A cable production scheduling modeling method

Abstract

The present application relates to a kind of cable production scheduling modeling method, the method comprises the following steps: step 1: integration production data, step 2: integration order data, step 3: create order production constraint model, step 4: based on production process feature constructs scheduling mathematical model, step 5: based on ant colony algorithm iteration optimization;The method includes the mathematical model of cable production process and ant colony optimization algorithm, and the production scheduling of cable scheduling process is completed by combining two kinds of algorithm models.

Description

TECHNICAL FIELD

[0001] The application relates to a cable production scheduling modeling method and belongs to the technical field of intelligent scheduling. BACKGROUND

[0002] Production scheduling is of great significance in manufacturing. Production scheduling can help enterprises make more effective use of their production resources, such as staff, equipment and materials. Effective scheduling can also ensure full use of resources, improve production efficiency, and avoid or reduce idle resources. A reasonable and effective production scheduling plan can help enterprises improve production efficiency, reduce waste, and also help ensure product or service quality. Production scheduling helps determine the production time and sequence of products, so that enterprises can complete production tasks within the specified period, meet customer orders on time, and increase customer satisfaction. Effective production scheduling can reduce work-in-process and finished product inventory levels, reducing inventory costs. In addition, reasonable production scheduling can also help reduce the additional costs generated by overproduction and production interruptions. By optimizing production processes, improving production efficiency and quality, reducing costs and meeting delivery dates, production scheduling can greatly improve the competitiveness of enterprises and thus gain a larger share of the market. Implementing effective production scheduling is very important for an enterprise, whether in terms of improving efficiency and profits or enhancing competitiveness.

[0003] The cable scheduling method aims to reasonably plan the production and manufacturing process of the cable by using appropriate methods, improve processing efficiency, and reduce unnecessary resource waste. It can be summarized as a production and manufacturing workshop scheduling problem. Arthanari and Salvador first proposed the scheduling problem of processes that can be processed on multiple machines in the 1970s, marking the beginning of the study of flexible flow shop scheduling problems. He and Babayan studied a two-stage flexible flow shop scheduling problem considering delay product differences, where there is only one machine in the first stage and multiple identical parallel machines in the second stage. Schulz et al. proposed an improved multi-phase iterative local search algorithm to solve the k-stage hybrid flow shop scheduling problem with maximum completion time, total energy consumption and peak load as objective functions.

[0004] The cable manufacturing enterprise mainly faces the user order, and carries out production plan according to the customer requirement. But the cable industry as a traditional manufacturing industry still depends on manual production scheduling and scheduling to a large extent in the manufacturing process, so that the production efficiency of equipment cannot be fully exerted, and the comprehensive benefit of the enterprise is affected. And in the actual process of cable manufacturing, there are random disturbance events such as inserting order, reducing order and advancing order, which greatly affect the production efficiency of the workshop. Therefore, the intelligent production scheduling technology can provide a more efficient and reliable solution for the dynamic scheduling plan update of the cable production workshop, effectively reduce the production cost, shorten the production cycle, guarantee the production quality, and improve the comprehensive competitiveness of the enterprise.

[0005] However, there are four difficulties in the cable production process, 1. Difficulty in defining production object, 2. Complexity of order merging and material substitution, 3. Different logic before and after key process, 4. Combination of process manufacturing and discrete manufacturing. The order information needs to be effectively extracted, the scheduling strategy before and after the key equipment is further analyzed, and the complex changes of order merging and material substitution in the cable production process are accurately processed, so as to realize the objective and accurate expression of the intelligent scheduling of the mathematical model for the cable production. SUMMARY

[0006] The present application is just for the problems existing in the prior art, and provides a cable production scheduling modeling method, which comprises a mathematical model of the cable production process and an ant colony optimization algorithm, and combines the two algorithm models to complete the production scheduling of the cable scheduling process.

[0007] The method solves the four difficulties of difficulty in defining production object, complexity of order merging and material substitution, different logic before and after key process, and combination of process manufacturing and discrete manufacturing in the cable production scheduling, realizes the intelligent scheduling of the cable production, improves the scheduling efficiency and production efficiency, and can effectively guarantee the utilization rate of the key equipment.

[0008] In order to achieve the above purpose, the technical scheme of the present application is as follows, a cable production scheduling modeling method, comprising the following contents:

[0009] Step 1: integrate production data

[0010] (1) production time

[0011] In the production process, each unit length needs to be spliced from the next section to the end of the current section, which takes mmin time, and this operation takes the same time on each device, so it is necessary to increase the packaging time of each device. Moreover, different devices also have their own production time when completing the same length of parts. When the production program starts, we need to judge the state of the device, which depends on the highest common factor HCF of all device production times and m, which we call MPTC (number of Minimum processing time cell). In this process, the device state may change each time through MPTC. Therefore, we use the number of MPTC to describe the production time of the device, and get the device update matrix T p And is the MPTC number of unit production length:

[0012]

[0013] (2) Changeover time

[0014] The number of MPTC needed to supplement when the production process changes is T c

[0015]

[0016] (3) Device state

[0017] E S = [1, 1, 1, 1, 1, 1, 1, 1] (3)

[0018] 1 represents that the device is available, and 0 represents that the device is busy or faulty

[0019] (4) Material state

[0020] M jn represents the number of the nth material in the jth process

[0021] Step 2: Integrate order data

[0022] (1) Order integration

[0023] Because the cable has both flow and discrete characteristics, the entire process operation must be completed according to the established flow in the production process, but the production process is not completed once for the entire cable, but is divided into several sections for processing. In the formula, Line i represents a cable, P ij represents the jth process in cable i, part ij1 represents the first part of the jth process in cable i, kij The values ​​for `processType` and `deadline` indicate the processing segments that each device needs to complete. `processType` represents the processing technology type, `deadline` represents the delivery time, and `class` represents the processing time. in Enter the material type, class out This represents the type of material output.

[0024] Line i =[P i1 ,P i2 ,P i3 ,P i4 ,P i5 ,P i6 ,P i7 ,P i8 (4)

[0025]

[0026] part ijk =[processType,deadline,class in ,class out ] ij (8)

[0027] Step 3: Create an order production business constraint model

[0028] (1) Hard constraints

[0029] Processing constraints:

[0030] 1) A single machine can only process one process at a time.

[0031] 2) A single machine can only process one segment of an order at a time.

[0032] 3) Each segment of the order must first complete the prerequisite steps.

[0033] 4) After processing, fragments from different orders can be applied to the next processing step of any order that meets the material requirements.

[0034] 5) The production completed by one piece of equipment is only one process within a segment of an order.

[0035] Switching constraints:

[0036] In actual production, there are four scenarios for different orders:

[0037] 1) Different materials, same process;

[0038] 2) Same materials, same process;

[0039] 3) Different materials require different processes;

[0040] 4) Same materials, different processes.

[0041] For options 1 and 2, the changeover time is fixed at m min, which is the time consumed by changing the material tray. For options 3 and 4, the changeover time is not fixed and depends on different equipment. The changeover time varies for different equipment. It is necessary to minimize the total time through scheduling, while ensuring that key equipment operates at full capacity as much as possible to improve the overall production efficiency of the workshop. Another key indicator is that orders must be completed within the deadline.

[0042] (2) Soft constraints

[0043] Key equipment processing logic constraints:

[0044] Because the crosslinking machine is chosen as the key equipment, its production process needs to be stable and uninterrupted to minimize the need for process changes and reduce changeover time. Simultaneously, it's crucial to ensure a sufficient supply of the required raw materials to prevent forced production changes due to material shortages. Therefore, during the scheduling process, the corresponding production part is selected. ijk At the same time, set a larger penalty coefficient for critical equipment to avoid selecting parts that require process switching as much as possible. ijk As shown in Table 1, the time taken by the preceding equipment to produce a unit length of crosslinking machine is less than that of the crosslinking machine. Therefore, it needs to prioritize the production of all possible raw materials used by the crosslinking machine, ensuring that there is at least one unit of each raw material. If there are multiple raw materials with less than one unit, then the production of the raw materials currently being used by the crosslinking machine should be prioritized, provided that there are still fragments of that type of raw material in the processed fragments. If each of the three equipments has at least one of the required raw materials, then the second equipment should proceed according to the principle of minimizing process changeovers. ijk To process.

[0045]

[0046] In the formula, Equipment2 represents the processing section selected by equipment 2. P represents the material used in the current processing of equipment 3, P(M) represents the production segment that produces raw material M, and [P] is an indicator function that is 1 when proposition P is true and 0 otherwise.

[0047] Step 4: Construct a scheduling mathematical model based on production process characteristics

[0048] (1) Calculation of the probability of processing segments

[0049] Due to the unique nature of cable production, most equipment can only process one section at a time. A single machine can only execute one cable order unit time period, and can only select one cable order unit time period from within that time period. Furthermore, the selection of a section requires two conditions: sufficient material preparation and that the order section has not yet been completed.

[0050]

[0051] Where j represents the corresponding equipment, and n represents the nth material type for the corresponding equipment. This type of material needs to be determined each time the equipment starts or finishes processing. When M... jn When the value is greater than 1, the required material M can be selected from production equipment j. jn The order. In the formula, j represents the corresponding equipment, and m represents the m-th process mode of the corresponding equipment. This mode needs to be determined each time the equipment starts or finishes processing. When Parts jm When .num>1, device j also needs to produce this type of product. jm This equipment can be selected for production. When the above-mentioned material preparation status, equipment segment selection status, and time segment processing status are all available, Parts can be selected. jm Production begins.

[0052] (2) Processing segment selection

[0053] Each Parts jm The probability of being selected is shown in Equation 13:

[0054]

[0055] In the formula WT am steps j It refers to the time required to switch production from the previous production process a to the selected process m on equipment j, where μ is the distance penalty coefficient, thus obtaining the probability of each processable part being selected.

[0056] (3) Equipment / Material Status Update

[0057] After selecting the corresponding Parts, the production data, production equipment, and remaining unfinished orders need to be updated to ensure that all information is synchronized, as shown in equations 14, 15, and 16.

[0058]

[0059] Parts in the formula ij .num refers to the number of Parts that process i needs to complete in equipment j. When it is selected, its number is reduced by one.

[0060] (4) Scheduling scheme record

[0061]

[0062] Record each Part switch of each device, record the complete results of the entire simulated production scheduling, and generate a scheduling plan as shown in Equation 17.

[0063] To record changeover time, after analyzing the orders, the parts are obtained. Each part requires corresponding equipment for its production and processing. Different parts require different processing technologies. Therefore, it is necessary to construct a production exchange time matrix using Formula 2 to record the production exchange time between different parts, providing guidance for the selection of part production processing technologies, as shown in Formula 18, ρ ijk-i'j'k' This refers to the time consumed when switching production between the k-th processing segment in order i and the k'-th processing segment in order i' on equipment j. ik (tpye.P j () refers to the processing method used for the k-th processing segment in order i:

[0064]

[0065] Step 5: Iterative optimization based on ant colony optimization algorithm

[0066] The mathematical model constructed based on formulas (1)-(18) can complete one production scheduling operation, but its scheduling result is highly random and difficult to meet the requirement of minimizing production time. Ant colony algorithm is needed to optimize its scheduling result.

[0067] (1) Heuristic information definition, let ρ ijk-i'j'k' Become with The relevant heuristic value, through the heuristic value ρ ijk-i'j'k' To evaluate The advantages and disadvantages, ρ ijk-i'j'k' yes The reciprocal of is shown in Equation 19.

[0068]

[0069] (2) Update the pheromone matrix, let Read as pheromone, it is a positive real value that indicates the usefulness of making the following decisions. Selected as The next operation is performed by the same machine. In the ACO algorithm, M ants learn pheromones collaboratively, thus gaining a probabilistic advantage in discovering better scheduling schemes. The pheromone update rules are shown in Equations 20 and 21.

[0070]

[0071] (3) Definition of the probability of random selection: When ant r selects the next... The following rules, i.e., the action rules, will be used. Random selection is made according to the distribution given by the formula. This formula gives the distribution when... When Ant was first selected, it chose... This is the probability of the next operation. Here, α and β are parameters that weigh the relative importance of the learned pheromone and the heuristic value. ijk This refers to whether the order itself meets the selection criteria, whether it has been completed, and whether the materials are ready.

[0072]

[0073] Compared with the prior art, the advantages of the present invention are as follows:

[0074] This invention proposes a cable production scheduling optimization algorithm for multi-order, multi-product scenarios, solving the problems of low production efficiency and low resource utilization in traditional production lines. Based on the actual cable production process, this invention abstracts a mathematical model that accurately expresses the technological and discrete characteristics of the production process. It also proposes specific scheduling schemes for key equipment on the production line to ensure their long-term stable operation. Finally, the ACO algorithm is used to continuously optimize the scheduling results, resulting in a 10.04% improvement in production efficiency in production scenario test cases. Attached Figure Description

[0075] Figure 1 This is a flowchart of the algorithm operation in an embodiment of the present invention;

[0076] Figure 2 This is a Gantt chart of the scheduling results in an embodiment of the present invention. Detailed Implementation

[0077] To enhance understanding of the present invention, the embodiments will be described in detail below with reference to the accompanying drawings.

[0078] Example 1: To verify the feasibility and optimization effect of the above method, production scheduling and optimization were completed in the medium-voltage workshop of a cable manufacturer. Different products require different processing techniques in terms of quantity and process parameters. However, there are cases where some processes are the same but the raw materials differ, and vice versa. This poses a significant challenge to production scheduling. Relying solely on experience and manual calculations makes it difficult to arrive at a suitable scheduling plan that balances production efficiency and delivery time, often resulting in idle equipment during production.

[0079] Step 1: Integrate production data

[0080] (1) Production time

[0081] Table 1 Equipment Processing Time

[0082]

[0083] (2) Production change time

[0084] Table 2 Time for Equipment Process Switching

[0085]

[0086] T c =[9,13,64,0,0,13,0,13]

[0087] (3) Equipment status

[0088] E S =[1,1,1,1,1,1,1,1]

[0089] 1 indicates the device is available, 0 indicates the device is busy or malfunctioning.

[0090] (4) Material status

[0091]

[0092] Step 2: Integrate order data

[0093] (1) Order consolidation

[0094] Therefore, we optimized the scheduling based on ant colony for the production orders received by the workshop on July 18, 2024, as shown in Table 3.

[0095] Table 3 Order Requirements

[0096]

[0097] The order information is converted into an order matrix and stored in a file for later retrieval.

[0098] Step 3: Construct an order production business constraint model, including processing constraints and production change constraints in hard constraints, and key equipment processing logic constraints in soft constraints.

[0099] Step 4: Record the scheduling plan

[0100]

[0101] Step 5: The ant colony algorithm is used to optimize the existing scheduling model by setting the ant colony parameters. In this verification, the ant colony size is set to 50, the number of iterations to 150, the pheromone coefficient to 10, the distance influence coefficient to 1, the pheromone index parameter to 4, the distance influence index parameter to 1, and the pheromone evaporation coefficient to 0.5. Then, based on the information in Table X and Figure X, the scheduling scheme code is edited and integrated into the ant colony iteration process. Finally, the results of the ant colony iteration process are converted into a Gantt chart outputting the total production time and scheduling scheme for all orders, as shown below. Figure 1 As shown.

[0102] Table 4 Ant Colony Optimization Process

[0103]

[0104]

[0105] The iteration results are shown in Table 4. The result of the first round (589 MPTCs) was 2.8632 days, while the actual workshop scheduling required 3 days, which was a significant improvement over the result of direct manual scheduling. With further iterations of optimization, in the 5th iteration, the resulting production plan (575 MPTCs) required 2.7951 days to complete production, an improvement of 6.83% compared to manual scheduling, at which point the optimization progress began to slow down. In the 10th iteration, the production plan was further optimized to require 2.7465 days (565 MPTCs) to complete the production of all orders. Finally, in the 37th iteration, the optimal solution under the algorithm was found, and the generated production plan required 2.6882 days (553 MPTCs) to complete the production of all tasks, an increase in productivity of 10.04% compared to the initial manual scheduling.

[0106] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.

Claims

1. A cable production scheduling modeling method, characterized in that, The method includes the following steps: Step 1: Integrate production data. Step 2: Integrate order data. Step 3: Create a constraint model for order production. Step 4: Construct a scheduling mathematical model based on the characteristics of the production process. Step 5: Iterative optimization based on the ant colony algorithm; Step 1: Integrating production data, specifically as follows: (1) Production time During the production process, each unit length needs to be spliced ​​from the next segment to the end of the current segment, which takes st min time. This operation takes exactly the same time on each machine, thus increasing the packaging time for each machine. Furthermore, different machines have different production times when completing parts of the same length. When the production program starts, the machine status is determined based on the highest common factor (HCF) and st of the production times of all machines, called MPTC, or Minimum Processing Time Unit. During this process, the machine status may change after each MPTC. The number of MPTCs describes the machine's production time, resulting in the machine update matrix. ,and This refers to the number of MPTCs per unit production length. (1) (2) Production change time, The amount of MPTC that needs to be replenished when the production process changes is: (2) (3) Equipment status, (3) 1 indicates the device is available, 0 indicates the device is busy or malfunctioning. (4) Material state, This represents the quantity of the nth type of material in the p-th process; Step 4: Construct a scheduling mathematical model based on the characteristics of the production process, as detailed below. (1) Calculation of the probability of processing segments, Due to the unique nature of cable production, most equipment can only process one section at a time. A single machine can only execute one cable order unit time period, and can only select one cable order unit time period. Furthermore, the selectable section must meet two conditions: sufficient material preparation and the order section not yet being completed. (10) (11) (12) Where e represents the corresponding equipment, and n represents the nth material type for the corresponding equipment. This needs to be determined each time the equipment starts or finishes processing. When the value is greater than 1, the required materials can be selected from production equipment e. The order, where e represents the corresponding equipment and m represents the m-th process mode of the corresponding equipment, needs to be judged each time the equipment starts or finishes processing. At that time, equipment e also needs to produce this type of product. This equipment can be selected for production. When the aforementioned material preparation status, equipment segment selection status, and time segment processing status are all available, this equipment can be selected. To carry out production, (2) Selection of processing segments, Each The probability of being selected is shown in Equation 13: (13) In the formula This refers to the time required to switch production from the previous production process a to the selected process m on equipment e. This is the distance penalty coefficient, which determines the probability of selecting each processable Part. (3) Equipment / material status update After selecting the corresponding Parts, the production data, production equipment, and remaining unfinished orders need to be updated to ensure that all information is synchronized, as shown in equations 14, 15, and 16. (14) (15) (16) In the formula, This refers to the number of Parts that process p in equipment e needs to complete. When a Part is selected, its quantity decreases by one. (4) Scheduling scheme record (17) Record every Part switch for each device, comprehensively record the entire simulated production scheduling results, and generate a scheduling plan as shown in Equation 17. To record changeover time, after analyzing the orders, the parts are obtained. Each part requires corresponding equipment to complete its production and processing. Different parts require different processing technologies. Therefore, it is necessary to construct a production exchange time matrix using Formula 2 to record the production exchange time between different parts, providing guidance for the selection of part production and processing technologies, as shown in Formula 18. This refers to the k-th processing segment in order o on device e, and the order... The Middle The time consumed when switching production between processing segments This refers to the processing method used for the k-th processing segment in order o: (18)。 2. The cable production scheduling modeling method according to claim 1, characterized in that, Step 2: Integrate order data, as detailed below. (1) Order consolidation, Due to the dual characteristics of both flow and discrete processes, the production of cables follows a predetermined process to complete all technological operations. During production, cables are divided into several sections based on their length for processing. In the formula, Represents a cable. This represents the j-th process in cable i. This represents the first part of the j-th process in cable i. The value of k is different in different processes, and the processing segments that each piece of equipment needs to complete are also different. Represents the type of processing technology. Indicates delivery time. Enter the material type. Represents the output material type. (4) (5) (6) (7) (8) 。 3. The cable production scheduling modeling method according to claim 2, characterized in that, Step 3: Create the business constraint model for order production, as follows: (1) Hard constraints Processing constraints: 1) A single machine can only process one process at a time. 2) A single machine can only process one segment of an order at a time. 3) Each segment of the order must first complete the prerequisite steps. 4) After processing, fragments from different orders can be applied to the next processing step of any order that meets the material requirements. 5) The production completed by one piece of equipment is only one process within a segment of an order. Switching constraints: In actual production, there are four scenarios for different orders: 1) Different materials, same process; 2) Same materials, same process; 3) Different materials require different processes; 4) Same materials, different processes Among them, the changeover time used for 1) and 2) is fixed at m min, which is the time consumed by changing the material tray; the changeover time used for 3) and 4) is not fixed and depends on different equipment. The changeover time of different equipment is also different. It is necessary to achieve the minimum total time through scheduling, while making the key equipment operate at full load as much as possible, improving the production efficiency of the entire workshop, and another key indicator is that the order must be completed within the deadline. (2) Soft constraints Key equipment processing logic constraints: During the scheduling process, select the production corresponding to At the same time, a larger penalty coefficient should be set for critical equipment to prevent it from choosing processes that require switching. The preceding equipment to the crosslinking machine takes less time to produce a unit length than the crosslinking machine itself. Therefore, it needs to prioritize the production of all possible raw materials used by the crosslinking machine, ensuring that there is at least one unit of each raw material. If there are multiple raw materials with less than one unit, then the equipment should prioritize the production of the raw materials currently being used by the crosslinking machine, provided that fragments of that type of raw material still exist in the processed fragments. If each of the three required raw materials has at least one type, then the equipment should proceed according to the principle of minimizing process changeovers. Processing, (9) In the formula, The processing section selected for equipment 2. P represents the material used in the current processing of equipment 3, P(M) represents the production segment that produces raw material M, and [P] is an indicator function that is 1 when proposition P is true and 0 otherwise.

4. The cable production scheduling modeling method according to claim 3, characterized in that, Step 5: Iterative optimization based on the ant colony algorithm, as follows: The mathematical model constructed based on formulas (1)-(18) completes a production scheduling operation, but its scheduling result is highly random and difficult to meet the requirement of minimizing production time. Therefore, the ant colony algorithm is needed to optimize its scheduling result. (1) Heuristic information definition, let Become with Related heuristic values, through heuristic values To evaluate The advantages and disadvantages, yes The reciprocal of is shown in Equation 19. (19) (2) Update the pheromone matrix, let , read as pheromone, is a positive real value that indicates the usefulness of making the following decisions. Selected as The next operation is processed by the same machine. In the ACO algorithm, A ants learn pheromones through cooperation, thus gaining a probabilistic advantage in discovering better scheduling schemes. The pheromone update rules are shown in Equations 20 and 21. (20) (21) (3) Definition of the probability of random selection: When ant r selects the next... The following rules, i.e., the action rules, will be used to randomly select an action from a distribution given by a formula, which gives the distribution when... When ant r is first selected, The probability of the next operation is given by α and β, where α and β are parameters that weigh the relative importance of the learned pheromone and the heuristic value. This refers to whether the order itself meets the selection criteria, whether it has been completed, and whether the materials are ready. (22)。 5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements a cable production scheduling modeling method as described in any one of claims 1 to 4 above.

6. A computer-readable storage medium storing computer instructions thereon, characterized in that: When the computer instruction is executed by the processor, it implements a cable production scheduling modeling method as described in any one of claims 1-4.

Images