A method for scheduling parallel processing of multiple machines in a foam material production workshop

Abstract

This invention specifically relates to a method for scheduling parallel processing of multiple machines in a foamed material production workshop, belonging to the field of intelligent manufacturing technology. It includes: based on the digital workshop model and hierarchical production tasks, generating multiple initial production scheduling schemes that meet core production constraints through preset scheduling rules combined with heuristic calculations. This invention adapts to the industry-specific characteristics of foamed material production, addressing the strong dependence on foamed production molds, the rigidity of core process sequences, and the coupling constraints of multiple production resources. It constructs a digital workshop model covering all production elements, achieving precise mapping between scheduling and the physical production scenario from the source of scheduling, ensuring a high degree of matching between the scheduling scheme and actual production.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a method for scheduling multiple machines to process in parallel in a foam material production workshop. Background Technology

[0002] Foamed materials, as lightweight and multifunctional polymer materials, are widely used in core areas such as automotive interiors, home appliance insulation, building energy conservation, and new energy cushioning and protection. With the rapid development of downstream industries, the market demand for foamed materials continues to grow, and the production model is gradually shifting from traditional large-volume single-variety production to multi-variety, small-batch, customized flexible production. The core production process of foamed materials is based on the parallel processing of multiple foaming machines. The production process has the dual characteristics of continuous raw material allocation in a flow-type process and batch molding in a discrete mold type. It has industry-specific production control characteristics such as strong dependence on molds, rigid core process sequence, coupling constraints of multiple production resources, and many disturbance factors in the production process. This places extremely high demands on the accuracy, scenario adaptability, and dynamic flexibility of workshop production scheduling.

[0003] Currently, workshop production scheduling technology in the field of intelligent manufacturing has formed a relatively complete technical system. Rule-driven scheduling methods, heuristic scheduling algorithms, and intelligent optimization algorithms have been applied on a large scale in multiple fields such as discrete manufacturing and process industries, providing effective technical support for capacity improvement, order delivery assurance, and production operation cost control in various production scenarios. For scheduling optimization in multi-machine parallel processing scenarios, existing technologies have conducted extensive research and practical implementation around multi-objective collaborative optimization and multi-constraint compliance management, forming a variety of mature technical solutions. This has laid a solid technical foundation for the intelligent upgrading of production scheduling and provided mature technical references for customized optimization of scheduling solutions in specific industries.

[0004] As the demands of downstream applications of foamed materials continue to upgrade, the need for rapid order response, dynamic adaptation to anomalies, and closed-loop optimization throughout the production process is becoming increasingly prominent. This necessitates scheduling solutions that not only optimize production scheduling in static production scenarios but also deeply adapt to the process characteristics and resource constraints of the entire foamed material production cycle. This requires collaborative management of all production elements, balanced optimization of multi-dimensional production goals, rapid response to sudden disturbances, and continuous iterative optimization based on production execution data. Therefore, developing a multi-machine parallel processing scheduling method deeply adapted to the foamed material production workshop scenario can better match the industry's specific production characteristics, further release production capacity, and improve the precision of production management. This has significant practical application value for the intelligent upgrading of the foamed material industry. Summary of the Invention

[0005] The purpose of this invention is to provide a method for scheduling multiple machines in parallel processing in a foam material production workshop in order to solve the above-mentioned problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for scheduling parallel processing of multiple machines in a foam material production workshop, comprising: Digital modeling is performed on all production elements in the foam material production workshop to construct a digital workshop model that maps one-to-one with the physical workshop; at the same time, the orders to be produced are broken down into hierarchical production tasks that can be scheduled, and the constraints and production requirements of each production task are clarified. Based on the digital workshop model and hierarchical production tasks, multiple initial production scheduling schemes that meet core production constraints are generated by combining preset scheduling rules with heuristic calculations. The initial production scheduling schemes of each group are subjected to full-dimensional hard constraint verification, resource conflicts and timing conflicts in the schemes are identified, and conflicts are resolved and repaired according to the preset hierarchical strategy to obtain multiple groups of feasible production scheduling schemes without constraints and conflicts. Starting with multiple feasible production scheduling schemes, the algorithm employs a parallel and collaborative approach using multiple intelligent optimization algorithms to iteratively optimize the multi-objective optimization system of foaming production, generating multiple Pareto optimal production scheduling schemes. A comprehensive quantitative evaluation and visualization of multiple Pareto optimal scheduling schemes are performed. Based on the evaluation results, the final execution scheme is selected, and the final execution scheme is decomposed into hierarchical production execution instructions and issued to the corresponding production units.

[0007] Preferably, the digital modeling of all production elements in the foam material production workshop specifically involves: standardizing and digitally defining the core production equipment, tooling, logistics and transportation resources, production materials, human resources, and public works resources in the workshop, and configuring a unique identifier, static inherent attributes, real-time dynamic status, and rigid constraint boundaries for each type of resource.

[0008] Preferably, the step of breaking down the orders to be produced into hierarchical production tasks that can be scheduled specifically involves: breaking down the orders to be produced into order-level, work order-level, and process-level tasks in sequence, clarifying the process dependencies, production constraints, and priority mappings of each level of tasks, and performing pre-clustering processing on production tasks with the same mold and the same formula.

[0009] Preferably, the preset production scheduling rules include general classic production scheduling rules and customized production scheduling rules for foaming production. The customized production scheduling rules for foaming production include priority clustering rules for the same mold and same formula, priority rules for equipment and process adaptation, coordination rules for curing time, and pre-control rules for utility load. The heuristic calculation specifically involves: using a task comprehensive priority calculation model with configurable weights to quantify and sort the priorities of each production task, and based on the sorting results, completing the initial allocation of production tasks and production equipment to generate multiple sets of differentiated initial production scheduling schemes.

[0010] Preferably, the full-dimensional hard constraint verification includes equipment capacity constraints, mold resource constraints, material supply constraints, human resource constraints, utility constraints, and process timing constraints; the verification process is performed using at least one of the following methods: time axis traversal verification, constraint satisfaction problem modeling verification, and work order-by-work order full-link verification.

[0011] Preferably, the step of resolving and repairing conflicts according to a preset hierarchical strategy specifically involves: first, classifying the conflicts according to their impact on order delivery, and then repairing each level of conflict in descending order of priority; the repair process prioritizes a local repair strategy with the smallest possible adjustment range, and after each conflict repair is completed, a secondary constraint verification is performed on the adjustment range to ensure that no new conflicts are generated during the repair process.

[0012] Preferably, the parallel and collaborative method of the multiple intelligent optimization algorithms is as follows: different optimization focuses are assigned to different intelligent optimization algorithms, and each feasible scheduling scheme is used as the optimization starting point of the corresponding algorithm to start iteration synchronously; during the iteration process, a common elite solution pool is set up, and each algorithm periodically uploads the high-quality non-dominated solutions obtained from the iteration to the common elite solution pool, while extracting high-quality solutions from the common elite solution pool to optimize its own population, until the preset iteration termination condition is reached, and the final Pareto optimal scheduling scheme is output.

[0013] Preferably, the multi-objective optimization system for foam production includes core optimization objectives and auxiliary optimization objectives; the core optimization objectives include minimizing the maximum completion time, minimizing the order delay rate, minimizing the overall production cost, and maximizing the equipment load balance; the auxiliary optimization objectives include minimizing work-in-process inventory, minimizing production energy consumption, and maximizing the product qualification rate.

[0014] Preferably, the indicators for the comprehensive quantitative evaluation include delivery indicators, capacity indicators, cost indicators, and operational indicators; the visualization includes equipment scheduling Gantt charts, multi-scheme comparison radar charts, resource load dashboards, and production risk warning prompts; the hierarchical production execution instructions include equipment-level execution instructions, mold management instructions, material delivery instructions, personnel scheduling instructions, post-processing instructions, and management-level monitoring instructions.

[0015] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. By adapting to the industry-specific characteristics of foam material production, this invention constructs a digital workshop model covering all production elements, addressing the characteristics of strong dependence on foam production molds, rigid timing of core processes, and coupling constraints of multiple production resources. It achieves accurate mapping between production scheduling and physical production scenarios from the source of production scheduling, ensuring a high degree of matching between production scheduling plans and actual production.

[0016] 2. This invention addresses core industry pain points such as mold and material change losses and raw material availability management by combining customized production scheduling rules for foaming production. Furthermore, it ensures the feasibility of the production scheduling plan through a comprehensive hard constraint verification and hierarchical conflict resolution mechanism. This effectively connects the entire chain from order demand to production execution, enabling refined collaborative management of multi-machine parallel processing and ensuring the stability and controllability of the production process. Attached Figure Description

[0017] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which: Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0018] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0019] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0020] Example 1 Its specific implementation method is combined with the appendix Figure 1 Please provide a detailed explanation.

[0021] Appendix Figure 1The flowchart of a multi-machine parallel processing scheduling method in a foam material production workshop provided in this embodiment of the invention shows the complete steps from digitally modeling all production elements in the foam material production workshop to conducting full-dimensional quantitative evaluation and visualization of multiple Pareto optimal scheduling schemes.

[0022] In this embodiment, it includes: Step 1: Initialize resource and task data This step forms the digital foundation of the entire scheduling system. Its core objective is to build a digital twin model that maps 1:1 to the physical workshop, ensuring that all production scheduling actions are based on real, accurate, and comprehensive fundamental data, thus preventing a disconnect between the production plan and actual production from the outset. This step consists of two core modules: comprehensive digital modeling of resources and hierarchical task breakdown modeling.

[0023] Standardized and calculable digital definitions are used for all production elements in the foaming workshop, covering six major categories of core resources. Each category of resources has four core pieces of information: a unique identifier, static inherent attributes, real-time dynamic status, and rigid constraint boundaries, thereby achieving full-element digital management of production resources.

[0024] The first category is core production equipment resources, centered around the foaming machine, and covering the entire production process including supporting mold temperature control systems, raw material premixing systems, high-pressure / low-pressure foaming main units, curing chambers, cutting and trimming equipment, etc. In terms of static attributes, fixed parameters such as the equipment's unique code, equipment type, rated injection volume, clamping force, compatible mold size range, temperature control accuracy, rated power, design processing efficiency, maintenance cycle, and certification requirements must be entered. In terms of dynamic status, dynamic information such as equipment operating status, currently mounted mold number, current processing work order, elapsed running time, remaining maintenance window, and real-time energy consumption data must be synchronized in real time. The core rigid constraint is that a single piece of equipment can only execute one processing task at a time; the time for core processes such as injection and curing cannot be compressed; and production tasks cannot be scheduled during non-working hours or maintenance periods.

[0025] The second category is tooling and mold resources. As a core bottleneck resource in foam production, these directly determine product compatibility and production scheduling flexibility. In terms of static attributes, fixed information such as the mold's unique code, compatible product model, number of cavities, compatible foaming machine model, standard mold closing / opening time, rated curing and insulation parameters, design lifespan, and historical mold repair records must be entered. In terms of dynamic status, information such as the mold's current location, number of uses, current availability status, and estimated availability time must be synchronized in real time. The core rigid constraint is that only one mold can be mounted on one machine at a time, and production tasks must use compatible molds; molds in unqualified states cannot be included in the production schedule.

[0026] The third category is logistics transfer resources, covering in-workshop transfer equipment such as AGVs / shuttles, raw material conveying systems, and mold transfer vehicles. In terms of static attributes, fixed parameters such as unique equipment codes, rated load capacity, operating speed, transfer path, and rated turnover efficiency must be entered. In terms of dynamic status, information such as real-time equipment location, operating status, currently executing task, and idle time window must be synchronized. The core rigid constraint is that the transfer time between processes must be included in the process connection time of the production schedule to avoid process waiting timeouts.

[0027] The fourth category is material resources, covering all categories of production materials such as core foaming raw materials, foaming agents, additives, release agents, and cleaning agents, adapting to the special characteristic constraints of foaming raw materials. In terms of static attributes, fixed information such as unique material code, specifications, formula compatibility, shelf life, applicable period after mixing, standard consumption per mold, and safety stock threshold must be entered. In terms of dynamic status, information such as real-time material inventory quantity, delivery time in transit, inspection status, and remaining applicable period of premixed batches must be synchronized in real time. The core rigid constraint is that sufficient material inventory must be met before the task starts, premixed raw materials must be injected into production within their applicable period, and expired materials cannot be included in the production schedule.

[0028] The fifth category is human resources, covering key positions such as foaming machine operators, mold adjusters, quality inspectors, and material delivery personnel. In terms of static attributes, fixed information such as unique personnel codes, certifications, operable equipment range, job skill levels, standard mold change / operation efficiency, and shift schedules must be entered. In terms of dynamic status, information such as personnel on-duty status, currently responsible equipment / tasks, and idle time windows must be synchronized in real time. The core rigid constraint is that key processes must be operated by certified personnel, and there is a clear upper limit to the number of devices a single shift can oversee; overstaffing is prohibited.

[0029] The sixth category is public utility resources, which serve as the fundamental guarantee for foam production and directly determine the upper limit of parallel operation of equipment. In terms of static attributes, fixed information such as the rated maximum supply capacity of workshop electricity, steam, and compressed air, peak and off-peak electricity price periods, and supply stability parameters must be entered. In terms of dynamic status, information such as the workshop's real-time total load and remaining supply capacity for each time period must be synchronized in real time. The core rigid constraint is that the total load of all operating equipment at the same time period cannot exceed the maximum supply capacity of public utilities to avoid product scrapping due to tripping or insufficient pressure.

[0030] Customer orders are broken down from top-level requirements into executable and scheduleable process-level tasks, achieving a full-link mapping of order-work order-process, and avoiding a disconnect between production planning and order requirements.

[0031] First, the order layer information needs to be standardized. The core constraint information of customer orders must be fully entered, including the unique order code, customer level, product model and core technical indicators, total demand, delivery date, urgency level, quality acceptance standards, latest completion time, and earliest start time, so as to clarify the full constraint boundaries of the order.

[0032] Secondly, the work order layer is broken down, dividing orders into independent production work orders as the core unit of production scheduling. Each work order must have a unique code, corresponding order number, product BOM and raw material formula, standard material consumption per mold, total production cycles, compatible mold number, standard process route, standard single-piece processing time, dependencies between preceding and subsequent processes, and priority mapping of the corresponding order. Simultaneously, specific optimizations are made for the characteristics of foam production. Work orders with the same mold and formula are pre-clustered to provide a data foundation for reducing losses during mold and material changes. Work orders using premixed raw materials are batch-bound to ensure that the entire batch of production is completed within the raw material's applicable period.

[0033] Finally, the process-level task decomposition further breaks down the work order into the smallest execution unit, corresponding to the entire foaming production process, including raw material premixing, mold installation and adjustment, mold closing and locking, high-pressure injection, heat preservation and curing, mold opening and demolding, curing, trimming and quality inspection, and warehousing. The standard duration, dependencies, required resources, and constraints of each process are clearly defined to achieve precise production scheduling at the process level.

[0034] Step 2: Initial Production Scheduling Plan Generation The core objective of this step is to quickly generate multiple feasible initial production scheduling schemes that meet the core hard constraints. It does not pursue global optimization, but focuses on solving the "from 0 to 1" problem of production scheduling schemes, providing a high-quality starting point for subsequent in-depth optimization, and adapting to the large-scale, multi-task, and multi-equipment production scheduling scenarios in foaming workshops. This step is divided into two main modules: rule-driven rapid scheduling and heuristic computation-based batch scheme generation.

[0035] Based on the production pain points and management priorities of the foaming workshop, we preset general production scheduling rules and industry-customized rules. By matching these rules, we can quickly complete the initial allocation of tasks and equipment, which is the core foundation for generating the initial plan.

[0036] The general classic scheduling rules can be flexibly adapted to workshop management goals, with different rules corresponding to different production scenarios. The first-in, first-out (FIFO) rule sorts orders by their placement time, prioritizing the earliest placed orders, suitable for regular orders and steady-state production scenarios without urgent priorities; the earliest delivery date priority rule sorts orders by their latest completion time in ascending order, prioritizing the orders with the tightest delivery dates, suitable for scenarios with many urgent orders and high delivery pressure; the shortest processing time priority rule prioritizes work orders with the shortest processing time, enabling the rapid completion of small-batch orders and reducing work-in-process inventory, suitable for multi-variety, small-batch order structures; the critical ratio priority rule calculates the critical ratio using "(delivery date - current time) / remaining processing time," with a smaller value indicating higher priority, balancing delivery date and processing time, suitable for scenarios with large differences in order urgency.

[0037] Customized production scheduling rules for the foaming workshop are designed to address the core pain points of foaming production and are key to ensuring the feasibility and economy of the initial plan. The same mold and same formula priority clustering rule prioritizes work orders using the same mold and raw material formula to be continuously assigned to the same equipment, minimizing time and material loss from mold changes, material changes, and cleaning of material pipes, thus solving the core efficiency bottleneck of 1-4 hours for a single mold change and adjustment of foaming machines. The equipment-process adaptation priority rule prioritizes high-precision, high-value-added orders to high-pressure foaming machines, while assigning low-precision orders such as conventional insulation boards and fillers to low-pressure foaming machines, ensuring product quality and avoiding equipment resource mismatch. The curing time coordination rule prioritizes work orders with long curing and insulation times to be scheduled before the equipment's shift ends, ensuring the curing process is completed during off-peak hours, without occupying effective equipment working time, thus improving equipment utilization. The utility load pre-control rule avoids the simultaneous start-up of high-power equipment during initial scheduling, initially smoothing out the electricity and steam load curves and avoiding large-scale utility conflicts during subsequent feasibility checks.

[0038] For large-scale production scheduling scenarios involving dozens of foaming machines and hundreds of work orders, a heuristic algorithm is used to quickly calculate task priorities and generate multiple differentiated initial feasible solutions in batches, avoiding the limitations of a single solution. First, a configurable weighted task priority calculation model is constructed to achieve quantitative ranking of tasks. The calculation formula is as follows: ; in To ensure configurable weights, the workshop can flexibly adjust these weights according to management objectives. All dimensions are standardized, with higher values ​​indicating higher priority. Specifically, these include: satisfy The workshop can be configured using experience-based presets, analytic hierarchy process (AHP), or dynamic adaptive methods according to management objectives. Typical preset combinations include: delivery priority mode (0.5, 0.3, 0.1, 0.1), cost priority mode (0.1, 0.1, 0.6, 0.2), capacity priority mode (0.2, 0.2, 0.2, 0.4), and balanced mode (0.25, 0.25, 0.25, 0.25).

[0039] Delivery urgency = processing time / remaining delivery time (if the remaining delivery time is 0 or negative, the maximum value is taken). The larger this ratio is, the more urgent the delivery is and the higher the urgency value is. Order importance is assigned based on customer level, order profit, and strategic significance. Mold change cost savings are assessed based on the compatibility between the work order and the previous task on the equipment; shared molds / formulas that do not require mold change are assigned a high score, while those requiring mold change are assigned a low score. Equipment compatibility is the degree of matching between the work order's process requirements and the equipment's processing capacity; higher compatibility results in higher scores. Based on priority ranking, a classic parallel machine scheduling heuristic algorithm is used to allocate work orders to currently available equipment that meets core constraints in descending priority order, quickly completing initial task allocation. Simultaneously, by adjusting weight combinations and switching core rules, 3-5 sets of differentiated initial solutions are generated in batches, such as delivery-priority solutions, cost-priority solutions, capacity-priority solutions, and load-balancing-priority solutions, providing a multi-dimensional starting point for subsequent optimization.

[0040] When a workshop needs to prioritize multiple objectives simultaneously (e.g., both delivery time and cost require high priority), the analytic hierarchy process (AHP) combined with objective weight vector reconstruction is used to determine the overall priority weights. Let the objective weight vector be... In multi-objective collaborative scenarios, the weights are determined by the following formula: ; in: The basic preference coefficient for workshop management objectives is set directly by managers based on current operational priorities (such as delivery, cost, capacity, and balance). It is a task-level dynamic correction coefficient, calculated in real time based on the average delivery time tension of the current queued tasks, the difference in mold change cost, and the equipment load status.

[0041] Example of a scenario where delivery time and cost are both prioritized: - Set a basic preference coefficient: (Delivery date) (Cost), the rest is 0.2; If the current task has a high average delivery time pressure, then Upgraded to 1.2 Lower; The final generated weights are as follows .

[0042] Sorting mechanism within tasks of the same priority: When multiple tasks have the same priority on the same optimization objective, secondary feature values ​​are introduced for further ranking: When delivery dates are of the same priority, they are sorted in ascending order by the ratio of remaining delivery time to processing time, with the smaller the ratio, the more urgent the delivery. When costs have the same priority, they are ranked in ascending order of estimated mold change time plus raw material loss cost, with the smaller value having higher priority. When production capacity has the same priority, the orders are sorted in descending order by processing time × equipment compatibility, with priority given to larger and more compatible tasks.

[0043] The above-mentioned secondary feature value sorting is only activated when the primary priority objectives are completely consistent, ensuring the uniqueness and interpretability of the production scheduling decision.

[0044] Rules for quantifying order importance: Order Importance The calculation is based on a weighted average of three factors: customer level, order profit, and strategic significance, as shown in the following formula: ; The definition and assignment rules for each sub-item are as follows: Customer Level

[0045] Strategic clients: Value assigned 1.0, applicable to long-term cooperation and high-value orders; Key clients: assigned a value of 0.6, suitable for orders with stable cooperation and high potential; Regular customers: assign a value of 0.3, applicable to small, scattered orders.

[0046] Order Profit

[0047] High profit margin: Assign a value of 1.0, corresponding to a profit margin >30%; Medium profit margin: assigned a value of 0.6, corresponding to a profit margin of 10% to 30%; Low profit margin: Assign a value of 0.3, corresponding to a profit margin of <10%.

[0048] Strategic significance

[0049] Strategic new product: Valued at 1.0, used to expand into new markets; For standard products: assign a value of 0.5 to ensure stable supply; Clearance inventory products: assign a value of 0.2 to reduce inventory.

[0050] Weight The configuration can be flexibly set by the workshop management based on the current business strategy. A typical configuration example is as follows: Market expansion phase: ; Profit-oriented period: ; Stable service period: .

[0051] Step 3: Feasibility Check and Conflict Resolution This step is crucial for ensuring the production scheduling plan can be implemented. Its core objective is to identify and eliminate all conflicts in the initial plan that violate hard constraints, ensuring the plan 100% meets rigid production requirements and outputs a conflict-free, feasible production scheduling plan, avoiding a disconnect between "paper scheduling" and actual production. This step consists of two main modules: full-dimensional constraint verification and hierarchical conflict resolution and repair.

[0052] First, it's crucial to clearly distinguish between hard and soft constraints. Hard constraints are rules that absolutely cannot be violated; violating them renders the solution infeasible. Soft constraints are optimization goals that don't affect the fundamental feasibility of the solution. This step only performs a full, dimension-by-dimensional verification of hard constraints, marking all conflict points and conflict types. The core hard constraints in the foaming workshop fall into six categories: First, equipment capacity constraints: only one work order can be assigned to a single machine at a time, the task processing time must meet the minimum process requirements, and core times such as injection and curing cannot be compressed; production cannot be scheduled during equipment maintenance or off-peak hours. Second, mold resource constraints: only one mold can be assigned to one machine at a time, and work orders must use compatible and qualified molds; incompatible or unusable molds cannot be assigned. Third, material supply constraints: when a work order starts, there must be sufficient qualified inventory of the corresponding raw materials, including premixed raw materials. Injection must be completed within the applicable period to avoid situations where there is "no materials to start production"; the fourth category is human resource constraints, key processes must have certified personnel on duty, and the number of equipment scheduled for production at the same time cannot exceed the maximum number of certified personnel on duty; the fifth category is utility constraints, the total power, steam, and compressed air load of all operating equipment at the same time cannot exceed the workshop's rated maximum supply capacity; the sixth category is process sequence constraints, the dependencies between processes cannot be reversed, the preceding process must be completed before the following process can be started, and the process connection time must meet the logistics and transfer requirements. Constraint verification is performed collaboratively in three ways. The first is timeline traversal verification, which is performed minute by minute, traversing each piece of equipment and each time period in chronological order to check for overlapping task times and resource conflicts, and marking all conflict points in all time dimensions; The second approach is constraint satisfaction problem modeling and verification. This involves transforming all resources, tasks, and constraints into a mathematical model, and then using a constraint satisfaction problem solver to iterate through all variables and identify unsatisfiable constraints. The process of transforming all resources, tasks, and constraints into a mathematical model is as follows: Variables: the equipment assigned to each work order, the start time, the completion time, and the order of work orders on the same equipment; Value range: the range of legal values ​​for each variable (e.g., time from 0 to the sum of total processing time, equipment refers to all available equipment in the workshop). Constraints: Mathematical expressions are used to precisely describe equipment capacity constraints (at most one work order per piece of equipment at the same time), mold constraints, material inventory constraints, human resource quantity constraints, utility load limit constraints, and process sequence dependency constraints. After the transformation is complete, an open-source or commercial constraint solver (such as the CP-SAT module of Google OR-Tools) is called. The solver automatically traverses all variable assignment combinations through backtracking search and constraint propagation, and determines whether there is a feasible solution that satisfies all constraints at the same time. If the constraint does not exist, the solver will return the conflicting constraint for subsequent conflict resolution.

[0053] The third method is work order-by-work order full-chain verification. For each work order, the constraint satisfaction is checked from all dimensions, including raw materials, molds, equipment, personnel, and processes, and conflict items in each work order are marked.

[0054] For conflicts identified during verification, conflict repair is performed in a tiered and categorized manner according to the principles of "local first, then global; high priority first, then low priority; repair first, then adjust." A second verification is required after each repair to ensure no new conflicts arise, ultimately outputting a fully feasible production schedule. First, conflicts are categorized based on their impact on order delivery: critical conflicts, severe conflicts, and minor conflicts. Critical conflicts are repaired first. Critical conflicts directly cause order delays, severe conflicts affect the use of core resources, and minor conflicts only affect specific processes. The repair process follows a local priority principle, prioritizing repair strategies with minimal adjustments. Only the work orders and equipment affected by the conflict are adjusted, without altering other feasible production schedules, ensuring the stability of the plan. After each conflict repair, a second constraint verification is immediately performed on the adjustment scope to ensure no new conflicts are generated. After all conflicts are repaired, 3-5 feasible production schedules without hard constraint conflicts are output, proceeding to the next optimization stage. For different types of conflicts, corresponding foaming workshop-specific repair strategies are matched. To address equipment time conflicts, i.e., scenarios where multiple work orders are assigned to the same equipment at the same time and task times overlap, three remediation methods can be adopted. The first is task diversion, which diverts low-priority work orders to parallel equipment of the same model, compatibility, and availability. The second is staggered scheduling, which adjusts the start time of low-priority work orders to stagger production without violating delivery deadlines. The third is work order splitting, which splits large batches of work orders into multiple sub-work orders and diverts them to multiple machines for parallel production to avoid time conflicts.

[0055] For mold resource conflicts—scenarios where the same mold is assigned to multiple work orders or equipment at the same time—three remedial methods can be adopted: First, replacement with a spare mold: directly call a qualified spare mold of the same specification and assign it to the conflicting work order. Second, time-sequencing: prioritize work orders sharing the same mold to avoid time overlap. Third, work order diversion: transfer the work order to equipment corresponding to other compatible molds. For material supply conflicts—scenarios where the work order start time is earlier than the raw material arrival / inspection time and inventory is insufficient—three remedial methods can be adopted: First, adjusting the start time: postpone the work order until after the raw material availability time, and simultaneously verify the impact on delivery dates. Second, batch production: complete part of the production using existing inventory, and supplement the remaining production after the raw materials arrive. Third, cross-warehouse transfer: urgently transfer qualified raw materials of the same specification to meet production needs.

[0056] To address the conflict of utility loads, i.e., the scenario where the total load exceeds the workshop's rated supply limit at the same time, three repair methods can be adopted. The first is staggered production scheduling, which involves staggering the start times of high-energy-consuming injection and mold heating processes by 15-30 minutes to flatten the load curve. The second is priority guarantee, which prioritizes the supply of utility work for high-priority work orders and staggers the production of low-priority work orders. The third is parameter optimization, which involves slowing down the mold heating rate within the allowable range of the process to reduce the instantaneous peak load.

[0057] To address human resource conflicts, where the number of production equipment exceeds the maximum number of certified personnel on duty, three remedial methods can be adopted. The first is shift adjustment, where work orders are rescheduled to daytime shifts with sufficient personnel. The second is priority screening, prioritizing the allocation of personnel for high-priority work orders and postponing the scheduling of low-priority work orders. The third is job coordination, where certified auxiliary personnel are reassigned to supplement core operation positions.

[0058] Step 4: Multi-algorithm fusion optimization This step is the core of improving the quality and efficiency of the scheduling scheme. The core objective is to find the Pareto optimal solution set that takes into account multiple conflicting objectives by using multi-intelligent algorithm collaboration and multi-objective comprehensive optimization on the basis of feasible solutions, thereby solving the problem of production scheduling schemes "from feasible to high-quality" and adapting to the scheduling pain points of multi-objective conflicts in the foaming workshop.

[0059] Parallel scheduling in a foaming workshop is a typical multi-objective optimization problem, with multiple core objectives conflicting with each other. For example, the shortest completion time and the lowest mold change cost, as well as the highest delivery rate and optimal equipment load balancing, are mutually exclusive. Therefore, this step first clarifies the quantitative optimization objective system, which is divided into core optimization objectives and auxiliary optimization objectives. The core optimization objectives include four categories. The first category is minimizing the maximum completion time, that is, minimizing the total time for all parallel equipment to complete all work orders, thereby maximizing the overall capacity of the workshop. The second category is to minimize the order delay rate, that is, to maximize the proportion of on-time delivered orders, minimize the number of delayed orders and the delay time, and ensure customer satisfaction. The third category is minimizing overall production costs, with a focus on reducing costs associated with mold and material changes, raw material losses, and energy consumption. This is the core of cost control in the foaming workshop. The fourth category is to maximize the load balance of the equipment, that is, to minimize the difference in load rate among the foaming machines, to avoid some equipment being overloaded and others being idle, to extend the service life of the equipment and reduce the risk of failure.

[0060] The auxiliary optimization objectives include three categories. The first category is to minimize work-in-process inventory, reduce waiting time between processes, and reduce work-in-process backlog. The second category is to minimize production energy consumption, reduce peak load by staggering electricity use, and reduce energy consumption. The third category is to maximize product qualification rate, reduce trial mold scrap caused by frequent production changes by stabilizing continuous production scheduling, and improve product yield.

[0061] Single intelligent optimization algorithms have inherent limitations. For example, genetic algorithms are strong in global optimization but weak in local search, simulated annealing is strong in local optimization but slow in convergence, and particle swarm optimization converges quickly but is prone to getting trapped in local optima. Therefore, this step adopts a multi-algorithm fusion architecture of "parallel iteration + elite sharing + complementary division of labor" to leverage the strengths of each algorithm and achieve global optimization. First, parallel initialization and division of labor are performed. The multiple feasible solutions output from step three are used as the initial solutions or initial populations of different algorithms, and iteration is started simultaneously. Based on the characteristics of bubble scheduling, different optimization focuses are assigned to different algorithms to achieve precise division of labor. The genetic algorithm is responsible for global optimization, focusing on the global allocation of work orders and equipment, and the overall timing optimization of processes. Its core optimization targets include global objectives such as maximum completion time and order delay rate. The simulated annealing algorithm is responsible for local deep optimization, focusing on the work order sorting optimization on a single machine. Its core optimization targets include local objectives such as mold change frequency and material change cost, adapting to the optimization needs of single-machine work order sorting. The particle swarm optimization algorithm is responsible for rapid convergence optimization, focusing on equipment load balancing and utility energy consumption optimization, quickly flattening the load curve, and achieving peak-shifting cost reduction. The tabu search algorithm is responsible for avoiding local optima, recording the searched inferior solution space, avoiding repeated searches by the algorithm, and improving the overall optimization efficiency.

[0062] An elite solution sharing mechanism is implemented during the iteration process. First, a public elite solution pool is constructed to store high-quality non-dominated solutions found by each algorithm during iteration. After a fixed number of iterations, each algorithm uploads its current optimal solution and elite solutions to the public pool. Each algorithm then extracts high-quality solutions from the elite pool to replace inferior solutions in its own population, enabling information exchange between algorithms. This improves convergence speed and avoids getting trapped in local optima. The iteration terminates when the optimal solution in the elite pool shows no significant improvement for several consecutive iterations, or when the preset maximum number of iterations or computation time is reached. At this point, iteration stops, and the final Pareto optimal solution set is output from the elite pool.

[0063] Multi-objective optimization does not have an absolutely unique optimal solution; only Pareto non-dominated solutions exist, meaning these solutions are not inferior to other solutions across all optimization objectives. This step standardizes the solution set. First, the solution set is categorized. For Pareto optimal solutions, they are classified according to their optimization focus, generating differentiated high-quality solutions, such as optimal delivery time, optimal cost, optimal capacity, and a comprehensive equilibrium solution. The optimal delivery time solution achieves a 0% order delay rate, the optimal cost solution minimizes mold changes, the optimal capacity solution minimizes completion time, and the comprehensive equilibrium solution achieves above-average performance across all objectives. Second, weight preference adaptation is supported. The workshop can assign weights to different optimization objectives based on current production and operational goals. A weighted summation method is then used to generate a recommended optimal solution that aligns with management preferences. For example, when pushing for sales targets at the end of the month, higher weight is given to delivery time and production capacity targets; during the off-season, higher weight is given to cost and equipment load.

[0064] Simultaneously, specific optimizations were implemented to address the characteristics of foam production. The optimization focused on three core areas: first, optimizing mold change costs, achieved through continuous clustering of work orders, including the following steps: Cluster labeling: During the task decomposition phase, work orders that use the same tools and the same raw material formula are labeled as the same "continuous cluster family"; Continuous scheduling constraint: During the scheduling and optimization process, work orders of the same family are forced to be processed continuously on the same machine, and work orders of different families are not inserted in between. Mold change downgrade: Adjacent work orders within the same family only perform a "quick transition process" (mold is not disassembled or cooled, and the material pipe is only quickly flushed or the material is not changed), which takes 5-15 minutes; while work orders from different families or before the start of the first work order of a family perform a complete mold change (including mold disassembly, installation, preheating, trial molding, etc.), which takes 1-4 hours. Quantitative Analysis: Taking 5 work orders from the same cluster as an example, decentralized scheduling requires 5 complete mold changes (totaling approximately 900 minutes). After continuous clustering, only 1 complete mold change + 4 quick transitions are needed (totaling approximately 220 minutes), reducing the total mold change time by approximately 75%. The average time for a single mold change is reduced from hours (approximately 3 hours) to minutes (approximately 44 minutes). The larger the cluster size, the more significant the effect. In extreme cases, a single quick transition can be as low as 5 minutes, completely achieving the goal of "reducing the time from hours to minutes." Secondly, we optimize raw material loss by ensuring continuous production of work orders for the same premixed batch and completing all injections within the applicable period of the raw materials to avoid them expiring and becoming unusable. Thirdly, we optimize equipment utilization by coordinating the curing and insulation process with non-working hours to maximize equipment time and reduce the occupation of effective working time.

[0065] Step 5: Production Scheduling Plan Decision and Output This step is the final stage of implementing the scheduling plan. The core objective is to transform the optimized optimal solution set into production instructions that managers can make decisions on and workshops can execute, thus realizing the implementation from digital solutions to physical production. It is divided into two main modules: quantitative evaluation of multiple solutions and visual decision support, and solution locking and execution instruction issuance.

[0066] This system provides managers with a comprehensive and visualized solution comparison framework, lowering the decision-making threshold and ensuring that the final solution matches the workshop's current production and operational goals. First, it conducts a comprehensive KPI quantitative evaluation, generating standardized KPI reports for each optimal Pareto solution, covering four core dimensions: Delivery KPIs include on-time order delivery rate, average order lead time, maximum delay time, and number of delayed orders; Capacity KPIs include maximum completion time, overall workshop equipment efficiency, effective utilization rate of a single foaming machine, and mold turnover rate; Cost KPIs include total mold changeovers, total mold changeover time, raw material loss rate, unit product energy consumption, and total labor cost; Operational KPIs include equipment load balancing rate, work-in-process inventory, peak utility load, and production anomaly risk coefficient. Second, through multi-dimensional visualization, it adapts to the foaming workshop management scenario, intuitively presenting the advantages and disadvantages of solutions and assisting managers in making quick decisions. The equipment scheduling Gantt chart uses time as the horizontal axis and each foaming machine or piece of equipment as the vertical axis. It distinguishes work orders by color blocks, labeling work order numbers, product models, mold numbers, and processing times. Different colors differentiate order priorities, and users can click to view full work order information. The multi-solution comparison radar chart standardizes the core KPIs of each solution, visually showcasing their advantages and disadvantages, helping managers quickly identify the optimal solution for current objectives. The resource load dashboard displays real-time equipment load rates, mold occupancy, material inventory consumption, and utility load curves, intuitively identifying production bottlenecks and idle resources. Risk warning alerts highlight potential risks within the solutions. For example, if the interval between work order commencement and raw material arrival is too short, or if equipment operates continuously without a maintenance window, this provides a risk reference for management decision-making. After completing the solution evaluation, managers or planners can directly select the optimal solution recommended by the system based on current production targets, or they can compare multiple solutions and make their own selection. Simultaneously, the system supports manual fine-tuning of the selected solution, such as advancing important customer orders, postponing low-priority work orders, and adjusting equipment allocation. After fine-tuning, the system automatically triggers constraint checks to ensure that the adjusted solution still meets all hard constraints, avoiding conflicts caused by manual adjustments.

[0067] Once the final plan is confirmed, the system locks in the plan and breaks down the overall production schedule into executable instructions for each level and department. These instructions are then distributed throughout the entire process via the workshop information system, achieving closed-loop management. First, the core elements of the plan are locked in: the time windows for high-priority work orders, equipment allocation, and mold configurations to avoid arbitrary adjustments; the sequence of key processes to ensure production continuity; and critical nodes for material delivery and mold installation to prevent delays in preparation. Second, hierarchical instructions are decomposed and distributed, breaking down the overall production schedule into six categories of execution instructions. These instructions are then precisely distributed to the corresponding departments, teams, personnel, and equipment through the MES system, workshop digital dashboards, equipment HMI interfaces, and handheld terminals. The first type is equipment-level execution instructions, issued to the HMI interface of each foaming machine, specifying the processing sequence of the work orders for the shift or day, the process parameters for each work order, the start and completion times, the corresponding operators, and the quality inspection requirements. The second type is mold management instructions, issued to the mold workshop, specifying the time nodes for the requisition, installation, adjustment, and return of each mold, requiring trial molding and inspection to be completed in advance to ensure the molds are ready before the work order starts. The third type is material delivery instructions, issued to the warehousing and materials departments, specifying the material requirements, delivery time, and delivery location for each work order, requiring the original material delivery to be completed in advance. The first category is material inspection and premixing to ensure that materials are in place before the work order starts; the second category is personnel scheduling instructions, which are issued to production teams to clarify the job responsibilities, equipment, and tasks for each shift, ensuring that certified personnel are on duty for key processes; the third category is post-processing instructions, which are issued to curing, trimming, and quality inspection teams to clarify the post-processing requirements and time nodes for each work order, closely linking with the preceding foaming process to reduce work-in-process waiting; the sixth category is management-level monitoring instructions, which are synchronized to the workshop management dashboard to display production plans, progress requirements, and key nodes in real time, achieving transparent management of the entire workshop.

[0068] Finally, a closed loop for receiving and confirming instructions is established. Each receiving department, personnel, and equipment must confirm the receipt of the issued instructions. If there are any problems, such as equipment failure or insufficient materials, they must be reported to the planner immediately. The planner can then make quick adjustments through the online rescheduling mechanism, forming a complete closed loop of "issuance-confirmation-feedback-adjustment".

[0069] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0070] It should be noted that, in this document, the use of relational terms such as "first" and "second" is merely for distinguishing one entity or operation from another, and does not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0071] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0072] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0073] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for scheduling parallel processing of multiple machines in a foamed material production workshop, characterized in that, include: Digital modeling is performed on all production elements in the foam material production workshop to construct a digital workshop model that maps one-to-one with the physical workshop; at the same time, the orders to be produced are broken down into hierarchical production tasks that can be scheduled, and the constraints and production requirements of each production task are clarified. Based on the digital workshop model and hierarchical production tasks, multiple initial production scheduling schemes that meet core production constraints are generated by combining preset scheduling rules with heuristic calculations. The initial production scheduling schemes of each group are subjected to full-dimensional hard constraint verification, resource conflicts and timing conflicts in the schemes are identified, and conflicts are resolved and repaired according to the preset hierarchical strategy to obtain multiple groups of feasible production scheduling schemes without constraints and conflicts. Starting with multiple feasible production scheduling schemes, the algorithm employs a parallel and collaborative approach using multiple intelligent optimization algorithms to iteratively optimize the multi-objective optimization system of foaming production, generating multiple Pareto optimal production scheduling schemes. A comprehensive quantitative evaluation and visualization of multiple Pareto optimal scheduling schemes are performed. Based on the evaluation results, the final execution scheme is selected, and the final execution scheme is decomposed into hierarchical production execution instructions and issued to the corresponding production units.

2. The method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, Digital modeling is carried out for all production elements in the foam material production workshop. Specifically, the core production equipment, tooling, logistics and transportation resources, production materials, human resources, and public works resources in the workshop are defined in a standardized digital manner, and each type of resource is assigned a unique identifier, static inherent attributes, real-time dynamic status, and rigid constraint boundaries.

3. The method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, The production orders are broken down into hierarchical production tasks that can be scheduled. Specifically, the production orders are broken down into order level, work order level and process level tasks in sequence. The process dependencies, production constraints and priority mappings of each level of tasks are clarified. At the same time, production tasks with the same mold and the same formula are pre-clustered.

4. The method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, The preset production scheduling rules include general classic production scheduling rules and customized production scheduling rules for foam production. The customized production scheduling rules for foam production include priority clustering rules for the same mold and same formula, priority rules for equipment and process adaptation, coordination rules for curing time, and pre-control rules for utility load. The heuristic calculation specifically involves: using a task comprehensive priority calculation model with configurable weights to quantify and sort the priorities of each production task, and based on the sorting results, completing the initial allocation of production tasks and production equipment to generate multiple sets of differentiated initial production scheduling schemes.

5. The method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, Full-dimensional hard constraint verification includes constraints on equipment capacity, mold resources, material supply, human resources, utilities, and process timing. The verification process is performed using at least one of the following methods: timeline traversal verification, constraint satisfaction problem modeling verification, and work order-by-work order full-link verification.

6. The method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, The conflict is resolved and repaired according to the preset hierarchical strategy. Specifically, the conflict is first classified according to its impact on order delivery, and the conflict at each level is repaired in order of priority from high to low. The repair process prioritizes the local repair strategy of the smallest scope adjustment. After each conflict repair is completed, the adjustment scope is checked twice to ensure that no new conflict is generated during the repair process.

7. The method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, The parallel and collaborative approach of multiple intelligent optimization algorithms is as follows: different optimization focuses are assigned to different intelligent optimization algorithms, and each feasible scheduling scheme is used as the optimization starting point of the corresponding algorithm to start iteration synchronously; during the iteration process, a common elite solution pool is set up, and each algorithm periodically uploads the high-quality non-dominated solutions obtained from the iteration to the common elite solution pool, while extracting high-quality solutions from the common elite solution pool to optimize its own population, until the preset iteration termination condition is reached, and the final Pareto optimal scheduling scheme is output.

8. The method for scheduling multiple machines in parallel processing in a foamed material production workshop according to claim 1, characterized in that, The multi-objective optimization system for foam production includes core optimization objectives and auxiliary optimization objectives. The core optimization objectives include minimizing the maximum completion time, minimizing the order delay rate, minimizing the overall production cost, and maximizing the equipment load balance. The auxiliary optimization objectives include minimizing work-in-process inventory, minimizing production energy consumption, and maximizing the product qualification rate.

9. A method for scheduling parallel processing of multiple machines in a foamed material production workshop according to claim 1, characterized in that, The comprehensive quantitative evaluation indicators include delivery indicators, capacity indicators, cost indicators, and operational indicators; the visualization displays include equipment scheduling Gantt charts, multi-scheme comparison radar charts, resource load dashboards, and production risk warning prompts. The hierarchical production execution instructions include equipment-level execution instructions, mold management instructions, material distribution instructions, personnel scheduling instructions, post-processing instructions, and management-level monitoring instructions.

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