A Robust Optimization Method for the Duration of Complex Equipment Maintenance Projects

Abstract

The present invention discloses a robust optimization method for the duration of complex equipment maintenance projects, comprising the following steps: 1) Analyze complex equipment maintenance projects to determine relevant parameters for the duration of maintenance projects; 2) Draw a network planning model for complex maintenance projects according to the relevant parameters determined in step 1); 3) Establish start-end time constraint relationships for optimizing the duration of maintenance projects; 4) Adopt the robust duality transformation theory, with the shortest duration and the highest completion confidence level as the objectives, to establish a multi-objective robust duality optimization model for maintenance operations under determined operation durations; 5) Solve the model based on Monte Carlo simulation and the critical path method; 6) Comprehensively and preferably select the maintenance operation plan with the shortest duration according to risk assessment and duration expectations. The method of the present invention can provide technical support for effectively shortening the duration during ship maintenance and play an important role in improving the in-service rate of ships, reducing maintenance funds, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of complex equipment maintenance engineering, and particularly to a robust optimization method for the construction period of complex equipment maintenance projects. Background Technique

[0002] Complex equipment maintenance engineering projects have the characteristics of being complex and diverse, having a relatively high degree of uncertainty in the maintenance process, frequent rework, and strict requirements for the construction period progress. It is a unique, time-limited, non-repetitive, and high-risk maintenance activity. During the complex equipment maintenance process, the maintenance operation duration varies greatly from the maintenance project, and the maintenance time of key maintenance operations often affects the overall maintenance construction period. In a certain equipment modernization transformation abroad, the concept of project management was first applied, and the construction period was saved by nearly 25% with a similar cost investment. Therefore, drawing on the project management idea provides a new idea for the construction period optimization of complex equipment maintenance engineering.

[0003] At present, for the uncertainty of the maintenance task duration during the complex equipment maintenance process, common processing methods include fuzzy numbers, three-point method, etc., which simply process the uncertain maintenance task time as a definite task duration. Secondly, methods such as program evaluation and review technique (PERT), expected value, scenario reasoning, etc. are also used to calculate the construction period of maintenance tasks in order to achieve the purpose of construction period optimization. Taking the PERT as an example, it was first developed when a certain equipment was developed abroad. The PERT shortened the originally estimated equipment development time by two years. This technology assumes that the maintenance task duration follows a certain probability distribution and uses the mathematical expectation to calculate the project construction period. The existing common methods are widely used in the general project scheduling problem.

[0004] In fact, the disassembly and maintenance of a key piece of equipment may affect the maintenance operations of other equipment, causing problems such as unreachable maintenance, task rework, etc., resulting in the inability to implement the maintenance plan and construction period delay. From the perspective of the overall project, exploring the essence of the construction period delay reveals that there is a large deviation between the estimated maintenance operation duration and the actual maintenance operation duration of the project, and there is a game. Therefore, the present invention adopts the method of increasing the redundancy of the maintenance operation duration. On the one hand, it ensures that there is enough float time to absorb the uncertainty of the operation duration during the maintenance process and increases the robustness of the maintenance plan. On the other hand, it reasonably distributes the redundancy to ensure the construction period optimization of the maintenance engineering project. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a robust optimization method for the construction period of complex equipment maintenance projects in view of the defects in the prior art.

[0006] The technical solution adopted by the present invention to solve its technical problems is: a robust optimization method for the construction period of complex equipment maintenance projects, including the following steps:

[0007] 1) Analyze the complex equipment maintenance projects and determine the relevant parameters for the duration of the maintenance projects: maintenance tasks, precedence relationships between maintenance operations, and the operation duration of maintenance tasks;

[0008] 2) Draw a network planning model for complex maintenance projects based on the relevant parameters for the duration of the maintenance projects determined in step 1) to visualize the complex equipment maintenance projects;

[0009] 3) Based on the precedence relationship between maintenance operations i and j, establish the start - end time constraint relationship for optimizing the duration of the maintenance project, that is:

[0010]

[0011]

[0012] Among them, i and j are the maintenance operation numbers. For the convenience of expression and calculation, maintenance operations 1 and n are defined as virtual maintenance operations, which do not occupy time and resources and only represent logical relationships, that is, maintenance operation 1 is the immediate predecessor operation of all maintenance operations, and maintenance operation n is the immediate successor operation of all maintenance operations. Therefore, the actual number of maintenance operations is n - 2; ST i and FT i are the start time and end time of the maintenance operation; represents the uncertain maintenance duration of the maintenance operation;

[0013] Equation (1) means that any maintenance operation must satisfy the precedence relationship constraint, that is, it can only start after all previous maintenance work is completed;

[0014] Equation (2) means that once a maintenance operation starts, it cannot be interrupted.

[0015] Describe the uncertain maintenance operation duration through the theoretical activity duration d i of the maintenance operation, the degree of fluctuation ε, and the disturbance amount δ, that is:

[0016]

[0017] Among them, the processing maintenance operation time disturbance amount δ follows a uniform distribution on [-1, 1]. Introduce the completion confidence level parameter k, and the corresponding quantile is:

[0018]

[0019] 4) Adopt the robust duality transformation theory, and establish a multi - objective robust duality optimization model for maintenance operations with determined operation durations with the goal of the shortest duration and the highest completion confidence level;

[0020] Objective function: min C max = FT n

[0021] max k

[0022] Constraint:

[0023]

[0024]

[0025]

[0026] ST1 = 0 (8)

[0027] FT1 = 0 (9)

[0028] φ >> 0 (10)

[0029] where C max is the repair duration, k is the confidence level of the completion of the repair operation, d i represents the theoretical duration of the repair operation, and φ is a sufficiently small positive real number;

[0030] Equation (5) represents the precedence relationship of the repair operation at the confidence level k. Equation (6) represents the end time constraint of the repair operation at the confidence level. Equation (7) represents the 0-1 variable constraint. Equations (8) and (9) represent that the start time and end time of the virtual repair operation 1 are both zero.

[0031] 5) Based on Monte Carlo simulation and the critical path method, solve the model to obtain the minimum duration under different confidence levels;

[0032] 6) According to the risk assessment and the duration expectation, comprehensively and preferentially select the repair operation plan with the shortest duration.

[0033] According to the above solution, the specific steps of step 5) are as follows:

[0034] 5.1) Set a random variable whose confidence level follows a uniform distribution [0,1]. According to the actual situation, randomly generate the confidence level k, and the confidence level k generally takes [0.8,1];

[0035] 5.2) Calculate the duration of the repair activity according to the confidence level and the fluctuation degree of the repair operation

[0036] 5.3) According to the repair activity network planning model, starting from the left in sequence, calculate the earliest start time and the earliest end time of each repair operation;

[0037] 5.4) When the earliest start time and the earliest end time of all repair activities are calculated, obtain the duration of the entire repair project;

[0038] 5.5) Repeat steps 5.2) to 5.4) until the simulation requirements are met;

[0039] 5.6) Output the Pareto optimal solution set of the maintenance operation plan.

[0040] The beneficial effects of the present invention are as follows:

[0041] 1. The robust optimization model proposed by the present invention fully considers the fluctuation degree of maintenance operations, reasonably distributes robust redundancy to key maintenance operations, avoids waste of project duration, and provides valuable reference for project duration optimization guidance;

[0042] 2. The Pareto optimal solution set of the present invention, Monte Carlo simulation, fully considers different confidence levels, helps decision-makers identify risks, can effectively ensure the completion probability with a confidence level higher than 95%, and avoid project duration delays;

[0043] 3. A complex equipment maintenance project duration optimization method provided by the present invention can assist in carrying out maintainability project duration optimization work during ship maintenance, provide technical support for effectively shortening the project duration, and play an important role in improving the ship's in-service rate and reducing maintenance costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0045] Figure 1 is the flowchart of the method of the embodiment of the present invention;

[0046] Figure 2 is the flowchart of the Monte Carlo simulation and critical path method algorithm of the embodiment of the present invention;

[0047] Figure 3 is the maintenance engineering network diagram of the embodiment of the present invention;

[0048] Figure 4 is the Gantt chart of the best optimization plan of the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0050] As Figure 1 shown, a robust optimization method for the project duration of a complex equipment maintenance project includes the following steps:

[0051] 1) Analyze the complex equipment maintenance project to determine the relevant parameters of the project duration of the maintenance project: maintenance tasks, precedence relationships between maintenance operations, and operation durations of maintenance tasks;

[0052] 2) Draw a complex maintenance project network planning model based on the relevant parameters of the maintenance project duration determined in step 1) to visualize the complex equipment maintenance project;

[0053] 3) For the complex equipment maintenance project duration optimization model, establish the start - end time constraint relationship of the model according to the precedence relationship between maintenance operations i and j, that is:

[0054]

[0055]

[0056] where i and j are maintenance operation numbers; ST i and FT i are the start time and end time of the maintenance operation; represents the uncertain maintenance duration of the maintenance operation;

[0057] Equation (1) means that the earliest possible start time of any operation must be later than the end time of the previous operation;

[0058] Equation (2) means that the end time of the maintenance operation is equal to the sum of its start time and operation duration;

[0059] Describe the uncertain maintenance operation duration through the theoretical activity duration d i of the maintenance operation, the degree of fluctuation ε and the disturbance amount δ, that is:

[0060]

[0061] where the processing maintenance operation time disturbance amount δ follows a uniform distribution on [-1, 1], introduce the completion confidence level parameter k, and the corresponding quantile is:

[0062]

[0063] 4) Adopt the robust dual - transformation theory, and establish a multi - objective maintenance operation robust dual optimization model with a fixed operation duration with the goal of the shortest duration and the highest completion confidence level;

[0064] Objective function: min C max = FT n

[0065] max k

[0066] Constraints:

[0067]

[0068]

[0069]

[0070] ST1 = 0 (8)

[0071] FT1 = 0 (9)

[0072] φ >> 0 (10)

[0073] where C max is the repair duration, k is the confidence level of the completion of the repair operation, d i represents the theoretical duration of the repair operation, and φ is a sufficiently small positive real number;

[0074] Equation (5) represents the precedence relationship of the repair operations at the confidence level k. Equation (6) represents the end time constraint of the repair operations at the confidence level. Equation (7) represents the 0-1 variable constraint. Equations (8) and (9) represent that both the start time and the end time of the dummy repair operation 1 are zero.

[0075] 5) Based on Monte Carlo simulation and the critical path method, solve the model to obtain the minimum duration at different confidence levels;

[0076] Step 5) is specifically as follows:

[0077] 5.1) Set a random variable whose confidence level follows a uniform distribution [0,1], and randomly generate the confidence level k according to the actual situation. The confidence level k generally takes [0.8,1];

[0078] 5.2) Calculate the duration of the repair activities according to the confidence level and the degree of fluctuation of the repair operations

[0079] 5.3) According to the repair activity network planning model, starting from the left in sequence, calculate the earliest start time and the earliest end time of each repair operation;

[0080] 5.4) When the earliest start time and the earliest end time of all repair activities are calculated, obtain the duration of the entire repair project;

[0081] 5.5) Repeat steps 5.2) to 5.4) until the simulation requirements are met;

[0082] 5.6) Output the frontier solution set of the repair operation plan;

[0083] 6) According to the risk assessment and the duration expectation, comprehensively and preferably select the repair operation plan with the shortest duration.

[0084] Taking the minor repair of a certain type of ship as an example, this repair project is characterized by complex technological processes and a relatively long estimated construction period, which has drawn high attention from the shipowner and the repair factory. In this embodiment, taking a certain link as an example, the activity parameters of its repair items are sorted out as shown in Table 1.

[0085] Table 1 Project Activity Time Parameter Table

[0086]

[0087] Based on the above data, the specific implementation steps of this embodiment are as follows:

[0088] Step 1: Network Diagram of Complex Equipment Repair Project

[0089] According to the project activity time parameter table of the minor repair of a certain type of ship, draw the network plan model diagram of its complex repair project as Figure 3 shown.

[0090] Step 2: Model Construction

[0091] According to the above data and the network diagram, Activity 1 and Activity 14 are dummy activities. Therefore, FT 14 is the construction period of this minor repair project.

[0092] Objective function: min C max = FT 14

[0093] max k

[0094] Constraint conditions:

[0095]

[0096]

[0097]

[0098] ST1 = 0 (14)

[0099] FT1 = 0 (15)

[0100]

[0101] Among them, C max is the repair construction period, k is the confidence level of the completion of the repair task, i and j are the repair task numbers, i = 0 and i = n are dummy repair tasks, which do not occupy time and resources. ST i and FT i are the start time and end time of the repair task. d i represents the theoretical duration of the repair task. is a sufficiently small positive real number. Equation (11) represents the precedence relationship of maintenance tasks at the confidence level k. Equation (12) represents the end-time constraint of maintenance tasks at the confidence level. Equation (13) represents the 0-1 variable constraint. Equations (14) and (15) represent that the start time and end time of the virtual maintenance task 0 are both zero.

[0102] Step 3: Solving the model

[0103] Based on the present invention, the frontier solution set of the above multi-objective model is generated by using Monte Carlo simulation and the critical path method.

[0104] Step 1: Determine the fluctuation degree of maintenance operations according to the actual project.

[0105] Step 2: Obtain the x ij matrix as follows:

[0106]

[0107] Step 3: Generate 20 random numbers that follow a uniform distribution on [0.8, 1], and assume that the generated random number vector A = [0.9558 0.8847 0.8182 0.8533 0.8307 0.8562 0.8880 0.9054 0.8915 0.9751 0.9036 0.9887 0.9275 0.9915 0.8481 0.9352 0.8578 0.9344 0.9390 0.8136].

[0108] Step 4: Let t = 1;

[0109] Step 5: Take k = A[t], where A is the random number vector generated in Step 2.

[0110] Step 6: Calculate the earliest start time and earliest end time of each activity;

[0111] Step 7: Calculate the project duration;

[0112] Step 8: If t > 20, output the frontier solution set; otherwise, t = t + 1, and jump to Step 4.

[0113] Fourth step: In this minor repair case, the fluctuation degrees of maintenance operations are 0.05, 0.10, 0.15, and 0.20 respectively. Using the model solving steps in the third step, the frontier solution sets are shown in Tables 2 - 5 respectively.

[0114] Table 2 Frontier solution set under the condition of a fluctuation degree of 0.05

[0115] 95.58％ 88.47％ 81.82％ 85.33％ 83.07％ 85.62％ 88.80％ 141.1533 140.1935 139.2957 139.7696 139.4645 139.8087 140.238 90.36％ 98.87％ 92.75％ 99.15％ 84.81％ 93.52％ 85.78％ 140.4729 140.2853 141.4139 140.4486 141.5975 140.7713 141.6353 90.54％ 89.15％ 97.51％ 93.44％ 93.90％ 81.36％ 139.6994 140.8752 139.8303 140.8644 140.9265 139.2336

[0116] Frontier solution set under the condition that the fluctuation degree is 0.10 in Table 3

[0117] 95.58％ 88.47％ 81.82％ 85.33％ 83.07％ 85.62％ 88.80％ 147.3066 145.3869 143.5914 144.5391 143.9289 144.6174 145.476 90.36％ 98.87％ 92.75％ 99.15％ 84.81％ 93.52％ 85.78％ 145.9458 145.5705 147.8277 145.8972 148.1949 146.5425 148.2705 90.54％ 89.15％ 97.51％ 93.44％ 93.90％ 81.36％ 144.3987 146.7504 144.6606 146.7288 146.853 143.4672

[0118] Frontier solution set under the condition that the fluctuation degree is 0.15 in Table 4

[0119] 95.58％ 88.47％ 81.82％ 85.33％ 83.07％ 85.62％ 88.80％ 153.4599 150.5804 147.8871 149.3087 148.3934 149.4261 150.714 90.36％ 98.87％ 92.75％ 99.15％ 84.81％ 93.52％ 85.78％ 151.4187 150.8558 154.2416 151.3458 154.7924 152.3138 154.9058 90.54％ 89.15％ 97.51％ 93.44％ 93.90％ 81.36％ 149.0981 152.6256 149.4909 152.5932 152.7795 147.7008

[0120] Frontier solution set under the condition that the fluctuation degree is 0.20 in Table 5

[0121] 95.58％ 88.47％ 81.82％ 85.33％ 83.07％ 85.62％ 88.80％ 159.6132 155.7738 152.1828 154.0782 152.8578 154.2348 155.952 90.36％ 98.87％ 92.75％ 99.15％ 84.81％ 93.52％ 85.78％ 156.8916 156.141 160.6554 156.7944 161.3898 158.085 161.541 90.54％ 89.15％ 97.51％ 93.44％ 93.90％ 81.36％ 153.7974 158.5008 154.3212 158.4576 158.706 151.9344

[0122] Step 5: Select the best solution;

[0123] As can be seen from Table 2 to Table 5, the greater the fluctuation degree of the maintenance activities, the greater the fluctuation range of the maintenance duration. The decision maker needs to determine, according to the actual situation, that the fluctuation degree of the maintenance activities is 0.20, the confidence level reaches 90.54%, and the shortest duration is 153.7974. Its Gantt chart is as Figure 4 shown.

[0124] In summary, the effectiveness of a method for robust optimization of the duration of a complex equipment maintenance project of the present invention is verified.

[0125] It should be understood that those of ordinary skill in the art can make improvements or changes according to the above description, and all such improvements and changes should fall within the protection scope of the appended claims of the present invention.

Claims

1. A robust optimization method for the duration of complex equipment maintenance projects, characterized in that, It includes the following steps: 1) Analyze the complex equipment maintenance project, and determine the relevant parameters of the maintenance project duration: maintenance tasks, the precedence relationship between maintenance operations, and the operation duration of maintenance tasks; 2) Draw a network planning model of the complex maintenance project based on the relevant parameters of the maintenance project duration determined in step 1) to visualize the complex equipment maintenance project; 3) Based on the precedence relationship between maintenance operations i and j, establish the start-end time constraint relationship for optimizing the maintenance project duration, that is: Among them, i and j are the maintenance operation numbers. Maintenance operation 1 and maintenance operation n are defined as virtual maintenance operations, which do not occupy time and resources and only represent logical relationships, that is, maintenance operation 1 is the immediate predecessor operation of all maintenance operations, and maintenance operation n is the immediate successor operation of all maintenance operations. The actual number of maintenance operations is n - 2; ST i and FT i are the start time and end time of the maintenance operation; represents the uncertain maintenance duration of the maintenance operation; The duration of uncertain maintenance operations is described by the theoretical activity duration d i of the maintenance operation, the degree of fluctuation ε, and the disturbance amount δ, i.e.: where the processing maintenance operation time perturbation amount δ follows a uniform distribution of [-1, 1], introduce the completion confidence level parameter k, and the corresponding quantile is: 4) Adopt the robust equality transformation theory, and establish a multi-objective maintenance operation robust equality optimization model with the shortest duration and the highest completion confidence level as the objectives under the determined operation duration; Objective function: min C max = FT n ; max k; Constraints: ST1 = 0 (8) FT1 = 0 (9) Among them, C max is the maintenance duration, k is the confidence level of the completion of the maintenance operation, d i represents the theoretical duration of the maintenance operation, is a positive real number small enough; 5) Based on Monte Carlo simulation and the critical path method, solve the model to obtain the minimum duration under different confidence levels; Specifically as follows: 5.1) Set a random variable whose confidence level follows a uniform distribution of [0, 1], and randomly generate the confidence level k according to the actual situation; 5.2) Calculate the duration of the maintenance activity based on the confidence level and the degree of fluctuation of the maintenance operation 5.3) According to the maintenance activity network planning model, starting from the left in sequence, calculate the earliest start time and the earliest end time of each maintenance operation; 5.4) When the earliest start time and the earliest end time of all maintenance activities are calculated, obtain the duration of the entire maintenance project; 5.5) Repeat steps 5.2) to 5.4) until the simulation requirements are met; 5.6) Output the frontier solution set of the maintenance operation plan; 6) According to the risk assessment and duration expectation, comprehensively and preferentially select the maintenance operation plan with the shortest duration.

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