CN116954166A

CN116954166A - Flow shop production and maintenance joint scheduling method considering plug order disturbance

Info

Publication number: CN116954166A
Application number: CN202310641239.6A
Authority: CN
Inventors: 李波; 张竞一; 刘民岷; 洪涛; 胡家文
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2023-06-01
Filing date: 2023-06-01
Publication date: 2023-10-27

Abstract

The invention discloses a joint scheduling method for flow shop production and maintenance that takes into account the disturbance of insertion orders, and relates to a hybrid assembly line joint scheduling model optimization solution method and a dynamic scheduling method. Aiming at the integrated optimization problem of production scheduling and equipment preventive maintenance in a dynamic scheduling scenario, the present invention conducts disturbance analysis and determines the main disturbance events existing in the research object of the present invention. At the same time, rolling window technology and rescheduling are introduced on the basis of the integrated model. Based on the deviation penalty cost, a basic dynamic scheduling model was established, and then a rescheduling driving mechanism was formulated, a rescheduling method was determined, and a parallel particle swarm-genetic hybrid algorithm with embedded simulation was designed to obtain a complete rescheduling plan.

Description

Flow shop production and maintenance joint scheduling method considering plug order disturbance

Technical Field

The invention relates to the field of mixed flow shop preventive maintenance and production joint scheduling, in particular to a mixed flow shop production and preventive maintenance joint dynamic scheduling method considering plug-in disturbance.

Technical Field

The preventive maintenance strategy and the production scheduling strategy of the mixed flow shop are two important factors influencing the production cost, in the traditional production and manufacturing process, production managers usually independently formulate the two strategies and neglect the correlation between the two strategies, so that higher production cost is caused, meanwhile, with the rising of production modes such as customization, multiple varieties, small batches and the like, the disturbance caused by the change of demands in the production process is more and more, such as order withdrawal, emergency bill insertion, change of delivery date and the like, and the static scheduling which only takes a production plan as input is more and more unsuitable for the production environment at present. When the static scheduling scheme is executed, dynamic disturbance occurs, so that the original production and processing plan and the actual production process come in and go out, and if a reasonable disturbance processing strategy is not formulated, the production cost is greatly increased. Therefore, the method has important practical significance for the production and preventive maintenance combined dynamic scheduling research of the mixed flow shop.

At present, the related research of the dynamic scheduling problem is concentrated in the field of pure production scheduling, and the dynamic scheduling research aiming at the production workshop production and preventive maintenance combined scheduling is very rare; meanwhile, the existing dynamic scheduling problem only considers the influence of disturbance on a production scheduling scheme, and neglects the influence on a maintenance plan; in addition, the existing dynamic scheduling strategy usually only formulates a single rescheduling driving mechanism and rescheduling method, thereby resulting in higher dynamic scheduling deviation cost.

Disclosure of Invention

Aiming at the problem of production scheduling and equipment preventive maintenance integrated optimization in a dynamic scheduling scene, the invention provides a mixed flow production line maintenance and production combined dynamic scheduling method considering plug-in disturbance. The method takes the minimum equipment maintenance cost, the total workpiece early and late penalty cost and the dynamic scheduling deviation penalty cost as optimization targets, establishes a mathematical model, and optimizes and solves to obtain a rescheduling scheme after the insertion order disturbance occurs, thereby realizing the maintenance and production combined dynamic scheduling management of the mixed flow shop.

The technical scheme of the invention is a flow shop production and maintenance joint scheduling method considering plug-in disturbance, which comprises the following steps:

step 1: establishing a combined dynamic scheduling basic model of a mixed flow shop;

step 1.1: determining constraint conditions of a combined dynamic scheduling basic model;

step 1.2: performing preventive maintenance modeling, and updating an initial scheduling sequence;

step 1.2.1: let the machine failure rate function obey two-parameter weibull distribution:the machine reliability function is: r (t) =e- (t/η) ^φ T is 0.ltoreq.t, where t denotes the service life of the plant, provided that +.>In the case of a certain process, i.e. at the time of completion of a certain process, there is +.>The system performs a j-th maintenance shutdown at which point beta _j,xy ＝1，T _j ＝t，n _s ＝n _s +1, performing opportunistic maintenance judgment on other devices:

device state factor beta _j,xy Indicating equipment E during the jth shutdown maintenance of the system _xy Whether maintenance activities are performed or not, wherein 1 represents that maintenance is performed, and 0 represents that maintenance is not performed;

wherein ,represent arbitrary values, phi represents the shape parameter in the Weibull distribution, phi>0, η represents the size parameter in the weibull distribution, η>0，R _xy (t) represents the apparatus E _xy Reliability function of C _xy[l] Represents O _xy[l] End time of the process, R ^pt Representing a preventive maintenance threshold, T _j Represents the jth preventive maintenance time of the system, E _xy The first step of the process xy stage apparatus, n _s Indicating the total shutdown times of the system, wherein the initial value is 0, < ->The working life of the y-th station apparatus in the process x at the time t is represented by R ^ot Representing a device opportunity maintenance threshold;

step 1.2.2: modeling maintenance effects using virtual service life models, and after the jth shutdown maintenance of the system, based on the equipment status factor beta _j,xy After updating the jth maintenance, i.e. t=t _j +T ^m Virtual working years of each equipment at moment, T ^m Representing the average maintenance time of the device:

①β _j,xy =0, i.e. the j-th system maintenance time, equipment E _xy No maintenance is performed:

②β _j,xy =1, i.e. the j-th system maintenance, equipment E _xy And (3) maintaining:

ε _x for improving factor of service life, the method is used for describing the reliability change condition of equipment after imperfect maintenance, and the equipment epsilon in the same process _x The same and constant value is 0 < epsilon _x ＜1，The y-th station apparatus indicating process x is at T _j Service life at moment;

step 1.2.3: after adding the preventive maintenance strategy to the original production schedule, the process start time S is set after each system shutdown maintenance _xy[l] And working procedure finishing time C _xy[l] Updating:

step 1.2.4: calculating the equipment E in the whole production scheduling period _xy Expected number of times of unexpected failure n _xy ：

wherein Representing machine E _xy At C _mk Age of moment lambda _x (t) represents a failure rate function of step x;

step 1.3: constructing a joint dynamic scheduling basic model objective function;

(1) Computing device maintenance Total cost C ^m ：

C ^m ＝C ^dm +C ^pm

wherein ,

wherein ,c_us Representing equipment repair costs by considering post-fault repair emergency dispatch costs c _s C, representing the preventive maintenance cost of the equipment, taking the preventive maintenance scheduling cost into consideration ^dm Representing the total cost of post-hoc repair, C ^pm Represents the total cost of preventive maintenance, m represents the total number of processes, n _x Representing the total number of devices, n _xy The expected number of unexpected failures of the y-th equipment in the process x is represented, the initial value is 0,representing the equipment overhaul cost of process x, c _s Representing a single maintenance schedule charge,/->Indicating the equipment maintenance cost of the process x;

(2) Calculating the total early and late punishment cost C of workpieces ^ta ：

wherein ,representing the workpiece J _i Is>Representing the workpiece J _i Unit stall penalty cost,/->Representing the workpiece J _i Unit advance penalty cost, x _ixy[l] Representing the workpiece J _i Processing the first position of the y-th stage equipment in the process x to be 1, otherwise, processing the first position to be 0;

(3) Calculating a dynamic scheduling deviation punishment cost:

cost of machine offset penalty C ^ed Refers to the product of the quantity change of the workpiece processed by a rescheduling scheme and an initial scheduling scheme of a certain device and a penalty factor:

equipment maintenance departure penalty cost C ^md Refers to the product of the preventive maintenance time change and penalty factor of rescheduling scheme and initial scheduling scheme arrangement of a certain device:

thus, the overall weight of the production system deviates from penalty cost C ^d The method comprises the following steps:

wherein ,machine deviation penalty factor, ED, representing process x _xy Representing device E _xy The number of changes in the work piece after rescheduling, +.>Maintenance deviation penalty factor representing process x, MD _xy Representing device E _xy The number of maintenance times changes after rescheduling;

(4) The objective function F is;

F＝min(C ^ta +C ^m +C ^d )；

step 2: formulating a combined dynamic scheduling strategy of the mixed flow shop;

step 2.1: initializing the length of a scheduling processing window and rescheduling period;

step 2.2: acquiring workpiece processing information;

step 2.3: updating a scheduling processing window;

step 2.4: solving the objective function obtained in the step 1 by adopting a parallel particle swarm-genetic hybrid method;

step 2.5: generating a static scheduling scheme;

step 2.6: executing a dispatch plan;

step 2.7: determine if a rescheduling period is reached? If yes, turning to the step 2.8, and if not, turning to the step 2.9;

step 2.8: determining whether the fitness difference reaches a threshold? If yes, turning to the step 2.3, otherwise, returning to the step 2.7;

step 2.9: determine whether a disturbance has occurred? If yes, performing tail insertion rescheduling, then turning to step 2.8, and if not, turning to step 2.10;

step 2.10: determining whether all work pieces are finished? If yes, the technology is scheduled, and if not, the step 2.6 is performed.

Further, the detailed method of the step 2.4 is as follows:

step 2.4.1: the method adopts a double-chromosome form to represent the feasible solution coding, and divides the population into two sub-populations according to the self-adaptive population distribution factors, wherein one sub-population is updated by using a particle swarm algorithm, one sub-population is updated by using a genetic algorithm, and the self-adaptive population distribution factors have the following calculation formula:

wherein ,d_i Represents the Euclidean distance of the ith individual, K represents the adaptive population distribution factor, f _i ·、 _f j represents the fitness value of the ith individual, the fitness value of the jth individual, d _avg Represents the average Euclidean distance of the population, d _min Representing the minimum value of Euclidean distance in the population, d _max Representing the maximum value of Euclidean distance in the population; when the population quantity is N, KN individual components in the population form a sub-population 1 to enter a particle swarm algorithm for updating, and the rest individual components form a sub-population 2 to enter a genetic algorithm for updating;

step 2.4.2: constructing an improved particle swarm algorithm to optimize the sub population 1 in the step 3.1;

step 2.4.3: constructing an improved genetic algorithm to optimize the sub population 2 in the step 3.1;

step 2.4.4: combining the sub population 1 with the sub population 2;

step 2.4.5: judging whether the current population reaches the maximum iteration times, if so, executing the step 3.6, otherwise, continuing the step 3.1;

step 2.4.6: and obtaining the combined rescheduling scheme of the mixed flow shop after the single-plug disturbance.

Further, the detailed method of the step 2.4.2 is as follows:

a1: according to the maintenance threshold combination, calculating the fitness of each particle through the preventive maintenance model simulation established in the step 1.2, and updating the processing starting time and the processing finishing time of each workpiece obtained by decoding;

a2: updating self-adaptive weights;

a3: particle velocity update and position update.

Further, the detailed method of the step 2.4.3 is as follows:

b1: according to the maintenance threshold combination, calculating the fitness of each chromosome through the preventive maintenance model simulation established in the step 1.2, and updating the processing starting time and the processing finishing time of each decoded workpiece;

b2: chromosome selection operations are performed by using a random competition selection mode, and elite retention strategies are introduced;

b3: performing cross operation by using a single-point cross mode;

b4: chromosome mutation operation.

The invention provides a method for joint dynamic scheduling of preventive opportunity maintenance and production in a mixed flow shop taking account of plug-in disturbance, which uses a rolling window technology to statically process a dynamic scheduling process, constructs a mixed rescheduling driving mechanism combining a period and an event, formulates a combined rescheduling method combining complete rescheduling and tail plug-in rescheduling, and designs an embedded simulated parallel type self-adaptive particle swarm-genetic hybrid algorithm for model solving according to model characteristics to realize joint dynamic scheduling of the mixed flow shop.

Drawings

FIG. 1 is a diagram of an example scrolling window division;

FIG. 2 is a flow chart of a hybrid rescheduling driving mechanism;

FIG. 3 is a flow chart of a combined rescheduling method;

FIG. 4 is a flow chart of a hybrid flow shop joint dynamic scheduling;

FIG. 5 is a flow chart of a particle swarm-genetic algorithm of an embedded simulation;

FIG. 6 is a flow chart of a simulation algorithm;

FIG. 7 is a flow chart of a specific embodiment of the method of the present invention.

Detailed Description

The following describes the implementation routine of the present invention in detail (fig. 6), and the implementation routine is implemented on the premise of the technical solution of the present invention, and a detailed implementation and a specific operation procedure are given, but the scope of protection of the present invention is not limited to the implementation routine described below.

The implementation routine can be mainly divided into the following steps:

step 1: model constraints are determined.

(1) In any process, each workpiece can only occupy one machining position of one machine;

wherein ,x_ixy[l] Representing the workpiece J _i Processing the first position of the y-th stage equipment in the process x to be 1, otherwise, processing the first position to be 0, and taking the first position as a decision variable;

(2) In any process, only one workpiece can be processed at any position of any machine;

(3) Standard machining time of the workpiece process corresponding to the first machining position of the y-th machine in the process x;

wherein ,P_xy[l] Represents O _xy[l] Standard processing time of the procedure;

(4) The start time of a workpiece in a certain process is not earlier than the finish time of the process immediately before the equipment;

(5) The end time of the workpiece process corresponding to the first processing position of the y-th machine in the process x;

(6) The start time of a workpiece in a certain process is not earlier than the finish time of the workpiece in a previous process;

C _xy[l] ≥S _xy[l] +p _xy[l]

(7) Machine preventative maintenance threshold and opportunity maintenance threshold constraints;

0≤R ^pt ，R ^ot ≤1

R ^pt ＜R ^ot

(8) Maximum system completion time;

C _mk ＝max{C _my[l] }

(9) Disturbance occurs in the process of production scheduling execution;

wherein ,t_o Representing the occurrence time of the disturbance;

(10) Process start time constraints when a disturbance occurs. When the workpiece J _i When the disturbance occurs during the processing in the x working procedure, the starting time of the next working procedure of the workpiece is not earlier than the maximum value of the ending time of the workpiece on the working procedure and the disturbance occurrence time;

(11) Equipment processing time constraint when disturbance occurs; when equipment E _xy When the first task is processed, disturbance occurs, and the starting time of the next processing task of the equipment is not earlier than the maximum value of the finishing time of the current task of the equipment and the disturbance occurrence time;

step 2: when a plug-in disturbance event occurs, the initial scheduling scheme is windowed using a rolling window technique (FIG. 1). And (3) processing the plug-in single disturbance by using a tail plug-in rescheduling method, judging a threshold value of the disturbance degree, if the disturbance degree is smaller than or equal to the threshold value, not processing, and if the disturbance degree is larger than the threshold value, entering a step (4), and performing complete rescheduling on the workpieces in the scheduling processing window in the step (2).

Step 2.1: determining the plug-in disturbance as the main dynamic disturbance of the plug-in disturbance:

disturbance of the production process is generally divided into external factors and internal factors according to sources of the disturbance, wherein the external factors can be divided into two aspects of inherent factors and market factors, and the internal factors can be divided into environment factors, equipment factors and personnel factors;

step 2.2: introducing a rolling window technology, and statically processing the dynamic scheduling problem (figure 1):

first, the process needs to be classified according to its state: a set of processed processes, a set of in-process processes, a set of unprocessed processes, and a set of waiting for scheduling processes; three static scheduling windows are then defined for storing these process sets:

(1) A finishing window for storing a finished set of processes;

(2) A scheduling processing window for storing the processing procedure set and the unprocessed procedure set;

(3) A waiting window for storing a waiting scheduling procedure set;

the initialization of the length of the dispatching processing window can be set according to the production capacity of a processing workshop, the delivery period of the workpiece, the experience of a manager and the like by taking the workpiece or the procedure as a unit; when the scheduling starts, the scheduling processing window firstly takes out the workpiece sets with the number equal to the window set length from the waiting window according to a certain rule, performs static scheduling, and starts to execute the scheduling plan. When the set period is reached or rescheduling is needed due to disturbance, firstly, part of working procedures which are finished in the scheduling processing window are put into the finishing window, then, a part of workpieces are selected from the waiting window according to a certain rule and added into the scheduling processing window, and finally, the working procedures in the scheduling processing window are rescheduled according to a static scheduling method, so that disturbance events occurring in the whole production process can be dynamically absorbed; dynamic scheduling based on a rolling window technology is to repeat the process until all workpieces finish processing;

in order to illustrate the specific use of the rolling window technology, assuming that the production system is disturbed and needs to be rescheduled, dividing an initial scheduling scheme into three static windows according to the principle of the rolling window technology, wherein the window division is shown in fig. 1;

according to the above, the process can be divided into four sets according to the production state of each process at the rescheduling moment, and the specific division is as follows;

(1) Set of processed procedures: {1.1,2.1,3.1,4.1,5.1,6.1 (1),4.2 (1) }

(2) The working procedure is assembled: {6.1 (2),4.2 (2) }

(3) Waiting for a set of scheduling procedures: {7.1,7.2,8.1}

(4) Raw process set: all procedures except the above set

Wherein "1.1" represents the first process of the workpiece 1, and the rest are the same; at the rescheduling time, splitting the finished part and the unfinished part of the working procedure in processing into 2 independent working procedures for scheduling, wherein '4.2 (1)' in the set represents the finished part of the second working procedure of the workpiece 4 at the rescheduling time, and '4.2 (2)' represents the unfinished part in processing, and the rest is the same;

when rescheduling is carried out, firstly, the finished working procedure in the scheduling processing window is put into the finishing window, and then the workpiece is filled in the waiting window and scheduling is carried out;

step 2.3: constructing a hybrid driving mechanism based on disturbance degree threshold judgment (figure 2):

considering that rescheduling is based on a production and maintenance integrated model, and simultaneously relates to two dimensions of production scheduling and equipment maintenance, when a disturbance event occurs in the production process, the production scheduling and the equipment preventive maintenance are interfered, so that a quantitative index of disturbance degree should represent two aspects of influence on the production scheduling and influence on the equipment preventive maintenance at the same time; the influence of disturbance on production scheduling is finally reflected as the change of the delivery time of the workpiece, and the influence on equipment maintenance is finally reflected as the change of the equipment maintenance times and the expected times of unexpected faults, so that the sum of the total early and late punishment cost of the workpiece and the equipment maintenance cost is used as a quantitative index of the disturbance degree; as can be seen from fig. 2, when the set rescheduling period arrives or a dynamic disturbance event occurs, firstly, calculating the difference between the adaptability of the scheduling scheme and the original scheduling scheme, namely the disturbance degree, and comparing the calculated difference with a preset disturbance degree threshold value, if the difference exceeds the threshold value, it indicates that the current system needs rescheduling, and if the difference does not exceed the threshold value, it does not need rescheduling;

step 2.4: a combined rescheduling method (fig. 3) is established in which the full rescheduling method is combined with the tail-inserted rescheduling method:

a combined rescheduling method is designed by using a complete rescheduling method and a tail-inserted rescheduling method. In combination with the hybrid rescheduling driving mechanism based on the disturbance degree threshold judgment proposed in step 2.3, the workflow of the combined rescheduling method designed by the invention is shown in fig. 3.

As can be seen from fig. 3, when a disturbance event occurs, the disturbance is processed by a tail-inserted rescheduling method, then the difference between the adaptation degree before and after rescheduling is calculated and compared with a preset threshold value, if the difference between the adaptation degree is greater than the threshold value, the complete rescheduling is performed, otherwise, a tail-inserted rescheduling scheme is used as a rescheduling result; when the rescheduling period arrives, calculating the final fitness according to the execution condition of the current scheduling scheme, comparing the difference value between the final fitness and the fitness of the last complete rescheduling scheme with a threshold value, and if the final fitness is larger than the threshold value, performing complete rescheduling, otherwise, not performing rescheduling operation;

step 2.5: combining the step 2.3 with the step 2.4 to obtain a combined dynamic scheduling overall flow of the mixed flow shop; (fig. 4) step 3: and constructing an embedded simulated parallel particle swarm-genetic algorithm optimization solution (figure 5).

Step 3.1: initializing a maintenance threshold combination according to the model constraint determined in the step 1;

step 3.2: initializing a scheduling scheme population according to the model constraint determined in the step 1;

step 3.3: dividing a population into two sub-populations, wherein one sub-population is updated by using a particle swarm algorithm, one sub-population is updated by using a genetic algorithm, and in order to improve the local searching capability of the algorithm when the populations are scattered and the global searching capability of the algorithm when the populations are concentrated, the self-adaptive allocation factors are adopted for carrying out population division:

when the population quantity is N, KN individuals in the population enter a particle swarm algorithm for updating, and the rest individuals enter a genetic algorithm for updating.

Step 3.4: iterative sub-population 1 using an improved particle swarm algorithm;

step 3.4.1: calculating fitness of each particle by simulation (fig. 6);

(1) When (when)There is->The system performs the j-th maintenance shutdown and recordsT _j ＝t，n _s ＝n _s +1, performing opportunistic maintenance judgment on other devices:

device state factor beta _j,xy Indicating equipment E during the jth shutdown maintenance of the system _xy Whether maintenance activities are performed.

(2) After the jth shutdown maintenance is carried out on the system, the system is controlled according to the equipment state factor beta _j,xy Update jth post-maintenance t=t+t ^m Service life of the time equipment:

ε _x for improving factor of service life, the method is used for describing the reliability change condition of equipment after imperfect maintenance, and the equipment epsilon in the same process _x The same and constant value is 0 < epsilon _x ＜1。

(3) Start machining time S _xy[l] And finishing time C _xy[l] Updating:

(4) Equipment E _xy Unexpected failure occursDesired number of times:

wherein Representing machine E _xy At C _mk Age of moment.

(5) Calculating a total cost of maintenance of the machine C ^m ：

C ^m ＝C ^dm +C ^pm

wherein ：

(6) Calculating the total early and late punishment cost C of workpieces ^ta ：

wherein ：

(7) Calculating dynamic scheduling deviation penalty cost C ^d ：

The machine deviation punishment cost refers to the product of the quantity change of the workpiece processed by a rescheduling scheme and an initial scheduling scheme of a certain equipment and a punishment factor:

the equipment maintenance deviation penalty cost refers to the product of the preventative maintenance frequency change and penalty factor of a certain equipment rescheduling scheme and an initial scheduling scheme arrangement:

thus, the total weight adjustment deviation penalty cost of the production system can be expressed as:

(8) Calculating the fitness f:

f＝C ^ta +C ^m +C ^d

step 3.4.2: updating omega by adopting a nonlinear dynamic inertia weight coefficient formula:

step 3.4.3: particle velocity update, position update:

x _id (t+1)＝x _id (t)+v _id (t+1)

step 4.4.4: because the particle swarm algorithm aims at continuous variables, real numbers are generated in the searching process, and illegal solutions are often brought at the same time, updated particles need to be adjusted after the primary optimizing operation is finished so as to correct the illegal solutions:

(1) Rounding down each code

(2) Removing still illegal solutions in coding

(3) Randomly generating chromosomes according to coding rules to complement the solutions removed in (2)

Step 3.5: iterative sub-population 2 using an improved genetic algorithm;

step 3.5.1: the fitness of each chromosome is calculated through simulation, and the calculation method is the same as that of the step 4.4.1;

step 3.5.2: selecting by using a random competition selection mode, so that the probability of reserving chromosomes with larger fitness is larger, randomly selecting a certain number of chromosomes as new father, and simultaneously introducing elite reservation strategy to enable a certain number of high-quality solutions to directly enter the next generation so as to accelerate the convergence rate of the algorithm;

step 3.5.3: the interleaving is performed using a single point interleaving approach, as the encoding herein requires certain constraints to be maintained: the first dimension code indicates that the value of each element required to be met by the processing equipment code selected by the workpiece in each process is not more than the number of the process equipment where the element is located, and the second dimension code indicates that the value of each element required to be met by the processing sequence code of the workpiece in each process has uniqueness in the column where the element is located. Therefore, the first dimension code randomly selects a longitudinal crossing mode and a transverse crossing mode to perform single-point crossing operation, and the second dimension code performs single-point crossing operation in the longitudinal crossing mode;

step 3.5.4: two gene exchange sequences were randomly selected to achieve the effect of variation. The constraint condition of the codes can prove that the first dimension codes can only carry out line genetic variation, and the second dimension codes can carry out variation in rows and columns;

step 3.6: fusing the population 1 with the population 2, judging whether the current population meets the termination condition, if not, continuing the step 4.3, otherwise, stopping iteration;

step 3.7: the full rescheduling scheme is output.

Claims

1. A method for joint scheduling of production and maintenance in a flow shop considering order insertion disturbances, the method comprising the following steps:

Step 1: Establish a basic model for joint dynamic scheduling of hybrid production lines;

Step 1.1: Determine the constraints of the joint dynamic scheduling basic model;

Step 1.2: Perform preventative maintenance modeling and update the initial scheduling order;

Step 1.2.1: Assume the machine failure rate function follows a two-parameter Weibull distribution: The machine reliability function is then: 0≤t, where t represents the service life of the equipment, and assume that when At that time, that is, at the moment when a certain process is completed, there is The system then performs the j-th maintenance shutdown, at which point _βj,xy = 1, _Tj = t, _ns = _ns + 1, and opportunistic maintenance is assessed for other equipment.

The equipment status factor βj _,xy indicates whether equipment _Exy performs maintenance activities during the j-th system shutdown maintenance, with 1 representing maintenance and 0 representing no maintenance;

in, Let represent any value, φ represent the shape parameter in the Weibull distribution (φ>0), η represent the size parameter in the Weibull distribution (η>0), _Rxy (t) represent the reliability function of equipment _Exy , _Cxy[l] represent the end time of process _Oxy[l] , ^Rpt represent the preventive maintenance threshold of the equipment, _Tj represent the time of the j-th preventive maintenance of the system, _Exy represent the y-th equipment in process x, and _ns represent the total number of system downtimes, with an initial value of 0. Let represent the service life of the y-th equipment in process x at time t, and R ^ot represent the equipment opportunity maintenance threshold;

Step 1.2.2: Use a virtual service life model to model the maintenance effect. After the j-th downtime maintenance, update the virtual service life of each device at time t = _Tj + ^Tm based on the device state factors βj _,xy. ^Tm represents the average maintenance time of the device.

①βj _,xy = 0, meaning that during the j-th system maintenance, device _Exy does not undergo maintenance:

②βj _,xy = 1, meaning that during the j-th system maintenance, device _Exy undergoes maintenance:

ε _x is the service life improvement factor, used to describe the reliability change of equipment after imperfect maintenance. Within the same process, ε _x is the same and a constant value, where 0 <ε _x < 1. This represents the service life of the y-th piece of equipment in process x at time _Tj ;

Step 1.2.3: After adding the equipment preventive maintenance strategy to the original production scheduling plan, update the process start time S _xy[l] and process completion time C _xy[l] after each system shutdown for maintenance:

Step 1.2.4: Calculate the expected number of unexpected failures _nxy of equipment _Exy during the entire production scheduling cycle:

in Let E _xy represent the service life of machine Exy at time C _mk , and let λ _x (t) represent the failure rate function of process x.

Step 1.3: Construct the objective function of the joint dynamic scheduling basic model;

(1) Calculate the total equipment maintenance cost C ^m :

C ^m = C ^{dm} + C^pm

in,

Where, _CUSUs represents the cost of emergency dispatching for minor repairs after a failure, _CS represents the cost of preventative maintenance dispatching after a failure, ^Cdm represents the total cost of minor repairs, ^Cpm represents the total cost of preventative maintenance, m represents the total number of processes, _nx represents the total number of devices, and _nxy represents the expected number of unexpected failures of the y-th device in process x, with an initial value of 0. Let represent the minor repair cost of equipment in process x, and _CS represent the cost of a single maintenance scheduling operation. This represents the equipment maintenance cost for process x.

(2) Calculate the total cost of advance and delay penalties for the workpiece, C ^{ta} :

in, This indicates the expected completion time of workpiece _Ji . This represents the unit delay penalty cost for workpiece _J. Let xi represent the unit advance penalty cost of workpiece _J i, and x _{ixy[l]} represent that workpiece J _i is processed at the l-th position of the y-th machine in process x, and is 1 otherwise;

(3) Calculate the cost of dynamic scheduling deviation penalty:

The machine deviation penalty cost C ^ed refers to the product of the change in the number of workpieces processed by a certain machine under the rescheduling plan and the initial scheduling plan, and the penalty factor:

The equipment maintenance deviation penalty cost C ^{md} refers to the product of the change in the number of preventive maintenance operations scheduled for a certain piece of equipment under the rescheduling plan and the initial scheduling plan, and the penalty factor.

Therefore, the total rescheduling deviation penalty cost ^Cd of the production system is:

in, Let Exy represent the machine deviation penalty factor for process x, and ED_xy represent the change in the number of workpieces processed after rescheduling of equipment E _xy . MDxy represents the maintenance deviation penalty factor for process x, and _MDxy represents the change in the number of maintenance operations after rescheduling of equipment _Exy ;

(4) The objective function F is:

F = min(C ^{ta} + C ^m + C^d);

Step 2: Develop a joint dynamic scheduling strategy for hybrid production lines;

Step 2.1: Initialize the scheduling processing window length and rescheduling cycle;

Step 2.2: Obtain workpiece machining information;

Step 2.3: Update the scheduling processing window;

Step 2.4: Solve the objective function obtained in Step 1 using a parallel particle swarm optimization-genetic hybrid method;

Step 2.5: Generate a static scheduling scheme;

Step 2.6: Execute the scheduling plan;

Step 2.7: Determine if the rescheduling cycle has been reached? If yes, proceed to step 2.8; otherwise, proceed to step 2.9.

Step 2.8: Determine if the fitness difference has reached the threshold. If yes, proceed to step 2.3; otherwise, return to step 2.7.

Step 2.9: Determine if a disturbance has occurred. If yes, a tail-insertion rescheduling is performed, and then proceed to step 2.8; otherwise, proceed to step 2.10.

Step 2.10: Determine if all processed workpieces are complete. If yes, use scheduling technology; otherwise, proceed to step 2.6.

2. The method for joint scheduling of production and maintenance in a flow workshop considering order insertion disturbances as described in claim 1, characterized in that the detailed method of step 2.4 is as follows:

Step 2.4.1: Represent the feasible solution using a dual-chromosome form. Simultaneously, divide the population into two subpopulations based on the adaptive population allocation factor. One subpopulation is updated using the particle swarm optimization algorithm, and the other subpopulation is updated using a genetic algorithm. The formula for calculating the adaptive population allocation factor is as follows:

Where d _i represents the Euclidean distance of the i-th individual, K represents the adaptive population allocation factor, f _i and f _j represent the fitness values of the i-th and j-th individuals, d _{avg} represents the average Euclidean distance of the population, d _min represents the minimum Euclidean distance in the population, and d_max represents the maximum Euclidean distance in the population; when the population size is N, KN individuals in the population form subpopulation 1 and enter the particle swarm optimization algorithm for updating, and the remaining individuals form subpopulation 2 and enter the genetic algorithm for updating;

Step 2.4.2: Construct an improved particle swarm optimization algorithm to optimize subpopulation 1 in step 3.1;

Step 2.4.3: Construct an improved genetic algorithm to optimize subpopulation 2 in step 3.1;

Step 2.4.4: Merge subpopulation 1 and subpopulation 2;

Step 2.4.5: Determine whether the current population has reached the maximum number of iterations. If yes, proceed to step 3.6; otherwise, continue to step 3.1.

Step 2.4.6: Obtain the joint rescheduling scheme for the mixed flow workshop after the interruption.

3. The method for joint scheduling of production and maintenance in a flow workshop considering order insertion disturbances as described in claim 2, characterized in that the detailed method of step 2.4.2 is as follows:

a1: Based on the maintenance threshold combination, the fitness of each particle is calculated by simulation using the preventive maintenance model established in step 1.2, and the start and finish times of each workpiece obtained by decoding are updated.

a2: Adaptive weight update;

a3: Particle velocity update, position update.

4. The method for joint scheduling of production and maintenance in a flow workshop considering order insertion disturbances as described in claim 2, characterized in that the detailed method of step 2.4.3 is as follows:

b1: Based on the maintenance threshold combination, the fitness of each chromosome is calculated by simulation using the preventive maintenance model established in step 1.2, and the start and finish times of each workpiece obtained by decoding are updated.

b2: Use random competitive selection for chromosome selection and introduce an elite retention strategy;

b3: Perform crossover operations using a single-point crossover method;

b4: Chromosomal aberration operations.