheet production line and the tire production line. Since any sub-solution cannot independently determine its multi-objective fitness after separating from its collaborators, a dual-population co-evolutionary framework is adopted. This framework allows the rubber sheet sub-population and the tire sub-population to evolve separately, forming a complete solution through collaborator pairing. A unified evaluation is then performed via joint decoding to guide the collaborative search of the two sub-populations. It should be noted that genetic algorithms, NSGA-II, or other multi-objective intelligent optimization algorithms can be used as the solution framework, but the core of this invention lies in the dual-production-line collaborative modeling, joint decoding, and feedback correction mechanism, rather than relying on a specific optimization algorithm.

[0110] IV. Jointly decode and evaluate candidate scheduling schemes.

[0111] In this step, the production of rubber packs, inventory updates, and tire batch processing are carried out synchronously on a unified timeline, and a scheduling record structure is established to record the batch, equipment, start time, and completion time corresponding to each process.

[0112] Rubber sheath terminal decoding is used to generate pre-production intentions and type priority descriptions, while tire terminal decoding is used to generate actual demand, processing sequences, and completion information by tire type. Both types of outputs are jointly decoded on a unified timeline to synchronously advance rubber sheath production, inventory updates, and tire batch processing, thereby obtaining complete production, inventory, and equipment operation trajectories.

[0113] A process overlap strategy is introduced during the decoding process.

[0114] To reduce process waiting time and equipment idleness caused by traditional batch completion and transfer, this invention employs a process overlap strategy for time advancement in both the rubber packaging and tire production lines. The core of this strategy is to further treat batches as sub-batch units that can be transferred ahead of time. Once a sub-batch is completed in a previous process, it is allowed to proceed to the next process ahead of time, provided that subsequent resources are available and the process sequence is met, thus achieving parallel processing and transfer. This strategy effectively reduces inter-process waiting time and improves equipment utilization.

[0115] Set batch Classified as Each batch, the first Individual batches in the process The completion time is recorded as Then the start time for it to enter the next process satisfies:

[0116] Furthermore, the first The actual start time of a sub-batch in the next process depends on the greater of the resource availability time and the material availability time, which can be expressed as:

[0117] in, This indicates the earliest time when resources become available for subsequent processes. This indicates the earliest executable time when the kitting or preconditions are met. This strategy allows completed sub-batches to be moved to the next process as early as possible, provided that the constraints are met.

[0118] Introducing a dynamic machine selection strategy during the decoding process In this invention, both the rubber packaging production line and the tire production line employ a unified machine selection strategy for equipment allocation. This strategy comprehensively considers the machine's current status, estimated completion time, processing capacity, and serial number priority to select the optimal equipment for the batch or sub-batch to be processed, while satisfying both process and resource constraints. The machine selection strategy sequentially determines the processing equipment for the batch or sub-batch to be processed, based on estimated completion time, processing time, and preset equipment priority, while also satisfying both process and resource constraints.

[0119] Let the processing unit to be assigned be a batch. In the process The task on the surface, the set of processing equipment is as follows ,equipment The estimated completion time is The processing time is The equipment number is Then the optimal device can be expressed as:

[0120] The strategy prioritizes selecting the equipment with the shortest estimated completion time. If multiple candidate equipment have the same estimated completion time, the equipment with the smallest processing time among them is selected. If multiple candidate equipment still exist, the equipment with the larger equipment number is selected. This strategy balances processing efficiency, equipment load balancing, and feasibility.

[0121] A unified evaluation and feasibility test are conducted based on the joint decoding results.

[0122] In a preferred embodiment, the complete production scheduling scheme obtained after joint decoding can be used to calculate corresponding evaluation values ​​based on the three optimization objectives defined in step S2, and form a multi-objective fitness vector. .

[0123] When a candidate solution violates constraints such as overlapping equipment processing times, out-of-bounds inventory, or unmet demand, a comprehensive constraint violation rate is introduced. As a penalty:

[0124] in, For a constraint set, Indicates the first Class constraint violation quantity These are the corresponding weighting coefficients. When the solution satisfies all constraints, we have: Furthermore, the revised evaluation vector is:

[0125]

[0126] in, This is the penalty coefficient. This mechanism encourages the evolutionary search to gradually converge towards the feasible solution space and ensures the output solution is practically executable.

[0127] V. Perform iterative updates and feedback corrections based on the evaluation results.

[0128] Before joint decoding, the packaging end first determines the predicted demand. With output scaling factor Forming a continuous planned production benchmark This continuous planned production baseline is used to express the pre-production intensity of each bag type within the forecast window, rather than directly as the final executed production.

[0129] Error correction weights, feedback correction weights, and feedback gain coefficients are introduced to provide feedback correction for the planned production of rubber bales.

[0130] In a preferred embodiment, the feedback correction process simultaneously considers the prediction baseline term, the error correction term, and the feedback correction term, and their weights satisfy the following... ,in, To predict the baseline weights, For error correction weights, To provide feedback and adjust the weights, This is the feedback gain coefficient. By introducing the above weighting relationship and feedback gain coefficient, the pre-fabrication quantity of rubber packs can be dynamically corrected based on actual tire consumption, current inventory status, and previous deviations, thereby mitigating the impact of accumulated forecast errors. Continuous planned production can be written as:

[0131] in, This refers to the feedback signal and the prediction bias term.

[0132] After feedback and correction, the actual output is generated by further combining capacity reduction rules and type selection rules. This ensures that production at the rubber pack end meets the single-line feasibility and total capacity constraints at any given time. The final output includes rubber pack prefabrication plan, tire batch scheduling scheme, rubber pack inventory trajectory, tire finished product inventory trajectory, order completion time, and equipment switchover and operation information, and can be further output in Gantt charts or other visualization methods.

[0133] Through the above iterative optimization and feedback correction process, the demand forecasting at the planning level and the scheduling results at the execution level are coordinated with each other, thereby gradually obtaining the optimal scheduling scheme that takes into account inventory control, equipment utilization and order delivery capability.

[0134] Example 3 To verify the effectiveness and superiority of the dual-production-line collaborative batch scheduling method for tire production oriented towards pre-fabricated rubber packs provided in Embodiment 2 of the present invention, simulation experiments were conducted using standard examples and actual factory data. By constructing a test environment that includes multiple tire types, multiple rubber pack types, and collaborative relationships between the two production lines, the proposed method was validated and compared with other scheduling strategies.

[0135] 1. Data Preparation Due to the lack of real order data from enterprises, this paper uses an externally anchored synthesis mechanism to generate historical demand sequences aggregated by type. Based on this, historical order instances are constructed. The expression of the demand sequence is consistent with the prediction model, both consisting of trend changes, periodic fluctuations, and random disturbances; the difference lies in that the experimental data further incorporates external statistical information to constrain the seasonal amplitude and fluctuation intensity, thereby enhancing the realistic rationality and reproducibility of the generated samples.

[0136] External anchoring mainly consists of two parts: first, extracting the annual cyclical pattern using publicly available monthly automobile production and sales statistics to constrain the seasonal structure of the demand sequence; second, adjusting the intensity of random disturbances using the price fluctuation levels of upstream raw materials such as natural rubber to characterize the impact of market volatility on demand uncertainty. Quarterly sales statistics for the tire industry are further used to verify the consistency between the overall magnitude and fluctuation range of the generated sequence.

[0137] After obtaining the historical demand vector aggregated by type Then, it is further broken down into order sets. For any order Let its type requirement be ,satisfy:

[0138] During the order decomposition process, the number of orders, type coverage, and degree of mixing are controlled according to the experimental scale, thereby generating reproducible small-scale and large-scale test instances.

[0139] The aforementioned historical demand sequence serves as the input to the rolling forecasting model, while the generated order instances serve as the input to the experimental task of dual production line collaborative scheduling, thereby ensuring that the data sources of the forecasting layer and the scheduling layer are consistent in the experiment.

[0140] 2. Parameter sensitivity analysis To analyze the impact of key parameters on scheduling results, sensitivity analysis can be performed on key factors such as candidate solution size, number of iterations, probability of disturbance of candidate schemes, and feedback correction parameters. Figure 4 As shown in the figure. Experimental results show that different parameters have a significant impact on the maximum completion time and inventory cost, and reasonable parameter configuration can effectively improve scheduling performance and solution stability.

[0141] 3. Ablation test To verify the impact of prefabrication of rubber packs and tire batch organization on the overall scheduling results, the effects of different batch division strategies and coordination strategies on scheduling performance were further examined, such as... Figure 3-6 As shown in the figure. The results indicate that a reasonable batch organization method can achieve a better balance between inventory levels and production cycle time, and the collaborative scheduling mechanism can significantly reduce inventory fluctuations and material shortages compared to individual scheduling methods.

[0142] 4. Representative scheduling schemes and explanations of key time parameters To enhance the interpretability of the results for small-scale benchmark examples, this paper provides Gantt charts and explanations of key time metrics for representative scheduling schemes. For the predictive guidance modes M-All and M-noFB, pre-production Gantt charts for the rubber pack production line and the tire production line are presented, respectively, to characterize the time scale required for advance material preparation and the response completion time after order arrival. For the predictive guidance-removed mode M-noPred, a joint Gantt chart for rubber packs and tires is presented to represent the impact of initiating material preparation only after order arrival on the tire-end start-up time and the waiting time for key processes. The final completion time is uniformly defined as the maximum completion time of the tire production line. This ensures consistency in response time comparisons across different modes.

[0143] The implementation and verification results show that the dual-production-line collaborative batch scheduling method for tire production oriented towards pre-molded tire pouches proposed in this invention can coordinate the supply of tire pouches, inventory evolution, and tire batch processing under a unified time axis. While ensuring completeness before molding, it also considers maximum completion time, inventory control, and equipment operating costs. Compared to independent scheduling methods for upstream and downstream processes, this invention has better overall effects in reducing inventory holdings, minimizing material shortages, and improving equipment utilization.

[0144] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for collaborative batch scheduling of dual production lines in tire production for pre-fabricated rubber packs, characterized in that, Specifically, the following steps are included: S1. Obtain basic tire production data, convert tire demand into rubber pack demand based on the mapping relationship between tire type and rubber pack type, and generate predicted demand for each rubber pack type within the scheduling time window. S2. Based on the predicted demand and the basic data, establish a dual-line collaborative batch scheduling model for the rubber packaging production line and the tire production line. The model takes completion time, inventory cost and equipment operating cost as optimization objectives, and sets order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, rubber packaging inventory recursion constraints and pre-forming kitting constraints. S3. Construct a set of candidate scheduling schemes, which are used to characterize the rubber pack pre-production strategy and the tire batch scheduling strategy; S4. Jointly decode each candidate scheduling scheme on a unified time axis, synchronously promote rubber pack production, inventory update and tire batch processing, dynamically update the inventory of each rubber pack type according to the rubber pack inventory recursion constraint, and determine whether the tire batch enters the molding process according to the pre-molding kitting constraint, determine the start time, completion time and equipment allocation of each batch in each process, and evaluate according to the optimization target. S5. Based on the evaluation results, and according to the actual consumption of rubber bales, the current inventory status and the prediction deviation, the production of rubber bales is corrected by feedback, the candidate scheduling scheme is updated and iteratively solved, and the optimal scheduling scheme is output.

2. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 1, characterized in that, The tire production basic data in step S1 includes customer order set, historical demand data, consumption mapping relationship between tire type and rubber pack type, workshop process flow information and equipment operating parameters. The workshop process flow information includes at least the raw material preparation, mixing and cooling processes in the rubber packaging production line, as well as the processing sequence and corresponding process parameters of the extrusion, calendering, cutting, molding and vulcanization processes in the tire production line. The equipment operating parameters include at least the equipment's executable processes, planned available time, processing capacity parameters, mold change time parameters, and parallel processing capacity parameters of the vulcanization equipment.

3. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 2, characterized in that, The predicted demand for each type of adhesive pack within the scheduling time window in step S1 includes: Based on historical demand data, trend and periodic terms are modeled for the demand sequence of rubber packaging types to obtain baseline forecast results; Based on the deviation between the actual demand and the predicted demand at the current moment, and combined with the rolling time window, the predicted demand for subsequent periods is dynamically corrected to generate the predicted demand for each type of pack within the scheduling time window.

4. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 1, characterized in that, The optimization objectives of the dual-production-line collaborative batch scheduling model in step S2 include completion time, inventory cost, and equipment operating cost. The inventory costs include the cost of rubber pack inventory, the cost of finished tire inventory, and the cost of delayed delivery. The equipment operating costs include the cost of equipment processing and operation, and the cost of equipment switching.

5. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 4, characterized in that, The order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, pack inventory roll-forward constraints, and pre-molding kitting constraints in step S2 include: Divide orders into batches and maintain quantity conservation; process each batch sequentially according to a pre-defined process order. Each process is assigned to the equipment capable of performing that process; ordinary equipment is limited to processing only one batch of one process at a time; vulcanizing equipment is allowed to process multiple batches of the same process in parallel at the same time, and the number of parallel processes does not exceed the preset capacity; the cooling process of the rubber packaging production line is allowed to cool multiple batches simultaneously at the same time. The inventory of each type of rubber pack is updated recursively based on the production volume of rubber packs and the consumption of tire production, and the inventory is kept non-negative. Before a tire batch enters the molding process, a completeness check of the required rubber packs is performed. Only when the corresponding rubber pack inventory meets the demand is the tire batch allowed to enter the molding process.

6. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 1, characterized in that, The candidate scheduling scheme set in step S3 includes multiple collaborative scheduling schemes, and the collaborative scheduling schemes include rubber packaging production line substructure and tire production line substructure. The rubber pack production line substructure is used to characterize the rubber pack pre-production priority and pre-production intensity, while the tire production line substructure is used to characterize the tire batch division results, batch priority, and process sequence.

7. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 1, characterized in that, The joint decoding in step S4 includes: Simultaneously advance the rubber pack production process, inventory update process, and tire batch processing process on a unified timeline; Based on the process route, equipment availability, and resource occupancy status of each batch, determine the start time, completion time, and corresponding equipment for each process of each batch. During the decoding process, the inventory status of each type of packaging and the resource occupancy status of each device are dynamically updated.

8. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 7, characterized in that, The joint decoding in step S4 includes a process overlap strategy and a dynamic machine selection strategy; The process overlap strategy includes dividing batches into sub-batches and allowing sub-batches that have completed the preceding process to enter the next process in advance, provided that the process sequence constraints and subsequent resource availability conditions are met. The dynamic machine selection strategy includes prioritizing the selection of the device with the shortest expected completion time from the candidate device set. When there are multiple candidate devices with the same expected completion time, the device with the smallest processing time among the multiple candidate devices with the same expected completion time is selected. If there are still multiple candidate devices, the selection is made according to the preset device priority.

9. The method for collaborative batch scheduling of dual production lines for pre-fabricated tire production according to claim 1, characterized in that, The feedback correction in step S5 includes: An error feedback item is constructed based on the predicted demand for rubber bags, actual consumption, and current inventory status, and the production of rubber bags is dynamically adjusted based on the error feedback item. Based on the evaluation results of the candidate scheduling schemes, the candidate scheduling schemes are selected, perturbed, and reorganized to generate new candidate scheduling schemes and iteratively solve them until the preset termination conditions are met.

10. A dual-line collaborative batch scheduling system for tire production oriented towards pre-fabricated rubber packs, characterized in that, The system is used to implement the dual-line collaborative batch scheduling method for tire production oriented towards pre-fabricated rubber packs as described in any one of claims 1-9, the system comprising: The demand forecasting module is used to acquire basic tire production data, convert tire demand into rubber pack demand based on the mapping relationship between tire type and rubber pack type, and generate forecasted demand for each rubber pack type within the scheduling time window. The scheduling model construction module is used to establish a dual-line collaborative batch scheduling model for the rubber packaging production line and the tire production line based on the predicted demand and the basic data. The model takes completion time, inventory cost and equipment operation cost as optimization objectives, and sets order batching constraints, process sequence constraints, equipment allocation constraints, equipment capacity constraints, rubber packaging inventory recursion constraints and pre-forming kitting constraints. The candidate scheme generation module is used to construct a set of candidate scheduling schemes, which are used to characterize the pre-production strategy of rubber packs and the batch scheduling strategy of tires; The joint decoding module is used to jointly decode each candidate scheduling scheme on a unified time axis, simultaneously promote the production of rubber packs, inventory updates and tire batch processing, dynamically update the inventory of each type of rubber pack according to the recursive constraint of rubber pack inventory, determine whether the tire batch enters the molding process according to the pre-molding kitting constraint, determine the start time, completion time and equipment allocation of each batch in each process, and evaluate according to the optimization objectives. The feedback correction module is used to correct the production of rubber bales based on the evaluation results, actual consumption of rubber bales, current inventory status and prediction deviation, update candidate scheduling schemes and solve them iteratively. The results output module is used to output the optimal scheduling scheme.

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