阅读说明：本技术 基于spt规则的双代理开放车间工件加工排序方法 (The open workshop work pieces process sort method of dual-proxy based on SPT rule ) 是由 张妍 任涛 杨丹丹 董普庆 王柳婷 于 2019-09-11 设计创作，主要内容包括：本发明公布了一种基于SPT规则的双代理开放车间工件加工排序方法。首先确定开始处理时间,然后根据两个代理的最大完工时间确定出权重θ系数的取值范围,再根据SPT规则结合稠密排序得到两个代理的优先等级,选择开始时间小的工件先加工,在开始时间相同的情况下,先加工优先级高的工件,若优先级相同的工件中存在相同的开始时间,则优先加工处理时间短的工件,得出按照优先级排序后的两个代理的最大完工时间,并确定出权重θ系数和目标函数,最后根据目标函数求出极小化双代理的最大完工时间。本发明采用与优先级相结合的稠密排序,优化了双代理开放车间的排序,有利于缩短制造期限,提高生产效率。(The invention discloses a kind of, and the dual-proxy based on SPT rule opens workshop work pieces process sort method.Determination starts to process the time first, then the Maximal Makespan acted on behalf of according to two determines the value range of weight θ coefficient, dense sequence is combined to obtain the priority level of two agencies further according to SPT rule, the workpiece for selecting the time started small is first processed, in time started identical situation, the first high workpiece of processing priority, if there are at the beginning of identical in the identical workpiece of priority, then short workpiece of preferential working process time, obtain the Maximal Makespan according to two agencies after priority ranking, and determine weight θ coefficient and objective function, the Maximal Makespan of minimization dual-proxy is finally found out according to objective function.The present invention uses the dense sequence combined with priority, optimizes the sequence in the open workshop of dual-proxy, is conducive to shorten the manufacture time limit, improves production efficiency.)

1. a kind of open workshop work pieces process sort method of the dual-proxy based on SPT rule, which is characterized in that including following step It is rapid:

Step 1: initialize all work pieces process processes starts to process time S (i, j)=0, and wherein i indicates i-th machine, j It indicates workpiece j, initializes the machining state flag (i, j)=0 of all workpiece, wherein flag (i, j)=0 indicates that workpiece is in not Machining state, flag (i, j)=1 indicate that workpiece is in machined state, and it is equal that initialization, which acts on behalf of A with the priority for acting on behalf of B,；

Step 2: matrix H=(O (i, j) is defined_m*n), the matrix H indicates the manufacturing procedure of n workpiece of m platform machining Set, O (i, j) indicate the manufacturing procedure of workpiece, are looked in the matrix H according to SPT rule combination priority and dense sequence To the manufacturing procedure of the corresponding workpiece of the smallest S (i, j), if the corresponding workpiece of the smallest S (i, j) be two pieces and two pieces with On, the manufacturing procedure for the workpiece for selecting priority high is denoted as O (i, j) '；

Step 3: update starts to process time S (i, j) with the O (i, j) ' the process with identical workpiece and same machines, And the O (i, j) ' corresponding flag (i, j) is set to 1；

Step 4: it constantly repeats step 2 and step 3 is obtained until the flag (i, j)=1 of all process steps in the matrix H Act on behalf of the total workpiece n of A processing_AManufacturing procedure on each machine obtains the total workpiece n for acting on behalf of B processing_BAdding on each machine Work process；

Step 5: A processing n is being acted on behalf of_AThe n of a workpiece_AMaximal Makespan is found out in a completion date, is denoted as C_maxA, acting on behalf of B processes n_BThe n of a workpiece_BMaximal Makespan is found out in a completion date, is denoted as C_maxB, definition weight coefficient θ be section [0, 2*(C_maxB/C_maxA)] in random number, the workpiece number n of processing meets relationship n=n_A+n_B；

Step 6: the n for acting on behalf of A processing is found in the matrix H_AA workpiece, and to the n_AA workpiece is corresponding in matrix H Every row summation is X_A, to the n_AA workpiece is Y in the corresponding each column summation of matrix H_A, compare X_AAnd Y_ASize, take X_AAnd Y_A In maximum value be assigned to LB_A, LB_AIt indicates to act on behalf of the n that A is processed_AThe floor value of a workpiece finds in matrix H and acts on behalf of B processing n_BA workpiece, and to the n_BA workpiece is X in the corresponding every row summation of matrix H_B, to the n_BA workpiece is corresponding in matrix H Each column summation is Y_B, compare X_BAnd Y_BSize, take X_BAnd Y_BIn maximum value be assigned to LB_B, LB_BIt indicates to act on behalf of the n that B is processed_BA work The floor value of part；

Step 7: by comparing θ and LB_B/LB_ARatio size relation, judgement act on behalf of A with act on behalf of B priority height, if θ >LB_B/LB_A, then it represents that the priority for acting on behalf of B is high, if θ≤LB_B/LB_A, then it represents that the priority for acting on behalf of A is high；

Step 8: the machining state flag (i, j)=0 of all workpiece in matrix H is initialized again, acts on behalf of A and generation in judgement Step 2 and step 3 are constantly repeated under the premise of managing B priority, until the machining state flag of all workpiece in matrix H (i, j)=1 obtains the n that A processing is acted on behalf of under the premise of judging priority_AProcessing sequence of a workpiece on each machine, and The n of B processing is acted on behalf of under the premise of judging priority_BProcessing sequence of a workpiece on each machine；

Step 9: it finds out and acts on behalf of A processing n under the premise of judging priority_AThe n of a workpiece_AMaximum completion in a completion date Time, and update C_maxAValue, find out acted on behalf of under the premise of judging priority B processing n_BThe n of a workpiece_BIn a completion date Maximal Makespan, and update C_maxBValue, objective function F is found out according to formula (1), can be asked according to the objective function Minimization is obtained to act on behalf of A and act on behalf of the Maximal Makespan of B；

F=min (C_maxA+θC_maxB) (1)

In formula, θ indicates weight coefficient, and value range is section [0,2* (C_maxB/C_maxA)] in random number.

2. the open workshop work pieces process sort method of a kind of dual-proxy based on SPT rule according to claim 1, special Sign is, being found in the matrix H according to SPT rule combination priority with dense sequence in the step two is the smallest The manufacturing procedure of the corresponding workpiece of S (i, j) is specific to state are as follows: two or more works for having the identical time started if it exists Sequence, the then process in agency for selecting priority high；If in the high agency of the priority again there are two or two or more have phase The other process of same priority then selects the process that the processing time is shorter；If the processing time shorter process again there are two or The process of more than two same treatment times, then the sequence according to process in matrix H is processed, according to thick when work pieces process The rule of solid matter sequence is processed, and marks flag (i, j)=1 after processing is completed.

3. the open workshop work pieces process sort method of a kind of dual-proxy based on SPT rule according to claim 1, special Sign is that the step three updates and the O (i, j) ' when the starting to process of process with identical workpiece and same machines Between S (i, j), it is specific to state are as follows: to define C (i, j)=S (i, j)+P (i, j), C (i, j) indicates the complete working hour of work pieces process process Between, S (i, j) indicates the time that starts to process of work pieces process process, and P (i, j) indicates the processing time of work pieces process process, for There is the process of identical workpiece and same machines with the manufacturing procedure O (i, j) ' of workpiece, if S (i, j) < C (i, j), enables C (i, j)=S (i, j), if S (i, j) >=C (i, j), S (i, j) value is constant.

Technical field

The present invention relates to production scheduling field, specifically a kind of open workshop workpiece of the dual-proxy based on SPT rule Machining Sequencing method.

Background technique

Open job shop scheduling problem is the simplified model in many field scheduling problems, close with actual relationship.Assuming that existing It to open at certain in You Liangjia manufacturer and be processed on the assembly line of workshop, the product that each manufacturer is intended to oneself can deliver goods as early as possible, How should so arrange production as open workshop factory, the requirement of two clients of satisfaction of ability maximum possible here it is The opening Job-Shop problem of one very typical dual-proxy.

Open job shop scheduling problem general description are as follows: n workpiece is processed on m platform machine, and each workpiece is on machine Processing sequence is arbitrary, and workpiece can be processed since on any machine, terminates processing on any machine.In At any moment, each workpiece at most can only be by a machining, and every machine at most processes a workpiece.Workpiece starts to add It after work, cannot be interrupted in process, until work pieces process is completed, target is to find a scheduling so that some scheduling is quasi- It is then minimum.Open job shop scheduling problem is the generally acknowledged complexity of academia and all high optimal combination problem of difficulty, in addition to A small number of have the problem of special circumstances, most of open job shop scheduling problem be all np hard problem (NP-hard) wherein, NP refers to nondeterministic polynomial (non-deterministic polynomial, abridge NP).So-called uncertainty refers to, Can go to solve the problems, such as with a certain number of operations it is soluble in polynomial time, it is popular for be that the correctness of its solution can be by The problem of " being readily inspected ".

Summary of the invention

Aiming at the problem that solution dual-proxy open workshop minimization weighting manufacture phase, the present invention is provided one kind and is added based on most short The dense row of the minimization weighting manufacture phase problem for solving the open workshop of dual-proxy of priority rule (SPT rule) between working hour Sequence algorithm improves production efficiency for shortening the manufacture time limit.

The invention proposes a kind of, and the dual-proxy based on SPT rule opens workshop work pieces process sort method, technical side Case are as follows:

A kind of open workshop work pieces process sort method of the dual-proxy based on SPT rule, comprising the following steps:

Step 1: initialize all work pieces process processes starts to process time S (i, j)=0, and wherein i indicates i-th machine Device, j indicate workpiece j, initialize the machining state flag (i, j)=0 of all workpiece, and wherein flag (i, j)=0 is indicated at workpiece In rough, flag (i, j)=1 indicates that workpiece is in machined state, and initialization acts on behalf of A and is with the priority for acting on behalf of B It is equal；

Step 2: matrix H=(O (i, j) is defined_m*n), the matrix H indicates the processing work of n workpiece of m platform machining The set of sequence, O (i, j) indicate the manufacturing procedure of workpiece, according to SPT rule combination priority and dense sequence in the matrix H In find the manufacturing procedure of the corresponding workpiece of the smallest S (i, j), if the corresponding workpiece of the smallest S (i, j) is two pieces and two More than part, the manufacturing procedure for the workpiece for selecting priority high is denoted as O (i, j) '；

Step 3: update starts to process time S with the O (i, j) ' the process with identical workpiece and same machines (i, j), and the O (i, j) ' corresponding flag (i, j) is set to 1；

Step 4: constantly repeating step 2 and step 3, until the flag (i, j)=1 of all process steps in the matrix H, Obtain the total workpiece n for acting on behalf of A processing_AManufacturing procedure on each machine obtains the total workpiece n for acting on behalf of B processing_BOn each machine Manufacturing procedure；

Step 5: A processing n is being acted on behalf of_AThe n of a workpiece_AMaximal Makespan is found out in a completion date, is denoted as C_maxA, In Act on behalf of B processing n_BThe n of a workpiece_BMaximal Makespan is found out in a completion date, is denoted as C_maxB, definition weight coefficient θ is section [0,2*(C_maxB/C_maxA)] in random number, the workpiece number n of processing meets relationship n=n_A+n_B；

Step 6: the n for acting on behalf of A processing is found in the matrix H_AA workpiece, and to the n_AA workpiece is in matrix H pair The every row summation answered is X_A, to the n_AA workpiece is Y in the corresponding each column summation of matrix H_A, compare X_AAnd Y_ASize, take X_A And Y_AIn maximum value be assigned to LB_A, LB_AIt indicates to act on behalf of the n that A is processed_AThe floor value of a workpiece finds in matrix H and acts on behalf of B and add The n of work_BA workpiece, and to the n_BA workpiece is X in the corresponding every row summation of matrix H_B, to the n_BA workpiece is in matrix H pair The each column summation answered is Y_B, compare X_BAnd Y_BSize, take X_BAnd Y_BIn maximum value be assigned to LB_B, LB_BIt indicates to act on behalf of the n that B is processed_B The floor value of a workpiece；

Step 7: by comparing θ and LB_B/LB_ARatio size relation, it is high with the priority of acting on behalf of B that A is acted on behalf of in judgement It is low, if θ > LB_B/LB_A, then it represents that the priority for acting on behalf of B is high, if θ≤LB_B/LB_A, then it represents that the priority for acting on behalf of A is high；

Step 8: the machining state flag (i, j)=0 of all workpiece in matrix H is initialized again, acts on behalf of A in judgement Step 2 and step 3 are constantly repeated under the premise of B priority with acting on behalf of, until the machining state of all workpiece in matrix H Flag (i, j)=1 obtains the n that A processing is acted on behalf of under the premise of judging priority_AProcessing sequence of a workpiece on each machine, And the n of B processing is acted on behalf of under the premise of judging priority_BProcessing sequence of a workpiece on each machine；

Step 9: it finds out and acts on behalf of A processing n under the premise of judging priority_AThe n of a workpiece_AMaximum in a completion date Completion date, and update C_maxAValue, find out acted on behalf of under the premise of judging priority B processing n_BThe n of a workpiece_BA complete working hour Between in Maximal Makespan, and update C_maxBValue, objective function F is found out according to formula (1), can be according to the target letter Number acquires minimization and acts on behalf of A and act on behalf of the Maximal Makespan of B；

F=min (C_maxA+θC_maxB) (1)

In formula, θ indicates weight coefficient, and value range is section [0,2* (C_maxB/C_maxA)] in random number.

Minimum is found in the matrix H according to SPT rule combination priority and dense sequence in the step two The corresponding workpiece of S (i, j) manufacturing procedure, it is specific to state are as follows: two or more have the identical time started if it exists Process, the then process in agency for selecting priority high；If in the high agency of the priority again there are two or two or more have The other process of equal priority then selects the process that the processing time is shorter；If the processing time shorter process again there are two Or the process of more than two same treatment times, then the sequence according to process in matrix H is processed, when work pieces process according to The rule of dense sequence is processed, and marks flag (i, j)=1 after processing is completed.

The step three updates and the O (i, j) ' when the starting to process of process with identical workpiece and same machines Between S (i, j), it is specific to state are as follows: to define C (i, j)=S (i, j)+P (i, j), C (i, j) indicates the complete working hour of work pieces process process Between, S (i, j) indicates the time that starts to process of work pieces process process, and P (i, j) indicates the processing time of work pieces process process, for There is the process of identical workpiece and same machines with the manufacturing procedure O (i, j) ' of workpiece, if S (i, j) < C (i, j), enables C (i, j)=S (i, j), if S (i, j) >=C (i, j), S (i, j) value is constant.

Beneficial effects of the present invention:

The present invention is optimized for the open workshop sequencing problem of dual-proxy using the dense sequence combined with priority The sequence in the open workshop of dual-proxy, the Maximal Makespan of minimization dual-proxy is obtained by solving the objective function designed, Be conducive to shorten the manufacture time limit, improve production efficiency.

Detailed description of the invention

Fig. 1 is the stream of the open workshop work pieces process sort method of the dual-proxy based on SPT rule in the embodiment of the present invention Cheng Tu.

Fig. 2 is the open Job-Shop sequence Gantt chart of the dual-proxy based on SPT rule in the embodiment of the present invention.

Fig. 3 is that the open Job-Shop sequence of the dual-proxy based on SPT rule combination priority in the embodiment of the present invention is sweet Spy's figure.

Fig. 4 is the open Job-Shop sequence Gantt chart of randomly ordered lower dual-proxy in the embodiment of the present invention.

Specific embodiment

Here is that technical solution of the present invention is described in detail in conjunction with attached drawing.

Such as the stream of the open workshop work pieces process sort method of the dual-proxy based on SPT rule in Fig. 1 embodiment of the present invention Shown in journey figure, a kind of open workshop work pieces process sort method of the dual-proxy based on SPT rule, comprising the following steps:

Step 1: initialize all work pieces process processes starts to process time S (i, j)=0, and wherein i indicates i-th machine Device, j indicate workpiece j, initialize the machining state flag (i, j)=0 of all workpiece, and wherein flag (i, j)=0 is indicated at workpiece In rough, flag (i, j)=1 indicates that workpiece is in machined state, and initialization acts on behalf of A and is with the priority for acting on behalf of B It is equal；

Step 2: matrix H=(O (i, j) is defined_m*n), the m platform machine when matrix H indicates not according to priority ranking The set of the manufacturing procedure of n workpiece is processed, O (i, j) indicates the manufacturing procedure of workpiece, combines dense sequence according to SPT rule The manufacturing procedure of the corresponding workpiece of the smallest S (i, j) is found in the matrix H, if the corresponding work of the smallest S (i, j) Part is two pieces and two pieces or more, and the manufacturing procedure for the workpiece for selecting priority high is denoted as O (i, j) '；

SPT rule combination priority and dense sequence, it is specific to state are as follows: two or more have identical beginning if it exists The process of time, the then process in agency for selecting priority high；If in the high agency of the priority again there are two or two There is the other process of equal priority above, then selects the process that the processing time is shorter；If the processing time shorter process is again There are two or more than two same treatment time process, then the sequence according to process in matrix H is processed, work pieces process When processed according to the rule of dense sequence, after processing is completed mark flag (i, j)=1.

Step 3: update starts to process time S with the O (i, j) ' the process with identical workpiece and same machines (i, j), (i.e. the be expert at process that with column is related to of the O (i, j) ' in matrix H), and by the O (i, j) ' it is corresponding Flag (i, j) is set to 1, specific to state are as follows: defines C (i, j)=S (i, j)+P (i, j), C (i, j) indicates work pieces process process Completion date, S (i, j) indicates the time that starts to process of work pieces process process, when P (i, j) indicates the processing of work pieces process process Between, the process for having identical workpiece and same machines with the manufacturing procedure O (i, j) ' of workpiece, if S (i, j) < C (i, j), C (i, j)=S (i, j) is then enabled, if S (i, j) >=C (i, j), S (i, j) value is constant.

Step 4: constantly repeating step 2 and step 3, until the flag (i, j)=1 of all process steps in the matrix H, Obtain the total workpiece n for acting on behalf of A processing_AManufacturing procedure on each machine obtains the total workpiece n for acting on behalf of B processing_BOn each machine Manufacturing procedure；

As shown in table 1, Jobj (A) expression belongs to the workpiece j for acting on behalf of A in table for design parameter design；Jobj (B) expression belongs to Act on behalf of the workpiece j of B；Machine i indicates machine i；Data indicate process time of the workpiece on machine in table, as first in table The data of row secondary series indicate that belonging to process time of the workpiece 2 for acting on behalf of A on machine 1 is 1.

1 concrete case parameter list of table

Step 5: A processing n is being acted on behalf of_AThe n of a workpiece_AMaximal Makespan is found out in a completion date, is denoted as C_maxA, In Act on behalf of B processing n_BThe n of a workpiece_BMaximal Makespan is found out in a completion date, is denoted as C_maxB, definition weight coefficient θ is section [0,2*(C_maxB/C_maxA)] in random number, it is θ assignment that random number is taken in this interval range, and the workpiece number n of processing, which meets, to close It is n=n_A+n_B；

The value range of θ is sought according to the design parameter that table 1 provides, and workpiece sequencing is calculated using SPT rule first C_maxA=15, C_maxB=21, weight coefficient θ are the random number in section [0,2* (21/15)], for convenience of calculating, enable θ=1.Base In the open Job-Shop sequence Gantt chart of the dual-proxy of SPT rule as shown in Fig. 2, Mi represents machine i in figure, Ji represents workpiece i, Specific numerical value corresponds to process time of each workpiece on each machine in figure.

Step 6: the n for acting on behalf of A processing is found in the matrix H_AA workpiece, and to the n_AA workpiece is in matrix H pair The every row summation answered is X_A, to the n_AA workpiece is Y in the corresponding each column summation of matrix H_A, compare X_AAnd Y_ASize, take X_A And Y_AIn maximum value be assigned to LB_A, LB_AIt indicates to act on behalf of the n that A is processed_AThe floor value of a workpiece finds in matrix H and acts on behalf of B and add The n of work_BA workpiece, and to the n_BA workpiece is X in the corresponding every row summation of matrix H_B, to the n_BA workpiece is in matrix H pair The each column summation answered is Y_B, compare X_BAnd Y_BSize, take X_BAnd Y_BIn maximum value be assigned to LB_B, LB_BIt indicates to act on behalf of the n that B is processed_B The floor value of a workpiece；

Step 7: by comparing θ and LB_B/LB_ARatio size relation, it is high with the priority of acting on behalf of B that A is acted on behalf of in judgement It is low, if θ > LB_B/LB_A, then it represents that the priority for acting on behalf of B is high, if θ≤LB_B/LB_A, then it represents that the priority for acting on behalf of A is high；

2 concrete case lower bound calculating process of table

It can be obtained in conjunction with above-mentioned case parameter and table 2, LB_B=18, LB_A=11, then LB_B/LB_A=1.6, θ < 1.6 at this time, Then illustrate to act on behalf of A priority height, Mi represents machine i in table, and Ji represents workpiece i, and specific numerical value corresponds to each workpiece in each machine On process time, wherein corresponding data are the number for calculating lower bound and using in the process respectively in " row summation " and " column summation " According to two numbers of overstriking respectively correspond LB_AAnd LB_B。

Step 8: the machining state flag (i, j)=0 of all workpiece in matrix H is initialized again, acts on behalf of A in judgement Step 2 and step 3 are constantly repeated under the premise of B priority with acting on behalf of, until the machining state of all workpiece in matrix H Flag (i, j)=1 obtains the n that A processing is acted on behalf of under the premise of judging priority_AProcessing sequence of a workpiece on each machine, And the n of B processing is acted on behalf of under the premise of judging priority_BProcessing sequence of a workpiece on each machine；

Step 9: it finds out and acts on behalf of A processing n under the premise of judging priority_AThe n of a workpiece_AMaximum in a completion date Completion date, and update C_maxAValue, find out acted on behalf of under the premise of judging priority B processing n_BThe n of a workpiece_BA complete working hour Between in Maximal Makespan, and update C_maxBValue, objective function F is found out according to formula (1), can be according to the target letter Number acquires minimization and acts on behalf of A and act on behalf of the Maximal Makespan of B；

F=min (C_maxA+θC_maxB) (1)

In formula, θ indicates weight coefficient, and value range is section [0,2* (C_maxB/C_maxA)] in random number.

It combines Fig. 3 that can obtain in the present embodiment, under the premise of acting on behalf of A priority height, obtains the Maximal Makespan for acting on behalf of A It is 15, the Maximal Makespan for acting on behalf of B is 21, then objective function F=min (C_maxA+θC_maxB)=15+1*21=36, if according to Randomly ordered mode carries out the sequence of work pieces process sequence, it is randomly ordered under the open Job-Shop of dual-proxy sort Gantt chart As shown in figure 4, the Maximal Makespan for acting on behalf of A is 19 under randomly ordered, the Maximal Makespan for acting on behalf of B is 22, then target letter Number F=min (C_maxA+θC_maxB)=19+1*22=41, it can be seen that can reduce target in conjunction with the dense sort algorithm of priority Functional value illustrates that the present invention is effective.The open Job-Shop sequence Gantt chart of dual-proxy based on SPT rule combination priority As shown in figure 3, Mi represents machine i in figure, Ji represents workpiece i, and specific numerical value corresponds to each workpiece adding on each machine in figure Between working hour.

It is whether effective in order to verify the open workshop work pieces process sort method of the dual-proxy based on SPT rule, devise one The numerical simulation experiment of series, the number of machines for testing test is respectively 3/5/10；Workpiece number is respectively 100/500/1500/2000 When, the combination of each machine workpieces different scales.

The experiment is emulated using c language, and workpiece is generated in the process time of every machine by function at random, and section is [1,10].Every kind of scale carries out 5 experiments, and record acts on behalf of A, the floor value for acting on behalf of B, θ value, C_maxA、C_maxBAnd it is randomly ordered under Target function value and combine the target function value after the present invention, specific test data and test result such as table 3, table 4, table 5 It is shown.

From table 3, table 4, table 5 calculated result can be seen that using combine priority dense sequence can optimize dual-proxy The sequence in open workshop, so that objective function C_maxA+θC_maxBIt is smaller.

Table 3. emulates data result (number of machines 3)

Table 4. emulates data result (number of machines 5)

Table 5. emulates data result (number of machines 10)