A method and system for optimizing production scheduling of a packaging print job

Abstract

This invention discloses a production scheduling optimization method and system for packaging and printing operations, relating to the field of packaging and printing production scheduling technology. The invention collects task data, materials, ink color sequence, number of printing colors, and equipment parameters to generate a task set. It calculates the multi-dimensional coupling degree between tasks to construct a directed task coupling graph and establishes a nonlinear function for sequence-dependent preparation time based on historical data. Based on the coupling relationship, the invention groups tasks into process groups and assigns them to suitable printing presses. It employs inter-group sorting and intra-group double-ended insertion sorting to achieve joint scheduling optimization. The function parameters are corrected online, and the optimization effect is verified, outputting the final scheduling scheme. This effectively solves the problems of frequent ink changes and cleaning, long preparation time, uneven equipment load, and easy delivery delays in parallel multi-color printing presses. It significantly reduces the time spent on ink changes and equipment cleaning, improving production efficiency, equipment utilization, and order delivery timeliness.

Description

Technical Field

[0001] This invention relates to the field of packaging and printing production scheduling technology, specifically to a method and system for optimizing production scheduling in packaging and printing operations. Background Technology

[0002] In the packaging and printing industry, multicolor printing presses typically operate in parallel clusters. Faced with a diverse range of small-batch orders, the equipment frequently switches between different jobs. During these switches, operations such as ink roller cleaning, ink replacement, and paper feeding system adjustments are required based on the substrate materials of adjacent tasks (e.g., paper, film type and specifications), ink color sequence (arrangement of colors in each color group), and the number of printing colors (actual number of color groups used). This results in sequence-dependent setup time. This time directly impacts equipment utilization and on-time delivery rates, making it crucial for scheduling optimization.

[0003] Most existing scheduling methods simplify preparation time to a fixed value independent of sequence, or estimate it linearly based solely on color type differences. A few studies have considered color sequence similarity, but failed to reveal the coupling relationship between printing material, ink color sequence, and the number of printing colors. In actual production, material changes not only cause paper feeding system cleaning but may also force deep cleaning due to changes in ink adhesion characteristics. When switching color sequences, the cleaning burden of non-shared ink path colors and the number of non-overlapping color groups increase nonlinearly in a step-like manner. At the same time, the difference in the number of colors determines the number of units participating in cleaning and overlaps with the material and color sequence, resulting in preparation time exhibiting a complex nonlinear function between task sequences. Due to the lack of accurate modeling of this nonlinear coupling, existing grouping and sorting strategies often cause unnecessary multiple rounds of cleaning and excessively long ink change times, making it difficult to minimize the cumulative time of ink change and equipment cleaning globally.

[0004] To address the aforementioned shortcomings, a technical solution is provided. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of frequent ink changes and cleaning, long preparation time, uneven equipment load and easy delays in delivery of parallel multicolor printing presses, and to propose a production scheduling optimization method and system for packaging and printing operations.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A production scheduling optimization method for packaging and printing operations includes:

[0008] S1: By acquiring the task information, printing material parameters, ink color sequence parameters, printing color number parameters, and equipment capability parameters of the parallel multicolor printing press for the packaging and printing tasks to be scheduled, a set of tasks to be scheduled is generated.

[0009] S2: Calculate the coupling degree of any two tasks to be scheduled in the dimensions of printing material, ink color sequence, and number of printing colors, and construct a directed task coupling graph;

[0010] S3: Based on the directed task coupling graph, construct a nonlinear function for the preparation time of the sequence dependency between adjacent tasks;

[0011] S4: Based on the directed task coupling graph, the tasks to be scheduled are grouped into process coupling groups so that the ink inheritance and printing material transition compatibility between tasks in the same group are higher than the preset grouping threshold.

[0012] S5: Based on the task grouping results, each task group is assigned to the corresponding parallel multicolor printing press, and the grouping order and task order within each group on each parallel multicolor printing press are jointly optimized.

[0013] S6: The optimized scheduling scheme is sent to the production execution unit. During the production process, the actual ink change time and actual equipment cleaning time are collected, and the parameters of the nonlinear function of the sequence-dependent preparation time are corrected online.

[0014] S7: Verify the optimized scheduling scheme. When the cumulative ink replacement time and cumulative equipment cleaning time meet the preset optimization conditions, output the final production scheduling scheme.

[0015] Furthermore, the specific operation steps of S2 include:

[0016] Based on the set of tasks to be scheduled, the degree of coupling between any two tasks to be scheduled is calculated in terms of printing material, ink color sequence, and number of printing colors, and a directed task coupling graph is constructed.

[0017] Material coupling degree is calculated based on the type of printing material, normalized basis weight, surface energy, ink absorption rate and paper feed direction; color sequence coupling degree is calculated based on ink color code alignment and color group position attenuation coefficient; color number coupling degree is calculated by combining the increase or decrease of printing color number and subtractive cleaning coefficient.

[0018] An ink brightness crossing penalty term is introduced, and the material coupling degree, color sequence coupling degree, color number coupling degree, and interaction coefficient are integrated to obtain the comprehensive coupling degree through the Sigmoid function; at the same time, the residual ink risk value of ink switching is calculated;

[0019] Based on the comprehensive coupling degree and preset threshold, directed edges are marked as directly inheritable edges, local ink replacement edges, or strong cleaning edges, and the edge classification identifier, comprehensive coupling degree, and residual ink risk value are written into the directed task coupling graph.

[0020] Furthermore, the specific operation steps of S2 also include:

[0021] When constructing the directed task coupling graph, the ink color sequence coupling degree is based on the maximum number of color groups in the printing press. The task ink color sequence is aligned with the position of the color group, and the ink color code is compared group by group. If the codes are the same and not empty, they are counted as inheritable. The inheritance weight of the earlier color group is higher than that of the later color group.

[0022] The printing color coupling degree distinguishes between two switching scenarios: color increase and color decrease between tasks. Color increase is included in the ink consumption time for plate mounting, and color decrease is included in the time consumption for cleaning empty ink paths.

[0023] The overall coupling degree is limited to between 0 and 1 using the Sigmoid function. At the same time, the residual ink risk value is obtained by summing the washability difficulty of each color group ink switching. The washing difficulty is obtained based on the preset ink switching washing difficulty matrix.

[0024] When the overall coupling degree is higher than the first preset threshold, it is marked as a directly inheritable edge; when it is lower than the second preset threshold, it is marked as a strong cleaning edge; when it is between the first preset threshold and the second preset threshold, it is marked as a local ink replacement edge, and the first preset threshold is greater than the second preset threshold.

[0025] Furthermore, the specific operation steps of S3 are as follows:

[0026] Extract adjacent task switching samples from historical production records, including the previous task number, the next task number, the printing press number, the actual ink change time, the actual equipment cleaning time, the cleaning level, and the abnormal shutdown marker.

[0027] Remove samples containing downtime due to non-process reasons, and retain machine difference labels for samples of the same task pair switching on different printing presses;

[0028] Based on the comprehensive coupling degree and residual ink risk value, a nonlinear function for the sequence-dependent preparation time of task switching is established for each parallel multicolor printing press.

[0029] Based on the preparation time of adjacent tasks on all parallel multicolor printing presses, a joint optimization objective function is constructed, which includes adjacency indicator variables, load balancing weights, and delivery penalty weights.

[0030] Furthermore, the specific operation steps of S4 are as follows:

[0031] Traverse the nodes of tasks to be scheduled, count the number of directly inheritable edges, and filter the tasks whose number of directly inheritable edges meets the preset condition and whose equipment can process masks that can be matched with multiple parallel multi-color printing machines as group seed tasks.

[0032] Candidate tasks are expanded outward from the seed tasks of each group, and candidate tasks that can be directly inherited or have local ink change edges with the tasks within the group are absorbed. The distribution of ink color code is statistically analyzed simultaneously to construct a common color sequence skeleton corresponding to the group.

[0033] For any two candidate tasks to be merged, grouping and merging scores are performed based on comprehensive coupling degree, common color sequence skeleton conflict and delivery window conflict.

[0034] When the group merge score is higher than the preset threshold and meets the constraints of maximum number of color groups, maximum width, compatibility of printing materials, and delivery window, the merge is executed.

[0035] Virtual cleaning partitions are inserted between groups where there is a strong cleaning edge and the risk of residual ink cannot be eliminated, thus fixing the full-width cleaning at the group boundary;

[0036] After grouping, the candidate parallel multicolor printing presses are assigned based on the mask that the equipment can process, with priority given to the parallel multicolor printing press that can maintain the common color sequence skeleton and has a better historical cleaning time.

[0037] Furthermore, the specific operation steps of S5 are as follows:

[0038] Each task group is assigned to the corresponding parallel multi-color printing press. The first criterion is to minimize the sequence dependency preparation time from the tail task of the group to the first task of the next group, and the second criterion is to maximize the number of common color order skeletons. This completes the sorting of groups on each printing press.

[0039] Within each group, a double-ended insertion sorting strategy is adopted. The task with the lowest residual ink risk value and the highest matching degree with the common color order skeleton is selected as the initial task. Then, the remaining unsorted tasks are inserted from the head and tail of the sequence respectively.

[0040] Calculate the look-ahead insertion increment of the candidate task at each possible insertion position, select the position with the smallest look-ahead insertion increment as the optimal insertion position, and if the increments are the same, prioritize the arrangement method that reduces the number of transitions from dark ink to light ink.

[0041] Furthermore, the specific operation steps of S6 are as follows:

[0042] In actual production, the actual ink change time and actual equipment cleaning time of each parallel multicolor printing press during the switching between adjacent tasks are collected in real time, and the corresponding on-site working condition data are recorded simultaneously.

[0043] The actual preparation time data collected on-site is compared in real time with the predicted preparation time output by the sequence-dependent preparation time nonlinear function of S3, and the deviation between the actual value and the function prediction value is calculated.

[0044] When the deviation exceeds the preset deviation threshold, the online correction mechanism for function parameters is activated, and the model parameters of the sequence-dependent preparation time nonlinear function are iteratively updated using a restricted step size gradient descent method.

[0045] Furthermore, the specific operation steps of S7 are as follows:

[0046] Based on the results of task grouping, printing press allocation, grouping and sorting and in-machine task sorting, the adjacent task switching process of each printing press is traversed, the cumulative time of global ink replacement and equipment cleaning is calculated, and the data is compared with the corresponding data of the benchmark scheduling scheme to calculate the optimization improvement rate.

[0047] Simultaneously calculate the evaluation values ​​of auxiliary indicators for equipment load balancing and task delivery delay;

[0048] The scheduling scheme is validated based on the optimization improvement rate, auxiliary indicator evaluation values, and constraints.

[0049] If the optimization conditions and constraints are met, the scheduling scheme is deemed to have passed verification, and the task grouping, equipment allocation, sorting results, and virtual cleaning baffle positions are locked.

[0050] If the optimization conditions or constraints are not met, return to correct the nonlinear function parameters of the sequence dependency preparation time, and iterate through S4 to S7 again until the optimization conditions and constraints are met.

[0051] The optimal scheduling plan is output synchronously and sent to the production execution unit as the basis for printing press production scheduling, ink changing and cleaning control.

[0052] A second aspect of the present invention provides a production scheduling optimization system for packaging and printing operations, comprising:

[0053] Production data acquisition and processing module: Acquires task, printing material, ink color sequence, number of printing colors and printing machine equipment parameters, generates task set and equipment processable mask, uniformly encodes ink information and generates task process fingerprint;

[0054] Task Coupling Analysis Module: Calculates the multi-dimensional coupling degree between tasks, constructs a directed task coupling graph, marks edge types, and calculates the comprehensive coupling degree and residual ink risk value;

[0055] The scheduling optimization calculation module constructs a sequence-dependent preparation time nonlinear function based on the directed task coupling graph, and fits the function parameters by combining historical ink change and cleaning data to complete task process grouping, equipment allocation, inter-group sorting and intra-group double-ended insertion sorting to form a scheduling scheme.

[0056] Online correction and verification output module: Collects actual production data to calibrate function parameters, verifies the optimization improvement rate and constraint compliance, outputs the final scheduling plan and sends it out for execution.

[0057] Compared with the prior art, the beneficial effects of the present invention are:

[0058] This invention collects parameters such as packaging printing tasks, substrate materials, ink color sequence, number of printing colors, and equipment capabilities to construct a multi-dimensional task coupling relationship and a directed task coupling graph. It establishes a nonlinear function for sequence-dependent preparation time to predict ink change and cleaning times. Tasks are grouped and equipment allocated according to process coupling. Scheduling is jointly optimized using inter-group optimization sorting and intra-group double-ended insertion sorting. Through online correction of function parameters and closed-loop iteration to verify optimization effects, this invention significantly reduces ink change and equipment cleaning times for parallel multi-color printing presses, minimizing the risk of residual ink contamination and unnecessary downtime. Simultaneously, it balances equipment load, ensures order delivery dates, and significantly improves the automation scheduling level and process continuity of packaging printing production. This increases overall equipment utilization and production efficiency, reduces production changeover costs, and enhances overall workshop production control capabilities and order delivery stability. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Example:

[0062] like Figure 1 As shown, a production scheduling optimization method for packaging and printing operations includes:

[0063] S1: The production scheduling data processing unit obtains the task information, substrate parameters, ink color sequence parameters, printing color number parameters, and equipment capability parameters of the parallel multicolor printing press for the packaging and printing tasks to be scheduled, and generates a set of tasks to be scheduled. The specific implementation process is as follows:

[0064] The production scheduling data processing unit obtains basic data for packaging and printing tasks to be scheduled from the enterprise resource planning unit, production execution unit, prepress unit, and color management unit, including:

[0065] Printing material parameters include: type of printing material, material thickness, basis weight, width, surface energy, surface roughness, ink absorption rate, moisture content, and paper feed direction;

[0066] Ink color sequence parameters: including ink color codes, spot color identification, ink system, ink brightness level, and ink drying method for each printing color group;

[0067] Printing color parameters: including the actual number of printing color groups used in the task, the location of empty color groups, and whether there are reverse white, varnishing or spot color overprinting processes.

[0068] Color information from different sources is uniformly encoded, and standard four-color inks, spot colors, and functional inks are mapped to unified ink color codes respectively, with unused color group positions filled with empty ink markers; the unified ink color code adopts a segmented composite encoding rule;

[0069] A task process fingerprint is generated based on the printing material parameters, ink color sequence parameters, and printing color number parameters of each task to be scheduled.

[0070] Based on the maximum number of color groups, printable width, supported substrate types, and ink system compatibility of each parallel multicolor printing press, a device processing mask is generated between the task and the parallel multicolor printing press to exclude scheduling combinations that do not meet the device capability constraints.

[0071] S2: Based on the printing material parameters, ink color sequence parameters, and printing color number parameters, calculate the coupling degree between any two tasks to be scheduled in the dimensions of printing material, ink color sequence, and printing color number, and construct a directed task coupling graph. The specific implementation process is as follows:

[0072] Select any two tasks from the set of tasks to be scheduled, and denote them as tasks. and tasks And obtain the corresponding substrate parameters, ink color sequence parameters and printing color number parameters respectively;

[0073] Regarding the printing substrate dimension, based on the substrate type, normalized basis weight, surface energy, ink absorption rate, and paper feed direction, the formula is used... The task is obtained by calculation. To the mission The material coupling degree, where Represents an exponential function. This indicates a conditional indicator function. If the condition within the parentheses is true, the function evaluates to 1; otherwise, it evaluates to 0. Representing tasks and tasks The types of printing materials, Representing tasks and tasks Normalized weight, Representing tasks and tasks Normalized surface energy, Representing tasks and tasks Normalized ink absorption rate, Representing tasks and tasks The direction of paper movement. These represent the preset weighting coefficients for the type of printing material, basis weight, surface energy, ink absorption rate, and paper feed direction, respectively.

[0074] Regarding the ink color sequence dimension, the task and tasks The ink color sequence is aligned according to the color group position of the parallel multicolor printing press, from the first color group to the maximum number of color groups. Compare them one by one;

[0075] If two tasks have the same ink color code and neither is an empty ink identifier, the ink at the current color group position can be directly inherited; if at least one task uses ink at the current position, it is included in the base for color order comparison.

[0076] Through formula The task is obtained by calculation. To the mission Color sequence coupling The value ranges from 0 to 1; among them, This represents the color group position attenuation coefficient, used to ensure that the inheritance weight of earlier color groups is greater than that of later color groups. Indicates the color group position attenuation coefficient of The power is used to assign differentiated contribution weights to each color group position when calculating the color order coupling degree. Indicates task In the Uniform ink color code for each color group position Indicates task In the Uniform ink color code for each color group position;

[0077] If the formula for calculating color sequence coupling degree includes: ,but ;

[0078] The higher the color sequence coupling value, the greater the proportion of ink shared by the two tasks in the same color group position, and the smaller the ink replacement requirement.

[0079] Regarding the dimension of printing color number, when the task Switch to task At that time, if This indicates that more color groups need to be used, which will increase the time spent on plate mounting, inking, and other operations; if If there are excess color sets that need to be left idle and cleaned, the additional workload and time consumed by cleaning the idle ink paths when reducing from multiple color tasks to fewer color tasks; among them, Representing tasks With the task The number of printing colors;

[0080] Through formula The task is obtained by calculation. To the mission The chromatic coupling degree, where, Represents the maximum value function. Indicates the predicted subtractive washing coefficient;

[0081] After calculating the material coupling degree, color order coupling degree, and color number coupling degree, the tasks to be scheduled can be used as nodes to construct a directed task coupling graph; for any task and tasks If there is a task Pointing to task A directed edge represents a task. In the task The previous process inheritance relationship; the initial properties of directed edges are jointly characterized by material coupling degree, color order coupling degree, and color number coupling degree;

[0082] Based on material coupling degree, color sequence coupling degree, and color number coupling degree, and introducing an ink brightness crossing penalty term. The ink brightness exceeding the penalty item is defined as a task. Switch to task At that time, it is the weighted sum of the absolute values ​​of the lightness level differences of all the transitions from dark ink to light ink at the corresponding color group position;

[0083] Through formula The overall coupling degree is calculated, where, , These represent the linear influence weights of material coupling degree, color order coupling degree, and color number coupling degree, respectively. This represents the interaction coefficient between the material and the color sequence. This represents the interaction coefficient between color order and color number. This represents the coefficient for the brightness crossing penalty term, indicating the severity of the penalty imposed by the ink brightness crossing penalty term on the overall coupling degree. This represents a bias term used to provide a baseline level of overall coupling when no other coupling information is available. The Sigmoid function is used to limit the output value to between 0 and 1.

[0084] Simultaneously calculate the sum of the cleanability difficulties caused by ink changes at each color group position, i.e., the task. To the mission residual ink risk value The calculation formula is: ,in, Indicates the first The cleaning weight of color group positions, Indicates the difficulty level of cleaning, characterizing the ink. Switch to ink The degree of difficulty in cleaning at any given time is determined by querying a pre-constructed ink switching cleaning difficulty matrix;

[0085] Based on the magnitude of the overall coupling degree, each directed edge in the directed task coupling graph is classified and labeled:

[0086] When the overall coupling degree is higher than the first preset threshold, it indicates that the process inheritance between the two tasks is extremely strong, and there is almost no need to change ink or clean when switching. The current directed edge is marked as an edge that can be directly inherited.

[0087] When the overall coupling degree is lower than the second preset threshold, it indicates that the switching will involve a large amount of ink replacement and deep cleaning, and the current directed edge is marked as a strong cleaning edge.

[0088] When the overall coupling degree is between the first preset threshold and the second preset threshold, it indicates that only some color groups need to replace ink or perform local cleaning, and the current directed edge is marked as a local ink replacement edge.

[0089] Wherein, the first preset threshold is greater than the second preset threshold;

[0090] After the directed edges are classified and labeled, the classification identifier of the directed edges, along with the comprehensive coupling degree and the residual ink risk value, are written into the directed task coupling graph.

[0091] S3: Based on the directed task coupling graph and combining historical ink change records and historical equipment cleaning records, a nonlinear function for the sequence dependency preparation time between adjacent tasks is constructed to characterize the ink change time and equipment cleaning time generated during task switching. The specific implementation process is as follows:

[0092] Samples of adjacent task switching are extracted from historical production records, including the previous task number, the next task number, the printing press number, the actual ink change time, the actual equipment cleaning time, the cleaning level, and the abnormal shutdown flag. The cleaning level corresponds to different cleaning depths such as full-width cleaning, partial color group cleaning, or partial ink path cleaning. The abnormal shutdown flag is used to record the nature of the shutdown event accompanying the switching, which can be classified as shutdown caused by equipment failure, shutdown caused by raw material shortage, and other shutdowns caused by non-process reasons.

[0093] Remove samples containing downtime due to non-process reasons, and retain machine difference labels for samples of the same task pair switching on different printing presses;

[0094] Based on the comprehensive coupling degree and residual ink risk value, the task is constructed. Parallel multicolor printing press Switch to task The sequence-dependent preparation time is a non-linear function, and its expression is: ,in, Indicates task Parallel multicolor printing press Switch to task Preparation time, Indicates a parallel multicolor printing press Basic version change preparation time Indicates printing press The coupling lacks a scaling factor. Indicated with printing press The corresponding nonlinear exponent, Indicates printing press The residual ink risk scaling factor, Indicated with printing press The corresponding nonlinear index of residual ink risk, Indicates printing press The color number change time coefficient, This indicates the subtractive cleaning adjustment coefficient. Indicates printing press The material path cleaning time is fixed. Indicates the material path cleaning marker, when the task... With the task The value is 1 when the printing material is switched across categories, and 0 otherwise.

[0095] The All of these results were obtained by fitting historical switching sample data using nonlinear least squares regression, and were estimated independently for each parallel multicolor printing press.

[0096] Based on the preparation times of adjacent tasks on all parallel multicolor printing presses, a joint optimization objective function is constructed, and its expression is: ,in, Indicates the joint optimization objective value. Indicates the number of parallel multicolor printing presses. This represents the set of adjacent task pairs in a task sequence. This indicates an adjacency indicator variable, which is used when the task... With the task Parallel multicolor printing press When the processes are arranged in a preceding-following-adjacent processing relationship, ,otherwise , This represents the weight of the load balancing auxiliary constraint, used to adjust the importance of load balancing in the overall optimization objective. Indicates parallel multicolor printing, flashing the firmware. Total load, This represents the average load of all parallel multicolor printing presses. This indicates the weight of the auxiliary constraint for delivery time penalty. Indicates task The positive delay is defined as the task's... The portion of the planned completion time that exceeds its delivery date is taken as 0 if there is no delay.

[0097] S4: Based on the directed task coupling graph, the tasks to be scheduled are grouped into process coupling groups, so that the ink inheritance and substrate transition compatibility between tasks within the same group are higher than the preset grouping threshold. The specific implementation method is as follows:

[0098] Based on the directed task coupling graph, all task nodes to be scheduled are traversed, the number of directly inheritable edges associated with each task node is counted, and the condition judgment is completed in combination with the coverage of the mask that the device can process. Tasks that meet the preset number of directly inheritable edges and whose mask that the device can process can match multiple parallel multi-color printing machines are selected as group seed tasks.

[0099] Expand candidate tasks outward from the seed task of each group, and sequentially determine the coupling and association attributes between the remaining tasks not included in the group and all tasks in the current group. Prioritize the inclusion of candidate tasks that have direct inheritance edges or local ink-changing edges with the tasks within the group.

[0100] During the task expansion and absorption process, the distribution of repeated ink color codes in each printing color group position within the group is statistically analyzed. The set of identifiers in which the proportion of repeated ink color codes in the same color group position exceeds the preset threshold is used to construct the common color sequence skeleton corresponding to the group.

[0101] After completing the initial independent grouping, group any two candidate tasks to be merged. and Substitute the values ​​into the grouping and merging scoring formula for quantitative evaluation. The grouping and merging scoring formula is as follows: ,in, Indicates grouping and Grouped and merged scores, Indicates task To the mission The overall coupling degree, This represents the penalty coefficient for conflicts in the common color order skeleton. Indicates grouping and Common color sequence skeleton conflict markers, when grouping Common color sequence skeleton and grouping When a common color sequence skeleton contains different but not empty valid ink color codes at the same color group position, a color sequence skeleton process conflict is determined to exist. ,otherwise ; This represents the penalty coefficient for delivery window conflicts. Indicates grouping and The delivery window conflict flag is used when a common parallel multicolor printing press exists. Considering only the two groups of tasks and their delivery dates, and taking all constraints into account, a constraint satisfaction algorithm is used to find a feasible schedule. If a feasible schedule exists such that all tasks in both groups are not delayed, then... ,otherwise ;

[0102] Group merging is performed when the combined score exceeds a preset threshold, and the merged group meets the constraints of maximum number of color groups, maximum page width, compatible printing materials, and delivery window. Specific constraints are as follows:

[0103] Maximum number of color groups constraint: The number of printing color groups actually occupied by all printing tasks within the merged task group shall not exceed the maximum number of color groups hardware limit of the adapted parallel multicolor printing press.

[0104] Maximum width constraint: Within the merged task group, the printing width parameter of all printing tasks to be scheduled must not exceed the maximum printing width specification that the corresponding parallel multicolor printing press can support.

[0105] Material category compatibility constraints: Within the merged task group, all tasks must maintain a unified material category or belong to a preset compatible transition category;

[0106] Delivery window constraints: In the merged task group, the planned production delivery dates and time windows of each task are compatible with each other, and there is no overlap or conflict in delivery dates or mutual squeezing of order delivery times; the production scheduling requirements are met, and the original task delivery deadlines are not disrupted after the merger.

[0107] When there is a strong cleaning edge between two groups and the risk of residual ink cannot be eliminated by the common color sequence skeleton, a virtual cleaning partition is inserted between the two groups. The virtual cleaning partition is used to fix a complete equipment cleaning at the group boundary to avoid repeated full-width cleaning within the group.

[0108] After grouping, each task group is assigned to a candidate parallel multicolor printer based on the device-processable mask, with priority given to parallel multicolor printers that can maintain a common color sequence skeleton and have a shorter historical cleaning time.

[0109] S5: Based on the task grouping results, assign each task group to the corresponding parallel multicolor printing press, and jointly optimize the grouping order and the task order within each group on each parallel multicolor printing press; the specific implementation process is as follows:

[0110] On each parallel multicolor printing press, the assigned task groups are sorted between groups. The first criterion for sorting is to minimize the sequence dependency preparation time from the tail task of the group to the first task of the next group, and the second criterion is to maximize the number of common color order skeletons.

[0111] A double-ended insertion sorting strategy is adopted within each task group. First, the task with the lowest residual ink risk value and the highest matching degree with the common color sequence skeleton is selected as the initial task. Then, unsorted tasks are inserted from the head and tail of the sequence respectively. The matching degree of the common color sequence skeleton is defined as the number of times the ink color code of the task at each color group position is the same as the color code of the corresponding position of the common color sequence skeleton, minus the number of different ones.

[0112] For candidate tasks Insert into adjacent tasks and The situation between them can be determined by formula. Candidate tasks are obtained through calculation. Insert into adjacent tasks and The look-ahead insertion increment between , All of these are the corresponding task switching preparation times calculated based on a nonlinear function of sequence-dependent preparation time. Indicates the remaining unsorted task set Any of the pending tasks in the list, This indicates the current parallel multicolor printing press. The remaining set of tasks that have not yet been sorted. Indicates traversal All tasks And take the minimum value, This represents the preset forward-looking cleaning weighting coefficient;

[0113] Calculate the look-ahead insertion increment for all possible insertion positions, and select the position with the smallest look-ahead insertion increment as the optimal insertion position. If there are multiple insertion positions with equal look-ahead insertion increments, prioritize the arrangement that reduces the number of transitions from dark ink to light ink. The criterion for determining the transition from dark ink to light ink is: compare the brightness values ​​of the inks in the same color group position before and after the transition. If the brightness value of the preceding task is lower, it is determined as a transition from dark ink to light ink.

[0114] S6: The optimized scheduling scheme is distributed to the production execution unit. During the production process, the actual ink change time and actual equipment cleaning time are collected, and the parameters of the nonlinear function of the sequence-dependent preparation time are corrected online. The specific implementation process is as follows:

[0115] During actual production, the actual ink change time and actual equipment cleaning time of each parallel multicolor printing press during the switching process between adjacent tasks are collected in real time, and the corresponding task number, printing press number, ink color sequence switching type, substrate switching type and actual cleaning level and other on-site working condition data are recorded simultaneously.

[0116] The actual preparation time data collected on-site is compared in real time with the predicted preparation time output by the sequence-dependent preparation time nonlinear function of S3, and the deviation between the actual value and the function prediction value is calculated.

[0117] When the deviation between the actual preparation time and the predicted value of the sequence-dependent preparation time nonlinear function exceeds a preset deviation threshold, an online parameter correction mechanism is activated. This mechanism uses a restricted step-size gradient descent method to iteratively update the model parameters of the sequence-dependent preparation time nonlinear function. The online parameter correction calculation formula is as follows: ,in, Indicates the first The set of function parameters after the second iteration. Indicates the first The set of function parameters before the next correction iteration Indicates the iteration step size for parameter correction. This indicates the actual preparation time for switching tasks during on-site data collection. This represents the threshold cutoff function, used to constrain the deviation between the actual and predicted values ​​to a certain limit. Within the interval, This indicates the preset deviation cutoff threshold. This represents the gradient vector of the sequence-dependent preparation time with respect to the function parameters.

[0118] S7: Verify the optimized scheduling scheme. When the cumulative ink replacement time and cumulative equipment cleaning time meet the preset optimization conditions, output the final production scheduling scheme. The specific implementation process is as follows:

[0119] Based on the optimized task grouping results, the parallel multicolor printing press allocation relationship, and the in-machine task sorting sequence, all adjacent task switching processes on each parallel multicolor printing press are traversed. Relying on the sequence dependency preparation time nonlinear function of S3, the global ink replacement cumulative time and equipment cleaning cumulative time are calculated segment by segment. At the same time, the ink replacement cumulative time and equipment cleaning cumulative time corresponding to the baseline scheduling scheme are retrieved.

[0120] Through formula The optimization improvement rate of the current optimized scheduling scheme is calculated. ,in, These represent the cumulative ink replacement time and cumulative equipment cleaning time corresponding to the baseline scheduling scheme, respectively. These represent the cumulative ink replacement time and cumulative equipment cleaning time corresponding to the optimized scheduling scheme, respectively.

[0121] At the same time, through the formula The auxiliary indicator evaluation values ​​are obtained through calculation.

[0122] When the optimization improvement rate is greater than the preset threshold and the auxiliary indicator evaluation value is less than the preset threshold, it is determined that the cumulative ink replacement time and the cumulative equipment cleaning time meet the preset optimization conditions. Simultaneously, the constraints are verified layer by layer, including the maximum number of color groups of the parallel multi-color printing press, the maximum printing width constraint, the compatibility constraint of the substrate category, the matching constraint of the common color sequence skeleton, and the delivery window constraint of each task.

[0123] When the optimization improvement rate is greater than the preset threshold, the auxiliary indicator evaluation value is less than the preset threshold, and all constraints are verified to be qualified, the scheduling optimization verification is determined to be successful. The current task grouping result, parallel multi-color printing machine allocation result, machine grouping sorting result, and task sorting result within the group are locked. At the same time, the virtual cleaning partition position set at the group boundary is fixed.

[0124] If the optimization improvement rate is less than or equal to the preset threshold, or the evaluation value of the auxiliary indicator is greater than or equal to the preset threshold, or any constraint such as equipment capacity exceeding the limit, incompatible printing materials, or delivery window conflict is not met, then the current scheduling scheme is determined to have not met the optimization requirements. It returns to S3 to correct the function parameters of the nonlinear function of the sequence dependency preparation time, and then iterates through S4 to S7 in sequence until the preset optimization conditions and various constraint requirements are met.

[0125] After completing all verifications and locking in the optimal scheduling scheme, the final production scheduling scheme, the task switching sequence of each machine, the estimated ink change time, the estimated equipment cleaning time, and the virtual cleaning partition placement location are simultaneously output and sent to the production execution unit, providing a standardized scheduling and execution basis for the production scheduling, ink change control, and equipment cleaning management of parallel multi-color printing presses in the packaging and printing workshop.

[0126] A production scheduling optimization system for packaging and printing operations includes:

[0127] Production data acquisition and processing module: The production scheduling data processing unit acquires the task information, printing material parameters, ink color sequence parameters, printing color number parameters, and equipment capability parameters of the parallel multicolor printing machine for the packaging and printing tasks to be scheduled, and generates a set of tasks to be scheduled, uniformly encodes the ink information, and generates task process fingerprints.

[0128] Task Coupling Analysis Module: Calculates the multi-dimensional coupling degree between tasks to be scheduled in terms of material, color order, and color number, constructs a directed task coupling graph, calculates the comprehensive coupling degree and residual ink risk value, and classifies and marks each directed edge in the directed task coupling graph based on the magnitude of the comprehensive coupling degree.

[0129] The scheduling optimization calculation module constructs a sequence-dependent preparation time nonlinear function based on the directed task coupling graph and historical ink change and cleaning records, and fits the function parameters through historical data. With the goals of minimizing total preparation time, balancing equipment load, and minimizing delivery time penalty, it completes task process coupling grouping, printing press allocation, inter-group sorting, and double-ended insertion sorting within groups to generate an optimized scheduling scheme.

[0130] Online correction and verification output module: Real-time acquisition of actual ink change and cleaning times, comparison with predicted deviations and online correction of function parameters; calculation of optimization improvement rate and auxiliary indicators, verification of constraints such as equipment, materials, and delivery time, and output of final scheduling plan after verification and distribution to production execution unit.

[0131] 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 of optimizing production scheduling of a packaging print job, characterized by, include: S1: By acquiring the task information, printing material parameters, ink color sequence parameters, printing color number parameters, and equipment capability parameters of the parallel multicolor printing press for the packaging and printing tasks to be scheduled, a set of tasks to be scheduled is generated. S2: Calculate the coupling degree of any two tasks to be scheduled in the dimensions of printing material, ink color sequence, and number of printing colors, and construct a directed task coupling graph; S3: Based on the directed task coupling graph, construct a nonlinear function for the preparation time of the sequence dependency between adjacent tasks; S4: Based on the directed task coupling graph, the tasks to be scheduled are grouped into process coupling groups so that the ink inheritance and printing material transition compatibility between tasks in the same group are higher than the preset grouping threshold. S5: Based on the task grouping results, each task group is assigned to the corresponding parallel multicolor printing press, and the grouping order and task order within each group on each parallel multicolor printing press are jointly optimized. S6: The optimized scheduling scheme is sent to the production execution unit. During the production process, the actual ink change time and actual equipment cleaning time are collected, and the parameters of the nonlinear function of the sequence-dependent preparation time are corrected online. S7: Verify the optimized scheduling scheme. When the cumulative ink replacement time and cumulative equipment cleaning time meet the preset optimization conditions, output the final production scheduling scheme.

2. A method of optimizing production scheduling of a packaging print job according to claim 1, characterized in that, The specific operation steps of S2 include: Based on the set of tasks to be scheduled, the degree of coupling between any two tasks to be scheduled is calculated in terms of printing material, ink color sequence, and number of printing colors, and a directed task coupling graph is constructed. Material coupling degree is calculated based on the type of printing material, normalized basis weight, surface energy, ink absorption rate and paper feed direction; color sequence coupling degree is calculated based on ink color code alignment and color group position attenuation coefficient; color number coupling degree is calculated by combining the increase or decrease of printing color number and subtractive cleaning coefficient. An ink brightness crossing penalty term is introduced, and the material coupling degree, color sequence coupling degree, color number coupling degree, and interaction coefficient are integrated to obtain the comprehensive coupling degree through the Sigmoid function; at the same time, the residual ink risk value of ink switching is calculated; Based on the comprehensive coupling degree and preset threshold, directed edges are marked as directly inheritable edges, local ink replacement edges, or strong cleaning edges, and the edge classification identifier, comprehensive coupling degree, and residual ink risk value are written into the directed task coupling graph.

3. A method of optimizing production scheduling of a packaging print job according to claim 2, characterized in that, The specific operation steps of S2 also include: When constructing the directed task coupling graph, the ink color sequence coupling degree is based on the maximum number of color groups in the printing press. The task ink color sequence is aligned with the position of the color group, and the ink color code is compared group by group. If the codes are the same and not empty, they are counted as inheritable. The inheritance weight of the earlier color group is higher than that of the later color group. The printing color coupling degree distinguishes between two switching scenarios: color increase and color decrease between tasks. Color increase is included in the ink consumption time for plate mounting, and color decrease is included in the time consumption for cleaning empty ink paths. The overall coupling degree is limited to between 0 and 1 using the Sigmoid function. At the same time, the residual ink risk value is obtained by summing the washability difficulty of each color group ink switching. The washing difficulty is obtained based on the preset ink switching washing difficulty matrix. When the overall coupling degree is higher than the first preset threshold, it is marked as a directly inheritable edge; when it is lower than the second preset threshold, it is marked as a strong cleaning edge; when it is between the first preset threshold and the second preset threshold, it is marked as a local ink replacement edge, and the first preset threshold is greater than the second preset threshold.

4. The method of claim 1, wherein The specific operation steps of S3 are as follows: Extract adjacent task switching samples from historical production records, including the previous task number, the next task number, the printing press number, the actual ink change time, the actual equipment cleaning time, the cleaning level, and the abnormal shutdown marker. Remove samples containing downtime due to non-process reasons, and retain machine difference labels for samples of the same task pair switching on different printing presses; Based on the comprehensive coupling degree and residual ink risk value, a sequence-dependent preparation time nonlinear function for task switching is established for each parallel multicolor printing press. Based on the preparation time of adjacent tasks on all parallel multicolor printing presses, a joint optimization objective function is constructed, which includes adjacency indicator variables, load balancing weights, and delivery penalty weights.

5. The method of claim 1, wherein The specific operation steps of S4 are as follows: Traverse the nodes of tasks to be scheduled, count the number of directly inheritable edges, and filter the tasks whose number of directly inheritable edges meets the preset condition and whose equipment can process masks that can be matched with multiple parallel multi-color printing machines as group seed tasks. Candidate tasks are expanded outward from the seed tasks of each group, and candidate tasks that can be directly inherited or have local ink change edges with the tasks within the group are absorbed. The distribution of ink color code is statistically analyzed simultaneously to construct a common color sequence skeleton corresponding to the group. For any two candidate tasks to be merged, grouping and merging scores are performed based on comprehensive coupling degree, common color sequence skeleton conflict and delivery window conflict. When the group merge score is higher than the preset threshold and meets the constraints of maximum number of color groups, maximum width, compatibility of printing materials, and delivery window, the merge is executed. Virtual cleaning partitions are inserted between groups where there is a strong cleaning edge and the risk of residual ink cannot be eliminated, thus fixing the full-width cleaning at the group boundary; After grouping, the candidate parallel multicolor printing presses are assigned based on the mask that the equipment can process, with priority given to the parallel multicolor printing press that can maintain the common color sequence skeleton and has a better historical cleaning time.

6. The method of claim 1, wherein The specific operation steps of S5 are as follows: Each task group is assigned to the corresponding parallel multi-color printing press. The first criterion is to minimize the sequence dependency preparation time from the tail task of the group to the first task of the next group, and the second criterion is to maximize the number of common color order skeletons. This completes the sorting of groups on each printing press. Within each group, a double-ended insertion sorting strategy is adopted. The task with the lowest residual ink risk value and the highest matching degree with the common color order skeleton is selected as the initial task. Then, the remaining unsorted tasks are inserted from the head and tail of the sequence respectively. Calculate the look-ahead insertion increment of the candidate task at each possible insertion position, select the position with the smallest look-ahead insertion increment as the optimal insertion position, and if the increments are the same, prioritize the arrangement method that reduces the number of transitions from dark ink to light ink.

7. The method of claim 1, wherein the method further comprises: The specific operation steps of S6 are as follows: In actual production, the actual ink change time and actual equipment cleaning time of each parallel multicolor printing press during the switching between adjacent tasks are collected in real time, and the corresponding on-site working condition data are recorded simultaneously. The actual preparation time data collected on-site is compared in real time with the predicted preparation time output by the sequence-dependent preparation time nonlinear function of S3, and the deviation between the actual value and the function prediction value is calculated. When the deviation exceeds the preset deviation threshold, the online correction mechanism for function parameters is activated, and the model parameters of the sequence-dependent preparation time nonlinear function are iteratively updated using a restricted step size gradient descent method.

8. The method of claim 1, wherein the method further comprises: The specific operation steps of S7 are as follows: Based on the results of task grouping, printing press allocation, grouping and sorting and in-machine task sorting, the adjacent task switching process of each printing press is traversed, the cumulative time of global ink replacement and equipment cleaning is calculated, and the data is compared with the corresponding data of the benchmark scheduling scheme to calculate the optimization improvement rate. Simultaneously calculate the evaluation values ​​of auxiliary indicators for equipment load balancing and task delivery delay; The scheduling scheme is validated based on the optimization improvement rate, auxiliary indicator evaluation values, and constraints. If the optimization conditions and constraints are met, the scheduling scheme is deemed to have passed verification, and the task grouping, equipment allocation, sorting results, and virtual cleaning baffle positions are locked. If the optimization conditions or constraints are not met, return to correct the nonlinear function parameters of the sequence dependency preparation time, and iterate through S4 to S7 again until the optimization conditions and constraints are met. The optimal scheduling plan is output synchronously and sent to the production execution unit as the basis for printing press production scheduling, ink changing and cleaning control.

9. A system applied to the production scheduling optimization method for packaging and printing operations according to any one of claims 1-8, comprising: Production data acquisition and processing module: Acquires task, printing material, ink color sequence, number of printing colors and printing machine equipment parameters, generates task set and equipment processable mask, uniformly encodes ink information and generates task process fingerprint; Task Coupling Analysis Module: Calculates the multi-dimensional coupling degree between tasks, constructs a directed task coupling graph, marks edge types, and calculates the comprehensive coupling degree and residual ink risk value; The scheduling optimization calculation module constructs a sequence-dependent preparation time nonlinear function based on the directed task coupling graph, and fits the function parameters by combining historical ink change and cleaning data to complete task process grouping, equipment allocation, inter-group sorting and intra-group double-ended insertion sorting to form a scheduling scheme. Online correction and verification output module: Collects actual production data to calibrate function parameters, verifies the optimization improvement rate and constraint compliance, outputs the final scheduling plan and issues it for execution.

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