Low-entropy state operation evaluation method for discrete workshop manufacturing system

Abstract

The invention discloses a scheduling evaluation method for low-entropy state operation of a discrete workshop manufacturing system, and the method comprises the following steps: 1) constructing operation conditions and following principles of the discrete workshop manufacturing system, analyzing the operation state of the discrete workshop manufacturing system, and constructing a static entropy function of the discrete workshop manufacturing system; 2) constructing a discrete workshop manufacturing system operation dynamic entropy function according to the situation that the system is in an out-of-control state and a fuzzy event occurs; 3) calculating the maximum feasible scheduling time limit of the scheduling scheme; and 4) analyzing and comparing the static entropy, the operation entropy and the maximum feasible scheduling time limit aiming at the problem of scheduling scheme selection, and selecting an execution scheme with small system entropy increase as an optimal execution scheduling scheme for guiding actual production scheduling. According to different scheduling schemes of the discrete workshop manufacturing system, the low-entropy state operation evaluation method is provided, the scheduling scheme with low uncertainty and high system order degree is selected, and low-entropy efficient ordered production of the discrete workshop manufacturing system is achieved.

Description

Technical Field

[0001] The invention belongs to the field of production scheduling and manufacturing dispatching, and in particular relates to a dispatching evaluation method for low-entropy operation of a discrete workshop manufacturing system. Background Art

[0002] Against the backdrop of rapid economic development, continuous technological innovation, and increasingly fierce market competition, the manufacturing industry has encountered new challenges. The discrete production model with multiple varieties, small batches, and customization is gradually taking a dominant position in the market. The product market is increasingly inclined to customized production needs, which has led to the increasing complexity of workshop production. Discrete manufacturing has the characteristics of multiple varieties and small batches, and its production process presents many characteristics, such as staggered production of multiple products, rich and diverse production processes, massive production data, numerous uncertain factors, complex and changeable production management, and parallel production. At present, the production efficiency of discrete workshop manufacturing systems has not yet reached a satisfactory level, and the effectiveness of scheduling plans is precisely the key factor that determines the production operation of workshops. However, some plans ignore the complexity of the actual production scheduling link and the uncertain factors in the workshop when making decisions, which will cause many problems in the actual workshop production operation. Determining the production status of the manufacturing system can help select a scheduling plan. Entropy is a tool to measure the degree of disorder in a system. Information entropy can be used to quantify the uncertainty or randomness of information. Applying information entropy to manufacturing systems can describe the degree of order in the system. The larger the information entropy, the higher the uncertainty of the system and the higher the probability of failure or collapse. Summary of the invention

[0003] In view of the above-mentioned problems, the shortcomings of the existing scheduling scheme selection are optimized to provide theoretical support for enterprise production decision-making. The purpose of the present invention is to provide a low-entropy operation evaluation method for discrete workshop manufacturing systems. The method proposes a low-entropy operation evaluation method for different scheduling schemes of discrete workshop manufacturing systems, aiming to select a scheduling scheme with low uncertainty and high system order, so as to realize low-entropy, efficient and orderly production of discrete workshop manufacturing systems.

[0004] Aiming at the workshop scheduling problem in the production process of discrete workshop manufacturing system, the present invention uses the evaluation method of low entropy operation, takes the processing situation of a single production unit and process optimization as an example, and compares and selects different process optimization schemes.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A scheduling evaluation method for low entropy operation of a discrete workshop manufacturing system includes the following steps:

[0007] Step 1: According to the discrete workshop manufacturing system problem, analyze the operating status of the discrete workshop manufacturing system and construct the static entropy function of the discrete workshop manufacturing system;

[0008] Step 2: According to the situation that the system is out of control and fuzzy events occur, the dynamic entropy function of the discrete workshop manufacturing system operation is constructed;

[0009] Step 3: Calculate the maximum feasible scheduling time limit of the scheduling scheme;

[0010] Step 4: In order to solve the problem of scheduling scheme selection, the static entropy, dynamic entropy and maximum feasible scheduling time limit are analyzed and compared, and the execution scheme with the smallest system entropy increase is selected as the optimal execution scheduling scheme to guide the actual production scheduling.

[0011] Furthermore, the above step 1 is specifically as follows:

[0012] Based on the current diversified and personalized needs of users, the manufacturing industry is forced to transform to a discrete manufacturing model with multiple varieties and small batches. However, the current workshop production situation is often high in energy consumption and low in efficiency. There is a lot of room for optimization, but the R&D cost of process optimization and machine performance improvement is high and the cycle is long. In contrast, workshop scheduling can achieve multiple indicators optimization in the production process at a lower cost and achieve efficiency growth by rationally planning workshop production resources. The discrete workshop scheduling problem fully considers the flexibility of parts processing procedures and machine flexibility, which is in line with the development trend of the current market. The discrete workshop manufacturing system is a production system that includes personnel, materials, equipment, environment and related production resources, implements the production plan, and turns raw materials into corresponding products. For a given discrete workshop manufacturing system, the operating state of the system is usually determined by the production factors (system resources, variety and quantity of processed products, selection of processing equipment for each product, staff, etc.) and their operating conditions.

[0013] The situation of a discrete manufacturing workshop can be described as follows: there are s parts and r processing machines in a certain production process. Each machine can undertake a specific process processing task of the part, and the production sequence needs to be properly planned to ensure that the parts can be processed and assembled smoothly. However, in the production process, there will be dynamic disturbances such as sudden machine failure, process processing exceeding the specified time, and rework due to substandard part quality during assembly. Therefore, after the dynamic disturbance event occurs, it is necessary to minimize its adverse impact on production and strive to optimize the target, and the following assumptions must be met: (a) The working conditions of the processing workshop and the assembly workshop are complete, and any part can be processed or assembled; (b) If there is no failure in the machine during operation, the machine will continue to run until the processing process is completed; (c) The transportation time of each component is included in the processing time; (d) The workpieces, operations, machines and tools required for processing and assembly are all known in advance.

[0014] Since the discrete workshop manufacturing system is a discrete system, the transmission of information in the system exhibits the characteristics of discrete information transmission. This process can be described with the help of Markov process, which means that the current state of the system depends only on the previous state and has no correlation with any other state.

[0015] Based on the information entropy theory, the information entropy of discrete random variables X is defined as the following formula:

[0016]

[0017] Where: x i is the i-th possible value of variable X, and variable X selects at least one variable parameter of a single manufacturing unit, a single processing step, or a single processing part. i ∈X; p(x i ) is the variable X with value x i The probability when p(x i )≥0; r is the logarithm base; n is the variable X i The number of possible values ​​of i The number is n; variable X represents the variable parameter of the discrete workshop manufacturing system, all x i It is represented as n different states of the manufacturing system, p(x i) is the probability value of each state corresponding to the system, H(X) represents the amount of uncertain information of the entire system. The larger H(X) is, the greater the uncertainty of the system is. Based on the actual structural characteristics of the manufacturing system and the recursive principle of equivalent partitioning, each workstation is regarded as a subsystem, and the system can be equivalently divided into multiple subsystems connected in series or in parallel, and each subsystem is composed of several devices connected in series or in parallel. Then, the calculation of the static entropy of the system can be converted into a mixed calculation process of the complexity of multiple devices in series or in parallel.

[0018] The discrete manufacturing process follows the following principles:

[0019] (1) The processing time of each process of the workpiece is non-negative;

[0020] (2) A workpiece cannot be processed on two machines at the same time;

[0021] (3) Each process of each workpiece cannot be processed repeatedly;

[0022] (4) Once the workpiece process starts on the machine tool, the machine cannot be stopped until it is completed;

[0023] (5) The execution of this process must ensure that the previous process has been completed;

[0024] (6) There is no priority relationship between the processes of different workpieces, and the same workpiece must meet the process relationship between the processes;

[0025] (7) There is a buffer area of ​​a certain capacity in front of each machine to temporarily store the workpieces to be processed.

[0026] The static entropy of part production status can be expressed as:

[0027]

[0028] p i It is the probability that a certain part i goes through the production state, and its calculation value is the ratio of the maximum completion time of a certain part i going through the production state to the total maximum production time of the normal production plan.

[0029] The static entropy of the part process production state can be expressed as:

[0030]

[0031] p j It is the probability that a certain process j goes through the production state, and its calculation value is the ratio of the maximum completion time of a certain process j going through the production state to the total maximum production time of the normal production plan.

[0032] The static entropy of the production state of processing equipment can be expressed as:

[0033]

[0034] p k It is the probability that a certain processing equipment k will go through the production state during the production cycle. Its calculation value is the ratio of the maximum completion time of a certain processing equipment k going through the production state to the total maximum production time of the normal production plan.

[0035] The normal production plan refers to the normal production process without considering the state of out-of-control and fuzzy events.

[0036] Then the system static entropy of a production plan can be expressed as:

[0037]

[0038] Where: H s is the static entropy: C is a constant related to the measurement unit, C>0; s is the total number of all processed parts, m is the total number of processes related to the processing of a certain part; r is the total number of equipment used under a known part batch; n is the maximum number of parts processed simultaneously in the manufacturing system; l is the number of parts processed simultaneously in the system; p ijkl It is the probability that the manufacturing system is processing l parts simultaneously when the j-th process of producing the i-th part is in the k-th equipment. It is calculated as the ratio of the maximum completion time of the system processing l parts simultaneously when the manufacturing system is producing the i-th part in the j-th process of producing the i-th part is in the k-th equipment to the total maximum production time of the normal production plan.

[0039] Furthermore, the above step 2 is specifically as follows:

[0040] The production process can be divided into two categories: one is the normal state (i.e. controlled state) executed according to the expected scheduling plan; the other is the abnormal state that deviates from the expected scheduling plan (i.e. out-of-control state, such as equipment failure in the system, staff operation timeout, temporary task insertion, etc.).

[0041] For discrete workshops, when executing the scheduling plan, the manufacturing system will carry out production operations through a series of objects involving production elements such as objects, machines, and people. In this process, as time goes by, the elements in the system continue to increase, which increases the chaos of the system. This process is the process of increasing system entropy. Until the product arrives at the storage area and the processing plan is completed, the elements in the system begin to decrease, and the entropy value of the system will gradually decrease. After the system completes the processing task, the system entropy value returns to stability.

[0042] This process is the exchange of materials, energy and information between the manufacturing system and the outside world, introducing negative entropy from the outside world to offset the increase of system entropy and keep the system in an orderly operation state. For the system, if the amount of state information of the system operation can be controlled (that is, the system has strong anti-interference ability), the operation complexity will be lower, the entropy value will be less, the operation efficiency of the system can reach the optimal value, and the discrete workshop manufacturing system will operate in a low entropy state.

[0043] Therefore, the low-entropy operation of discrete workshops is to achieve the highest scheduling execution of the manufacturing system, and the complexity of the scheduling process is relatively low. At the same time, the probability of internal uncertainty factors occurring during the system scheduling process is low, and the economic benefits are maximized.

[0044] The key to judging whether a discrete workshop manufacturing system is operating in a low entropy state is to determine the state of manufacturing resources in the system. For discrete workshop manufacturing systems, under a specific production plan, that is, a scheduling plan, the information state of each production factor in the system can be determined. If the system is always in a controlled state, the expected entropy value of the system is determined by the total number of parts in the production plan, the number of processes for parts, the number of machines involved in processing, and other manufacturing resource states and the probability of occurrence of each state, and increases with the increase of processed parts, machines, and processes.

[0045] When the discrete workshop manufacturing system executes the scheduling plan for production, the system entropy value of the manufacturing system under the expected scheduling plan can be determined. However, in actual production, there are production disturbance factors, that is, uncertainties in the production process. Situations such as equipment failures, product processing timeouts, and material flow delays may occur within the system. These uncertainties within the system will cause production chaos, increase the system entropy value, and then an abnormal state will occur in which the actual production deviates from the scheduling plan.

[0046] Furthermore, if the resource status in the manufacturing system is further determined, the probability of its controlled state is p ijkl and the probability of out-of-control state p' ijkl , assuming that the normal number of parts processing steps in the entire system is m i Then the number of delayed states of the processing step is m' i , the number of controlled states of the device is r i , then the number of out-of-control states of the equipment is r' i , then the dynamic entropy of the entire manufacturing system is:

[0047]

[0048] Where: H tis the system operation dynamic entropy: C is a constant related to the measurement unit, C>0; m is the total number of processes related to the processing of a certain component, m' is the total number of processes in which the processing state is uncontrolled, r' is the uncontrolled state of the processing equipment; n is the number of parts processed simultaneously in the manufacturing system; p' ijkl It is the probability that the manufacturing system is in an out-of-control state when the j-th process of producing the i-th part is in the k-th equipment and l parts are processed simultaneously in the system. It is calculated as the ratio of the maximum operating time of the system in an out-of-control state to the total maximum production time of the production plan in this state when the j-th process of producing the i-th part is in the k-th equipment and l parts are processed simultaneously in the system.

[0049] The system operation dynamic entropy can reflect the degree of system uncertainty when the system executes the production scheduling plan, and can also reflect the impact of the internal disturbance on the system.

[0050] Furthermore, in actual production, there is uncertainty in the occurrence of internal disturbance factors, namely fuzzy events. The entropy of the system operation state is further analyzed, and the concept of fuzzy theory is introduced to analyze and process the system processing state.

[0051] Events that make the production processing time uncertain in the production plan, including a series of situations such as production equipment processing timeout, logistics transportation delays, and manual operation delays, are defined as fuzzy events.

[0052] For production units, triangular fuzzy functions can be used to represent the uncertainty within the operating time range of parts, processes, and equipment, thereby quantifying their impact on production status;

[0053] Let μ be a fuzzy set on the universe U, and x is a mapping from U to the interval [0,1].

[0054] μ A :U→[0,1],x→μ A ∈[0,1],

[0055] For any u∈U, there is a number μ(x)∈[0,1] corresponding to it. μ(x) is called the membership degree of x to U, and μ is called the membership function of x, which is also a fuzzy number.

[0056] Introducing triangular fuzzy number B = (a, b, c), B is a fuzzy subset, and the prior probability of x can be described by the triangular fuzzy membership function μ(x):

[0057]

[0058] Where a, b, c are the value ranges of x, a <b<c;

[0059] For the system, it is easy to obtain the ideal, most likely and longest operation time in the production process. Therefore, triangular fuzzy numbers can be used to represent the fuzzy processing time, where a represents the ideal operation time, b represents the maximum possible operation time, and c represents the maximum operation time. This measures the uncertainty within the operation time range and quantifies the impact of the processing time on the production status.

[0060] According to the probability of occurrence of fuzzy events and their impact on operation time, the originally estimated operation time is adjusted. If the probability of a certain fuzzy event causing the operation time to be extended is high, the maximum possible operation time should be appropriately increased, and thus the maximum operation time of the fuzzy event is also increased accordingly.

[0061] The ideal operation time of a fuzzy event refers to the shortest time required when a fuzzy event occurs under optimal conditions, that is, without considering any uncertain factors including machine processing errors and human errors. The ideal operation time of a fuzzy event is set based on the historical data of system production or the experience of field engineers and is an expected value.

[0062] The maximum possible operation time of a fuzzy event refers to the expected operation time under control due to a small range of production fluctuations that may occur when a fuzzy event occurs, which is a delay compared to normal production. This is the expected operation time that is still under control despite the possible uncertainty within a small range (for example, slight manual delays or equipment performance fluctuations). The maximum possible operation time of a fuzzy event is set based on the mode or median obtained from the historical data of system production, reflecting the most likely scenario.

[0063] Substituting the ideal operation time and the maximum possible operation time of the fuzzy event into the above triangular fuzzy number, the maximum operation time under the fuzzy event condition can be obtained through calculation. The maximum operation time of the fuzzy event refers to the maximum tolerable time in the case of large disturbances, such as serious machine failure repair, major human error, etc. It refers to the maximum acceptable delay time without affecting subsequent processing, that is, when all fuzzy events occur, the system processing is at the maximum operation time.

[0064] The fuzzy information entropy of the system is

[0065]

[0066] Among them, P e It represents the probability of fuzzy event e occurring within the production cycle. Its calculation value is the ratio of the maximum processing time under the state of fuzzy event e occurring within the production cycle to the total maximum production time of the production plan when the fuzzy event occurs. g is the total number of all fuzzy events. C is a constant related to the measurement unit, C>0.

[0067] That is, the maximum operating entropy of the system is:

[0068] H z =H s +H d +H z .

[0069] Furthermore, the above step 3 is specifically as follows:

[0070] From the perspective of information theory and manufacturing system complexity, the essence of the deviation of the production scheduling plan during the actual operation is that part of the static information contained in the initial scheduling plan is converted into dynamic information during the operation of the production system. It can be seen that as long as the conversion rate of the production system structural entropy to operational entropy can be measured, the rationality of the scheduling time limit can be evaluated accordingly.

[0071] The system entropy in the scheduling scheme can be expressed as (H s ) is calculated to be the static entropy value of the production system at a certain moment. For a scheduling scheme with a scheduling time limit of T and a time interval (i.e., scheduling accuracy) of Δt for dynamic observation of the actual operating status of the production system, the static entropy of the system is H' s for:

[0072]

[0073] The time interval generated when the production system deviates from the expectation is the average operation entropy H' with a scheduling accuracy of Δt. d for:

[0074]

[0075] That is, within the scheduling expectation T, due to various disturbances in the production process, the expected system entropy in the scheduling plan is H' d The rate of change is towards dynamic entropy, so the maximum feasible scheduling time limit of the production system is:

[0076]

[0077] When the system running time exceeds T max The system production completely deviates from the expected operation, so it is necessary to max System production maintenance was previously performed.

[0078] The system static entropy, operating entropy and maximum feasible scheduling time limit can be used to quantitatively analyze and evaluate the current scheduling plan. By selecting an execution plan with a smaller system entropy increase, the system chaos can be kept at a lower range.

[0079] Compared with the prior art, the present invention has the following beneficial effects and advantages:

[0080] 1. By analyzing the operating status of the discrete workshop manufacturing system, the information entropy is used to quantify the operating status of the number of processed parts, processes and processing equipment during the production scheduling process, and a system static entropy function is established to quantitatively evaluate the operating status of the discrete workshop manufacturing system.

[0081] 2. Based on the uncertainty of processing time, the processing time is represented by fuzzy function, and the dynamic entropy function of system operation is established. The uncertainty of the workshop manufacturing system is combined with the execution expectation of the scheduling plan. Before the actual system operation, the changes of unstable factors between related processes can be obtained to guide the actual production process.

[0082] 3. By calculating the static entropy and dynamic entropy of the production system, the actual maximum effective operation time limit can be obtained. By evaluating the difference in system entropy increase, the system low entropy operation plan can be selected to provide reference value for actual production. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a flow chart of a scheduling evaluation method for low entropy operation of a discrete workshop manufacturing system according to the present invention;

[0084] Figure 2 It is a schematic diagram of the fuzzy function membership of the present invention;

[0085] Figure 3 This is a simplified diagram of the process distribution in the factory's machining workshop;

[0086] Figure 4 This is a schematic diagram of the process flow of the STR production line;

[0087] Figure 5 This is a schematic diagram of the processing position layout of the six-station bottleneck process;

[0088] Figure 6 It is a schematic diagram of the production unit scheduling plan;

[0089] Figure 7 Schematic diagram of actual production time of production unit. DETAILED DESCRIPTION

[0090] The present invention is described in detail below in conjunction with the attached drawings and specific implementation methods.

[0091] Embodiment 1:

[0092] Based on the current diversified and personalized needs of users, the manufacturing industry is forced to transform to a discrete manufacturing model with multiple varieties and small batches. However, the current workshop production situation is often high in energy consumption and low in efficiency. There is a lot of room for optimization, but the R&D cost of process optimization and machine performance improvement is high and the cycle is long. In contrast, workshop scheduling can achieve multiple indicators optimization in the production process at a lower cost and achieve efficiency growth by rationally planning workshop production resources. The discrete workshop scheduling problem fully considers the flexibility of parts processing procedures and machine flexibility, which is in line with the development trend of the current market. The discrete workshop manufacturing system is a production system that includes personnel, materials, equipment, environment and related production resources, implements the production plan, and turns raw materials into corresponding products. For a given discrete workshop manufacturing system, the operating state of the system is usually determined by the production factors (system resources, variety and quantity of processed products, selection of processing equipment for each product, staff, etc.) and their operating conditions.

[0093] The problem of discrete manufacturing workshop can be described as follows: there are s parts in a production process, and there are r processing machines (i.e., equipment), referred to as "machines" for short. Each machine can process part of the process of the parts, and the production sequence is reasonably arranged so that the parts are processed and assembled. However, dynamic disturbance events such as machine failure, process processing timeout, and rework due to unqualified parts quality during assembly may occur during the production process. Therefore, it is necessary to minimize the impact of dynamic disturbance events on production as much as possible after the occurrence of dynamic disturbance events, and optimize the objectives as much as possible. At the same time, the following assumptions need to be met: (a) The working conditions of the processing workshop and the assembly workshop are already in place, and any parts can be processed or assembled; (b) If the machine does not fail during operation, it will continue to run until the processing process is completed; (c) The transportation time of each component is included in the processing time; (d) The workpieces, operations, machines, and tools required for processing and assembly are all known in advance.

[0094] Based on the actual structural characteristics of the manufacturing system and the recursive principle of equivalent division, each operating station can be regarded as a subsystem, that is, the system can be equivalently divided into multiple subsystems connected in series or in parallel, and each subsystem is composed of several devices connected in series or in parallel, and then the calculation of the static entropy of the system can be converted into a mixed calculation of the complexity of multiple devices in series or in parallel. Furthermore, assuming that the machines in a given mechanical processing manufacturing system organize production in a serial or parallel manner, on a single machine k, the probability that part i is produced by machine k is: when the part is produced on the machine in a serial manner, P ik =1 / Ms, where Ms is the number of machines in the production line that are organized in serial fashion. If parts are processed in parallel on the machines, then P jk=1 / Mp, where Mp is the number of parallel machines. If the machines in the system are a mix of serial and parallel arrangements, when a part is processed on one of the parallel machines, then P jk =1 / (Mp*Ms). The discrete manufacturing process follows the following principles:

[0095] (1) The processing time of each process of the workpiece is non-negative;

[0096] (2) A workpiece cannot be processed on two machines at the same time;

[0097] (3) Each process of each workpiece cannot be processed repeatedly;

[0098] (4) Once the workpiece process starts on the machine tool, the machine cannot be stopped until it is completed;

[0099] (5) The execution of this process must ensure that the previous process has been completed;

[0100] (6) There is no priority relationship between the processes of different workpieces, and the same workpiece must meet the process relationship between the processes;

[0101] (7) There is a buffer area of ​​a certain capacity in front of each machine to temporarily store the workpieces to be processed.

[0102] Here are the specific implementation steps:

[0103] 1) Analyze the operating status of the discrete workshop manufacturing system, construct a static entropy model of the discrete workshop manufacturing system, and establish relevant constraints.

[0104] Take the production scheduling plan of a factory in Zhejiang as an example. The factory produces various types of wheel products, mainly relying on two production lines, S and T (see Figure 3 ), the S line has an annual production capacity of 230,000 pieces, and the T line has an annual production capacity of 90,000 pieces. Taking the S line production and processing as an example, the line has a total of 8 processes, namely milling anti-counterfeiting grooves, rough turning, fine turning, six-station, chamfering, milling steel stamps, adjustment, and tapping. The workshop system can be divided into eight processing units according to its processing technology (see Figure 4 ), the production scheduling plan of the workshop is 20h / d, and the scheduling accuracy is 1h. The production static entropy of the system can be described as the sum of the static entropies of each processing unit. There are eight processing units in total, so the static entropy of the part production state can be expressed as:

[0105]

[0106] p i It is the probability that a certain part i goes through the production state, and its calculation value is the ratio of the maximum completion time of a certain part i going through the production state to the total maximum production time of the normal production plan.

[0107] The static entropy of the part process production state can be expressed as:

[0108]

[0109] p j It is the probability that a certain process j goes through the production state, and its calculation value is the ratio of the maximum completion time of a certain process j going through the production state to the total maximum production time of the normal production plan.

[0110] The static entropy of the production state of processing equipment can be expressed as:

[0111]

[0112] p k It is the probability that a certain processing equipment k will go through the production state during the production cycle. Its calculation value is the ratio of the maximum completion time of a certain processing equipment k going through the production state to the total maximum production time of the normal production plan.

[0113] Then the system static entropy of the production plan can be expressed as formula (1), as follows:

[0114]

[0115] where p ijkl It represents the probability that l parts are processed simultaneously in the system when the jth process of producing the i-th part is in the k-th equipment in the process manufacturing unit. s is the static entropy: C is a constant related to the measurement unit, C>0; s is the total number of all processed parts, m is the total number of processes related to the processing of a certain part; r is the total number of equipment used under a known part batch; n is the maximum number of parts processed simultaneously in the manufacturing system; i is a single part, j is a single process, k is the processing equipment, and l is the number of parts processed simultaneously in the system. ijkl It is the probability that the manufacturing system is processing l parts simultaneously when the j-th process of producing the i-th part is in the k-th equipment. It is calculated as the ratio of the maximum completion time of the system processing l parts simultaneously when the manufacturing system is producing the i-th part in the j-th process of producing the i-th part is in the k-th equipment to the total maximum production time of the normal production plan.

[0116] The normal production plan refers to the normal production process without considering the state of out-of-control and fuzzy events.

[0117] Select the key bottleneck process and the six-station professional processing machine tool workbench for specific calculation instructions, and the station diagram (see Figure 5) are connected in series, and the main processes are 6: loading and unloading, drilling threaded bottom holes and tapered bottom holes, milling semicircles, expanding holes, milling oil drain grooves, and drilling large tapered holes. The daily production scheduling plan (see Figure 6 ), where: the horizontal axis is the scheduling and operation duration, the vertical axis is the different states of the manufacturing unit, Ⅰ~VI are the parts processed in the corresponding processes, A1~A6 represent the parts clamping and processing station adjustment period between processes, S1~S6 represent the system state of the parts in the production unit, and m1~m6 represent the processing equipment corresponding to different processes. As the scheduling plan proceeds, the manufacturing unit has different states when it goes through different manufacturing resources.

[0118] According to formula (1), the static entropy of processing in each workstation can be calculated, that is, the static entropy of the production unit (see Table 1).

[0119]

[0120] 2) Construct the operation state entropy model of the discrete workshop manufacturing system. In order to solve the operation state entropy of the scheduling plan, the discrete events of all scheduling plans in the actual workstation processing production are taken as separate operation states (see Figure 6 ) One week of scheduling measurement data is selected as the statistical probability of occurrence of different states, and the probability of occurrence of each state is calculated according to the average duration t of the scheduling plan of different states (see Figure 7 ). Among them: the horizontal axis is the scheduling and operation duration of the processing unit, the vertical axis is the different states of the manufacturing unit, Ⅰ~VI are the parts processed in the corresponding processes, A1~A6 represent the parts clamping and processing station adjustment period between processes, S1~S6 represent the system state of the parts in the processing process of the production unit, m1~m6 represent the processing equipment corresponding to different processes, because the operating difficulty of different equipment and the actual execution process have errors in the actual processing, and the actual execution time of each part will fluctuate compared with the ideal time.

[0121] In actual production, the state of internal disturbance factors is uncertain. To further analyze the entropy of the system operation state, the concept of fuzzy theory is introduced to analyze and process the system processing state.

[0122] For this production unit, the uncertainty within the operating time range of a process is represented by a fuzzy trigonometric function, thereby quantifying the entropy impact of a single part production process on the production status.

[0123] Let μ be a fuzzy set on the universe U, and x is a mapping from U to the interval [0,1].

[0124] μ A :U→[0,1],x→μ A(x)[0,1],

[0125] For any u∈U, there is a number μ(x)∈[0,1] corresponding to it. μ(x) is called the membership degree of x to U, and μ is called the membership function of x, which is also a fuzzy number.

[0126] Introducing triangular fuzzy number B = (a, b, c), B is a fuzzy subset, the prior probability of x can be described by the triangular fuzzy function membership μ (x):

[0127]

[0128] Where a, b, and c are the value ranges of x, respectively. a represents the ideal operation time of the process, b represents the most likely processing time of the process, and c represents the longest operation time of the process.

[0129] The ideal operation time of a fuzzy event refers to the shortest time required when a fuzzy event occurs under optimal conditions, that is, without considering any uncertain factors including machine processing errors and human errors. The ideal operation time of a fuzzy event is set based on the historical data of system production or the experience of field engineers and is an expected value.

[0130] The maximum possible operation time of a fuzzy event refers to the expected operation time that is still under control despite the small-scale production fluctuations that occur when a fuzzy event occurs, resulting in a delay in the operation time compared to normal production. The maximum possible operation time of a fuzzy event is set based on the mode or median obtained from the historical data statistics of the system's production, reflecting the most likely situation.

[0131] In Example 1 of the present invention, the fuzzy event is set as the interruption of process I. The ideal operation time for processing the fuzzy event is 0 seconds, the maximum possible operation time is 20 seconds, and the calculated maximum operation time is 50 seconds.

[0132] The maximum operating entropy of the system is:

[0133] H d =H s +H t +H c

[0134] H s is the static entropy function, H t To run the dynamic entropy function, H in Example 1 of the present invention t =0, that is, to examine the normal processing state and the state where a fuzzy event may occur.

[0135] According to the comprehensive analysis of production experience, the factors affecting the delay of each part of the six-station processing are processed to obtain the expected processing time range. At the same time, the processing influence of fuzzy events on the system is combined and processed, and then the maximum dynamic entropy value of the six-station processing is calculated. The results are as follows: (see Table 2)

[0136] Table 2 Dynamic entropy results of six stations

[0137]

[0138] The fuzzy operation time in each row in Table 1 corresponds to the ideal operation time, the maximum possible operation time and the maximum operation time from left to right.

[0139] 3) The system entropy in the scheduling scheme can be expressed as (H s ) is calculated as the static entropy value of the production system at a certain moment. For a scheduling scheme with a scheduling time limit of T = 20h and a time interval for dynamic observation of the actual operating status of the production system (i.e., scheduling accuracy) of Δt = 1h, the system entropy H' s for:

[0140]

[0141] The time interval generated when the production system deviates from the expectation is the average operation entropy H' with a scheduling accuracy of Δt. d for:

[0142]

[0143] The maximum feasible scheduling time limit for this production system is:

[0144]

[0145] The part that does not deviate during the actual operation is the scheduling execution degree, which is expressed by the relative value Y:

[0146] The scheduling compliance is:

[0147]

[0148] That is, if the equipment process of the production unit is not adjusted, for the entire production unit, when executing the scheduling plan for 20 hours a day with a scheduling accuracy of 1 hour, the maximum execution time is 18.59 hours, that is, the production plan needs to be adjusted after 18.59 hours.

[0149] By analyzing the entropy value of the bottleneck process, we can know that in actual processing, the entropy value generated by the loading and unloading station is relatively high, which has the greatest impact on maintaining the efficiency and order of the entire production process. The actual loading and unloading situation is highly related to the worker's operating proficiency. There are large differences between workers with different proficiency levels, and training is required. At the same time, the last process of drilling a large tapered hole will also generate a large entropy value, which needs to be improved.

[0150] Two combined machine tools and one ordinary CNC milling machine were selected to replace the six-station machine. Composite tools were used to combine the two previous countersunk hole processing procedures into one, so that the original six procedures were optimized to three procedures, shortening the processing time. After optimization, the six-station processing procedures became: loading and unloading-drilling threaded holes, tapered holes and drilling taper bottom holes-milling grooves.

[0151] The static entropy of the six stations after optimization is shown in Table 3:

[0152] Table 3 Optimized static entropy results

[0153]

[0154] The dynamic entropy of the six stations after optimization is shown in Table 4:

[0155] Table 4 Dynamic entropy results after optimization

[0156]

[0157]

[0158] After optimization, under the same scheduling time limit T = 20h and scheduling accuracy of 1h, the system entropy H' s2 for:

[0159]

[0160] The average operating entropy H' generated by the deviation of the production system from the expected d2 for:

[0161]

[0162] The maximum feasible scheduling time limit of the production system is:

[0163]

[0164] That is, when the equipment process of the production unit is optimized, the maximum execution time for the entire production unit is 27.51 hours when the scheduling plan is executed 20 hours a day with a scheduling accuracy of 1 hour.

[0165] 4) In order to solve the problem of scheduling scheme selection, the static entropy, dynamic entropy, maximum feasible scheduling time limit and scheduling execution degree are analyzed and compared to obtain the optimal execution scheduling scheme to guide the actual production scheduling.

[0166] Comparison table of evaluation indicators for low entropy operation of scheduling schemes

[0167] Scheduling plan Static entropy / bit Dynamic entropy / bit Maximum feasible scheduling time limit / h Initial plan 2.564 2.593 18.59 Optimization plan 1.503 1.863 27.51

[0168] By comparing the initial plan and the optimized plan, it can be seen that all indicators of the optimized plan are better than those of the initial plan, which means that after the optimization adjustment, the degree of system chaos can be reduced, which is conducive to achieving low-entropy production operation.

[0169] The above embodiments are only used to illustrate the present invention, and each step can be changed. On the basis of the technical solution of the present invention, any improvement and equivalent transformation of individual steps based on the principle of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing systems, characterized in that The following steps are involved: Step 1: Construct the operating conditions and principles of the discrete workshop manufacturing system, analyze the operating status of the discrete workshop manufacturing system, and construct the static entropy function of the discrete workshop manufacturing system; Step 2: According to the situation that the system is out of control and fuzzy events occur, the dynamic entropy function of the discrete workshop manufacturing system operation is constructed; Step 3: Calculate the maximum feasible scheduling time limit of the scheduling scheme; Step 4: In order to solve the problem of scheduling scheme selection, the static entropy, operating entropy and maximum feasible scheduling time limit are analyzed and compared, and the execution scheme with the smallest system entropy increase is selected as the optimal execution scheduling scheme to guide the actual production scheduling.

2. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing systems as claimed in claim 1, characterized in that The specific process of step 1 is: Based on the information entropy theory, the information entropy of discrete random variables X is defined as the following formula: Where: x i is the i-th possible value of variable X, and variable X selects at least one variable parameter of a single manufacturing unit, a single processing step, or a single processing part, x i ∈X; p(x i ) is the variable X with value x i The probability when p(x i )≥0; r is the logarithm base; n is the variable X i The number of possible values ​​of i The number is n; variable X represents the variable parameter of the discrete workshop manufacturing system, all x i It is represented as n different states of the manufacturing system, p(x i ) is the probability value of each state corresponding to the system, H(X) represents the uncertainty information of the whole system. The larger H(X) is, the greater the uncertainty of the system is. Based on the actual structural characteristics of the manufacturing system and the recursive principle of equivalent partitioning, each workstation is regarded as a subsystem, and the system can be equivalently divided into multiple subsystems connected in series or in parallel, and each subsystem is composed of several devices connected in series or in parallel. Then, the calculation of the static entropy of the system can be converted into a mixed calculation process of the complexity of multiple devices in series or in parallel. Construct the following static entropy functions for each state: The static entropy of the part production state is expressed as: p i is the probability that a part i goes through a production state, and its calculation value is the ratio of the maximum completion time of a part i going through a production state to the total maximum production time of the normal production plan; The static entropy of the part process production state is expressed as: p j is the probability that a process j goes through the production state, and its calculation value is the ratio of the maximum completion time of a process j going through the production state to the total maximum production time of the normal production plan; The static entropy of the production state of processing equipment can be expressed as: p k It is the probability that a certain processing equipment k experiences a production state during the production cycle. Its calculation value is the ratio of the maximum completion time of a certain processing equipment k experiencing a production state to the total maximum production time of the normal production plan; Then the static entropy of a production plan system is expressed as: Where: H s is the static entropy: C is a constant related to the measurement unit, C>0; s is the total number of all processed parts, m is the total number of processes related to the processing of a certain part; r is the total number of equipment used under a known part batch; n is the maximum number of parts processed simultaneously in the manufacturing system; l is the number of parts processed simultaneously in the system; p ijkl is the probability that the system processes l parts at the same time when the j-th process of producing the i-th part is on the k-th equipment. Its calculation value is the ratio of the maximum completion time of the system processing l parts at the same time when the j-th process of producing the i-th part is on the k-th equipment to the total maximum production time of the normal production plan; The normal production plan refers to the normal production process without considering the state of out-of-control and fuzzy events.

3. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing system as claimed in claim 1, characterized in that Step 1 Discrete workshop manufacturing system, including the following assumptions: (a) The working conditions of the processing workshop and assembly workshop are already available, and any part can be processed or assembled; (b) If there is no failure in the machine during operation, the machine will continue to run until the processing process is completed; (c) The transportation time of each part is included in the processing time; (d) The workpieces, operations, machines and tools required for processing and assembly are all known in advance.

4. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing systems as claimed in claim 1, characterized in that Step 1 Discrete workshop manufacturing system, whose discrete production and manufacturing process follows the following principles: (1) The processing time of each process of the workpiece is non-negative; (2) A workpiece cannot be processed on two machines at the same time; (3) Each process of each workpiece cannot be processed repeatedly; (4) Once the workpiece process starts on the machine tool, the machine cannot be stopped until it is completed; (5) The execution of this process must ensure that the previous process has been completed; (6) There is no priority relationship between the processes of different workpieces, and the same workpiece must meet the process sequence relationship between the processes; (7) There is a buffer area of ​​a certain capacity in front of each machine to temporarily store the workpieces to be processed.

5. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing system as claimed in claim 1, characterized in that Step 2 The specific process of establishing the dynamic entropy function of the discrete workshop manufacturing system operation is: The production process of the discrete workshop manufacturing system is divided into two categories: one is the normal state executed according to the expected scheduling plan, that is, the controlled state; the other is the abnormal state deviating from the expected scheduling plan, that is, the out-of-control state, including at least one of the abnormal states of equipment failure, staff operation timeout, and temporary task insertion in the system; The low entropy state operation of the discrete workshop means that the scheduling execution of the manufacturing system is the highest, and the complexity of the scheduling process is low. At the same time, the probability of internal uncertainty factors occurring during the system scheduling process is low. The key to judging whether the discrete workshop manufacturing system is in a low entropy state is to determine the state of the manufacturing resources in the system. In order to further determine the state of the resources in the manufacturing system, the following parameters are defined: The probability of the controlled state is p ijkl and the probability of out-of-control state p' ijkl , assuming that the normal number of parts processing steps in the entire system is m i Then the number of delayed states of the processing step is m' i , the number of controlled states of the device is r i , then the number of out-of-control states of the equipment is r' i , then the dynamic entropy of the entire manufacturing system is: Where: H t is the system operation dynamic entropy: C is a constant related to the measurement unit, C>0; m is the total number of processes related to the processing of a certain component, m' is the total number of processes in which the processing state is uncontrolled, r' is the uncontrolled state of the processing equipment; n is the number of parts processed simultaneously in the manufacturing system; p' ijkl It is the probability that the system is in an out-of-control state when the j-th process of producing the i-th part is in the k-th equipment and l parts are processed simultaneously in the system. It is calculated as the ratio of the maximum operation time of the system in an out-of-control state to the total maximum production time of the production plan in this state when the j-th process of producing the i-th part is in the k-th equipment and l parts are processed simultaneously in the system. The dynamic entropy of system operation can reflect the degree of system uncertainty when the system executes the production scheduling plan, and can also reflect the impact of the internal disturbance of the system on the system.

6. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing systems as claimed in claim 5, characterized in that In the process of constructing the system operation dynamic entropy in step 2, in actual production, the state of internal disturbance factors is uncertain. The system operation dynamic entropy is further analyzed, and the fuzzy theory concept is introduced to analyze and process the system processing state; Events that make the production processing time uncertain in the production plan, including a series of situations such as production equipment processing timeout, logistics transportation delay, and manual operation delay, are defined as fuzzy events; For production units, triangular fuzzy functions can be used to represent the uncertainty within the operating time range of parts, processes, and equipment, thereby quantifying their impact on production status; Let μ be a fuzzy set on the universe U, and x is a mapping from U to the interval [0,1]. m A :U→[0,1],x→μ A ∈[0,1], For any u∈U, there is a number μ(x)∈[0,1] corresponding to it. μ(x) is called the membership degree of x to U, and μ is called the membership function of x, which is also a fuzzy number. Introducing triangular fuzzy number B = (a, b, c), B is a fuzzy subset, and the prior probability of x can be described by the triangular fuzzy membership function μ(x): Where a, b, c are the value ranges of x, a <b<c; For the system, it is easy to obtain the ideal, most likely and longest operation time in the production process. Therefore, the fuzzy processing time can be represented by triangular fuzzy numbers, a represents the ideal operation time, b represents the maximum possible operation time, and c represents the maximum operation time, thereby measuring the uncertainty within the operation time range and quantifying the impact of the processing time on the production status; The ideal operation time of a fuzzy event refers to the shortest time required when a fuzzy event occurs under optimal conditions, that is, without considering any uncertain factors including machine processing errors and human errors. The ideal operation time of a fuzzy event is set based on the historical data of system production or the experience of field engineers and is an expected value. The maximum possible operation time of a fuzzy event refers to the expected operation time that is still under control, but delayed compared to normal production due to a small range of production fluctuations when a fuzzy event occurs. The maximum possible operation time of a fuzzy event is set based on the mode or median obtained from the historical data of system production, reflecting the most likely situation. Substituting the ideal operation time and the maximum possible operation time of the fuzzy event into the above triangular fuzzy number, the maximum operation time under the condition of the fuzzy event can be obtained through calculation. The maximum operation time of the fuzzy event refers to the maximum tolerable time in the case of a large disturbance. System fuzzy information entropy: Among them, P e It represents the probability of fuzzy event e occurring in the production cycle. Its calculation value is the ratio of the maximum processing time under the state of fuzzy event e occurring in the production cycle to the total maximum production time of the production plan when the fuzzy event occurs. g is the total number of all fuzzy events. C is a constant related to the measurement unit, C>0. That is, the maximum operating entropy of the system is: H d =H s +H t +H c H s The static entropy function established in step 1.

7. A scheduling evaluation method for low entropy operation of discrete workshop manufacturing system as claimed in claim 1, characterized in that Step 3 The process of calculating the maximum feasible scheduling time limit and scheduling execution degree of the scheduling scheme is as follows: The system entropy in the scheduling scheme can be expressed as s Calculate the static entropy value of the production system at a certain moment; for a scheduling scheme with a scheduling time limit of T and a time interval for dynamic observation of the actual operating status of the production system, that is, a scheduling accuracy of Δt, the static entropy of the system is H' s for: The time interval generated when the production system deviates from the expectation is the average operation entropy H' with a scheduling accuracy of Δt. d for: That is, within the scheduling expectation T, due to various disturbances in the production process, the expected system entropy in the scheduling plan is H' d The rate of change is towards dynamic entropy, so the maximum feasible scheduling time limit of the production system is: When the system running time exceeds T max The system production completely deviates from the expected operation, so it is necessary to max Previously, system production maintenance was performed; The system static entropy, operating entropy and maximum feasible scheduling time limit can be used to quantitatively analyze and evaluate the current scheduling plan. By selecting an execution plan with a smaller system entropy increase, the system chaos can be kept at a lower range.

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