CN102566560B - A kind of production line scheduling method based on structure type heuritic approach - Google Patents

A kind of production line scheduling method based on structure type heuritic approach Download PDF

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CN102566560B
CN102566560B CN201210061685.1A CN201210061685A CN102566560B CN 102566560 B CN102566560 B CN 102566560B CN 201210061685 A CN201210061685 A CN 201210061685A CN 102566560 B CN102566560 B CN 102566560B
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唐聃
舒红平
罗飞
刘魁
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Chengdu Information Technology Co Ltd of CAS
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention provides a kind of production line scheduling method based on structure type heuritic approach, if the method comprises the steps: that a S1 n workpiece is processed on m platform machine, if p i, jfor the execution time of a jth workpiece on i-th machine, form matrix P, wherein i=1,2, Λ, m; J=1,2, Λ, n; Two column elements in S2, arbitrarily selection matrix P, i.e. workpiece a, the b execution time P respectively on m platform machine aand P b, wherein 1≤a, b≤n, a ≠ b; S3, determine workpiece a, the processing sequence of b; Whether the n column element in S4, judgment matrix P all compares between two, if so, then terminates to judge, adjusts, and process on m platform machine successively by the processing sequence determined to workpiece, otherwise, return step S2.The present invention realizes the scheduling of Flow Shop production line, by reducing each workpiece stand-by period before processing to the adjustment of work pieces process order so that total complete time is minimum for target.Relative to prior art, computation complexity of the present invention is low, and computing time is short, and has good scheduling performance.

Description

A kind of production line scheduling method based on structure type heuritic approach
Technical field
The present invention relates to and automatically control and areas of information technology, particularly relate to a kind of production line scheduling method based on structure type heuritic approach.
Background technology
Production line scheduling is very important problem in manufacturing enterprise's production run, and good scheduling strategy will be enhanced productivity greatly.Total complete time (makespan) is very important performance index in scheduling process, and the most I of total complete time makes that resource more effectively utilizes, task is transmitted more rapidly and Work in Process is minimum.Current production line scheduling method is divided into two types, one is the method for exhaustion, as dynamic programming, branch and bound method etc., although optimum scheduling can be obtained to the processing sequence of workpiece, but the search volume of these methods can along with the increase of piece count exponentially formula sharp increase, computation complexity is high, higher to the requirement of machine hardware, is difficult to be applied on large-scale production line scheduling; Another kind method is heuritic approach, comprise meta-heuristic algorithm and structure type heuritic approach, the structure type heuritic approach of current proposition is as (1) Palmer algorithm---Palmer D S.Sequencing Jobs through a Multi-Stage Process in the Minimum Total Time-a Quick Method of Obtaining a near Optimum [J] .Operational Research Quarterly, 1965,16:101-107; (2) Gupta algorithm---Gupta J.A Functional Heuristic Algorithm for the Flowshop Scheduling Problem [J] .Operational Research Quarterly, 1971,22:39-47; (3) CDS algorithm---Campbell H G, Dudek R A, Smith M L.A Heuristic Algorithm for then-Job, m-Machine Scheduling Problem. [J] .Management Science, 1970,16:630-637; (4) RA algorithm---Dannenbring D G.An Evaluation of Flow Shop Sequencing Heuristics [J] .Management Science, 1977,23 (11): 1174-1182; (5) NEH algorithm---Nawaz M, Enscore E, Ham I.A Heuristic Algorithm for the m Machine, n Job Flow Shop [J] .OMEGA:The International Journal of Management Sciences, 1983,11 (1): 91-95 etc., best with the performance of NEH algorithm in above several structure type heuritic approach.But, NEH algorithm need in implementation procedure by repeatedly calculate draft workpiece sequence total complete time and compare, therefore, computation complexity will much larger than other structure type heuritic approaches.
Summary of the invention
For prior art Problems existing, fundamental purpose of the present invention is that providing a kind of has higher scheduling performance, the production line scheduling method based on structure type heuritic approach that computation complexity is lower simultaneously.
For achieving the above object, the invention provides a kind of embodiment of the production line scheduling method based on structure type heuritic approach, the method comprises the steps:
If a S1 n workpiece is processed on m platform machine, if p i, jfor the execution time of a jth workpiece on i-th machine, form matrix P, wherein i=1,2, Λ, m; J=1,2, Λ, n;
Two column elements in S2, arbitrarily selection matrix P, i.e. workpiece a, the b execution time P respectively on m platform machine aand P b, wherein 1≤a, b≤n, a ≠ b;
S3, determine workpiece a, the processing sequence of b;
Whether the n column element in S4, judgment matrix P all compares between two, if so, then terminates to judge, otherwise, return step S2,
Wherein step S3 comprises following steps:
S31, by two column element P in matrix P a, P bvalue substitute into respectively calculate S aand S b;
S32, judge S a* S bwhether <=0 sets up, if set up, then enters step S321, if be false, then enters step S33;
S321, judge S awhether > 0 sets up, if set up, then before the processing sequence of element a being placed in element b, if be false, then before the processing sequence of element b being placed in element a;
S33, judge S a, S bwhether > 0 sets up, if set up, then enters step S34, if be false, then enters step S35;
S34, by two column element P in optional matrix P a, P bvalue substitute into respectively calculate sum_c aand sum_c b;
S341, judge sum_c a< sum_c bwhether set up, if set up, then before the processing sequence of element a being placed in element b; If be false, then enter step S342;
S342, judge sum_c a> sum_c bwhether set up, if set up, then, before the processing sequence of element b being placed in element a, if be false, then remove P aand P bthe last element arranged also returns step S31;
S35, by two column element P in optional matrix P a, P bvalue substitute into respectively calculate sum_f aand sum_f b;
S351, judge sum_f a> sum_f bwhether set up, if set up, then, before the processing sequence of element a being placed in element b, if be false, then enter step S352;
S352, judge sum_f a< sum_f bwhether set up, if set up, then, before the processing sequence of element b being placed in element a, if be false, then remove P aand P bthe first element arranged also returns step S31.
Further, when the n column element in judgment matrix P all compares between two, then by the processing sequence determined, workpiece is adjusted, and process on m platform machine successively.
The present invention realizes the scheduling of Flow Shop production line, by reducing each workpiece stand-by period before processing to the adjustment of work pieces process order so that total complete time is minimum for target.Relative to prior art, computation complexity of the present invention is low, and computing time is short, and has good scheduling performance.
Accompanying drawing explanation
Fig. 1 is Flow Shop production line scheduling schematic diagram.
Fig. 2 is the production line scheduling method process flow diagram that the present invention is based on structure type heuritic approach.
Fig. 3 is the process flow diagram of step S3 in the production line scheduling method that the present invention is based on structure type heuritic approach.
Embodiment
Below in conjunction with accompanying drawing, describe the specific embodiment of the present invention in detail.
As shown in Figure 1, for Flow Shop production line scheduling schematic diagram of the present invention, be expressed as n workpiece to process on m platform machine, namely each workpiece needs through m procedure, the machine that per pass procedure calls is different, but n workpiece is identical by the order of m platform machine, and namely the processing sequence of n workpiece on every platform machine is identical.Namely workpiece 1, workpiece 2...... workpiece n are in order respectively through the processing of machine 1, machine 2...... machine m, but this processing sequence is not likely best, in order to make total elapsed time the shortest, must adjust the processing sequence of workpiece.
Definition O i, jfor a jth workpiece operates on i-th machine, p i, jfor O i, jexecution time, c i, jfor O i, jdeadline, c i, jfor O i, jadd the stand-by period.Wherein i=1,2, Λ, m; J=1,2, Λ, n.In order to determine the optimum processing sequence of the processing tasks of n workpiece on every platform machine, make the shortest time that the processing tasks of all workpiece all completes.When carrying out work pieces process, the processing sequence of each processing tasks on machine is identical, is 1,2, Λ, m; Every platform machine can only carry out a processing tasks simultaneously; A processing tasks can not carry out simultaneously on different machines; Each processing tasks send next process immediately after processing; Task starts processing on machine, must be performed until the completion of this operation, and midway does not allow to stop and inserts other task; All tasks are ready in 0 moment, and setup time is included in process time; Permission task is waited between operation; Allow machine idle when task does not arrive.Longest finishing time makespan (C max) that is to say the deadline c of last work pieces process m, n, find the processing sequence of a workpiece, workpiece a, workpiece b...... workpiece n, make total complete time (makespan) minimum.
If the total complete time (makespan) when piece count is i is C i, wherein 1≤i≤n, as i=n, definition C i=C n=C; If a jth workpiece process on i-th machine before stand-by period be t i, j, wherein t i, 1=0,1≤i≤m, 1≤j≤n; If the n-th workpiece process on i-th machine before stand-by period be D i, wherein D 1=0, namely the stand-by period of all workpiece on First machine is 0,1≤i≤m; If the process time matrix of n workpiece on m platform machine is P, wherein: P = p 1,1 p 1,2 &Lambda; p 1 , n p 2,1 p 2,2 &Lambda; p 2 , n M M O M p m , 1 p m , 2 &Lambda; p m , n , In matrix P, p i, jrepresent the process time of a jth workpiece on i-th machine, 1≤i≤m, 1≤j≤n.
When piece count is 1, namely during n=1, workpiece process on each machine before stand-by period be 0, therefore total complete time (makespan) is the process time sum of this workpiece on all machines: C 1 = p 1,1 + p 2,1 + &Lambda; + p m , 1 = &Sigma; i = 1 m p i , 1 ;
When piece count is 2, namely, during n=2, total complete time (makespan) is stand-by period sum: C before the processing in the end on a machine of process time in the end on a machine of sum process time of the 1st workpiece on all machines, second workpiece and second workpiece 2=C 1+ p m, 2+ D 2, and D 2=t 2, n, can calculate as follows: t 2,2=max (p 2,1-p 1,2, 0), t 2,3=max (t 2,2+ p 2,2-p ' 1,3, 0), Λ, t 2, n=max (t 2, n-1+ p 2, n-1-p ' 1, n, 0), wherein p ' i, j=p i, j+ max (p i-1, j-p j, i-1, 0), 2≤i≤m, 1≤j≤n;
By that analogy, when piece count is n, C n=C n-1+ p m, n+ D n, and D n=t m, n, can calculate as follows: t m, 2=max (p m, 1-p ' m-1,2, 0), t m, 3=max (t m, 2+ p m, 2-p ' m-1,3, 0), Λ, t m, n=max (t m, n-1+ p m, n-1-p ' m-1, n, 0).That is:
makespan = C =
C n = C n - 1 + p m , n + D n
= C n - 2 + p m - 1 , n + p m , n + D n - 1 + D n
= C n - 3 + p m - 2 , n + p m - 1 , n + p m , n + D n - 2 + D n - 1 + D n
M
= p 1,1 + p 2,1 + &Lambda; + p m , 1 + p m , 2 + p m , 3 + &Lambda; + p m , n + D 1 + D 2 + &Lambda; + D n
= &Sigma; i = 1 m p i , 1 + &Sigma; j = 2 n p m , j + &Sigma; k = 1 n D k
To make total complete time (makespan) minimum, then needing to look for a work pieces process sequence, making the deadline of the n-th workpiece on m platform machine try one's best close to or equal namely the process time sum and other workpiece except unit one except stand-by period sum before processing of unit one at sum process time of all machines, other workpiece except unit one in the end machine will be reduced.
As shown in Figure 2, for the present invention is based on the production line scheduling method process flow diagram of structure type heuritic approach, the method comprises the steps:
If a S1 n workpiece is processed on m platform machine, if p i, jfor the execution time of a jth workpiece on i-th machine, form matrix P, P = p 1,1 p 1,2 &Lambda; p 1 , n p 2,1 p 2,2 &Lambda; p 2 , n M M O M p m , 1 p m , 2 &Lambda; p m , n , Wherein i=1,2, Λ, m; J=1,2, Λ, n;
Two column elements in S2, arbitrarily selection matrix P, i.e. workpiece a, the b execution time P respectively on m platform machine aand P b, wherein 1≤a, b≤n, a ≠ b;
S3, determine workpiece a, the processing sequence of b;
Whether the n column element in S4, judgment matrix P all compares between two, if so, then terminates to judge, adjusts, and process on m platform machine successively by the processing sequence determined to workpiece, otherwise, return step S2.
As shown in Figure 3, for the present invention is based on structure type heuritic approach production line scheduling method in the process flow diagram of step S3.Step S3, namely determines workpiece a, and the processing sequence of b, specifically comprises following steps:
S31, by two column element P in matrix P a, P bvalue substitute into respectively (S jweighted value for jth row in matrix P), calculate S aand S b;
S32, judge S a* S bwhether <=0 sets up, if set up, then enters step S321, if be false, then enters step S33;
S321, judge S awhether > 0 sets up, if set up, then enters step S322, before being placed in element b, if be false, then enters step S323 by the processing sequence of element a, before being placed in element a by the processing sequence of element b;
S33, judge S a, S bwhether > 0 sets up, if set up, then enters step S34, if be false, then enters step S35;
S34, by two column element P in optional matrix P a, P b, substitute into (sum_c jfor constantly remove jth in matrix P arrange last element and), calculate sum_c aand sum_c b;
S341, judge sum_c a< sum_c bwhether set up, if set up, then enter step S343, before being placed in element b by the processing sequence of element a; If be false, then enter step S342;
S342, judge sum_c a> sum_c bwhether set up, if set up, then enter step S345, before being placed in element a by the processing sequence of element b, if be false, known sum_c a=sum_c b, then enter step S344, namely remove P aand P bthe last element arranged also returns step S31;
S35, by two column element P in optional matrix P a, P b, substitute into (sum_f jfor constantly remove the most previous element of the row of jth in matrix P and), calculate sum_f aand sum_f b;
S351, judge sum_f a> sum_f bwhether set up, if set up, then enter step S353, before being placed in element b by the processing sequence of element a, if be false, then enter step S352;
S352, judge sum_f a< sum_f bwhether set up, if set up, then enter step S355, before being placed in element a by the processing sequence of element b, if be false, known sum_f a=sum_f b, then enter step S354, namely remove P aand P bthe first element arranged also returns step S31.
Result illustrates the actual schedule performance of the production line scheduling method based on structure type heuritic approach of the present invention by experiment.Wherein Y is optimum rate, and namely in specific sample scale, optimum solution accounts for the ratio of all sample sizes to use certain dispatching method to draw, this numerical value is higher, then the ratio of optimum solution is higher to show to use this dispatching method to draw, performance is more excellent.In addition, optimum deviation ratio E=(MK-MKp) 100/MKp, wherein MK is the actual total complete time using the rear workpiece of certain dispatching method sequence, MKp is the total complete time of this group workpiece when optimum processing sequence, optimum deviation ratio E is less, and show to use certain dispatching method better to the arrangement of work pieces process order, E=0 then shows that the processing sequence of certain subjob is arranged as optimum.
Workpiece used by experiment each element Pi of the process time on each machine in matrix P, j is the random integers (1≤i≤m of 0 to 9,1≤j≤n), following table gives multiple test data in units of sample size 20, as can be seen from following table, utilize that the production line scheduling method based on structure type heuritic approach of the present invention optimum deviation ratio E >'s 10% is considerably less, average optimal deviation ratio, substantially all below 5%, shows that the scheduling performance of the method is more excellent.In addition, the production line scheduling method algorithm complex based on structure type heuritic approach of the present invention is nlog (n)+nm, and computation complexity is low, and computing time is short.
Embodiment one
Suppose that the process time matrix P of 5 workpiece on 4 machines is as follows, P irepresent i-th row of P.
P = 1 1 3 7 7 3 9 9 2 3 9 7 3 7 7 10 6 8 7 2
Two column element P in any selection matrix P 1, P 2;
By P 1, P 2value substitute into respectively calculate S 1=33, S 2=13;
Because S 1, S 2> 0, by P 1, P 2value substitute into respectively calculate sum_C 1=13, sum_C 2=17;
Because sum_C 1< sum_C 2, therefore by P 1processing sequence be placed in P 2before;
Two column element P in any selection matrix P 1, P 3;
By P 1, P 3value substitute into respectively calculate S 1=33, S 3=9;
Because S 1, S 3> 0, by P 1, P 3value substitute into respectively calculate sum_C 1=13, sum_C 3=15;
Because sum_C 1< sum_C 3, therefore by P 1processing sequence be placed in P3 before;
Two column element P in any selection matrix P 1, P 4;
By P 1, P 4value substitute into respectively calculate S 1=33, S 4=4;
Because S 1, S 4> 0, by P 1, P 4value substitute into respectively calculate sum_C 1=13, sum_C 4=16;
Because sum_C 1< sum_C 4, therefore by P 1processing sequence be placed in P 4before;
Two column element P in any selection matrix P 1, P 5;
By P 1, P 5value substitute into respectively calculate S 1=33, S 5=-10;
Because S 1s 5<=0, and S 1> 0, therefore by P 1processing sequence be placed in P 5before;
Two column element P in any selection matrix P 2, P 3;
By P 2, P 3value substitute into respectively calculate S 2=13, S 3=9;
Because S 2, S 3> 0, by P 2, P 3value substitute into respectively calculate sum_C 2=17, sum_C 3=15;
Because sum_C 2> sum_C 3, therefore by P 3processing sequence be placed in P 2before;
Two column element P in any selection matrix P 2, P 4;
By P 2, P 4value substitute into respectively calculate S 2=13, S 4=4;
Because S 2, S 4> 0, by P 2, P 4value substitute into respectively calculate sum_C 2=17, sum_C 4=16;
Because sum_C 2> sum_C 4, therefore by P 4processing sequence be placed in P 2before;
Two column element P in any selection matrix P 2, P 5;
By P 2, P 5value substitute into respectively calculate S 2=13, S 5=-10;
Because S 2s 5<=0, and S 2> 0, therefore by P 2processing sequence be placed in P 5before;
Two column element P in any selection matrix P 3, P 4;
By P 3, P 4value substitute into respectively calculate S 3=9, S 4=4;
Because S 3, S 4> 0, by P 3, P 4value substitute into respectively calculate sum_C 3=15, sum_C 4=16;
Because sum_C 3< sum_C 4, therefore by P 3processing sequence be placed in P 4before;
Two column element P in any selection matrix P 3, P 5;
By P 3, P 5value substitute into respectively calculate S 3=9, S 5=-10;
Because S 3s 5<=0, and S 3> 0, therefore by P 3processing sequence be placed in P 5before;
Two column element P in any selection matrix P 4, P 5;
By P 4, P 5value substitute into respectively calculate S 4=4, S 5=-10;
Because S 4s 5<=0, and S 4> 0, therefore by P 4processing sequence be placed in P 5before;
5 column elements in matrix P all compare between two, and the final processing sequence of each workpiece is P 1p 3p 4p 2p 5.
The processing sequence of adjustment workpiece is P 1p 3p 4p 2p 5, process on m platform machine successively.
Be described above the production line scheduling method based on structure type heuritic approach.The present invention is not limited to above embodiment, does not anyly depart from technical solution of the present invention, namely only carries out improvement that those of ordinary skill in the art know or change to it, all belongs within protection scope of the present invention.

Claims (2)

1., based on a production line scheduling method for structure type heuritic approach, comprise following steps:
If a S1 n workpiece is processed on m platform machine, if p i,jfor the execution time of a jth workpiece on i-th machine, form matrix P, wherein i=1,2 ..., m; J=1,2 ..., n;
Two column elements in S2, arbitrarily selection matrix P, i.e. workpiece a, the b execution time P respectively on m platform machine aand P b, wherein 1≤a≤n, 1≤b≤n, a ≠ b;
S3, determine workpiece a, the processing sequence of b;
Whether the n column element in S4, judgment matrix P all compares between two, if so, then terminates to judge, otherwise, return step S2,
It is characterized in that, described step S3 comprises following steps:
S31, by two column element P in matrix P a, P bvalue substitute into respectively calculate S aand S b;
S32, judge S a* S bwhether <=0 sets up, if set up, then enters step S321, if be false, then enters step S33;
S321, judge S awhether >0 sets up, if set up, then before the processing sequence of element a being placed in element b, if be false, then before the processing sequence of element b being placed in element a;
S33, judge S a>0 and S bwhether >0 sets up, if set up, then enters step S34, if be false, then enters step S35;
S34, by two column element P in optional matrix P a, P bvalue substitute into respectively calculate sum_c aand sum_c b;
S341, judge sum_c a<sum_c bwhether set up, if set up, then before the processing sequence of element a being placed in element b; If be false, then enter step S342;
S342, judge sum_c a>sum_c bwhether set up, if set up, then, before the processing sequence of element b being placed in element a, if be false, then remove P aand P bthe last element arranged also returns step S31;
S35, by two column element P in optional matrix P a, P bvalue substitute into respectively calculate sum_f aand sum_f b;
S351, judge sum_f a>sum_f bwhether set up, if set up, then, before the processing sequence of element a being placed in element b, if be false, then enter step S352;
S352, judge sum_f a<sum_f bwhether set up, if set up, then, before the processing sequence of element b being placed in element a, if be false, then remove P aand P bthe first element arranged also returns step S31.
2. as claimed in claim 1 based on the production line scheduling method of structure type heuritic approach, it is characterized in that: when the n column element in judgment matrix P all compares between two, then by the processing sequence determined, workpiece is adjusted, and process on m platform machine successively.
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