CN110597218A - Scheduling optimization method based on flexible scheduling - Google Patents
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Abstract
The invention discloses a scheduling optimization method based on flexible scheduling, which comprises the following steps: on the basis of a time decomposition method, taking a CR value as a convergence formula of an optimal solution for searching particle swarm for a customer order; embedding the optimized particle swarm into an artificial immune algorithm based on a process decomposition method and a mathematical model structure decomposition method to obtain an initial production scheduling sequence; establishing a multi-objective optimization model; calculating a production bottleneck process and a highest efficiency process; matching product models with complementary bottleneck procedures and highest efficiency procedures, and carrying out variation on the original solution by combining artificial immunity to generate a plurality of scheduling sequences; and calculating the affinity of the plurality of scheduling sequences, so as to screen the solution and finally generate the optimal scheduling sequence. The invention combines the scheduling optimization method based on flexible scheduling with the actual work piece production process, reasonably generates the scheduling plan, and achieves the effects of reducing the production idle time, reducing the production energy consumption and reducing the production cost.
Description
Technical Field
The invention relates to the technical field of production scheduling, in particular to a scheduling optimization method based on flexible scheduling.
Background
In the context of the german industry 4.0, the global market is increasingly competitive, and reasonable production planning and scheduling are increasingly paid more attention by enterprises and academia as one of the advantages of occupying the market. Where data-driven production scheduling is particularly important. Because the production schedule under big data can give more detailed data information to enterprises, and can take the factors of capacity, personnel skill, material availability and tooling and mold constraints into consideration, the preplanned schedule is formulated through an intelligent optimization algorithm.
Production scheduling is the process of assigning production tasks to production resources. The most basic basis and principle is the cost priority principle, and the market and customer satisfaction are taken as the guidance for scheduling production. In most cases, customer satisfaction tends to be positively correlated with delivery time with product quality assurance. And therefore, delivery on schedule is the subject of production scheduling by many scholars. Some of the researchers have worked on the solution from the point of view of processing time period. For example, the article [ himmicche s, austry a, scale Marang, et al, using static-model-packing-based maintenance for evaluating the robustness of the project schedule [ J ],2018,762 ] proposes a system incomplete preventive maintenance model applicable to the change of the production speed with time, in order to determine the robustness of the project, but the consideration in resource scheduling is still deficient; researchers have also addressed the problem from a Production facility perspective, the article [ Ioannou G, Dimitriou, Stavrianna. lead time estimation in MRP/ERP for make-to-order manufacturing systems [ J ]. International Journal of Production economies, 2012,139(2): 551. 563 ] proposes a method for a multi-machine, multi-product manufacturing environment without specially configuring the Production conditions for the resources, using a simple iterative algorithm to replace the fixed delivery time estimate of a typical Material demand planning (MRP) system, thereby assigning an accurate completion time estimate to the order based on its current state; also, researchers plan scheduling from the perspective of processing workpieces, such as the article [ Louly M a, Dolgui a. optimal time planning and periodic property for MRP with POQ policy [ J ]. International Journal of Production Economics,2012,131(1):76-86 ] discussed the problem of component supply planning for assembly systems, using MRP methods and Periodic Order Quantity (POQ) strategies to plan the supply of components. The optimal values of the order period and the planned lead time are found in the offset step of the MRP program, and the time phase and period optimization effect is achieved under the condition that the lead time is uncertain; finally, a solution method using the production process as a guide is provided, and a rolling planning algorithm using the steel production sequence as a guide is developed in an article [ LeYang, Guozhang Jiang, Xiaowu Chen, Gongfa Li. Intelligent optimization and optimization project for steel integrated production. IJWMC,2019,16(4):364 and 368], so that not only the calculation efficiency is improved, but also the reliability of understanding is improved.
From the above article, it can be seen that most of the optimization objectives of the optimization research on production schedule are to deliver the product on schedule, and although it is the most important and basic condition in industrial production to complete the production task on schedule before the delivery time, on this basis, shortening the idle time of production, reducing the energy consumption of production and reducing the production cost are also very critical links in the intelligent production path of factories. Because the knowledge of non-factory workers on the specific production process of the production line has certain deviation with the real production process, and the data of the production schedule has the characteristics of complex and variable types, how to combine the actual situation on the production line to generate a production schedule sequence with high efficiency, high productivity and low cost becomes a problem which needs to be solved urgently at present.
At present, most scheduling methods are solved by using a single solving flexible scheduling algorithm, such as simulated annealing, tabu search, simulated annealing, particle swarm optimization and the like. Compared with the traditional enterprise scheduling method according to the shortest construction period, delivery date and the like, the method improves the accuracy of the scheduling result. However, because the factors influencing production in the actual workshop production process are many and complex, the scheduling sequence generated by a single algorithm is difficult to consider most factors of stirring production, and the method still lacks reliable guiding significance for the execution of actual production.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a scheduling optimization method based on flexible scheduling, which is characterized in that under the combination of a time-based decomposition method, a process decomposition-based method and a mathematical model structure decomposition method, after a particle swarm algorithm is optimized through workpiece emergency degree parameters, an artificial immune algorithm for improving a bottleneck process by utilizing a highest-efficiency process is embedded, and a multi-objective optimization mathematical model is established to be used as an adjusting mechanism of the artificial immune algorithm. And finally, according to the actual execution factors of the workpiece factory production and the judgment standard of the production efficiency, combining the scheduling optimization method based on flexible scheduling with the actual workpiece production process to reasonably generate a scheduling plan, thereby achieving the effects of reducing the production idle time, reducing the production energy consumption and reducing the production cost.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a scheduling optimization method based on flexible scheduling is characterized by comprising the following steps:
s1, on the basis of a time decomposition method, using CR values of three factors, namely a product construction period, a delivery date and a current date, of a customer order as a convergence formula for searching an optimal solution of a particle swarm;
s2, embedding the optimized particle swarm into an artificial immune algorithm based on a process decomposition method and a mathematical model structure decomposition method, taking the process of generating a solution of the particle swarm as the process of identifying an antigen and generating an antibody by the artificial immune algorithm, and obtaining a relatively efficient initial production scheduling sequence;
s3, establishing a multi-objective optimization model, and evaluating the performance of the initial production scheduling sequence;
s4, calculating a production bottleneck process and a highest efficiency process by utilizing the production time of different types of workpieces on each process and the corresponding equipment quantity;
s5, matching product models with complementary bottleneck procedures and highest efficiency procedures, and carrying out variation on an original solution by combining a variation function of artificial immunity to generate a plurality of scheduling sequences;
and S6, taking the multi-target optimization model as a concentration regulation mechanism of an artificial immune algorithm, and calculating the affinity of the multiple scheduling sequences, so as to screen solutions and finally generate an optimal scheduling sequence.
Further, in step S3, the constraint conditions of the multi-objective optimization model established in step S3 are: (1) the processes of the same workpiece are sequentially restricted; (2) the processes of different workpieces are not sequentially restricted; (3) each process can only be processed in one device at a time and cannot be interrupted during the processing; (4) at most, any equipment can only process one procedure at any time; (5) the earlier the cutoff time among different workpieces is, the higher the priority is; (6) besides capacity limitation, other resources such as raw materials and the like are not limited, and raw material suppliers can guarantee sufficient supply.
Further, in step S3, the multi-objective optimization model relates to scheduling influence factors such as order type, order quantity, production process, equipment type, equipment quantity, and equipment power, and can calculate the equipment idle time, total production time, wasted production power, and total consumed power corresponding to the scheduling sequence.
Further, in step S3, in the multi-objective optimization model, the calculation of the production time is as follows:
the production time comprises two types of equipment idle time and total production time, wherein the equipment idle time comprises equipment generation idle time in a start stage and a processing stage, and the total production time comprises ideal production time and actual waste total time;
the calculation formula of the idle time of the equipment in the start-up stage is as follows:
wherein, TjThe idle time of equipment in the start-up stage of the workpiece type j is set; m [ i ]]Is the processing procedure i instituteThe corresponding equipment number; s [ a ]][i]The machining time required by the type of the workpiece corresponding to the a-th batch of orders in the i-th procedure is set; 1, 8; a 1., Order _ sum; order _ sum is the total number of orders;
the formula for calculating the idle time of the equipment in the processing stage is as follows:
wherein, TkThe idle time of equipment for the kth production is shown, and sum is the total number of orders;
the whole production equipment idle time Timewasted is the sum of the total equipment idle time in the startup stage and the total processing equipment idle time, and the calculation formula is as follows:
wherein m is the total number of first batch of initial work required for producing the batch of orders, and n is the integer quotient of the number of workpieces in all the orders and the maximum equipment number corresponding to the working procedure;
the ideal production time TD is calculated as:
wherein sum is the total number of orders, and ListSum [ a ] is the number of the a-th order;
the calculation formula of the total production time T is as follows:
T＝TD+Timewasted/34。
further, in step S3, in the multi-objective optimization model, the calculation of the production consumption electric energy is:
producing and consuming the total electric energy comprises wasting the total electric energy and ideally consuming the total electric energy; the waste of the total electric energy is divided into waste of the electric energy in a start-up stage and waste of the electric energy in a processing stage, and the consumption of the total electric energy comprises ideal consumption of the total electric energy and production waste of the total electric energy;
the calculation formula of the waste electric energy in the start-up stage is as follows:
wherein E isjWasting electric energy for the work type j in the start-up phase, pfree[i]The average idle power of equipment corresponding to the production procedure of the ith step of the workpiece is obtained;
the formula for calculating the waste electric energy in the processing stage is as follows:
wherein E iskRepresenting that the equipment for the kth production wastes electric energy, wherein k is the total number of processing steps of the workpiece;
the calculation formula of the total wasted electric energy Ewaste is as follows:
the ideal consumed total electric energy ED is calculated by the formula:
wherein p isworkThe total average power of the equipment during operation;
the calculation formula of the total consumed electric energy E is as follows:
E＝ED+Ewasted。
adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
the scheduling optimization method based on flexible scheduling provided by the invention considers and makes a solution for two processes (one process of solution variation and multiple solutions and a process of screening multiple solutions) of the defects generated by the artificial immune algorithm, so that the artificial immune algorithm is not random when generating antibodies at the beginning, but is integrated into a high-efficiency algorithm by combining with an application background, and the generated initial antibodies are already a relatively high-efficiency solution; and then, a targeted mutation method is established according to the solution with the defect mutation of the initial solution, so that a very efficient final solution can be screened by mutating a small amount of solutions.
The whole large framework of the invention is therefore the framework of artificial immunization algorithms. After an antigen is initially identified, a particle swarm algorithm combined with a CR value is used as a method for generating an initial antibody by an artificial immune algorithm, then a multi-objective scheduling optimization mathematical model is established according to actual production factors to evaluate and analyze the advantages and the disadvantages of the initial antibody, a method for generating corresponding variant solutions by using key factors in the production of bottleneck equipment and highest-efficiency equipment is utilized, and the optimal scheduling sequence is screened out by utilizing the multi-objective optimization mathematical model after a plurality of solutions are obtained by means of variation. The effects of shortening the production time and reducing the production energy consumption are achieved.
The method provided by the invention is respectively applied to the scheduling of a hub production line and an injection molding production line, and through experimental analysis, on the basis of completion of the hub production line in time, compared with a particle swarm algorithm, the method reduces the equipment idle time by 9.6%, saves the waste electric energy by 11.7%, and compared with an artificial immune algorithm, reduces the equipment idle time by 9.53% and the electric energy by 11.12%. On the injection molding production line, compared with a particle swarm algorithm, the idle time of the equipment is reduced by 22.1%, the waste electric energy is saved by 21.3%, and compared with an artificial immune algorithm, the idle time of the equipment is reduced by 21.4% and the electric energy is reduced by 20.5%.
Drawings
FIG. 1 is a vortex data processing architecture of the present invention;
FIG. 2 is a diagram of a scheduling optimization method based on flexible scheduling according to the present invention;
FIG. 3 is a diagram of the equipment wait state during the start-up phase of the present invention;
FIG. 4 is a diagram of the equipment wait condition at the processing stage of the present invention;
FIG. 5 is a flowchart of a scheduling optimization method based on flexible scheduling according to the present invention;
FIG. 6 is a graph of the order quantity and CR value for the hub production line of the present invention;
FIG. 7 is a graph of the order sequence and CR values for the scheduled sequence on the hub production line of the present invention;
FIG. 8 is a graph of the order quantity and CR value for an injection molding line according to the present invention;
FIG. 9 is a graph of the order sequence and CR value for the scheduling sequence of the present invention on an injection molding line.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
In the design process of the scheduling optimization method based on flexible scheduling, the optimization algorithm uses a full data form. In the particle swarm optimization, the invention takes the full data as all data points in a closed two-dimensional space, wherein each data point comprises a plurality of sub-points, firstly a certain data point is found as an optimal data point, a certain sub-point in the data point is taken as a global optimal point and is taken out, then the data point is merged with the next optimal data point, the next optimal point is found from the merged sub-points, and the data points are sequentially transmitted to form a vortex-type data processing structure as shown in figure 1. The other parts of the model adopt the structural form that data points are processed in sequence in the full amount of data.
The operation of the present invention is shown in fig. 2, a scheduling optimization method based on flexible scheduling includes the following steps:
s1, aiming at the order of all clients to complete the aim in term, the method adopts a particle swarm algorithm to take CR values of three factors, namely a product construction period, a delivery date and a current date, of the client order as a convergence formula of a particle swarm for searching an optimal solution on the basis of a time decomposition method;
s2, embedding the optimized particle swarm into an artificial immune algorithm based on a process decomposition method and a mathematical model structure decomposition method, taking the process of generating a solution of the particle swarm as the process of identifying an antigen and generating an antibody by the artificial immune algorithm, and obtaining a relatively efficient initial production scheduling sequence;
s3, establishing a multi-objective optimization model, and evaluating the performance of an initial production scheduling sequence (an antibody generated by a particle swarm); the model relates to scheduling influence factors such as order type, order quantity, production process, equipment type, equipment quantity, equipment power and the like, and can calculate the equipment idle time, the total production time, the electric energy wasted by production and the total electric energy consumed corresponding to a scheduling sequence;
s4, calculating a production bottleneck process and a highest efficiency process by utilizing the production time of different types of workpieces on each process and the corresponding equipment quantity;
s5, matching product models with complementary bottleneck procedures and highest efficiency procedures, and carrying out variation on an original solution by combining a variation function of artificial immunity to generate a plurality of scheduling sequences;
and S6, taking the multi-target optimization model as a concentration regulation mechanism of an artificial immune algorithm, and calculating the affinity of the multiple scheduling sequences, so as to screen solutions and finally generate an optimal scheduling sequence.
Because flexible job shop scheduling is a relatively complex scheduling problem, the invention divides the flexible job shop scheduling into a plurality of sub-problems to solve by using a time-based decomposition method, a process-based decomposition method and a mathematical model structure decomposition method, thereby reducing the complexity of solution.
The invention establishes a particle swarm algorithm as a tool for generating antibodies to embed the framework of an artificial immune algorithm. The initial antibody generated by the particle swarm algorithm improves the accuracy of eliminating the antigen of the original initial antibody, so that the optimal antigen can be found only by mutating a small part of the antigen when the initial antigen is mutated by the later artificial immune algorithm, thereby improving the efficiency and the accuracy of generating the optimal solution by the algorithm.
The particle swarm optimization combines production elements such as production delivery date, construction period, workpiece number and the like, and the artificial immune algorithm comprises factors such as inventory, equipment number, equipment type, equipment power, workpiece procedures and the like, so that the solving process of the optimization algorithm is more suitable for the actual production situation.
The bottleneck process and the highest efficiency process of different types of workpiece types are calculated, and the bottleneck process and the highest efficiency process are utilized to match the workpiece types which can be produced together and to change the initial scheduling sequence. Therefore, the defect that a mutation function consisting of simple multipoint mutation, character string regeneration or simple replacement in the artificial immune algorithm generates a plurality of useless solutions can be overcome, and the burden of a concentration regulation mechanism is reduced.
A multi-objective optimization model is established, the model can not only evaluate the quality of the finally output optimal scheduling sequence, but also can be used as a concentration regulation mechanism in an artificial immune algorithm to screen antibodies.
The method for establishing the multi-objective optimization model in the step S3 comprises the following steps: in an actual industrial production line, because workpieces of different types need different processing time in the same process, the number of devices corresponding to different processes is different, the running power of different devices is different, and the power of the same device in a working state and an idle state is different. In this case, an unreasonable production schedule sequence can easily result in high energy consumption, high cost and non-lead-time production conditions in the plant. On the basis of analyzing the scheduling optimization method based on the flexible scheduling, the invention establishes a scheduling optimization mathematical model on the production line based on the flexible scheduling by taking the scheduled completion, the shortest production time and the least production electric energy consumption as the targets. The constraint conditions of the model are as follows: (1) the processes of the same workpiece are sequentially restricted; (2) the processes of different workpieces are not sequentially restricted; (3) each process can only be processed in one device at a time and cannot be interrupted during the processing; (4) at most, any equipment can only process one procedure at any time; (5) the earlier the cutoff time among different workpieces is, the higher the priority is; (6) besides capacity limitation, other resources such as raw materials and the like are not limited, and raw material suppliers can guarantee sufficient supply.
(1) In step S3, in the multi-objective optimization model, the production time is calculated:
the production time in the mathematical model of the present invention includes two categories of equipment idle time and total production time, which are substantially different. Device idle time refers to the time wasted by the device, such as device a being idle for d seconds, then it is wasted d seconds for device a. The total production time is the processing time for calculating the whole production and consists of ideal production time and production waste time. The ideal production time refers to the total time spent on the equipment in working condition in the whole production process. The wasted time of equipment production is positively correlated to the idle time of equipment, but is not equal because of their different bodies.
Idle time of equipment
The idle time of the plant is mainly generated by two phases, which are called start-up phase and processing phase by the present invention. The idle time generated by the two stage devices is different, and the calculation methods are also different. In the start-up stage, when all the devices are started, because the processes of the same workpiece are sequentially restricted, when the device corresponding to the previous process processes the workpiece, the device corresponding to the subsequent process has to be in a waiting state, so that the idle time of the device is caused. As shown in fig. 3, S [ a ] [ i ] is a processing time (i ═ 1.... 8) (a ═ 1.... 8) required by the workpiece type corresponding to the batch a of orders in the ith process, and Order _ sum is a total number of orders, a darkened circle indicates that the workpiece is processed on the device corresponding to the process in the ith process, and a darkened triangle corresponds to a device type that needs to wait. When a workpiece is machined on the equipment A, the following equipment is in a waiting state, the waiting time is the time spent by the type of the machined workpiece on the first process, when the workpiece is machined on the equipment B, the following equipment is also in the waiting state, the waiting time is the time spent by the type of the machined workpiece on the second process, and by analogy, the calculation formula for calculating the idle time of the equipment in the starting stage can be obtained as follows:
wherein, TjThe idle time of equipment in the start-up stage of the workpiece type j is set; m [ i ]]The number of devices corresponding to the processing step i.
In the machining stage, there should be a workpiece in the equipment corresponding to each production process theoretically, but the condition? for generating the equipment idle condition is satisfied under the constraint condition mentioned in the present invention, as shown in fig. 4, if the time efficiency of the current process is lower than the time efficiency of the next process, the part of the equipment corresponding to the next process waits to generate the equipment idle time, the calculation formula of the equipment idle condition in the machining stage is:
wherein, TkThe idle time of equipment for the kth production is shown, and sum is the total number of orders; fig. 4 shows 8 processing steps, so the total number of steps is 8.
The whole production equipment idle time (timespent) is the sum of the total idle time of equipment in the start-up stage and the total idle time of processing equipment, and the calculation formula is as follows:
wherein m is the total number of first batch of initial works required for producing the batch of orders, and n is the integer quotient of the number of workpieces in all the orders and the maximum equipment number corresponding to the working procedure.
Production total time
The total time actually wasted is also related to the number of devices to which the process corresponds, and the ideal total Time (TD) is calculated by:
the ideal production time TD is calculated as:
wherein sum is the total number of orders, and ListSum [ a ] is the number of the a-th order;
the total production time (T) comprises ideal production time and production waste time, and is calculated by the formula:
T＝TD+Timewasted/34。
(2) in step S3, in the multi-objective optimization model, calculation of the production power consumption:
in the actual production process, the power of the equipment in the working state and the idle state has certain difference, and therefore, the power is divided into ideal consumed total electric energy and wasted total electric energy.
Waste of total electric energy
The total wasted electric energy is generated when the equipment is in an idle state, and in the calculation process, the total wasted electric energy can be divided into wasted electric energy in a start-up stage and wasted electric energy in a processing stage. The calculation formula of the waste electric energy in the start-up stage is as follows:
the calculation formula of the waste electric energy in the start-up stage is as follows:
wherein E isjWasting electric energy for the work type j in the start-up phase, pfree[i]The average idle power of equipment corresponding to the production procedure of the ith step of the workpiece is obtained;
the formula for calculating the waste electric energy in the processing stage is as follows:
wherein E iskRepresenting that the equipment for the kth production wastes electric energy, wherein k is the total number of processing steps of the workpiece;
the calculation formula of the total wasted electric energy Ewaste is as follows:
② consuming total electric energy
The total consumed electric energy comprises ideal total consumed electric energy and production waste total electric energy, and the calculation formula of the ideal total consumed electric energy ED is as follows:
wherein p isworkThe total average power of the equipment during operation;
the calculation formula of the total consumed electric energy E is as follows:
E＝ED+Ewasted。
the test verification of the scheduling optimization method based on flexible scheduling comprises the following steps:
the steps of the schedule optimization method based on flexible scheduling provided by the invention are described as follows, and the flow chart of the algorithm is shown in FIG. 5.
Step 1: after receiving a plurality of batches of orders, checking inventory to determine a production task, simply sorting and selecting a client with the shortest delivery date, selecting a workpiece with the highest emergency degree according to a CR value, and deleting the workpiece from an original order;
step 2: selecting a next batch of orders according to the delivery date, and combining the tasks which are not selected in all the orders which are selected currently;
and step 3: calculating the CR value of each type of workpiece of each batch of orders, selecting the workpiece with the highest emergency degree, deleting the workpiece from the original order, continuing to the step 4 if all the orders are selected, and turning to the step 2 to execute if not;
and 4, step 4: outputting a scheduling sequence, and calculating affinity according to a fitness function in the multi-objective optimization model;
and 5: calculating the bottleneck process and the highest-efficiency process of each type of workpiece, and matching the types of workpieces which can be produced together;
step 6: generating other schemes similar to the scheduling sequence according to the matched workpiece types which can be produced together and the variation scheduling sequence;
and 7: calculating the affinity of the generated scheme, and removing the scheme with the affinity of later 50 percent;
and 8: determining the weight of each target in the multi-target optimization model, and selecting an optimal scheduling sequence.
The application performance of the scheduling optimization method based on flexible scheduling provided by the invention is subjected to simulation test analysis, the test selects the data of the hub production line and the injection molding production line, and the scheduling optimization method based on flexible scheduling is used for realizing reasonable generation of the scheduling plan, reducing the production idle time and reducing the production energy consumption. Then, a comparison test is carried out through a traditional particle swarm algorithm and an artificial immune algorithm, and the effectiveness of the scheduling optimization method based on flexible scheduling in the production scheduling of the workpieces is proved.
Hub production line test verification
Description of data: the test data was from a hub manufacturing company. The data is divided into four parts, namely order data, inventory data, process production time data, equipment number and power data. The order data comprises five data factors of a customer number, a hub workpiece type, an order quantity, an order number and a delivery date; the inventory data consists of a production place, a hub workpiece type and inventory; the process production time data comprises the types of the workpieces and the corresponding processing time of the workpieces in the processes of material cutting, aluminum bar preheating, forging and pressing into blanks, spinning forming, heat treatment, mechanical processing, drilling and surface treatment; the device number and power data includes device type, device average operating power, device average idle power, and device number.
The test process comprises the following steps:
order data is first processed, wherein one customer data corresponds to one or more of workpiece type data, a plurality of order number data, and a plurality of order quantity data, but one customer data corresponds to only one lead date data. Firstly, ordering the clients according to the delivery date according to a simple ordering algorithm, then selecting the order with the minimum CR value as the first order of a scheduling sequence from the orders of the clients with the shortest time, then combining the rest orders of the current client and all orders of the clients with the shortest time, and then continuing to select the order with the minimum CR value, and sequentially generating an initial scheduling sequence, wherein the formats of the scheduling sequence and the corresponding CR value are { 'P056': 7.6885428253615125, 'P055': 8.717558146347178, 'P052': 8.671256544745136, 'P214': 9.216599078940131, 'P068': 7.668798213157299. }, the corresponding workpiece models are { ' P056': 06016C03', ' P055': 02117C10', ' P052': 02114C06', ' P214': 02117C12', ' P068': 02116C10'. }, the order numbers are { ' P056':961, ' P055':909, ' P052':971, ' P214':881, ' P068':969. Fig. 6 is a scatter plot of the order quantity and CR value according to the initial scheduling sequence, since the smaller the CR value, the higher the urgency, and it can be seen from the plot that the order quantity is a positive correlation factor when producing models of the same product.
Fig. 7 is a diagram showing a relationship between the order sequence and the CR value in the scheduling sequence, and it can be seen from the diagram that at the beginning of the initial order sequence, there is no regular fluctuation of the CR value, because in the initial stage of the particle swarm algorithm, a value is selected in a small sample, the regularity is not strong, in the middle and later stages, the sample is larger and larger, and the trend that the order of the scheduling sequence is proportional to the CR value is more and more obvious.
Then, an initial scheduling sequence on the hub production line is calculated by using a multi-objective optimization model, and the obtained results of equipment idle time, total production time, production waste electric energy and total production energy consumption are shown in table 1:
TABLE 1 calculation of initial scheduling sequences by Multi-objective optimization model
| Total time(s) consumed by scheduling sequences | 6118127.462184876 |
| Total time(s) wasted by scheduling sequences | 1149927.0504201672 |
| Total electric energy (w) consumed by the scheduling sequence | 6297337521.877686 |
| Total wasted electrical energy (w) of scheduling sequences | 411788152.71428585 |
The purpose of generating the initial scheduling sequence is mainly to analyze the emergency degree of the order and then reasonably distribute the order so as to deliver the order according to the schedule. But have no specific effect on reducing production time and power. A bottleneck section or process can result due to imbalances in the throughput of equipment for the different processing steps. The "bottleneck process" determines the maximum capacity. Balance is an important guarantee of production progress, and in 100 links, as long as one link is low in efficiency, 99 links may fail to solve the problem of backward progress. When one process becomes a bottleneck process, idle time is generated in other processes. Because the bottleneck processes of different workpiece types are not identical, the corresponding highest efficiency processes are different. Therefore, if the bottleneck process of the workpiece type a is the same as the highest-efficiency process of the workpiece type b, if a and b are processed together, and a is clamped on the bottleneck process, b of the process is already processed, b can directly enter the next process for processing, and the waiting time of corresponding equipment of the next process of the bottleneck process of a, even all subsequent processes, can be effectively reduced. As can be seen from the above, allocating the scheduling sequence can effectively reduce the idle time of the device.
The bottleneck work procedure tables of different work piece types are obtained by calculating the ratio of the production time of the different work piece types in the working procedure to the number of corresponding devices, and are shown in table 2, and the highest efficiency work procedure tables of the different work piece types are shown in table 3.
According to table 2 and table 3 (bottleneck process and highest efficiency process), the types of the workpieces suitable for being processed together are matched. The specific contents are shown in table 4:
TABLE 4 matching of workpiece type and model suitable for machining together
| Type of the workpiece | Matched workpiece model |
| 02114F01 | 02114C06 |
| 02116C11 | 02114C06 |
| 00716C05 | 02114C06 |
| 02116C16 | 02114C06 |
| 02116C09 | 02116C11 |
| 02113C02 | 02114F01 |
| 02113C02 | 02114C09 |
| 02113C02 | 02116C09 |
| 02113C02 | 02116C10 |
| 02116C10 | 02114C06 |
According to table 4, a set of order numbers corresponding to the workpiece type models may be matched, for example, the order corresponding to the workpiece type 02114F01 is set a { ' P098', ' P033', ' P001', ' P050 ', ' P220 ', ' P236 ', ' P207 ', ' P194', ' P133', ' P072', ' P249', ' P144', ' P161', ' P117', ' P104', ' P177', ' P044', ' P052', the order corresponding to the workpiece type 02114C06 matched to the workpiece type 02114F01 is set B { (P052 ', ' P118', ' P004', ' P234', ' P148', ' P247', ' P034', ' P175', ' P129', ' P159', ' P074', ' P100', ' P038 '. The order of the order numbers in the set A and the set B is matched according to the order number set in the initial scheduling sequence, and the order is not freely changeable. The variant schedule sequence processes the bottleneck process and the most efficient process together. The ith order number in A should be processed with the ith order number in B, because if P098 in A and P038 in B are processed together, and the CR value of P098 is small, the order is an urgent order, but the CR value of P038 is far greater than that of P098, the process of P038 ahead of time can actually reduce production time and electric energy, but if other orders are so altered, it will actually affect the delivery of other urgent workpieces. The variation should be on the premise of delivery on schedule to improve production efficiency, i.e., high urgency in a should be matched with high urgency in B, and low urgency in a should be matched with low urgency in B. Finally generating a variant scheduled sequence, which has the structural form: [ ' P056', ' P055', ' P214', ' P068', ' P002', ' P213', ' P099', ' P165', ' P098', ' P052', ' P071', ' P134', ' P042', ' P037', ' P121', ' P078', ' P033', ' P118', ' P106', ' P036', ' P130', ' P066', ' P211', ' P115', ' P001', ' P004', etc. ' P089.
The matching process can be divided into two types of variation, namely bottleneck variation (high-efficiency process matched with bottleneck process) and high-efficiency variation (bottleneck process matched with high-efficiency process). The former is an order matched with the bottleneck process corresponding to the former according to the high-efficiency process of the order, and the latter is an order matched with the high-efficiency process corresponding to the latter according to the bottleneck process of the order. Finally, the optimal scheduling sequence is selected from the sequences generated by the two variations. The evaluation results of the multi-objective optimization model are shown in table 5. Because the initial scheduling sequence has no variation, the evaluation result is the result obtained by the traditional particle swarm algorithm.
TABLE 5 evaluation results of the multi-objective optimization model on two kinds of optimal variant sequences
| Scheduling sequences | Equipment idle time(s) | Wasting electric energy (w) |
| Initial scheduling sequence | 1149927.0504 | 411788152.7142 |
| Variation sequence (bottleneck) | 1039447.8361 | 363745174.4795 |
| Variant sequences (highest efficiency) | 1114164.2352 | 391925141.6775 |
According to the results shown in table 6, compared with the results obtained by the conventional particle swarm algorithm, the variation sequence obtained by bottleneck variation reduces the equipment idle time by 9.6%, and saves the waste electric energy by 11.7%. The variant sequence obtained by high-efficiency variation reduces the equipment idle time by 3.1%, saves the waste electric energy by 4.8%, and obviously the optimal scheduling sequence is the scheduling sequence varied according to the bottleneck process.
TABLE 6 analysis of the results of evaluation of two types of optimal variant sequences
According to the results shown in table 7, compared with the results obtained by the conventional artificial immune algorithm, the optimal result of the scheduling optimization method based on flexible scheduling reduces the equipment idle time by 9.53%, and saves the electric energy by 11.12%.
TABLE 7 comparison of the optimization algorithm with the conventional artificial immune algorithm
(II) injection molding production line test verification
Description of data: the test data were from a certain injection molding company. The data is divided into four parts, namely order data, inventory data, process production time data, equipment number and power data. The order data comprises five data factors of a customer number, an injection molding workpiece type, an order quantity, an order number and a delivery date; the inventory data consists of production areas, injection molding workpiece types and inventory; the process production time data comprises the types of the workpieces and the corresponding processing time of the workpieces in the processes of mold closing, filling, gas assistance, water assistance, cooling, mold opening, demolding and packaging; the device number and power data includes device type, device average operating power, device average idle power, and device number.
The test process comprises the following steps:
order data is first processed, wherein one customer data corresponds to one or more of workpiece type data, a plurality of order number data, and a plurality of order quantity data, but one customer data corresponds to only one lead date data. Firstly, ordering the clients according to the delivery date according to a simple ordering algorithm, then selecting the order with the minimum CR value as the first order of a scheduling sequence from the orders of the clients with the shortest time, then combining the rest orders of the current client and all orders of the clients with the shortest time, continuing to select the order with the minimum CR value, and sequentially generating an initial scheduling sequence, wherein the formats of the scheduling sequence and the corresponding CR value are { 'C055': 2.9598539964493686, 'C214': 2.9774686777790462, 'C246': 3.112426968062951, 'C052': 3.167430512237133, 'C068': 3.0020069387183597. }, the corresponding workpiece models are { ' C055': 17C10', ' C214': 17C12', ' C246': 13C02', ' C052': 14C06', ' C068': 16C10'. }, the order number is { ' C055':909, ' C214':881, ' C246':842, ' C052':971, ' C068':969. Fig. 8 is a scatter plot of the order quantity and the CR value according to the initial scheduling sequence, because the smaller the CR value, the higher the urgency, and it can be seen that the order quantity is a positive correlation factor when producing models of the same product.
Fig. 9 is a diagram showing a relationship between the order sequence and the CR value in the scheduling sequence, and it can be seen from the diagram that at the beginning of the initial order sequence, there is no regular fluctuation of the CR value, because in the initial stage of the particle swarm algorithm, the value is selected from a small sample, the regularity is not strong, in the middle and later stages, the sample is larger and larger, and the trend that the order of the scheduling sequence is proportional to the CR value is more and more obvious.
Then, an initial scheduling sequence on the injection molding production line is calculated by using a multi-objective optimization model, and the obtained results of the equipment idle time, the total production time, the production waste electric energy and the total production energy consumption are shown in table 8:
TABLE 8 calculation of initial scheduling sequences by the Multi-objective optimization model
| Total time(s) consumed by scheduling sequences | 15248217.579831934 |
| Total time(s) wasted by scheduling sequences | 2324162.5210084035 |
| Total electric energy (w) consumed by the scheduling sequence | 16215589757.309517 |
| Total wasted electrical energy (w) of scheduling sequences | 1143951319.392856 |
The purpose of generating the initial scheduling sequence is mainly to analyze the emergency degree of the order and then reasonably distribute the order so as to deliver the order according to the schedule. But have no specific effect on reducing production time and power. A bottleneck section or process can result due to imbalances in the throughput of equipment for the different processing steps. The "bottleneck process" determines the maximum capacity. Balance is an important guarantee of production progress, and in 100 links, as long as one link is low in efficiency, 99 links may fail to solve the problem of backward progress. When one process becomes a bottleneck process, idle time is generated in other processes. Because the bottleneck processes of different workpiece types are not identical, the corresponding highest efficiency processes are different. Therefore, if the bottleneck process of the workpiece type a is the same as the highest-efficiency process of the workpiece type b, if a and b are processed together, and a is clamped on the bottleneck process, b of the process is already processed, b can directly enter the next process for processing, and the waiting time of corresponding equipment of the next process of the bottleneck process of a, even all subsequent processes, can be effectively reduced. As can be seen from the above, allocating the scheduling sequence can effectively reduce the idle time of the device.
By calculating the ratio of the production time of different workpiece types in the process to the number of corresponding devices, the bottleneck process tables of different workpiece types are obtained as shown in table 9, and the highest efficiency process tables of different workpiece types are obtained as shown in table 10.
According to tables 9 and 10, the types of workpieces suitable for machining together are matched. The specific contents are shown in table 11:
TABLE 11 matching of workpiece type and model types for machining together
| Type of the workpiece | Matched workpiece model |
| 14C06 | 16C01 |
| 14C06 | 16C03 |
| 16C11 | 16C08 |
| 16C01 | 16C08 |
| 17C10 | 14C06 |
| 16C03 | 17C10 |
| 16C03 | 16C05 |
| 16C03 | 14C09 |
| 11C07 | 14C06 |
| 14C09 | 16C01 |
| 14C09 | 16C03 |
| 16C08 | 16C01 |
| 16C08 | 16C03 |
| 13C02 | 14C06 |
| 16C10 | 14C06 |
According to table 11, a set of order numbers corresponding to workpiece types may be matched, for example, the order corresponding to workpiece type 14C06 is set a1 { 'C052', 'C118', 'C004', 'C234', 'C148', 'C247', 'C034', 'C175', 'C129', 'C159', 'C074', 'C100', 'C196', 'C209', 'C038', 'C089', 'C167', 'C238', 'C190', 'C007', 'C151', 'C054', 'C120', 'C199', or 'C141', 'C199' corresponding to workpiece type 16C01 matched to workpiece type 14C06 is set B1 { 'C078', 'C121', 'C036', 'C089', 'C167', 'C238', 'C190', 'C007', 'C151', 'C054', 'C120', 'C199'. The order of the order numbers in set A1 and set B1 are matched according to the order number set in the initial scheduling sequence, and the order is not changeable. The variant schedule sequence processes the bottleneck process and the most efficient process together. Wherein the ith order number in A1 should most likely be processed with the ith order number in B1 because if C052 in A1 is processed with C228 in B1, and the CR value of C0528 is small, it is for a relatively urgent order, but the CR value of C228 is much greater than that of C0528, it does serve to reduce production time and power, but if other orders are so altered, it will actually affect the on-demand delivery of other urgent workpieces. The mutation should be to improve productivity on the premise of delivery on schedule, that is, the high urgency in a1 should be matched with the high urgency in B1, and the low urgency in a1 should be matched with the low urgency in B1. Finally generating a variant scheduled sequence, which has the structural form: "C055 '," C214', "C246 '," C052', "C078 '," C068', "C049 '," C056', "C098 '," C130', "C165 '," C040', "C122 '," C212', "C033 '," C001', "C108 '," C069', "C051 '," C118', "C121 '," C022', "C066 '," C062', "C220 '," C119', "C134 '," C236', "C099 '," C103', "C243 '," C002', "C004 '," C036' ], wherein the "C055 '," C078' and "C052 ' are processed together.
The matching process can be divided into two types of variation, namely bottleneck variation (high-efficiency process matched with bottleneck process) and high-efficiency variation (bottleneck process matched with high-efficiency process). The former is an order matched with the bottleneck process corresponding to the former according to the high-efficiency process of the order, and the latter is an order matched with the high-efficiency process corresponding to the latter according to the bottleneck process of the order. Finally, the optimal scheduling sequence is selected from the sequences generated by the two variations. The evaluation results of the multi-objective optimization model are shown in Table 12. Because the initial scheduling sequence has no variation, the evaluation result is the result obtained by the traditional particle swarm algorithm.
Table 12 evaluation results of the multi-objective optimization model on two types of optimal variant sequences
| Scheduling sequences | Equipment idle time(s) | Wasting electric energy (w) |
| Initial scheduling sequence | 2324162.5210 | 1143951319.3928 |
| Variation sequence (bottleneck) | 1809138.7090 | 899866891.0703 |
| Variant sequences (highest efficiency) | 2323345.9558 | 1143587047.1249 |
As shown in table 13, compared with the result obtained by the conventional particle swarm algorithm, the variation sequence obtained by the bottleneck variation reduces the idle time of the device by 22.1%, and saves the wasted electric energy by 21.3%. The variant sequence obtained by high-efficiency variation reduces the idle time of equipment by 0.35%, saves the waste electric energy by 0.318%, and obviously the optimal scheduling sequence is the scheduling sequence varied according to the bottleneck process.
TABLE 13 analysis of the results of evaluation of two types of optimal variant sequences
According to the results shown in table 14, compared with the results obtained by the conventional artificial immune algorithm, the optimal result of the scheduling optimization method based on flexible scheduling reduces the idle time of the equipment by 21.4%, and saves the electric energy by 20.5%.
TABLE 14 comparison of the optimization algorithm with the conventional artificial immunization algorithm
Conclusion
The invention provides a scheduling optimization method based on flexible scheduling, aiming at solving the problem that how to combine different decomposition methods to optimize an algorithm for solving FJSP (fuzzy inference processing) so as to improve the production efficiency under the conditions of reasonable scheduling speed and production reality. The particle swarm algorithm is used as a tool for generating the antigen and embedded into the artificial immune algorithm to serve as a large framework of the algorithm, and then the FJSP problem is decomposed into a plurality of sub-problems by using corresponding decomposition methods at different stages of the framework, so that the difficulty in solving is reduced. Secondly, introducing a workpiece urgency parameter and a method for eliminating bottleneck process in the highest-efficiency process in the algorithm, and establishing a multi-objective optimization model as a concentration regulation mechanism of the artificial immune algorithm and a screening standard of an optimal solution. Finally, a scheduling plan is reasonably generated by combining with actual production, and the aims of reducing production idle time and reducing production energy consumption are fulfilled. The effectiveness of the invention in production scheduling is verified through experimental analysis. On the basis of completion of the hub production line in time, compared with the traditional particle swarm algorithm, the idle time of the equipment is reduced by 9.6%, the waste electric energy is saved by 11.7%, and compared with the traditional artificial immunity algorithm, the idle time of the equipment is reduced by 9.53% and the electric energy is reduced by 11.12%. On the injection molding production line, compared with the traditional particle swarm algorithm, the idle time of the equipment is reduced by 22.1%, the waste electric energy is saved by 21.3%, and compared with the traditional artificial immune algorithm, the idle time of the equipment is reduced by 21.4% and the electric energy is reduced by 20.5%.
However, there are certain problems in applying the proposed method to the actual production schedule. Because the production scheduling of the system is that the production sequence of each production task is arranged under the condition of considering capacity and equipment and under the condition of a certain quantity of materials, but the conditions of insufficient materials, unstable production load of workers and the like often appear in an actual workshop, certain errors exist in the time and the electric energy calculated by the multi-objective optimization mathematical model.
Claims (5)
1. A scheduling optimization method based on flexible scheduling is characterized in that: the method comprises the following steps:
s1, on the basis of a time decomposition method, using CR values of three factors, namely a product construction period, a delivery date and a current date, of a customer order as a convergence formula for searching an optimal solution of a particle swarm;
s2, embedding the optimized particle swarm into an artificial immune algorithm based on a process decomposition method and a mathematical model structure decomposition method, taking the process of generating a solution of the particle swarm as the process of identifying an antigen and generating an antibody by the artificial immune algorithm, and obtaining a relatively efficient initial production scheduling sequence;
s3, establishing a multi-objective optimization model, and evaluating the performance of the initial production scheduling sequence;
s4, calculating a production bottleneck process and a highest efficiency process by utilizing the production time of different types of workpieces on each process and the corresponding equipment quantity;
s5, matching product models with complementary bottleneck procedures and highest efficiency procedures, and carrying out variation on an original solution by combining a variation function of artificial immunity to generate a plurality of scheduling sequences;
and S6, taking the multi-target optimization model as a concentration regulation mechanism of an artificial immune algorithm, and calculating the affinity of the multiple scheduling sequences, so as to screen solutions and finally generate an optimal scheduling sequence.
2. The method of claim 1, wherein the schedule optimization method based on flexible scheduling comprises: in step S3, the constraint conditions of the established multi-objective optimization model are: (1) the processes of the same workpiece are sequentially restricted; (2) the processes of different workpieces are not sequentially restricted; (3) each process can only be processed in one device at a time and cannot be interrupted during the processing; (4) at most, any equipment can only process one procedure at any time; (5) the earlier the cutoff time among different workpieces is, the higher the priority is; (6) besides capacity limitation, other resources such as raw materials and the like are not limited, and raw material suppliers can guarantee sufficient supply.
3. The method of claim 1, wherein the schedule optimization method based on flexible scheduling comprises: in step S3, the multi-objective optimization model relates to scheduling influence factors such as order type, order quantity, production process, equipment type, equipment quantity, and equipment power, and can calculate the equipment idle time, total production time, electric energy wasted in production, and total electric energy consumed corresponding to the scheduling sequence.
4. The method of claim 3, wherein the schedule optimization method based on flexible scheduling comprises: in step S3, in the multi-objective optimization model, the production time is calculated as follows:
the production time comprises two types of equipment idle time and total production time, wherein the equipment idle time comprises equipment generation idle time in a start stage and a processing stage, and the total production time comprises ideal production time and actual waste total time;
the calculation formula of the idle time of the equipment in the start-up stage is as follows:
wherein, TjThe idle time of equipment in the start-up stage of the workpiece type j is set; m [ i ]]The number of the devices corresponding to the processing procedure i; s [ a ]][i]The machining time required by the type of the workpiece corresponding to the a-th batch of orders in the i-th procedure is set; 1, 8; a 1., Order _ sum; order _ sum is the total number of orders;
the formula for calculating the idle time of the equipment in the processing stage is as follows:
wherein, TkThe idle time of equipment for the kth production is shown, and sum is the total number of orders;
the whole production equipment idle time Timewasted is the sum of the total equipment idle time in the startup stage and the total processing equipment idle time, and the calculation formula is as follows:
wherein m is the total number of first batch of initial work required for producing the batch of orders, and n is the integer quotient of the number of workpieces in all the orders and the maximum equipment number corresponding to the working procedure;
the ideal production time TD is calculated as:
wherein sum is the total number of orders, and ListSum [ a ] is the number of the a-th order;
the calculation formula of the total production time T is as follows:
T＝TD+Timewasted/34。
5. the method of claim 3, wherein the schedule optimization method based on flexible scheduling comprises: in the step S3, in the multi-objective optimization model, the calculation of the production power consumption:
producing and consuming the total electric energy comprises wasting the total electric energy and ideally consuming the total electric energy; the waste of the total electric energy is divided into waste of the electric energy in a start-up stage and waste of the electric energy in a processing stage, and the consumption of the total electric energy comprises ideal consumption of the total electric energy and production waste of the total electric energy;
the calculation formula of the waste electric energy in the start-up stage is as follows:
wherein E isjWasting electric energy for the work type j in the start-up phase, pfree[i]The average idle power of equipment corresponding to the production procedure of the ith step of the workpiece is obtained;
the formula for calculating the waste electric energy in the processing stage is as follows:
wherein E iskRepresenting that the equipment for the kth production wastes electric energy, wherein k is the total number of processing steps of the workpiece;
the calculation formula of the total wasted electric energy Ewaste is as follows:
the ideal consumed total electric energy ED is calculated by the formula:
wherein p isworkThe total average power of the equipment during operation;
the calculation formula of the total consumed electric energy E is as follows:
E＝ED+Ewasted。
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