CN106971235A - A kind of flexible job shop Optimization Scheduling in batches that there is intermediate storage constraint - Google Patents

Abstract

The invention discloses a kind of flexible job shop Optimization Scheduling in batches that there is intermediate storage constraint, belong to Job-Shop technical field.Including setting up flexible job shop Optimal Scheduling model and initiation parameter；Consider the limited constraints of intermediate storage warehouse amount of storage；Different types of work-piece batch machining path is any；Different types of workpiece is carried out in batches, to determine its batch splitting scheme；Each work-piece batch is with random sequence according to the production equipment in its preference probability selection each process；Equipment selects the sub- batch of suitable workpiece to be processed also according to its preference probability from its wait batch queue；Until completing batch number is equal to lot count, this scheduling scheme is obtained；Computing is iterated, optimal scheduling method is exported.By the above-mentioned means, the present invention can greatly improve utilization rate of equipment and installations, shorten the whole production cycle, improve production efficiency, realize flexible job shop Optimized Operation in batches.

Description

A kind of flexible job shop Optimization Scheduling in batches that there is intermediate storage constraint

Technical field

The invention belongs to Job-Shop field, more particularly to a kind of flexible job shop point that there is intermediate storage constraint Criticize Optimization Scheduling.

Background technology

Earlier 1900s, industrialization blank is just formed, and market is relatively single to the demand of product, and manufacturing enterprise is in order to full The sufficient market demand, raising production efficiency and saving manufacturing cost, start to produce using the rigid automatic streamline of high-volume, few kind Line carries out production.However, to the middle and later periods sixties, with the fast development of global economy and science and technology, consumer The single product of type is no longer satisfied with, their increasingly diversification of the demand to product are requiring that product possesses higher quality, more While short production cycle, also it is desirable to which product has distinct characteristic and style.In order to cater to consumer demand, accelerate product Update, manufacturers make great efforts to change current production status, and trial sets up one kind and accommodates multi items, small lot, can determine The new production pattern of inhibition and generation feature.

In manufacturing enterprise, the production of product is generally required for multiple working procedure to complete, and per procedure typically all Have and be generally provided with intermediate stores between many processing machines, adjacent process, for storing intermediate products, to ensure that each operation is given birth to The continuity of production.In traditional Flow Shop Scheduling, usually assume that the storage capacity between adjacent process be it is unlimited, But in actual industrial processes, in addition it is also necessary to consider the limited situation of intermediate stores storage capacity.

Because the essence of production scheduling problems is combinatorial optimization problem, if assigning single part as an independence during scheduling Individual, participate in sorting consistence, then scheduling problem scale can become very big, algorithm is in memory space and calculates spatially, all Unacceptably.So needing that some height batch will be divided into contained by workpiece in batches, with son batch for thread.It is this kind of workpiece The Batch Scheduling optimization problem of son batch is divided into, referred to as in batches optimization problem (Lot Streaming) was Reiter in 1966 Propose first.It is related to batch and divided and sorting consistence simultaneously, more complicated than traditional scheduler problem, but closer to actual life Production, it is adaptable to multi items, the productive prospecting of small lot.

Then, it is considered to which Optimal Scheduling arises at the historic moment the flexible job shop of intermediate storage constraint in batches.Such scheduling Different types of lots processed path is arbitrary in problem, but its contained process number and process processing sequence are predetermined 's.Scheduling is needed under being the limited constraints of under consideration warehouse amount of storage the problem of solution, in batches, determine all kinds of The batch splitting scheme of workpiece, is each procedure dispensation machines resource of each son batch, and determines that each son batch is most on processing machine Excellent processing sequence, so that regulation goal can be met.

At present, there was only a small number of scholars both at home and abroad, Optimized Operation is asked in batches to there is the flexible job shop of intermediate storage constraint Topic is more deeply studied.Two benches Flow Shop Scheduling with limited intermediate storage is established as one by Khosla Individual MILP model, and propose based on this model the two kinds of lower bounds and several heuritic approaches of problem. Nowicki proposes an effective tabu search algorithm, and to solve, to minimize makespan, (the maximum of all workpiece is completed Time) for target the scheduling with intermediate storage Flow Shop Scheduling.Tang and Xuan is utilized and is deposited centre Storage is considered as the modeling strategy for the parallel machine that processing time is 0, and the problem is established as to the paced beat of a static discrete time Model is drawn, and proposes an effective Lagrangian Relaxation Algorithm.Pan Quanke and Zhu Jianying to optimize the production cycle as target, Consider to start time, have studied flexible job shop Optimal Scheduling in batches, carried out according to minimum process batch impartial Divide, Machining Sequencing is determined using genetic algorithm optimization.Sun Zhijun etc., pacify into the batching Algorithm proposed based on genetic algorithm and Sort algorithm, the sub- lot number of each workpiece is optimized, and the batch of each son batch is determined using the partition strategy of impartial son batch. Lin Nan etc. considers production batch, starts time, in the case of given scheme in batches, with reference to heuristic dispatching rules and mould Intend annealing algorithm, propose that genetic algorithm solves the flexible scheduling problems of the Job-shop under Makespan performance indications.Shen L. in the case of to stator lot number, using consistent son batch partition strategy, propose to be processed by pre- division, tabu search algorithm optimization Sequence, three phase algorithms of the son batch part of adjustment in batches three composition solve Job-shop Optimal Schedulings in batches.White person of outstanding talent etc. Using the partition strategy of consistent son batch, by PSO Algorithm multi-objective flexible Optimal Scheduling in batches, base is devised Realize that batch is divided in the method for " vernier ".Huang R.H. are discussed when batch workpiece is divided into 1,2,3,4 The multiple target Job-shop scheduling problems in the case of four kinds are criticized Deng son, optimization is ranked up using ant group algorithm.

Existing research is mostly focused on the Flow Shop Scheduling in the presence of storage constraint, and existing batch processes Carry out, not batch splitting scheme is entered under conditions of sub- lot number or son batch batch size is manually determined in advance mostly The deep step research of row.The present invention is under conditions of storage resource-constrained is considered, to study flexible job shop Optimized Operation in batches Problem, will in batches optimize and be combined with batch scheduling, propose the dynamic batching Algorithm and flexible dispatching algorithm of monolithic batch.

The content of the invention

The defect existed for prior art, it is an object of the invention to provide a kind of flexibility that there is intermediate storage constraint Job shop Optimization Scheduling in batches, this method is under conditions of storage resource-constrained is considered, during work piece production Equipment, batch, intermediate stores are as entirety independent one by one, and each section all according to corresponding rule, performs corresponding row Will in batches to optimize and be combined with batch scheduling, and so as to greatly improve utilization rate of equipment and installations, shorten the process-cycle.

To reach above-mentioned purpose, the technical solution adopted by the present invention is：

A kind of flexible job shop Optimization Scheduling in batches that there is intermediate storage constraint, is characterized in：Same type Each height of workpiece batch, which need not be connected, to be processed, it is allowed to which machine inserts other between each son batch task for processing a class workpiece The son of type batch.Optimization determines batch of work-piece batch under the premise of under consideration warehouse position in storehouse number and the limited constraint of memory capacity Splitting scheme is measured, is each procedure dispensation machines resource of each son batch and the optimal processing sequence of each son batch of determination, minimizes Maximal Makespan.

Set up the mathematical modeling of following flexible job shop Optimal Scheduling：

Min Z=C_max (1)

R_s≤R_max (4)

R_s=R_o+R_r (6)

Formula (1) is object function, C_maxRepresent longest finishing time；When formula (2) represents the maximum completion of whole process Between computational methods, wherein：BN_nmFor machine u_mUpper batch n batch size, pt_nmIt is batch n in machine u_mOn processing when Between, N is total batch number；Formula (3) divides constraint for batch, represents carrying out when batch is divided same workpiece should being made to be assigned to respectively Batch summation on parallel machine is constant, remains the initial manufacture batch size of the workpiece；Formula (4) represents each production level correspondence The position in storehouse numbers of intermediate stores be limited；Formula (5) represents that the workpiece overall length deposited in per bin level is less than or equal to the length of position in storehouse Degree, L_RFor the length of position in storehouse；Formula (6) represents that position in storehouse number keeps constant.

Each batch of workpiece can select the process equipment per procedure and entrance according to oneself criterion and standard Its batch task waiting list.Each equipment can select batch to be processed from batch task waiting list.Per pass work After sequence, the sub- batch of workpiece is all likely to become final products, if final products, is directly entered finished parts warehouse；Otherwise, to centre Warehouse application position in storehouse resource, obtains after resource, can continue executing with the processing of subsequent handling, until it turns into final products.It is middle Warehouse is according to resource allocation standard distribution bin position resource, after the completion of the corresponding task of batch to be processed, then the resource of distribution is returned Receive.

Which process equipment work-piece batch selects from candidate device, and mainly the equipment state and equipment with equipment are to this The disposal ability of batch is relevant.The state of equipment is defined as：

Wherein：X_m(t) ∈ { 0,1 } is t equipment u_mAvailability, can be used as 1, unavailable is 0；1 effect in denominator It is by μ_m(t) number field restriction is in [0,1]；Q_m(t) it is t equipment u_mWaiting list in batch number；n_kFor equipment u_m Waiting list in k-th of batch Mission Number；For u_mUpper k-th of batch is performed the process time of needs,For u_mBatch switching time needed for upper -1 batch of kth to k batch switching.

In order to realize reasonable selection of the batch to equipment, batch is represented by the preference probability of equipment：

Wherein, δ_m∈ { 0,1 } represents u_mWhether the batch of the batch can be handled；α, β are to be set for the current of balancing equipment The relative importance of standby state and equipment to the disposal ability of the batch during equipment is selected, their value can basis Experience is determined by emulation experiment；JA_nsFor the cluster tool of the batch can be handled.

In order to realize reasonable selection of the equipment to batch, corresponding preference selection strategy is defined：

Selection strategy 1：The batch of prioritizing selection long processing time.That is, in production line balance, it is total on all machines Process time longer workpiece, it should which the workpiece shorter than total elapsed time obtains higher processing priority.

Selection strategy 2：In the case where position in storehouse is sufficient, prioritizing selection turns into the batch of intermediate products.

In batch partition problem, son batch batch and production cycle U-shaped relation.It is unfavorable when the batch of group batch is excessive In the load balance of machinery compartment；And the batch of group batch it is too small when, excessive sub- lot number can be caused so that machine is in different sons batch Between batch adjustment time increase and task inter process carrying increased frequency.Therefore rational scheme in batches be realize it is excellent Change scheduling, complete the guarantee of overall regulation goal.Based on the regulation goal for minimizing Maximal Makespan, definition is following several points Criticize scheduling rule：

Rule 1：Process equipment operation at full capacity, plays its characteristic as far as possible.

Rule 2：Process equipment is arranged for batch, makes batch switching time minimum as far as possible.

Rule 3：Process equipment is arranged for batch, makes the batch deadline earliest as far as possible.

Rule 4：Unnecessary free time is reduced in equipment process as far as possible.

Assuming that selecting an equipment composition one for every grade from the parallel batching equipment of each production level by production sequence Machining path, is designated as P_l, l is machining path numbering.Remember N_lminFor machining path P_lOn all intermediate stores single position in storehouse The minimum value of amount of storage.Thus optimized algorithm step in batches is constructed as follows：

Step 1：For each one predetermined queue of device definition, it is sky, queue deadline to initialize predetermined queue

Step 2：Randomly choose a BN_pq>0 initial workpiece batch.Selected work-piece batch is selected step by step according to formula (2) Go out an equipment and constitute a machining path p_l, and calculate

Step 3：Selected initial batches are divided intoBatch, the batch criticized per height isIfThen go to step 5；Otherwise step 4 is gone to.

Step 4：Will be remainingBefore individual workpiece is separately dispensed intoIt is individual In son batch.

Step 5：Update selected machining path p_lThe predefined queue deadline of middle equipment.

Step 6：If there is BN_pq>0 (p=1,2 ..., NS；Q=1,2 ..., n_p) batch, then go to step 2；Otherwise, Terminate.

Optimized algorithm, is each procedure dispensation machines resource and the determination of each son batch based on optimum choice strategy and in batches The optimal processing sequence of each son batch, flexible job shop given below Optimization scheduling algorithm flow in batches：

Step 1：Initialization.Current optimal objective value is set to+∞, cycle-index is providedWith each empirical parameter value, The attribute and state of all parts in Optimized model are initialized, current time is set to 0, equipment response time matrix is defined, And the equipment response time setting+∞ of all devices, all storages take number of resources and are set to 0 and are set batch number is completed It is set to 0.

Step 2：Batch operation is carried out to all kinds of workpiece according to algorithm 1, the sub- batch of different types of workpiece is obtained.

Step 3：The sub- batch of all workpiece obtained in step 2 is with random sequence by each production level of its preference probability selection On equipment, and reach the wait batch sequence of equipment, selected renewal of the equipment state, the response time is set to current execution The deadline of a procedure in the sub- batch of workpiece of selection；If the first procedure, then the response time be set to current execution The work-piece batch of selection enters the time of dispatch environment.

Step 4：Equipment performs processing behavior according to response time order, if being handled without the sub- batch of workpiece in equipment, Then directly go to step 5；Otherwise currently processed batch and more new equipment state are completed, the response time is set to the complete of the sub- batch Into the time, step 6 is gone to.

Step 5：The equipment chosen in step 4 is taken, suitable work is selected from batch queue is waited according to its preference probability Part batch is handled.If chosen, be set to the deadline of selected batch its response time；If not selecting In and its batch task waiting list not for sky, then the equipment response time of the equipment is set in its batch task waiting list The minimum value of the deadline of all sub- batch last process.

Step 6：If the procedure terminates rear work-piece batch as final products, finished parts warehouse is directly entered, on The corresponding storage release position in storehouse resource of equipment of procedure, completes batch number and adds 1, go to step 8；Otherwise to corresponding intermediate bin Position in storehouse resource is applied in storehouse, and application quantity is set toGo to step 7.

Step 7：If R_r≥R_a(R_r=R_s-R_o, wherein R_sFor the position in storehouse sum stored in a warehouse on production level s；R_oFor on production level s Store in a warehouse occupied number of resources), then difference is stored in different positions in storehouse the corresponding workpiece of the batch respectively by type, goes to step 8；Otherwise shut down and wait.

Step 8：If completing batch number is equal to lot count, this scheduling result is entered with current optimal scheduling result Row compares, if this scheduling result is better than current optimal scheduling result, preserves this scheduling result for optimal scheduling result, Otherwise, keep current optimal scheduling result constant.

Step 9：Reinitialize each several part state and equipment response time and complete batch number,IfStep 3 is then gone to, step 10 is otherwise performed.

Step 10：Optimal scheduling result and Gantt chart are exported, algorithm terminates.

The present invention beneficial outcomes be：

The characteristics of herein for flexible job shop process, " flexibility " thought is incorporated into flexible job shop scheduling Research field, it is proposed that flexible dispatching method, will in batches optimize and be combined with batch scheduling, not only solve speed with faster Degree, and with preferable optimizing performance, greatly improve utilization rate of equipment and installations, shorten the whole production cycle.And this method is flexibly, Scalability is strong, has preferable application prospect and promotional value solving the complicated scheduling problem field of multistage batch process.

Brief description of the drawings

Fig. 1 is dispatching method flow chart of the present invention.

Fig. 2 is case study on implementation glass post-processing of the present invention flexibility scheduling Gantt chart.

Embodiment

The present invention is described in detail with reference to the accompanying drawings and detailed description.The present embodiment is with the technology of the present invention side Implemented premised on case, give detailed embodiment and specific operating process, but protection scope of the present invention is not limited In following embodiments.

With reference to Fig. 1, a kind of flexible job shop Optimization Scheduling in batches that there is intermediate storage constraint, specific implementation step It is rapid as follows：

Step 1：Set up the mathematical modeling of following flexible job shop Optimal Scheduling：

Min Z=C_max (1)

R_s≤R_max (4)

R_s=R_o+R_r (6)

Formula (1) is object function, C_maxRepresent longest finishing time；When formula (2) represents the maximum completion of whole process Between computational methods, wherein：BN_nmFor machine u_mUpper batch n batch size, pt_nmIt is batch n in machine u_mOn processing when Between, N is total batch number；Formula (3) divides constraint for batch, represents carrying out when batch is divided same workpiece should being made to be assigned to respectively Batch summation on parallel machine is constant, remains the initial manufacture batch size of the workpiece；Formula (4) represents each production level correspondence The position in storehouse numbers of intermediate stores be limited；Formula (5) represents that the workpiece overall length deposited in per bin level is less than or equal to the length of position in storehouse Degree, L_RFor the length of position in storehouse；Formula (6) represents that position in storehouse number keeps constant.

Step 2：Initialization.Current optimal objective value is set to+∞, cycle-index is providedWith each empirical parameter value, The attribute and state of all parts in Optimized model are initialized, current time is set to 0, equipment response time matrix is defined, And the equipment response time setting+∞ of all devices, all storages take number of resources and are set to 0 and are set batch number is completed It is set to 0.

Step 3：All former piece initial batches press its preference probability selection cutting machine with random sequence, and reach equipment Batch queue, more selected cutting machine, new state are waited, the response time is set to currently perform the former piece initial batches of selection Entrance dispatch environment time.Batch is represented by the preference probability of equipment：

Wherein, δ_m∈ { 0,1 } represents u_mWhether the batch of the batch can be handled；α, β are to be set for the current of balancing equipment The relative importance of standby state and equipment to the disposal ability of the batch during equipment is selected, their value can basis Experience is determined by emulation experiment；JA_nsFor the cluster tool of the batch can be handled.

Equipment state is determined by below equation：

Wherein：X_m(t) ∈ { 0,1 } is t equipment u_mAvailability, can be used as 1, unavailable is 0；1 effect in denominator It is by μ_m(t) number field restriction is in [0,1]；Q_m(t) it is t equipment u_mWaiting list in batch number；n_kFor equipment u_m Waiting list in k-th of batch Mission Number；For u_mUpper k-th of batch is performed the process time of needs,For u_mBatch switching time needed for upper -1 batch of kth to k batch switching.

Step 4：Cutting machine is processed according to response time order, if on the cutting machine without former piece initial batches Processing, then directly go to step 5；Otherwise currently processed batch, and more new equipment state are completed, the former piece will be set to the response time The deadline of initial batches, go to step 6.

Step 5：The cutting machine chosen in step 4 is taken, conjunction is selected from batch queue is waited according to its preference selection strategy Suitable former piece initial batches are handled.If chosen, be set to the deadline of selected batch its response time； If not choosing and its batch task waiting list being not sky, the equipment response time of the cutting machine is set to its batch task The minimum value that all batches put into production in waiting list.Go to step 4.Equipment is to the preference selection strategy of batch：

Selection strategy 1：The batch of prioritizing selection long processing time.That is, in production line balance, it is total on all machines Process time longer workpiece, it should which the workpiece shorter than total elapsed time obtains higher processing priority.

Selection strategy 2：In the case where position in storehouse is sufficient, prioritizing selection turns into the batch of intermediate products.

Step 6：If the glass monolithic generated after the former piece initial batches cutting is final products, finished product is directly entered Part warehouse, completes batch number and adds 1, go to step 14；Otherwise to corresponding intermediate stores application position in storehouse resource, application quantity is set For

Step 7：If R_r≥R_a(R_r=R_s-R_o, wherein R_sFor the position in storehouse sum stored in a warehouse on production level s；R_oFor on production level s Store in a warehouse occupied number of resources), then difference is stored in different storehouses to the corresponding glass monolithic of the former piece initial batches respectively by type In position, step 8 is gone to；Otherwise shut down and wait.

Step 8：Batch operation is carried out to each monolithic initial batches, the sub- batch of different types of monolithic is obtained.Considering Optimization determines the batch splitting scheme of glass monolithic under the premise of intermediate stores position in storehouse number and the limited constraint of memory capacity.Assuming that pressing Production sequence selects equipment one machining path of composition for every grade from the parallel batching equipment of each production level, is designated as P_l, l is machining path numbering.Remember N_lminFor machining path P_lOn all intermediate stores single position in storehouse amount of storage minimum Value.Thus optimized algorithm step is as follows in batches for each monolithic initial batches for construction：

Step 8.1：For each one predetermined queue of device definition, it is sky, queue deadline to initialize predetermined queue

Step 8.2：Randomly choose a BN_pq>0 original one-piece batch.Selected monolithic batch according to formula (2) step by step Select an equipment and constitute a machining path p_l, and calculate

Step 8.3：Selected initial batches are divided intoBatch, the batch criticized per height isIfThen go to step 8.5；Otherwise step 8.4 is gone to.

Step 8.4：Will be remainingBefore individual workpiece is separately dispensed into In height batch.

Step 8.5：Update selected machining path p_lThe predefined queue deadline of middle equipment.

Step 8.6：If there is BN_pq>0 (p=1,2 ..., NS；Q=1,2 ..., n_p) monolithic batch, then go to step 8.2；Otherwise, terminate.

Step 9：The sub- batch of all monolithics obtained in step 8 is with random sequence by the next production level of its preference probability selection On equipment, and reach the wait batch sequence of equipment, selected renewal of the equipment state, the response time is set to current execution The deadline of a procedure in the sub- batch of monolithic of selection.

Step 10：Equipment performs processing behavior according to response time order, if being handled without the sub- batch of monolithic in equipment, Then directly go to step 11；Otherwise currently processed batch and more new equipment state are completed, the response time is set to the sub- batch Deadline, go to step 12.

Step 11：The equipment chosen in step 10 is taken, selects suitable from batch queue is waited according to its preference probability The sub- batch of monolithic is handled.If chosen, be set to the deadline of selected batch its response time；If no Choose and its batch task waiting list is not sky, then the equipment response time of the equipment is set to its batch task waiting list In all sub- batch last process of monolithic deadline minimum value.

Step 12：If the procedure terminates rear glass monolithic as final products, finished parts warehouse is directly entered, on The corresponding storage release position in storehouse resource of equipment of procedure, completes batch number and adds 1, go to step 14；Otherwise stored in a warehouse to next stage Apply for position in storehouse resource.Go to step 13.

Step 13：If R_r>=1, then the sub- batch of the monolithic, which enters, stores in a warehouse, and goes to step 9；Otherwise shut down and wait.

Step 14：If completing batch number is equal to lot count, by this scheduling result and current optimal scheduling result It is compared, if this scheduling result is better than current optimal scheduling result, preserves this scheduling result for optimal scheduling knot Really, otherwise, keep current optimal scheduling result constant.

Step 15：Reinitialize each several part state and equipment response time and complete batch number,IfStep 3 is then gone to, step 16 is otherwise performed.

Step 16：Optimal scheduling result and Gantt chart are exported, algorithm terminates.

Embodiment

1 order taking responsibility is accepted in certain glass post-processing manufacturing shop, contains 5 former piece initial batches.Have four in production level 1 Platform cutting machine, the working ability of each cutting machine and process time are as shown in Table 1 and Table 2.

The cutting machine working ability table (mm) of table 1

The cutting of table 2 machining time (single batch of process time)

- represent that cutting machine can not process the former piece of this kind

The monolithic of four types is generated after the former piece initial batches cutting of each in this example.Different processing machines is represented There is one or more parallel machine on different manufacturing procedures, each procedure.Glass post-processing technological process mainly have edging, It is cleaning, tempering, plated film, hollow.The workshop possesses each two of edge polisher, cleaning machine, coating machine, annealing furnace and hollow machine each one It is individual.Each monolithic size and its process time, the process time of machine represented the former piece initial batches correspondence for 0 as shown in table 3 Glass without the procedure.The process time of tempering process is single batch of process time, the manufacturing procedure time of remaining process It is monolithic process time.Table 4 is intermediate stores position in storehouse sizes at different levels.

The process time of table 3

The intermediate stores position in storehouse size (mm) of table 4

Arrange parameter is as follows：Cycle-indexα=β=1, carries out example with patent dispatching method of the present invention and tests Card, each batch of subvitreous machine choice, processing sequence and mass distributed such as glass post-processing are flexible to dispatch Gantt chart, i.e. Fig. 2 tables Show.Numeral 1 represents the first former piece and initially criticized in the batch that grid frame representative in figure in every equipment is being processed, square frame Secondary, 11 represent first son batch of the first glass types monolithic of the generation of initial batches 1, and 12 represent the generation of initial batches 1 2nd batch of the first glass types monolithic, other numerals the like, square frame upper values represent glass batch processing Time.As can be seen that the process equipment stand-by period in each process is shorter, and the distribution of each machine utilization is evener, equipment profit Increased substantially with rate, the whole production cycle is also reduced.

Claims (5)

1. a kind of flexible job shop Optimization Scheduling in batches that there is intermediate storage constraint, it is characterised in that including following Step：

Step 1：Set up the mathematical modeling of following flexible job shop Optimal Scheduling：

Min Z=c_max (1)

$C_{\max }=\underset{1\≤m\≤M}{\max }\underset{n=1}{\overset{N}{\Σ}}({\mathrm{BN}}_{nm}*{\mathrm{pt}}_{nm})---\left(2\right)$

$\underset{m=1}{\overset{M_s}{\Σ}}{\mathrm{BN}}_{nm}={\mathrm{BN}}_{pq}---\left(3\right)$

R_s≤R_max (4)

$\underset{n=1}{\overset{{\mathrm{BN}}_{nm}}{\Σ}}{L}_n\≤L_R---\left(5\right)$

R_s=R_o+R_r (6)

Formula (1) is object function, C_maxRepresent longest finishing time；Formula (2) represents the longest finishing time of whole process Computational methods, wherein：BN_nmFor machine u_mUpper batch n batch size, pt_nmIt is batch n in machine u_mOn process time, N is Total batch number；Formula (3) divides constraint for batch, represents carrying out when batch is divided same workpiece should being made to be assigned to each parallel machine On batch summation it is constant, remain the initial manufacture batch size of the workpiece；Formula (4) represents the corresponding centre of each production level The position in storehouse number in warehouse is limited；Formula (5) represents that the workpiece overall length deposited in per bin level is less than or equal to the length of position in storehouse, L_RFor The length of position in storehouse；Formula (6) represents that position in storehouse number keeps constant；

Step 2：Initialization, is set to+∞ by current optimal objective value, provides cycle-indexWith each empirical parameter value, initially Change the attribute and state of all parts in Optimized model, current time is set to 0, define equipment response time matrix, and handle The equipment response time of all devices is set to+∞, and all storages take number of resources and are set to 0 and will complete the setting of batch number For 0；

Step 3：Batch operation is carried out to each work-piece batch, the sub- batch of different types of workpiece is obtained；

Step 4：With random sequence, by its preference probability selection, each produces setting in level to all sub- batches obtained in step 3 It is standby, and the wait batch sequence of equipment, selected renewal of the equipment state are reached, the response time is set to currently perform selection The deadline of a procedure in the sub- batch of workpiece；If the first procedure, then the response time be set to currently perform selection Work-piece batch enters the time of dispatch environment；

Step 5：Equipment performs processing behavior according to response time order, if being handled without the sub- batch of workpiece in equipment, directly Switch through to step 6；Otherwise currently processed batch and more new equipment state are completed, when the response time is set into the completion of the sub- batch Between, go to step 7；

Step 6：The equipment chosen in step 5 is taken, suitable sub- batch is selected from batch queue is waited according to its preference probability Handled；If chosen, be set to the deadline of selected batch its response time；If not choosing and its batch Subtask waiting list is not sky, then is set into all sons batch in its batch task waiting list the equipment response time of the equipment The minimum value of the deadline of secondary last process；

Step 7：If the procedure terminates rear work-piece batch as final products, finished parts warehouse, upper track work are directly entered The corresponding storage release position in storehouse resource of equipment of sequence, completes batch number and adds 1, go to step 9；Otherwise to corresponding intermediate stores Shen Please position in storehouse resource, application quantity be set toGo to step 8；

Step 8：If R_r≥R_a, wherein R_r=R_s-R_o, R_sFor the position in storehouse sum stored in a warehouse on production level s, R_oFor quilt of being stored in a warehouse on production level s Number of resources is taken, then difference is stored in different positions in storehouse the corresponding workpiece of the batch respectively by type, goes to step 9；Otherwise Shut down and wait；

Step 9：If completing batch number is equal to lot count, this scheduling result is compared with current optimal scheduling result Compared with, if this scheduling result is better than current optimal scheduling result, this scheduling result is preserved for optimal scheduling result, it is no Then, keep current optimal scheduling result constant；

Step 10：Reinitialize each several part state and equipment response time and complete batch number,IfStep 4 is then gone to, step 11 is otherwise performed；

Step 11：Optimal scheduling result and Gantt chart are exported, algorithm terminates.

2. the flexible job shop Optimization Scheduling in batches according to claim 1 that there is intermediate storage constraint, it is special Levy and be, optimization determines the batch division side of workpiece under the premise of under consideration warehouse position in storehouse number and the limited constraint of memory capacity Case；Assuming that selecting one processing road of an equipment composition for every grade from the parallel batching equipment of each production level by production sequence Footpath, is designated as P_l, l is machining path numbering, remembers N_lminFor machining path P_lOn all intermediate stores single position in storehouse amount of storage Minimum value, thus optimized algorithm step is as follows in batches for each monolithic initial batches for construction：

Step 1：For each one predetermined queue of device definition, it is sky, queue deadline to initialize predetermined queue

Step 2：Randomly choose a BN_pq>0 initial workpiece batch, selected work-piece batch selects one step by step according to formula (2) Individual equipment constitutes a machining path P_l, and calculate

Step 3：Selected initial batches are divided intoBatch, the batch criticized per height isIfThen go to step 5；Otherwise step 4 is gone to；

Step 4：Will be remainingBefore individual workpiece is separately dispensed intoIn height batch；

Step 5：Update selected machining path P_lThe predefined queue deadline of middle equipment；

Step 6：If there is BN_pq>0 (p=1,2 ..., NS；Q=1,2 ..., n_p) monolithic batch, then go to step 2；Otherwise, Terminate.

3. the flexible job shop Optimization Scheduling in batches according to claim 1 that there is intermediate storage constraint, it is special Levy and be, in order to realize reasonable selection of the batch to equipment, batch is expressed as to the preference probability of equipment：

$p\left(u_m\right)=\frac{{\mathrm{\δ}}_m{\left({\mathrm{\μ}}_m\right)}^{\∂}{(1/{\mathrm{pt}}_{nm})}^{\mathrm{\β}}}{\underset{u_{m^{,}}\∈{\mathrm{JA}}_{ns}}{\Σ}{\mathrm{\δ}}_{m^{,}}{\left({\mathrm{\μ}}_{m^{,}}\right)}^{\∂}{(1/{\mathrm{pt}}_{{\mathrm{nm}}^{,}})}^{\mathrm{\β}}}$

Wherein, δ_m∈ { 0,1 } represents u_mWhether the batch of the batch can be handled；α, β are the current device shape for balancing equipment The relative importance of state and equipment to the disposal ability of the batch during equipment is selected, their value rule of thumb or Person is determined by emulation experiment；JA_nsFor the cluster tool of the batch can be handled.

4. the flexible job shop Optimization Scheduling in batches according to claim 3 that there is intermediate storage constraint, it is special Levy and be, equipment state is determined by below equation：

${\mathrm{\μ}}_m\left(t\right)=\frac{X_m\left(t\right)}{1+{\mathrm{pt}}_{n_{1}m}+\underset{k=2}{\overset{Q_m\left(t\right)}{\Σ}}({\mathrm{\τ}}_{n_{k-1}{n}_{k}m}+{\mathrm{pt}}_{n_{k}m})}$

Wherein：X_m(t) ∈ { 0,1 } is t equipment u_mAvailability, can be used as 1, unavailable is 0；In denominator 1 effect be by μ_m(t) number field restriction is in [0,1]；Q_m(t) it is t equipment u_mWaiting list in batch number；n_kFor equipment u_mEtc. Treat the Mission Number of k-th of batch in queue；For u_mUpper k-th of batch is performed the process time of needs,For u_m Batch switching time needed for upper -1 batch of kth to k batch switching.

5. the flexible job shop Optimization Scheduling in batches according to claim 1 that there is intermediate storage constraint, it is special Levy and be, equipment is to the preference selection strategy of batch：

Selection strategy 1：The batch of prioritizing selection long processing time, that is, in production line balance, total processing on all machines Time longer workpiece, it should which the workpiece shorter than total elapsed time obtains higher processing priority；

Selection strategy 2：In the case where position in storehouse is sufficient, prioritizing selection turns into the batch of intermediate products.