Evaluation method for multi-attribute maintenance plan of steel production line

By defining the deviation and balance of maintenance tasks in the steel production line, and combining equipment stability and concentration, a multi-level evaluation system is adopted to conduct quantitative comprehensive evaluation of the steel production line maintenance plan, solving the problem of inability to effectively coordinate multi-attribute requirements in the existing technology, and improving the efficiency of maintenance operations and the reliability of the production system.

CN114881253BActive Publication Date: 2025-04-08SHANGHAI JIAOTONG UNIV
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Patent Information

Application Number
CN202210221916.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-03-07
Publication Date
2025-04-08
Estimated Expiration
2042-03-07

AI Technical Summary

Technical Problem

The existing technology cannot effectively coordinate the deviation, balance and concentration requirements in steel production line maintenance plans, making it difficult for the maintenance plan evaluation results to guide subsequent optimization design.

Method used

By defining the deviation of maintenance tasks and the balance of working days during the planning period, and using a four-level evaluation system, the maintenance plan is initially evaluated and screened; the stability and concentration are defined at the equipment level, and the comprehensive evaluation value of the equipment is calculated based on the equipment importance weight at the system level to obtain the comprehensive evaluation value of the maintenance plan according to the equipment importance weight for scheme comparison.

Benefits of technology

It realizes a comprehensive and multi-attribute quantitative evaluation of steel production line maintenance plans, improves the executability and execution efficiency of maintenance operations, ensures the reliability of the production system, and provides guidance on the optimization design of subsequent maintenance plans.

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Abstract

A method for evaluating a multi-attribute maintenance plan for a steel production line, which defines the deviation of maintenance tasks and the balance of working days in a planning period and adopts a four-level evaluation system to perform preliminary evaluation and screening on the maintenance plan; then defines stability and concentration at the equipment level, and calculates the comprehensive evaluation value of all equipment in the maintenance plan in combination with attribute weights; finally, at the system level, the comprehensive evaluation value of the maintenance plan is obtained according to the equipment importance weights to compare the plans; the present invention can quantitatively integrate the multi-attribute performance of the steel production line maintenance plan and perform objective evaluation, so as to improve the executability and execution efficiency of the maintenance work and ensure the reliability of the production system.
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Description

Technical Field

[0001] The present invention relates to a technology in the field of steel manufacturing, and specifically to an evaluation method for a multi-attribute maintenance plan for a steel production line. Background Art

[0002] In the field of steel production, the maintenance plan of inspecting, repairing and maintaining the key parts of the specified equipment at a specific time is the basis for enterprises to improve equipment performance, thereby ensuring the quality of steel and even reducing production safety accidents. However, the steel production line occupies a large area, involves many processes, has complex equipment and many parts that need to be repaired, which leads to the need for maintenance plans to take into account a variety of interrelated but contradictory requirements. Therefore, in actual production, enterprises often generate a variety of maintenance alternatives according to the reserve of production resources (manpower, spare materials, etc.) and then make manual selection and judgment, which makes the evaluation of multiple alternative maintenance plans a key task in the equipment reliability analysis and maintenance and repair stage of the enterprise.

[0003] Specifically, the maintenance plan of the steel production line involves the following three aspects: ① Deviation / stability: The key parts of the equipment under different workloads and working mechanisms have different maintenance frequency requirements. The actual maintenance operation cycle should not deviate too much from the theoretical maintenance operation cycle determined by the equipment manufacturer, data diagnosis, etc.; ② Balance: It should be avoided that the maintenance tasks are too concentrated on a specific date, otherwise the maintenance work is easily interrupted due to resource shortages; ③ Concentration: The main plant area of ​​the steel enterprise covers thousands of acres, the equipment is complex and difficult to load and unload, and the maintenance tasks of different parts of the same equipment are concentrated as much as possible to improve the operation efficiency. However, the current subjective manual evaluation technology cannot effectively coordinate the above requirements, and the evaluation results are also difficult to provide guidance for the optimization design of subsequent maintenance plans. To this end, defining appropriate quantitative indicators from the above three perspectives and conducting effective synthesis to objectively evaluate the maintenance plan is an important prerequisite for ensuring the normal maintenance of the steel production line. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention proposes an evaluation method for multi-attribute maintenance plans for steel production lines, which can quantitatively integrate the multi-attribute performance of steel production line maintenance plans and conduct objective evaluation, so as to improve the feasibility and efficiency of maintenance operations and ensure the reliability of the production system.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to an evaluation method for a multi-attribute maintenance plan for a steel production line. The maintenance plan is preliminarily evaluated and screened by defining the deviation of maintenance tasks and the balance of working days in a planning period and adopting a four-level evaluation system; then stability and concentration are defined at the equipment level, and the comprehensive evaluation value of all equipment in the maintenance plan is calculated in combination with the attribute weight; finally, the comprehensive evaluation value of the maintenance plan is obtained at the system level according to the equipment importance weight to compare the plans; the method specifically comprises the following steps:

[0007] Step 1: Export the enterprise maintenance system data within the planning period and build the planning period collection in sequence Equipment Collection Maintenance task collection Maintenance cycle set R = {r i |i∈I}, equipment and maintenance task association matrix Γ={F ik |i∈I,k∈K} and the standard maintenance matrix E={e ij |i∈I,j∈J}, where: j=1 represents the first day of the planning period, represents the last day of the planning period; k corresponds to the equipment number in the enterprise maintenance system; for n k The equipment k (k∈K) with maintenance tasks is numbered as 1+∑ θ<k n θ ,…,n k +∑ θ<k n θ (θ,k∈K); r i is the maintenance cycle of maintenance task i, which is directly obtained from the enterprise system; when maintenance task i is related to equipment k, F ik =1, otherwise F ik =0; satisfies the condition r i -|dT′ i |+1=j when e ij =1, otherwise e ij =0,|dT′ i | represents the first day of the planning period d and the last operation execution date T′ of maintenance task i i The number of days between.

[0008] The enterprise maintenance system data includes: equipment number, maintenance task number, maintenance cycle, last maintenance date and the maximum number of maintenance tasks U that can be supported.

[0009] Step 2: Convert the maintenance plan to be evaluated into a maintenance task execution matrix And calculate the resource requirement set S = {s j |j∈J}, where: maintenance task i is scheduled to be executed on the jth day within the planning period x ij =1, otherwise x ij=0;

[0010] Step 3: Calculate the deviation of maintenance task i in the maintenance plan and the balance of working days during the planning period A four-level evaluation system is used to evaluate the deviation and balance of the maintenance plan.

[0011] The deviation evaluation level of the maintenance plan is as follows: the maximum deviation of all maintenance tasks is recorded as D max , when D max ≤10% is excellent, when 10% <D max ≤20% is good, when 20% <D max ≤30% is normal, when 30% <D max When the maintenance cycle is worse, the maintenance task operation cycle in the maintenance plan deviates greatly from the theoretical cycle, and the maintenance plan should be adjusted.

[0012] The balance evaluation level of the maintenance plan is specifically: calculate the average balance of all working days in the planning period And the balance of each working day B j With B u The absolute difference ratio of |B j -B u | / B u , where the maximum ratio is denoted as B max , when B max ≤10% is excellent, when 10% max ≤15% is good, when 15% max ≤20% is normal, when 20% max When the maintenance situation is worse, the maintenance tasks in the maintenance plan are over-concentrated and the maintenance plan should be adjusted.

[0013] Step 4: Calculate the stability of each maintenance task i in the maintenance plan After normalization, the stability of each device k is obtained

[0014] The normalization process is: The min-max method is used to normalize the stability of maintenance task i. where a min and a max They are Minimum and maximum values, when a max =a min When i =1.

[0015] Step 5: Calculate the concentration c of each equipment i in the maintenance plan k ​​​=∑ j∈J (∑ i∈I F ik X ij ) 2 , and normalized.

[0016] The normalization process is: k The concentration of device k is obtained by normalization using the min-max method. When the maintenance tasks related to equipment k are evenly distributed to each day, c k Minimum, specifically expressed as When the maintenance tasks related to equipment k are concentrated as much as possible on certain days, c k Maximum, specifically expressed as Where P k =∑ i∈I,j∈J F ik X ij , U is the maximum number of maintenance tasks that the enterprise can support, derived from the enterprise maintenance system, for The integer part, mod(P k ,U) is P k The remainder when divided by U.

[0017] Step 6: Calculate the comprehensive evaluation value M of each device k by combining the stability and concentration of the equipment in the maintenance plan k =W k1 A k +W k2 C k , and based on the importance weight of each device Quantitatively obtain the comprehensive evaluation value of the maintenance plan O = ∑ k∈K η k M k ; Finally, by comparing the evaluation values ​​of different maintenance plans, they can be ranked from high to low, and the best maintenance plan can be selected for implementation, where: weight W k1 and W k2 The sum of is 1.

[0018] Technical Effects

[0019] Compared with the prior art, the present invention introduces a four-level evaluation system of deviation and balance to conduct a preliminary assessment of the deviation and balance of maintenance plans, and realizes the preliminary screening of maintenance plans; the stability and concentration indicators are defined at the equipment level to quantitatively reflect the implementation effect of the maintenance plan, and attribute weights and equipment importance weights are proposed at the system level to obtain the comprehensive evaluation value of the maintenance plan for plan comparison. Compared with the traditional method of qualitative judgment based on experience, this method can intuitively and quantitatively integrate the multi-attribute performance of the steel production line maintenance plan and conduct an objective evaluation, which can improve the executability and execution efficiency of maintenance operations, ensure the reliability of the production system, and the evaluation results can further guide the optimization design of subsequent maintenance plans. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0021] This example takes the 1580 finishing rolling production line of a steel production enterprise as an example. According to the existing maintenance plan preparation criteria, the enterprise formulates four maintenance plans for the maintenance tasks of the week from 2021 / 5 / 24 to 2021 / 5 / 30, such as Figure 1 As shown, the evaluation method of this embodiment specifically includes the following steps:

[0022] Step 1: Export the enterprise maintenance system data (including equipment number, maintenance task number, maintenance cycle, last maintenance date, and the maximum number of maintenance tasks supported U=65) within the planning period 2021 / 5 / 24 to 2021 / 5 / 30, as shown in Table 2; and construct the planning period set J, equipment set K, maintenance task set I, maintenance cycle set R, equipment and maintenance task association matrix Γ and standard maintenance matrix E in turn, where:

[0023] ① The planning period set J = {1, 2, …, j, …, 7}, where j = 1 represents 2021 / 5 / 24 and j = 6 represents 2021 / 5 / 30;

[0024] ② Equipment set K = {1, 2, ..., k, ..., 15}, where k = 1 represents equipment 660159, k = 15 represents equipment 668750, and they correspond one-to-one to the equipment numbers in the enterprise maintenance system;

[0025] ③Maintenance task set I = {1, 2, ..., i, ..., 326}, where i = 1 represents the maintenance task I02D08 of equipment 660159, and i = 326 represents the maintenance task I32D01 of equipment 668750;

[0026] ④Maintenance cycle set R = {7, 14, …, 14}, directly obtained from the enterprise system;

[0027] ⑤ Correlation matrix Γ = {Fik |i∈I,k∈K}, where maintenance task i is related to equipment k, F ik =1, otherwise F ik =0, as shown in Table 3;

[0028] ⑥ Standard maintenance matrix E = {e ij |i∈I,j∈J}, where the condition r is satisfied i -|dT′ i |+1=j when e ij =1, otherwise e ij =0,|dT′ i |Represents the first day of the planning period d = 2021 / 5 / 24 and the last execution date of maintenance task i T′ i The interval between the two treatments is shown in Table 4.

[0029] Table 2 Enterprise maintenance system data during the planning period 2021 / 5 / 24 to 2021 / 5 / 30

[0030] Serial number Equipment No. Maintenance task number Maintenance cycle (days) Last maintenance date 1 660159 I02D08 7 2021 / 5 / 19 2 660159 I07D02 14 2021 / 5 / 14 3 660159 I07D03 14 2021 / 5 / 12 … … … … … 325 668750 I22D04 14 2021 / 5 / 12 326 668750 I32D01 14 2021 / 5 / 12

[0031] Table 3 Equipment and maintenance task correlation matrix Γ

[0032]

[0033] Table 4 Standard maintenance matrix E

[0034]

[0035]

[0036] Step 2: Convert the four maintenance plans to be evaluated (as shown in Table 5, where plan 1 is the maintenance plan obtained based on the theoretical maintenance cycle, and plans 2 to 4 are alternative plans prepared by the enterprise according to the existing compilation criteria) into the maintenance task execution matrix X 326×7 , and calculate the resource requirement set S, including:

[0037] ①Execution matrix X 326×7 ={x ij |i∈I,j∈J}, where maintenance task i is scheduled to be performed on the jth day within the planning period. ij =1, otherwise x ij =0, the execution matrix of Scheme 1 is shown in Table 4, and the execution matrices of the other three maintenance schemes are shown in Tables 6 to 8;

[0038] ② The resource requirement set of scheme 1 is S = {0, 1, 1, 1, 1, 0, 0}, and the resource requirement sets of the other three maintenance schemes are all S = {1, 1, 1, 1, 1, 0, 0}, where

[0039] Table 5 Maintenance solutions to be evaluated

[0040] Maintenance Task i Solution 1 Solution 2 Option 3 Option 4 1 2021 / 5 / 26 2021 / 5 / 27 2021 / 5 / 25 2021 / 5 / 27 2 2021 / 5 / 28 2021 / 5 / 26 2021 / 5 / 27 2021 / 5 / 25 3 2021 / 5 / 26 2021 / 5 / 26 2021 / 5 / 26 2021 / 5 / 26 … … … … 325 2021 / 5 / 26 2021 / 5 / 25 2021 / 5 / 25 2021 / 5 / 26 326 2021 / 5 / 26 2021 / 5 / 26 2021 / 5 / 27 2021 / 5 / 26

[0041] Table 6 Maintenance task execution matrix of scheme 2

[0042]

[0043] Table 7 Maintenance task execution matrix of scheme 3

[0044]

[0045]

[0046] Table 8 Maintenance task execution matrix of scheme 4

[0047]

[0048] Step 3: Calculate the deviation of maintenance tasks in the maintenance plan and the balance of working days in the planning period, and use the four-level evaluation system to evaluate the deviation and balance of the maintenance plan. As shown in Tables 9 and 10, the results show that the deviation and balance of all maintenance plans are max =0.29, the deviation evaluation is average; B max They are 0.50, 0.20, 0.20 and 0.20 respectively, and the balance evaluation is poor, fair, fair and fair, including:

[0049] ① Deviation of maintenance task i The deviation evaluation level of the maintenance plan is as follows: The maximum deviation of all maintenance tasks is recorded as D max , when D max ≤10% is excellent, when 10% <D max ≤20% is good, when 20% <D max ≤30% is normal, when 30% <D max When the maintenance task cycle in the maintenance plan deviates greatly from the theoretical cycle, the maintenance plan should be adjusted;

[0050] ② Average value of working day balance Balance degree of each working day B j With B u The absolute difference ratio of |B j -B u | / B u , where the maximum ratio is denoted as B max ; The balance evaluation level of the maintenance plan is as follows: max ≤10% is excellent, when 10% max ​≤15% is good, when 15% max ≤20% is normal, when 20% max When the maintenance situation is worse, the maintenance tasks in the maintenance plan are over-concentrated and the maintenance plan should be adjusted.

[0051] Table 9 Deviation of maintenance plan

[0052] Maintenance Task i Solution 1 Solution 2 Option 3 Option 4 1 0 0.14 0.14 0.14 2 0 0.14 0.07 0.21 3 0 0.00 0.00 0.00 … … … … … 325 0 0.07 0.07 0.00 326 0 0.00 0.07 0.00

[0053] Table 10 Balance of maintenance plan

[0054]

[0055] Step 4: Calculate the stability of all maintenance tasks in the maintenance plan, and obtain the stability of all equipment after normalization, as shown in Table 11, including:

[0056] ① The stability of maintenance task i without normalization Specifically expressed as

[0057] ② Normalization refers to The min-max method is used to normalize the stability of maintenance task i. where a min and a max They are Minimum and maximum values, when a max =a min When i =1;

[0058] ③Stability A of equipment k in the maintenance plan k It is obtained by weighted calculation of the stability of the related maintenance tasks, which is specifically expressed as

[0059] Table 11 Stability of maintenance plan

[0060]

[0061]

[0062] Step 5: Calculate the concentration of all equipment in the maintenance plan and perform normalization, as shown in Table 12, including:

[0063] ① The unnormalized concentration c of device k k =∑ j∈J (∑ i∈I F ik X ij ) 2 ;​​

[0064] ② Normalization refers to the k The concentration of device k is obtained by normalization using the min-max method. When the maintenance tasks related to equipment k are evenly distributed to each day, c k Minimum, specifically expressed as When the maintenance tasks related to equipment k are concentrated as much as possible on certain days, c k Maximum, specifically expressed as Where P k =∑ i∈I,j∈J F ik X ij , U is the maximum number of maintenance tasks that the enterprise can support, 65, derived from the enterprise maintenance system, for The integer part, mod(P k ,U) is P k The remainder when divided by U.

[0065] Table 12 Concentration of maintenance plans

[0066] Equipment Solution 1 Solution 2 Option 3 Option 4 1 0.19 0.44 0.03 0.23 2 0.20 0.48 0.42 0.16 3 0.12 0.45 0.10 0.20 4 0.33 0.22 0.22 0.22 5 0.18 0.34 0.09 0.20 6 0.11 0.39 0.15 0.15 7 0.18 0.39 0.08 0.18 8 0.66 0.82 0.17 0.39 9 0.25 0.38 0.29 0.10 10 0.19 0.44 0.10 0.24 11 0.33 0.38 0.38 0.38 12 0.11 0.44 0.03 0.24 13 0.19 0.24 0.10 0.10 14 0.17 0.22 0.06 0.06 15 0.33 0.38 0.38 0.38

[0067] Step 6: Calculate the comprehensive evaluation value of all equipment in the maintenance plan based on the stability and concentration of the equipment, and quantitatively obtain the comprehensive evaluation value of the maintenance plan based on the equipment importance weight. By comparing the evaluation values ​​of different maintenance plans, they can be ranked from high to low, and the best maintenance plan can be selected for implementation, including:

[0068] ① Comprehensive evaluation value M of device k k =W k1 A k +W k2 C k , weight W k1 and W k2 Allocated by the enterprise, both are 0.5;

[0069] ②Importance weight η of device k k is the proportion of maintenance tasks related to it to all maintenance tasks, specifically expressed as

[0070] ③The final comprehensive evaluation value of the maintenance plan is O=∑ k∈K η k M k ,The evaluation values ​​of the three maintenance schemes are 0.68, 0.66, 0.42, and 0.47, respectively.

[0071] Table 13 comprehensively shows the comprehensive evaluation of the deviation / stability, balance and centralization of the four maintenance schemes of the present invention. It can be seen from the table that although Scheme 1 has the highest comprehensive evaluation value, its balance evaluation level is "poor" and should not be adopted; among the other three schemes, Scheme 2 has the highest comprehensive evaluation value O, so Maintenance Scheme 2 should be selected as the maintenance execution standard between 2021 / 5 / 24 and 2021 / 5 / 30.

[0072] Table 13

[0073]

[0074] At the same time, combined with Table 11 and Table 12, for Scheme 2, the enterprise can further select the equipment with lower stability (equipment k =

[0075] 2 / 9 / 11) or with low concentration (equipment k = 4 / 13 / 14) to obtain a better maintenance plan. Compared with the existing conventional technical means that rely on subjective judgment, this method can intuitively and quantitatively integrate the multi-attribute performance of the steel production line maintenance plan and conduct an objective evaluation. The evaluation results also have the ability to further guide the optimization design of subsequent maintenance plans.

[0076] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for evaluating a multi-attribute maintenance plan for a steel production line, characterized in that: The maintenance plan is initially evaluated and screened by defining the maintenance task deviation and the working day balance of the planning period and using a four-level evaluation system. Then, stability and concentration are defined at the equipment level, and the comprehensive evaluation value of all equipment in the maintenance plan is calculated in combination with the attribute weights. Finally, at the system level, the comprehensive evaluation value of the maintenance plan is obtained according to the equipment importance weight to compare the plans, including: Step 1: Export the enterprise maintenance system data within the planning period and build the planning period collection in sequence Equipment Collection Maintenance task collection Maintenance cycle set R = {r i |i∈I}, equipment and maintenance task association matrix Γ={F ik |i∈I,k∈K} and the standard maintenance matrix E={E ij |i∈I,j∈J}, where: j=1 represents the first day of the planning period, represents the last day of the planning period; k corresponds to the equipment number in the enterprise maintenance system; for n k The equipment k with maintenance tasks, k∈K, is numbered as 1+∑ θ<k n θ ,…,n k +∑ θ< k n θ , r i is the maintenance cycle of maintenance task i, which is directly obtained from the enterprise system; when maintenance task i is related to equipment k, F ik =1, otherwise F ik =0; satisfies the condition r i -|dT' i |+1=j when e ij =1, otherwise e ij =0,|dT' i | represents the first day of the planning period d and the last operation execution date T' of maintenance task i i The number of days between Step 2: Convert the maintenance plan to be evaluated into a maintenance task execution matrix And calculate the resource requirement set S = {s j |j∈J}, where: Maintenance task i is scheduled to be executed on the jth day within the planning period. ij =1, otherwise X ij =0; Step 3: Calculate the deviation of maintenance task i in the maintenance plan and the balance of working days during the planning period A four-level evaluation system is used to evaluate the deviation and balance of maintenance plans; Step 4: Calculate the stability of each maintenance task i in the maintenance plan After normalization, the stability of each device k is obtained Step 5: Calculate the concentration c of each equipment i in the maintenance plan k =∑ j∈J (∑ i∈I F ik X ij ) 2 , and normalize it; Step 6: Calculate the comprehensive evaluation value M of each device k by combining the stability and concentration of the equipment in the maintenance plan k =W k1 A k +W k2 C k , and based on the importance weight of each device Quantitatively obtain the comprehensive evaluation value of the maintenance plan O = ∑ K∈K η k M k ; Finally, by comparing the evaluation values ​​of different maintenance plans, they can be ranked from high to low, and the best maintenance plan can be selected for implementation, where: weight W k1 and W k2 The sum of is 1.

2. The evaluation method for multi-attribute maintenance plan of steel production line according to claim 1, characterized in that: The enterprise maintenance system data includes: equipment number, maintenance task number, maintenance cycle, last maintenance date and the maximum number of maintenance tasks U that can be supported.

3. The evaluation method for multi-attribute maintenance plan of steel production line according to claim 1, characterized in that: The deviation evaluation level of the maintenance plan is as follows: the maximum deviation of all maintenance tasks is recorded as D max , when D max ≤10% is excellent, when 10% <D max ≤20% is good, when 20% <D max ≤30% is normal, when 30% <D max When the maintenance cycle is worse, the maintenance task operation cycle in the maintenance plan deviates greatly from the theoretical cycle, and the maintenance plan should be adjusted.

4. The evaluation method for multi-attribute maintenance plan of steel production line according to claim 1, characterized in that: The balance evaluation level of the maintenance plan is specifically: calculate the average balance of all working days in the planning period And the balance of each working day B j With B u The absolute difference ratio of |B j -B u | / B u , where the maximum ratio is denoted as B max , when B max ≤10% is excellent, when 10% max ≤15% is good, when 15% max ≤20% is normal, when 20% max When the maintenance situation is worse, the maintenance tasks in the maintenance plan are over-concentrated and the maintenance plan should be adjusted.​​​ 5. The evaluation method for multi-attribute maintenance plan of steel production line according to claim 1, characterized in that: The normalization process in step 4 refers to: The min-max method is used to normalize the stability of maintenance task i. Among them: a min and a max They are Minimum and maximum values ​​and a min ≠a max , when a max =a min When i =1.

6. The evaluation method for multi-attribute maintenance plan of steel production line according to claim 1, characterized in that: The normalization process in step 5 refers to: k The concentration of device k is obtained by normalization using the min-max method. When the maintenance tasks related to equipment k are evenly distributed to each day, c k Minimum, specifically expressed as When the maintenance tasks related to equipment k are concentrated as much as possible on certain days, c k Maximum, specifically expressed as Where P k =∑ i∈I,j∈J Fi kX i j , U is the maximum number of maintenance tasks that the enterprise can support, derived from the enterprise maintenance system, for The integer part, mod(P k ,U) is P k The remainder when divided by U.

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