A dynamic scheduling method of limited equipment resources considering time limit constraint

Abstract

The application discloses a kind of component assembly unit finite equipment resource dynamic scheduling method considering delivery time limit constraint, solve the problem of unreasonable allocation of finite equipment resources and unable to effectively respond to fault disturbance under existing production scene.For the finite equipment resource scheduling problem of flexible job shop with sudden equipment failure disturbance, first, a model is established with the optimization goal of minimizing the maximum delay time, a three-layer coding and decoding method is designed, and an improved particle swarm algorithm with adaptive inertia factor is used to solve the initial scheduling scheme;Then, considering the product delay cost and equipment switching cost caused by equipment failure disturbance, a re-scheduling model is constructed to minimize the comprehensive cost;Finally, based on the event-driven re-scheduling mechanism, partial / complete re-scheduling strategy and right-shift re-scheduling strategy are used to generate two alternative schemes for comparison and optimization.

Description

Technical Field

[0001] This invention belongs to the field of large civil aircraft assembly and manufacturing technology, specifically relating to a dynamic scheduling method for limited equipment resources of component assembly units that takes into account delivery time constraints. Background Technology

[0002] The aircraft nose assembly workshop is characterized by pulsed assembly line production and synchronous unit production. That is, in addition to parts and some outsourced components, the workshop also needs to assemble and deliver components of various sizes by assembly units. The smoothness of the main assembly line operation is affected by the timeliness of component supply. It is known that in the component assembly production unit, approximately 70%–80% of the processes are manual operations, while less than 30% are completed by automated equipment in the workshop; these are collectively referred to as machine operations. For a specific process, the workshop has M available backup machines. N different types of components require one of these machines to complete the process. Because the component processes are determined by the process design, different components require different machine sequence sequences, and the time spent on each machine varies. When all available machines are occupied, the current process must wait, and subsequent processes will also be affected accordingly.

[0003] In summary, on the one hand, component assembly is subject to strict time constraints and a clear sequence. Given the overlapping nature of human and machine processes, the time required for machine operations is influenced by the completion time of specific human operations. Furthermore, based on the production principle of sequential assembly by work teams, delays in machine operations are transitive. On the other hand, dynamic events commonly occur in workshops, such as machine malfunctions, material shortages, and order backlogs. These events prevent the original scheduling plan from being executed correctly. Most companies currently employ a simple "request-allocation" management method for scheduling workshop equipment resources, which is no longer suitable for the current production model with strict time constraints and lacks timely response methods to random disturbances in the workshop. Summary of the Invention

[0004] To address the shortcomings of the aforementioned background technology, this invention provides a dynamic scheduling method for finite equipment resources in component assembly units that considers mainline cycle time constraints and delivery time constraints. On one hand, considering the mainline pulsating cycle time, a static scheduling model for the finite equipment is established with the objective of minimizing component delivery delay time, and solved using a particle swarm optimization algorithm with an improved adaptive inertia factor. On the other hand, considering equipment failure disturbances during production, a rescheduling model is established with the objective of minimizing the overall cost (delay time cost and equipment changeover cost). Based on an event-driven rescheduling mechanism, two alternative schemes—partial / full rescheduling and right-shift rescheduling—are generated for comparison and selection.

[0005] The objective of this invention can be achieved through the following technical solution: a dynamic scheduling method for finite equipment resources considering delivery time constraints, comprising the following steps:

[0006] Step 1: Establish a dynamic scheduling model for limited equipment resources in the component assembly unit and determine the corresponding constraints;

[0007] Step 1.1: Establish the static objective function as follows:

[0008] f1 = min(max(0,ft) mj -pt mj )) (1)

[0009] Among them, ft mj This represents the completion time of component j belonging to flight m, pt mj This represents the cycle delivery time of component j belonging to flight m;

[0010] Step 1.2: Establish the rescheduling objective function as follows:

[0011] f2=min(μ1·Time t +μ2·Cost) (2)

[0012] in,

[0013] Time = max(0, Ft) m -Pt m (3)

[0014]

[0015]

[0016] Where μ1 and μ2 are weighting coefficients, and equation (2) represents the minimization of the combined cost of delay time and equipment changeover cost; equation (3) represents the minimization of product delay time, Pt m Ft represents the planned completion time for flight number m. m Indicates the completion time of sortie number m; flag amu For decision variables, denoted as aft; amu This refers to the equipment assigned to process number U, which is assembled by shift a and belongs to flight m after rescheduling. amu This refers to the equipment assigned to process number U of the component assembled by shift a and belonging to flight m in the initial plan; m a This indicates the sortie number of the first component to be assembled in shift A after the equipment failure. aEquation (4) indicates the first scheduled machine operation of the first component to be assembled in team a after the equipment failure; Equation (5) indicates the equipment change of the first scheduled machine operation of each component in the set of the first components to be assembled in each team after the equipment failure; Equation (6) indicates whether the equipment assigned to the u-number operation of the component assembled by team a and belonging to the m-number of the rack changes before and after the failure disturbance.

[0017] Step 1.3: Constraints include:

[0018] (1) Only one piece of equipment can be assigned to a process that requires equipment operation;

[0019]

[0020] Where, x jul The decision variable represents whether process u of component j is assigned to device l;

[0021] (2) Once any process begins, it must not be interrupted until it is completed;

[0022]

[0023] in, This indicates the end time of process u for the y-th component j assembled by team a and delivered to assembly line c. t represents the start time of process u for the delivery of the y-th component j assembled by team a to assembly line c. jul This represents the operation time of process u of component j on device l. y represents the manual assembly time of process u of component j in shift a. jua for

[0024] x jul Similar decision variables;

[0025] (3) Once each component is fully assembled, the work team will not start assembling the next component.

[0026]

[0027] (4) Any process can only begin after the preceding process has been completed;

[0028]

[0029] Step 2: Improve the particle swarm optimization algorithm in terms of adaptive inertia factor and three-layer coding form, and use the improved algorithm to solve the static scheduling model of limited equipment resources;

[0030] Step 3: Establish an event-driven dual scheduling method of partial / full rescheduling and right-shift rescheduling to respond to fault disturbances, and use the improved algorithm to solve the finite equipment resource rescheduling model.

[0031] Furthermore, the detailed method of step 2 is as follows:

[0032] Step 2.1: Set the values ​​of each parameter in the particle swarm optimization algorithm;

[0033] Step 2.2: Initialize the particle swarm, with the position and velocity of each particle represented by a two-dimensional array;

[0034] Step 2.3: Calculate the particle fitness value, which is equal to the objective function value;

[0035] Step 2.4: For each particle, compare its fitness value with the best position it has ever reached, pbest. If it is better, then take it as the current best position, pbest.

[0036] Step 2.5: Compare the historical best position pbest of all particles with the global best position gbest of the particle swarm. If pbest is better than gbest, then update gbest with pbest; otherwise, do not update gbest. Accumulate the number of times the fitness value of gbest remains unchanged and use it as the number of optimization attempts c.

[0037] Step 2.6: Update the position and velocity of each particle in each region, and return to Step 2.3. The inertia factor ω(t) is determined by both the number of algorithm iterations t and the number of times the overall optimal solution of the population remains unchanged, c.

[0038] The particles should gradually enhance their local search capability as the objective function value decreases. If the optimal position obtained by the particle swarm remains unchanged after multiple searches, it can be considered that the particle swarm has reached the global optimum or is trapped in a local optimum. In this case, the global search capability of the inertia factor ω should be restored to give the particles a mutation velocity to escape the local optimum. That is:

[0039] When c < C, ω(t) = (ω max -ω min (G) k -t) / G k +ω min t is the number of iterations in the current layer, G k The total number of iterations is set, and C is the upper limit of the number of iterations required for the overall optimal solution of the population to remain unchanged; otherwise, when c≥C, the global search capability of the particles is activated, and ω=(ω max -ω min (G) k -g) / G k +ω minWhere g = (c mod C) · G k / C;

[0040] Furthermore, the detailed method for step 3 is as follows:

[0041] Step 3.1: After a disturbance occurs, input the disturbance information; otherwise, execute the current scheduling plan until assembly is complete.

[0042] Step 3.2: Analyze the operating conditions at the time of the disturbance and update the process set and equipment set at the scheduling point;

[0043] Step 3.3: Generate a new scheduling scheme based on the partial / complete rescheduling policy;

[0044] Step 3.4: Compare the downtime caused by machine failure and repair with the time added by rescheduling;

[0045] Step 3.5: Select the better rescheduling scheme from the two schemes and execute the new scheme.

[0046] This invention, based on a real-world production scenario, first establishes a static scheduling model for equipment resources aimed at minimizing the maximum delay time for component delivery, and a rescheduling model that balances equipment change costs with product delay time costs. Then, based on the model characteristics, a three-layer encoding and decoding method is designed, and a particle swarm optimization algorithm with an improved adaptive inertia factor is used to solve the initial scheduling scheme. Next, an event-driven dual scheduling method of partial / complete rescheduling and right-shift rescheduling is established to generate the rescheduling scheme. Through these methods, the dynamic scheduling problem of limited equipment resources in flexible workshops with delivery deadlines and sudden equipment failure disturbances can be effectively solved. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the three-layer coding of particles.

[0048] Figure 2 This is a diagram illustrating machine code transcoding.

[0049] Figure 3 This is the flowchart of the particle swarm optimization algorithm.

[0050] Figure 4 This is a flowchart of equipment rescheduling based on equipment failure.

[0051] Figure 5 This is an example of partially rescheduled process sets and equipment sets being updated. Detailed Implementation

[0052] This invention pertains to the Flexible Job-shop Scheduling Problem (FJSP). Equipment resources are a crucial factor constraining workshop production progress, requiring a comprehensive consideration of the available equipment set and schedulable time for rational prioritization to minimize process delays due to resource scarcity. Furthermore, unexpected situations such as equipment failures can occur intermittently in actual production workshops. Therefore, to address these issues, this invention constructs an equipment resource scheduling model aiming to minimize the maximum component delay time, and a rescheduling model that balances product delay costs and equipment changeover costs. A dynamic scheduling scheme for limited resources is designed: encoding and decoding methods suitable for model solving are designed; sorting code adjustment and machine code conversion methods are designed for standard algorithm solutions; an improved adaptive particle swarm optimization algorithm is used to solve the scheduling scheme; and when equipment failure occurs, an event-driven rescheduling strategy is employed, generating scheduling schemes through partial / full rescheduling and right-shift rescheduling methods, and then comparing and selecting the optimal scheme.

[0053] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. The specific steps are as follows:

[0054] Step 1: Establish a static scheduling model for workshop equipment resources, with the goal of minimizing the maximum delay time of components. The formula is as follows;

[0055] f1 = min(max(0,ft) mj -pt mj ))

[0056] Establish constraints on equipment resource allocation and process operation, expressed by the following formulas. Specifically, each process requiring equipment operation can only be assigned to one piece of equipment; after each component starts operation, the work group will only begin assembling the next component after the previous component has been fully assembled; and any process can only begin after its preceding process has been completed.

[0057] a,

[0058] b、

[0059] c.

[0060] d、

[0061] Considering the delay time and rescheduling cost caused by machine failure disturbances, establish a rescheduling objective function;

[0062] f2 = min(μ1·Time + μ2·Cost)

[0063] in,

[0064] Time = max(0, Ft) m -Pt m )

[0065]

[0066]

[0067] Step 2: Based on the static scheduling objective function and constraints, an initial scheduling scheme is generated using a particle swarm optimization algorithm with an improved adaptive inertia factor. The specific process includes the following steps:

[0068] Step 2.1: Represent each particle with a two-dimensional array. The encoding needs to reflect three aspects of information: (1) the order of the sorties and the type of its components, (2) the equipment to which the machine process is assigned, and (3) the order in which the components utilize the assigned equipment.

[0069] Step 2.2: Initialize the particle swarm;

[0070] Step 2.3: Normalize the sorting code of each particle, following these principles;

[0071] (1) In a group of components assembled by the same work group, the sequence number of any machine process in the first-order assembly must be less than the sequence number of the second-order assembly.

[0072] (2) For different machine processes of the same component, the sequence number of the earlier process is smaller.

[0073] Step 2.4: Transcode the machine code: Divide the range of machine code values ​​into N uniform segments according to the number of machines N. When Code machine When the value falls within the range of the i-th segment, select the i-th machine in the machine set.

[0074] Step 2.5: Calculate the particle fitness value;

[0075] Step 2.6: For each particle, compare its fitness value with the best position it has passed through, pbest. If it is better, then take it as the current best position, pbest.

[0076] Step 2.7: Compare the historical best position pbest of all particles with the global best position gbest of the particle swarm, update gbest, and accumulate the number of optimization attempts c when the fitness value of gbest remains unchanged.

[0077] Step 2.8: Determine whether the jump condition (upper limit of iteration count or objective function value of zero) has been met. If not, proceed to step 2.9; otherwise, proceed to step 2.10.

[0078] Step 2.9: Update the position and velocity of each particle in each region, then return to step 2.5;

[0079]

[0080] The inertia factor ω(t) is determined by the number of algorithm iterations and the number of times the overall optimal solution of the population remains unchanged, c.

[0081] (1) When c < C, ω(t) = (ω max -ω min (G) k -t) / G k +ω min G k C represents the total number of iterations for the current layer, and C is the upper limit set for the number of times the overall optimal solution of the population remains unchanged.

[0082] (2) Otherwise, when c≥C, activate the global search capability of the particle, let ω=(ω max -ω min (G) k -g) / G k +ω min Where g = (c mod C) · G k / C.

[0083] Step 2.10: Output the results.

[0084] Step 3: When a device failure disturbance occurs during the operation of the initial scheduling scheme, a dual scheduling method of event-driven partial / full rescheduling and right-shift rescheduling is adopted to respond to the failure disturbance. The specific process includes the following steps:

[0085] Step 3.1: Analyze the operating conditions at the time of the disturbance and update the process set and equipment set at the scheduling point;

[0086] Step 3.1.1: Determine the timing of the machine failure: If all the workpiece processes required by the machine have been completed, the machine failure will not affect the assembly process, and the original schedule will continue; otherwise, proceed to step 3.1.2.

[0087] Step 3.1.2: The partial rescheduled process set G is updated following these steps:

[0088] Step 3.1.2.1: Define the rescheduled task set G, and initialize it as an empty set;

[0089] Step 3.1.2.2: Include processes that are interrupted or delayed due to equipment failure in G;

[0090] Step 3.1.2.3: Include the remaining processes on similar replaceable equipment of the faulty equipment into G;

[0091] Step 3.1.2.4: In the assembly teams to which each component belongs, all machine operations of all frames after the frames corresponding to the existing operations, and the subsequent operations on the corresponding equipment are added to G, and duplicate operations are removed.

[0092] Step 3.1.2.5: Repeat step 3.1.2.4 until no new process is added.

[0093] To illustrate Step 3.1.2, an example will be provided, such as... Figure 5 As shown. When equipment 3 malfunctions at time 5h, its ongoing processing step—machine step 2 (1.2) of a type 1 component belonging to the second sortie—and its subsequent processing step—machine step of a type 2 component belonging to the third sortie—are both affected (2.3), and according to Figure 4-5 It is known that equipment 4 and equipment 3 are of the same type and can be substituted, therefore process 1.3 (machine sequence 2) is indirectly affected. Furthermore, based on the characteristics of assembly components within a work group—components that are prioritized earlier within the same work group must complete all processes before the assembly of the next component can begin—the third batch of type 1 components within the same work group can only begin assembly after process 1.2 is completed. Therefore, the completion time of process 1.2 also indirectly affects process 1.3 (including machine sequence 1 and machine sequence 2) and subsequent processes on its equipment, such as 3.1. Other processes that are not within the same work group or are prioritized earlier within the same work group are not affected.

[0094] In summary, the rescheduled process set G in the example is {1.2,2.3,1.3,1.3,3.1}.

[0095] Step 3.1.3: Redetermine the start-up time for each piece of equipment, i.e., the earliest idle time for that equipment after the failure occurs. If the i-th equipment is idle at the time of the failure, its start-up time is 0; if the i-th machine is performing a process and the remaining time for that process is t, then its start-up time is t; the start-up time for the faulty equipment is its repair completion time t. * .

[0096] Step 3.2: Based on the updated process set and equipment set, a new scheduling scheme is generated using the particle swarm algorithm with improved adaptive inertia factor;

[0097] Step 3.3: Compare the downtime caused by machine failure and repair with the increased time and equipment changeover costs due to rescheduling, and select the best option to implement the new plan.

Claims

1. A method for dynamic scheduling of finite equipment resources in component assembly units considering delivery time constraints, comprising the following steps: Step 1: Establish a dynamic scheduling model for limited equipment resources in the component assembly unit and determine the corresponding constraints; Step 1.1: Establish the static objective function as follows: (1)； in, Indicates belonging to number of flights Component completion time, Indicates belonging to number of flights Component delivery time; Step 1.2: Establish the rescheduling objective function as follows: (2)； in, (3)； (4)； (5)； in, is the weighting coefficient, and equation (2) represents minimizing the combined cost of delay time and equipment changeover; equation (3) represents minimizing the product delay time. Indicates number The planned completion time for each flight Indicates number Completion time of each sortie; For decision variables; Indicates that after rescheduling, The team assembled and it belongs to the aircraft. The components The equipment assigned to process number [number] Indicates that in the initial scheme, there are... The team assembled and it belongs to the aircraft. The components The equipment assigned to process number 1; Indicates equipment failure The first aircraft to be assembled by the work team. Indicates equipment failure The first machine process to be scheduled for the first component to be assembled in the work group; Equation (4) represents the process by which the first component to be assembled in the work group is scheduled for the first machine process to be ... The team assembled and it belongs to the aircraft. The components The equipment assigned to the No. 1 process changes before and after the fault disturbance occurs; Equation (5) indicates the equipment change of the first scheduled machine process of each component in the first set of components to be assembled in each shift after the cumulative equipment fault. Step 1.3: Constraints include: (1) Only one piece of equipment can be assigned to a process that requires equipment operation; (6)； in, For decision variables, representing components of Has process number [number] been assigned to equipment? ; (2) Once any process begins, it must not be interrupted until it is completed; (7)； in, express The work team delivers the finished products to the assembly line. The Components of The end time of process number 1 express The work team delivers the finished products to the assembly line. The Components of The start time of process number 1 Representation Component process In the equipment On the operation time, Representation Component process exist The manual assembly time of the work team. for Similar decision variables; (3) The work group will only begin assembling the next component after all the components have been assembled. (8)； (4) Any process can only begin after the preceding process has been completed; (9)； Step 2: Improve the particle swarm optimization algorithm in terms of adaptive inertia factor and three-layer coding form, and use the improved algorithm to solve the static scheduling model of limited equipment resources; Step 3: Establish an event-driven dual scheduling method of partial / full rescheduling and right-shift rescheduling to respond to fault disturbances, and use the improved algorithm to solve the finite equipment resource rescheduling model.

2. The method for dynamic scheduling of finite equipment resources in component assembly units considering delivery time constraints as described in claim 1, characterized in that, The solution process for the static scheduling model of finite equipment resources in step 2 is as follows: Step 2.1: Represent each particle with a two-dimensional array. The encoding needs to reflect three aspects of information: (1) the order of the flight and its component type, (2) the equipment assigned to the machine process, and (3) the order in which the components utilize the assigned equipment. Step 2.2: Initialize the particle swarm; Step 2.3: Normalize the sorting code of each particle, following these principles; (1) In a group of components assembled by the same work group, the sequence number of any machine process of the first-order assembly must be less than the sequence number of the second-order assembly. (2) For different machine processes of the same component, the sequence number of the process that comes first is smaller; Step 2.4: Transcode the machine code: Convert the range of machine code values ​​according to the number of machines. Divided into uniform Duan, when Falling into When considering the range of values ​​for a segment, take the first value from the set of machines. 1 machine; Step 2.5: Calculate the particle fitness value; Step 2.6: For each particle, correlate its fitness value with the best position it has passed through. Compare the two positions, and if the former is better, then use it as the current best position. ; Step 2.7: Determine the historical best position of all particles With the global optimal position of the particle swarm Compare and update and accumulated The number of optimization attempts when the fitness value remains constant. ; Step 2.8: Determine if the jump condition has been met. If not, proceed to step 2.

9. Otherwise, proceed to step 2.10; Step 2.9: Update the position and velocity of each particle in each region, then return to step 3.5; ； Among them, inertia factor The number of algorithm iterations and the number of times the overall optimal solution of the population remains unchanged. Joint decision; (1) When hour, , This represents the total number of iterations for the current layer. This is the upper limit on the number of times the overall optimal solution for the population remains unchanged. (2) Otherwise, when At that time, the global search capability of particles is activated, making ,in ; Step 2.10: Output the results.

3. The method for dynamic scheduling of finite equipment resources in component assembly units considering delivery time constraints as described in claim 1, characterized in that, The rescheduling process in step 3 is as follows: Step 3.1: Analyze the operating conditions at the time of the disturbance and update the process set and equipment set at the scheduling point; Step 3.1.1: Determine the timing of the machine failure: If all the workpiece processes required by the machine have been completed, the machine failure will not affect the assembly process, and the original schedule will continue; otherwise, proceed to step 3.1.

2. Step 3.1.2: Partial rescheduling of process sets The update follows these steps: Step 3.1.2.1: Define the rescheduled process set Initialize to an empty set; Step 3.1.2.2: Include processes interrupted or delayed due to equipment failure. ; Step 3.1.2.3: Incorporate the remaining processes from similar alternative equipment to the faulty equipment. ; Step 3.1.2.4: Add all machine operations of all frames following the frames corresponding to the existing operations, and the subsequent operations on the corresponding equipment, to the assembly teams of the component types involved in the existing rescheduled operation set. ; Step 3.1.2.5: Repeat step 3.1.2.3 until no new processes are added; Step 3.1.3: Re-determine the start-up time for each piece of equipment, i.e., the earliest idle time for that equipment after a failure occurs; when a failure occurs, if the first... If a piece of equipment is currently idle, then the operating time of that equipment is 0; if the first piece of equipment is idle... A machine is performing a certain process, and the remaining time for that process is... Then the machine's start-up time is The start-up time of the faulty equipment is its repair completion time. ; Step 3.2: Based on the updated process set and equipment set, a new scheduling scheme is generated using the particle swarm algorithm with improved adaptive inertia factor; Step 3.3: Compare the downtime caused by machine failure and repair with the increased time and equipment changeover costs due to rescheduling, and select the best option to implement the new plan.

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