CN1529209A - Intergrated optimization control method for mixed-batch assembling line - Google Patents

Abstract

The integrated optimization method is for controlling production planning, dispatching and emulation on mixing batch assembly line (i.e. assembling multiple products on a assembly line at same time). The method includes procedures: smoothing customers' requirements on products; based on smoothed requirements on products, mixing integrated planning model of mixing batch assembly line is solved by using a branch delimit algorithm; obtaining best production planning, i.e. categories and quantities of products as well as dispatch or assembling sequence; observing best dispatching procedure for mixing batch assembly line by animated emulating the dispatch; determining whether customers' requirements on products are satisfied; if yes, formal plans and dispatch is ready to be excuted; based on formal plans and dispatch, arranging and controlling parts to be assembled on assembly line; based on moving speed determined by using animated emulation, controlling operation of assembly line.

Description

Mix the integrated optimization control method of batch assembly line

Technical field

The present invention relates to mix the integrated optimization control method of the production schedule, scheduling and the emulation of criticizing assembly line (promptly can assemble multiple product simultaneously on an assembly line), and can arrange production and control the operation that mixes batch assembly line according to this.Belong to production line optimal control method technical field.

Background technology

The existing overwhelming majority who mixes the production schedule, scheduling and the optimization document of batch assembly line only relates to production scheduling ^[1-8], seldom relate to the production schedule ^[9]In actual production, often optimization production plan separately earlier, optimization production scheduling on optimised project basis then, consequently planning and scheduling can not reach global optimization, even the situation that the production schedule causes dispatching infeasible or poor performance occurs ^[10,11]Tabu search (Tabu Search) is by Glover ^[12,13]A kind of senior heuristic that is used to obtain combinatorial optimization difficult problem approximate solution that proposes.At present, the tabu search method is mainly used in Flow shop scheduling, aspects such as Job shop scheduling and manufacturing cell's formation ^[14,15], the application aspect the mixed batch assembly line production schedule, scheduling is then very rare.The document of the Petri net modeling aspect of relevant mixed batch assembly line is very rare, only find that at present the coloured timing Petri of human net (Colored Timed Petri Net) such as Kuo set up automobile and mixed the model of batch assembly system, and developed one in view of the above and have different real-time simulators of assigning rule ^[16]But this model lacks decision point, and inconvenience incorporates scheduling rule etc. wherein.By contrast, expand senior at random judgement Petri net (ESHLEP-N) and comprised decision point, easier scheduling rule etc. is incorporated wherein, thereby be more suitable for setting up the scheduling simulation model that mixes batch assembly line.

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[9]Balakrishnan?A，Vanderbeck?F.Tactical?planning?model?for?mixed-model?electronics?assemblyoperations.Operations?Research，1999，47(3)，395-409.

[10]Lasserre?J?B.An?integrated?model?for?job-shop?planning?and?scheduling.?Management?Science，1992，38(8)，1201-1211.

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Summary of the invention

Technical matters: the purpose of this invention is to provide and a kind ofly on an assembly line, can assemble multiple product simultaneously, and make overfulfiling a production target, have a shortfall in output and setting up cost of product, the free time of each assembly station, the load deviation between scheduling span and each assembly station reaches minimized integrated optimization control method of mixing batch assembly line.

Technical scheme: the present invention has set up the mixed-integer programming model that mixes batch assembly line, to try to achieve the setting up cost that makes each assembly station with branch-bound algorithm and free time is the least possible and the thick production schedule of As soon as possible Promising Policy product demand.On the basis of considering the assembly line details, set up then and mixed the production schedule of batch assembly line and the integrated optimization model of scheduling, and propose three kinds of distinct methods such as embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method respectively and solve with the integrated optimization problem of the thick production schedule as the production schedule, scheduling and the emulation that mix batch assembly line of initial solution, provided the computational complexity of these three kinds of methods simultaneously.Integrated optimization control method of mixing batch assembly line of the present invention is characterized in that this method may further comprise the steps (see figure 3):

(1) level and smooth client's product demand;

(2), find the solution the mixed-integer programming model that mixes batch assembly line with branch-bound algorithm, to obtain the making setting up cost of each assembly station and free time is the least possible and the thick production schedule of As soon as possible Promising Policy product demand according to the product demand after level and smooth;

(3) on the integrated optimization model based of the production schedule of mixing batch assembly line and scheduling, at product category and quantity less, in, many etc. three in various degree, obtaining with the thick production schedule with embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method respectively is that product category and quantity and scheduling are assemble sequence as the best production schedule of mixing batch assembly line of initial solution;

(4) observe the optimal scheduling process of mixing batch assembly line by the animation scheduling simulation;

(5) judge whether to satisfy client's product demand;

(6) if, think not satisfy the demands through animation simulation, emulation again after then can doing suitably to revise to best planning and scheduling;

(7) if, think to satisfy the demands through animation simulation, then can be with it as formal plan and the scheduling of preparing to assign execution;

(8), arrange production and control reaching the standard grade of product to be installed, and the assembly line translational speed control of determining during according to animation simulation mixes the operation of batch assembly line according to formal plan and scheduling.

Since client's product demand (order) be at random and have suddenly, and production needs evenly and steadily carry out, therefore need the client at random with sudden demand be smoothed to can make production steadily, the demand of carrying out continuously.The level and smooth method of demand is according to the delivery period of product order requirements and importance and productive capacity, and the preferential the earliest and the heaviest principle of priority of importance according to delivery period smoothly is assigned to each plan interval with product order.

The basic thought of embedded tabu search simulation method is to seek a feasible scheme and scheduling with the thick production schedule as the initial production plan, seek best plan in plan layer with tabu search then, and plan layer is generated each adjacent plan to seek through high-speed simulation with another tabu search calculate scheduling with top performance index, until making the production schedule reach optimization simultaneously with dispatching.Because of tabu search nested another tabu search and calculate the scheduling index with high-speed simulation, so be named as embedded tabu search simulation method.The basic thought of alternative expression tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as the initial production plan; (2) plan that has the top performance index through high-speed simulation calculating is sought in given scheduling with tabu search; (3) worked out a scheme conversely, seek through high-speed simulation with another tabu search again and calculate scheduling with top performance index; (4) be used alternatingly (2), (3) two steps until finding best planning and scheduling.Owing to respectively planning and scheduling is used alternatingly two tabu search and calculates its performance index with high-speed simulation, so be called alternative expression tabu search simulation method.The basic thought of string type tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as the initial production plan; (2), seek rule-based scheduling and pass through the plan that high-speed simulation calculating has the top performance index with tabu search from feasible scheme; (3), use another tabu search to seek and calculate scheduling with top performance index through high-speed simulation for best plan.Owing to plan and scheduling are used tabu search successively and are calculated its performance index with high-speed simulation, so be called string type tabu search simulation method.The high-speed simulation of these three kinds of methods is all by setting up the realization of scheduling simulation model and OO technology rice with senior at random the judgements Petri net of expansion, and controls simulation process with variable time stream.Implication is that no literal and dynamic figures show fast herein, only calculates the performance index of given scheduling by high-speed simulation.Microsoft VisualC is all used in said method and emulation ⁺⁺5.0 weave into software.After the production schedule and scheduling best, just can arrange production and control the operation that mixes batch assembly line according to this with said method obtained performance index.Compare with classic method, advantage of the present invention is that analytic method, tabu search and fast dispatch emulation are organically combined, efficiently solve the integrated optimization problem of the production schedule, scheduling and the emulation that mix batch assembly line, and guarantee to have at least a feasible solution.The problem solving speed of embedded tabu search simulation method is the slowest, but the performance index that obtain are often best; The problem solving speed of string type tabu search simulation method and the performance index of acquisition are just in time opposite with embedded tabu search simulation method; And alternative expression tabu search emulation rule is between embedded tabu search simulation method and string type tabu search simulation method.Embedded tabu search simulation method is fit to find the solution minor issue, and alternative expression tabu search simulation method is fit to find the solution middle scale problem, and string type tabu search simulation method is fit to find the solution extensive problem.

Beneficial effect: the invention solves the integrated optimization control problem of mixing batch the assembly line production schedule, scheduling and emulation, provided the generation method of the thick production schedule, proposed embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method and provided their computational complexity and implementation method, mixed the ESHLEP-N model of batch assembly line and provided OO implementation method for realizing that scheduling simulation has been set up.On this basis, adopt Microsoft Visual C ⁺⁺5.0 developed the integration optimizing software that mixes the production schedule, scheduling and the emulation of batch assembly line.By these software, compare research with a large amount of examples, the result shows:

(1) compare with classic method, advantage of the present invention is that analytic method, tabu search and fast dispatch emulation are organically combined, and efficiently solves the integrated optimization problem of mixing batch assembly line production schedule and scheduling, and guarantees to have at least a feasible solution.

(2) the problem solving time average of embedded tabu search simulation method and alternative expression tabu search simulation method is grown 38.69 and 1.73 times respectively than string type tabu search simulation method, but the top performance index of embedded tabu search simulation method and alternative expression tabu search simulation method and average specific string type tabu search simulation method lack 7.78% and 5.16% respectively.

(3) embedded tabu search simulation method is fit to find the solution minor issue, and alternative expression tabu search simulation method is fit to find the solution middle scale problem, and string type tabu search simulation method is fit to find the solution extensive problem.If problem is very big, then suggestion uses the Step 1-2 of algorithm 4 to obtain feasible scheme and scheduling separating as problem.

(4) embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method is respectively 18.87%, 22.05% and 25.49% from feasible scheme and the average behavior index improvement rate that scheduling begins till the best planning and scheduling.

(5) the integrated optimization problem with the production schedule of mixing batch assembly line of random character and scheduling can be moved with the Monte Carlo of embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method and find the solution.

(6) ESHLEP-N has visual in imagely, simple in structure, and node is few, and descriptive good, decision-making capability is strong, and advantages such as dual token and dual sign very are fit to mix the modeling and the scheduling simulation of batch assembly line.

In addition, embedded tabu search simulation method of the present invention, alternative expression tabu search simulation method and string type tabu search simulation method also can be used for finding the solution the model that its objective function and constraint are different from formula (9)-(11).

After adopting embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method to obtain best planning and scheduling, can observe the optimal scheduling process of mixing batch assembly line by the animation scheduling simulation, judge whether to satisfy client's product demand.If, think not satisfy the demands through animation simulation, emulation again after then can doing suitably to revise to best planning and scheduling.If, think to satisfy the demands through animation simulation, then can be with it as formal plan and the scheduling of preparing to assign execution.Then, just can arrange production with scheduling (assemble sequence), and the assembly line translational speed control of determining during according to animation simulation mixes the operation of batch assembly line according to the above-mentioned formal plan (product category and quantity) that mixes batch assembly line.

Description of drawings

Fig. 1 is a line style assembly line synoptic diagram.

Fig. 2 is a U type assembly line synoptic diagram.

Fig. 3 is the integrated optimization control method main-process stream synoptic diagram that mixes plan, scheduling and the emulation of batch assembly line.

Fig. 4 is embedded tabu search simulation method process flow diagram.

Fig. 5 is based on the optimizing scheduling process flow diagram of tabu search.

Fig. 6 is an alternative expression tabu search simulation method process flow diagram.

Fig. 7 is a string type tabu search simulation method process flow diagram.

Fig. 8 is corresponding to determining algorithm flow chart for the scheduling of working out a scheme.

Fig. 9 is the ESHLEP-N graph model that mixes batch assembly line.

Figure 10 is the main flow chart that system's transition are handled.

Figure 11 is " assembly line on the product to be installed " transition t ₁Processing flow chart.

Figure 12 is " beginning assembling " transition t ₂Processing flow chart.

Figure 13 is " finishing assembling " transition t ₃Processing flow chart.

Figure 14 is " fault generation " transition t ₄Processing flow chart.

Figure 15 is transition " fault end " t ₅Processing flow chart.

Figure 16 is the processing flow chart of transition under the blocked state.

Figure 17 is the integration optimizing software structural drawing that mixes the production schedule, scheduling and the emulation of batch assembly line.

Embodiment

The technical solution adopted for the present invention to solve the technical problems and embodiment are as follows

1, mix batch assembly line:

Batch assembly line that mixes that the present invention relates to has two kinds, i.e. line style assembly line (see figure 1) and U type assembly line (see figure 2).Among the figure, (1＜k＜m) represents the reach the standard grade assembly station and the assembly station that rolls off the production line of product respectively, and arrow is represented the moving direction of product in assembling process for station 1 and m.Each assembly station can be distributed in the both sides of assembly line, also can be one-sided, and buffer zone is arranged.Each station at any time can only be adorned a product at the most.The station that product sum on the line at any time equals on the line is at the most counted m, just, if at a time each station all has a product, after a product such as then having only in the end station m installing and rolls off the production line, could be at station 1 product to be installed (promptly waiting product to be assembled) of reaching the standard grade.The synchronous translational speed of assembly line is variable and is definite by the assembling speed of its last station m when not having full buffer zone on line, and definite by the assembling speed of its bottleneck station when full buffer zone is arranged.Because the different product of each station assembling may need the different time, so the bottleneck station may shift when product category, mixed wholesale changing.The buffer zone here is in logic and a virtual notion.In fact, there is no real buffer zone, just allow workspace that the assembler exceeds oneself and finish fittage and logically form virtual buffering region in the workspace of other station.

2, the thick production schedule:

As noted earlier, one is mixed total m the assembly station of batch assembly line.Need adorn n kind product and i kind product need d altogether according to Assembly Order in now designing between partition _iIndividual.Again assembly line is reduced to a Flow shop problem, and the target of optimal plan be satisfy product demand to greatest extent and make the setting up cost of each assembly station and free time the least possible, it is as follows then can to set up the mixed-integer programming model of finding the solution the optimum thick production schedule:

$\min J=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[a_i^{+}{(x_i-d_i)}^{+}+a_i^{-}{(d_i-x_i)}^{+}]+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_{\mathrm{ij}}\mathrm{sgn}\left(x_i\right)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{c}_j{\mathrm{\τ}}_j......\left(1\right)$

$s.t.\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{ij}}{x}_i+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{t}_{\mathrm{ij}}\mathrm{sgn}\left(x_i\right)+{\mathrm{\τ}}_j={\mathrm{\β}}_j.......\left(2\right)$

x _i〉=0 and be integer, τ _j〉=0, j=1,2 ..., in m (3) formula: n is the product category number of the interval domestic demand assembling of plan; M is for mixing the millwright's figure place on batch assembly line; x _iFor planning the output of interval interior assembling i kind product, be integer; Sgn (x _i) be sign function, work as x _i＞0 o'clock, sgn (x _i) get 1, otherwise get 0; d _iFor planning interval interior demand, be integer to i kind product; τ _jFor planning the free time of interval interior j assembly station; β _jFor plan interval in the pot life of j assembly station, be from planning to deduct the production T.T. in interval the last time such as equipment failure servicing time; a _i ⁺Be the storage of an i kind product and the cost of the amount of circulating funds used of overfulfiling a production target; a _i ^-Be the cost that i kind product is broken a contract and is punished of having a shortfall in output; b _IjBe the setting up cost of i kind product on j assembly station; c _jFor with j assembly station resources idle cost related coefficient; t _IjBe that j assembly station assembles the needed time of i kind product; Δ t _IjIt is the setup time of i kind product on j assembly station; (c) ⁺For max (0, c).

It is as follows that the mixed integer nonlinear programming model of formula (1)-(3) can be converted into the MILP (Mixed Integer Linear Programming) model:

$\min J=$ $\underset{i=1}{\overset{n}{\mathrm{\Σ}}}$ $(a_i^{+}{\mathrm{\Δ}}^{+}{x}_i+a_i^{-}{\mathrm{\Δ}}^{-}{x}_i)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_{\mathrm{ij}}{y}_i+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{c}_j{\mathrm{\τ}}_j......\left(4\right)$

$s.t.\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{ij}}{x}_i+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{t}_{\mathrm{ij}}{y}_i+{\mathrm{\τ}}_j={\mathrm{\β}}_j---\left(5\right)$

x _i-Δ ⁺x _i+Δ ^-x _i＝d _i (6)

By _i≥x _i (7)

x _i〉=0 and be integer, y _i∈ (0,1), τ _j〉=0, Δ ⁺x _i〉=0, Δ ^-x _i〉=0, j=1,2 ..., m (8)

In the formula: y _iBe Boolean variable, work as x _i＞0 o'clock is 1, otherwise is 0; B is a big positive number.

Arrive this, find the solution the MILP (Mixed Integer Linear Programming) model of formula (4)-(8), to obtain the setting up cost that makes each assembly station and free time is the least possible and the thick production schedule of As soon as possible Promising Policy product demand with regard to available branch and bound method.

3, the integrated optimization method of the production schedule, scheduling and emulation and realization thereof:

For accelerating problem solving speed, in the model of formula (4)-(8), ignored the details of assembly line, and obtained the original plan of the thick production schedule thus as the integrated optimization problem iterative of subsequent production plan, scheduling and emulation.On the other hand, consider that the synchro assembling line of details is dispatched unstructured problems often, be difficult to find the solution that comparatively feasible way is to use the fast dispatch emulation based on variable time stream with the method for resolving.Implication is that no literal and dynamic figures show fast herein, only calculates the performance index of given scheduling by high-speed simulation.Select problem then to solve as for the iteration of optimal plan and scheduling by three kinds of distinct methods such as embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation methods.

3.1 embedded tabu search simulation method and realization thereof:

Assemble setup time for saving product, product of the same race is concentrated assembling, is not divided into a plurality of fittages, and only takies a sorting position when scheduling.With reference to formula (1)-(3), the mathematical model of then finding the solution the integrated optimization problem of mixing batch the assembly line production schedule, scheduling and emulation can be described below:

$\underset{x,S}{\mathrm{Min}}G(x,S)=\underset{x,S}{\mathrm{Min}}\left\{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\right[a_{\mathrm{\μ}(S,i)}^{+}(x_{\mathrm{\μ}(S,i)}-d_{\mathrm{\μ}(S,i)}{)}^{+}+a_{\mathrm{\μ}(S,i)}^{-}{(d_{\mathrm{\μ}(S,i)}-x_{\mathrm{\μ}(S,i)})}^{+}]$

$+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{b}_{\mathrm{\μ}(S,i)j}\mathrm{sgn}\left(x_{\mathrm{\μ}(S,i)}\right)+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{c}_j{\mathrm{\τ}}_j+\mathrm{rf}(x,S)$

$+q\underset{j=1}{\overset{m}{\mathrm{\Σ}}}[({\mathrm{\β}}_j-{\mathrm{\τ}}_j)-\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}({\mathrm{\β}}_j-{\mathrm{\τ}}_j){]}^2\}......\left(9\right)$

$s.t.$ $\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{t}_{\mathrm{\μ}(S,i)j}{x}_{\mathrm{\μ}(S,i)}+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\Δ}{t}_{\mathrm{\μ}(S,i)j}$ $\mathrm{sgn}$ $\left(x_{\mathrm{\μ}(S,i)}\right)$ $+{\mathrm{\τ}}_j$ $=$ ${\mathrm{\β}}_j......\left(10\right)$

x _{μ (S, i)}〉=0 and be integer, τ _j〉=0, j=1,2 ..., m (11)

In the formula: (S i) is n kind product or wherein part is by i the pairing product category in position among order (scheduling) S of assembly line to μ, and (S i)=0, then represent to dispatch among the S and at most only comprises h-1 kind product if for h≤i≤n μ is arranged; b _{μ (S, i) j}Be that (S i) plants the setting up cost of product on j assembly station to μ; Δ t _{μ (S, i) j}Be that (S i) plants the setup time of product on j assembly station to μ; X=(x _{μ (S, 1)}, x _{μ (S, 2),}, x _{μ (S, n)}) ^TBe production schedule vector; F (x, the S) time of all finishing for the product fittage (scheduling span) is by corresponding plan and the common decision of scheduling; R is a task deadline weight coefficient; Q is each assembly station load balancing weight coefficient.

Tabu search is a kind of senior heuristic that is used to obtain combinatorial optimization difficult problem approximate solution that is proposed by Glover.Using integrated optimization problem (9)-(11) that the tabu search method finds the solution the production schedule, scheduling and emulation before, at first introduce two notions, promptly adjacent plan and adjacent scheduling.P is drawn in design ^*=(x ₁, x ₂..., x _n) ^TAnd some i there is τ _j＞t _Ij＞0, to j=1,2 ..., m then defines p=(x ₁, x ₂..., x _I-1, x _I+1, x _I+1..., x _n) ^T, p=(x ₁, x ₂..., x _i± 1 ..., x _l 1 ..., x _n) ^TAnd p=(x ₁, x ₂..., x _I-1, x _I-1, x _I+1..., x _n) ^TBe p ^*Adjacent plan.Otherwise definition p=(x ₁, x ₂..., x _i± 1 ..., x _l 1 ..., x _n) ^TAnd p=(x ₁, x ₂..., x _I-1, x _I-1, x _I+1..., x _n) ^TBe p ^*Adjacent plan.As seen p ^*Adjacent plan have n at most ²+ n.

For scheduling S ^*, we only exchange S at definition ^*In two elements and being scheduling to of forming adjacent to S ^*Scheduling.Be without loss of generality, establish initial schedule S ₀In comprise three kinds of products, i.e. S altogether ₀={ c} is then according to definition, adjacent to S for a, b ₀Scheduling have three kinds: S ₁={ b, a, c}, S ₂={ c, b, a}, S ₃={ a, c, b}.Notice that adjacent scheduling only exchanges initial schedule S ₀In two elements and get.As S ₁Be only to exchange S ₀In a, two elements of b obtain, and are adjacent to S ₀Scheduling; But { c, a, b} are exchange S ₃In a, two elements of c obtain, and can not directly exchange S ₀In two elements and get, so { c, a, b} are not adjacent to S ₀Scheduling.Usually, for the scheduling S that comprises n kind product ^*, total n (n-1)/2 kind of then adjacent scheduling.

At present, the tabu search method is mainly used in Flow shop scheduling, aspects such as Job shop scheduling and manufacturing cell's formation, and the application aspect the mixed batch assembly line production schedule, scheduling is then very rare.What the present invention will solve again is the integrated optimization problem of plan, scheduling and emulation, solves so need to propose a kind of new embedded tabu search simulation method.Its basic thought is to seek a feasible scheme and scheduling with the thick production schedule as initial solution and with the tabu search simulation method of simplifying, seek best plan in plan layer with tabu search then, and plan layer is generated each adjacent plan to seek through high-speed simulation with another tabu search calculate scheduling with top performance index, until making the production schedule reach optimization simultaneously with dispatching.Because of tabu search nested another tabu search and calculate the scheduling index with high-speed simulation, so be named as embedded tabu search simulation method.

Algorithm 1: the embedded tabu search simulation method of integrated optimization problem (9)-(11) of the production schedule, scheduling and emulation

Step 1 initialization

(1) reads various data and parameter in formula (9)-(10).

(2) read algorithm parameter, comprise production schedule taboo table length PT_size, the mobile number of times PM-max of given plan, scheduling taboo table length ST_size and the given mobile number of times SM_max of scheduling.

(3) G_best=M_big is set, PM_ctr=0, PT_list={ φ }, P_best=φ, S_best={ φ }.

Step 2 initial feasible scheme of search and scheduling

(1) initial production plan p is set ₀=x.

(2) current planning p=p is set ₀, and call algorithm 2 is given the p that works out a scheme with search feasible schedule.

(3) if SC_flag=1 and G be (p, S ^{* *})＜G_best then is provided with p ^*← p, P_best ← p, S_best ← S ^{* *}, G_best ← G (p, S ^{* *}).Change Step 3 then.

(4) generate p ₀An adjacent plan p, p is set ₀=p.Change Step 2 (2) then.

The best planning and scheduling of Step 3 search

(1) generates one adjacent to p ^*Institute might plan collection, and put G (p ^*, S ^{* *})=M_big.

(2) for a plan p in this set, if p not in PT_list, then call algorithm 2 with search for giving the preferably scheduling of p of working out a scheme, and upgrade the preferably plan in the current Neighbor Set: p ^*← p, G (p ^*, S ^{* *}) ← G (p, S ^{* *}), if SC_flag=1 and G be (p, S ^{* *})＜G (p ^*, S ^{* *}); Otherwise abandon p.If the plan number among the plan taboo table PT_list is less than PT_size, p is added to the top of PT_list.So repeat, until finishing p ^*All adjacent plans.

(3) doing once plan moves: p is set ^*← p ^*, G (p ^*, S ^{* *}) ← G (p ^*, S ^{* *}If) and p ^*Not in PT_list then with p ^*Be added to the top of PT_list; If the plan number＞PT_size among the PT_list then deletes a plan the oldest from the bottom of PT_list.

(4) if plan has improvement, if i.e. G (p ^*, S ^{* *})＜G_best then upgrades and preferably separates: P_best ← p ^*, S_best ← S ^{* *}, G_best ← G (p ^*, S ^{* *}).

(5) the mobile number of times of plan that is updated to so far to be done: PM_ctr ← PM_ctr+1.If PM_ctr＞PM_max then stops iteration and changes Step 4, otherwise (1) of changeing Step 3.

Step 4 output results

Output P_best, S_best and G_best.

Here: M_big is a very big number; SC_flag is the sign for the scheduling that whether has satisfied constraint (10)-(11) to the p that works out a scheme, and SC_flag=1 represents to exist, and SC_flag=0 represents not exist; p ^*Be the preferably plan of concentrating in current adjacent plan; p ^*Be the concentrated preferably plan of adjacent plan before tight: the best production schedule of P_best for up to the present finding; S ^{* *}Preferably scheduling for corresponding plan; S_best is at the best production schedule that up to the present finds, the preferably scheduling of being found; (p S) is and production schedule p and the corresponding performance index of scheduling S: the best index of G_best for up to the present being reached G.

Algorithm 2: based on the optimizing scheduling of tabu search

Step 1 initialization

SM_ctr=0 is set, scheduling taboo table ST_list={ φ }.

Step 2 seeks initial schedule

(1) to given current production schedule p, press delivery period and minimum isopreference rule in batches the earliest successively, determine initial schedule S ₀, and put S ^*=S ₀, S ^{* *}=S ₀, SC_flag=0.

(2), calculate corresponding to p and S by fast dispatch emulation ₀Performance index G (p, S ₀), and put G (p, S ^{* *})=G (p, S ₀).

If S ₀Feasible (promptly satisfying constraint (10)-(11)) puts SC_flag=1.

Step 3 scheduling search

(1) generates a preferably scheduling S adjacent to adjacent dispatching concentration before tight ^*The collection of might dispatching, and put G (p, S ^*)=M_big.

(2) for a scheduling S in this set, if S not in ST_list, then by fast dispatch emulation, (p S), and upgrades preferably scheduling in the current Neighbor Set: S to calculate scheduling index G ^*← S, G (p, S ^*) ← G (p, S), if SC_flag=1 S is feasible and G (p, S)＜G (p, S ^*); S ^*← S, G (p, S ^*(if p is S) S and S for) ← G ^*All infeasible and G (p, S)＜G (p, S ^*); Otherwise abandon S.So repeat, until finishing S ^*All adjacent scheduling.

(3) doing once scheduling moves; S is set ^*← S ^*, G (p, S ^*) ← G (p, S ^*), and with S ^*Be added to the top of ST_list;

If the scheduling number＞ST_size among the ST_list then deletes a scheduling the oldest from the bottom of ST_list.

(4) if scheduling has improvement, i.e. S ^*Feasible and G (p, S ^*)＜G (p, S ^{* *}) or S ^*And S ^{* *}All infeasible and G (p, S ^*)＜G (p, S ^{* *}), then upgrade and preferably separate: S ^{* *}← S ^*, G (p, S ^{* *}) ← G (p, S ^*).

(5) upgrade the mobile number of times of scheduling that current planning is done: SM_ctr ← SM_ctr+1.If SM_ctr＞SM_max then stops iteration and changes Step 4; Otherwise change Step 3 (1).

Step 4 returns

X among algorithm 1 Step 2 is by finding the solution formula (4)-thick production schedule that (8) are obtained and the initial solution that is taken as algorithm accelerating the speed of finding the solution of problem, because the thick production schedule is often than the initial solution of selecting at random truly separating of proximity (9)-(11) more.However, because the details of aspects such as assembly line scheduling has been ignored in formula (4)-(8), the thus obtained thick production schedule is often still infeasible to formula (9)-(11).In addition, the effective ways that develop into feasible scheme from the thick production schedule reduce the load of assembly line beyond doubt, so the adjacent plan among algorithm 1 Step 2 can only be defined as p=(x ₁, x ₂..., x _I-1, x _I-1, x _I+1..., x _n) ^TTo accelerate to obtain the speed of initial feasible solution.

Have random character (as equipment failure, installation time change etc.) if mix batch assembly line, can move its integrated optimization problem of finding the solution by the Monte Carlo of algorithm 1.Specific practice is: (1) before the operation of each Monte Carlo, earlier according to the distribution function of each stochastic variable calculate separately sample value and with the analog value in these sample values replacement formula (9)-(10), call algorithm 1 then; (2) in Monte Carlo when operation first time, the x among algorithm 1 Step 2 is the thick production schedule, but for the second time and during the operation of later Monte Carlo, and x then finds the solution speed for the best production schedule that Monte Carlo operation back is last time obtained to accelerate it.Although because the sample value of current Monte Carlo operation different with Monte Carlo operation last time probably, last time preferably the production schedule often still than the thick production schedule more near this optimum solution; (3) behind all Monte Carlo end of runs, need calculating all except that preferably dispatching mean value as a result, and call algorithm 2 again to obtain accordingly preferably scheduling with the preferably plan mean value behind the rounding and stray parameter mean value as input, at last with the mean value of preferably planning mean value and other result of itself and rounding together as having mixing batch assembly line production schedule and dispatching separating of integrated optimization problem of random character.

The program flow diagram of algorithm 1 and algorithm 2 is respectively shown in Figure 4 and 5.Like this, according to algorithm 1 and algorithm 2 and program flow diagram thereof, the present inventor has adopted Microsoft Visual C ⁺⁺5.0 programming has realized finding the solution the above-mentioned batch assembly line production schedule and the embedded tabu search simulation method of dispatching the integrated optimization problem of mixing.

The computational complexity of algorithm 1 is o (0.5n ²(n ²-1) * SM_max * PM_max) inferior emulation.If n is bigger, finding the solution formula (9)-(11) with algorithm 1 can need the too many time so that can't obtain optimum solution in acceptable time.We will propose the algorithm that another kind is found the solution formula (9)-(11), i.e. alternative expression tabu search simulation method for this reason.

3.2 alternative expression tabu search simulation method and realization thereof:

The basic thought of alternative expression tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as the initial production plan and with the tabu search simulation method of simplifying; (2) plan that has the top performance index through high-speed simulation calculating is sought in given scheduling with tabu search; (3) worked out a scheme conversely, seek through high-speed simulation with another tabu search again and calculate scheduling with top performance index; (4) be used alternatingly (2), (3) two steps until finding best planning and scheduling.Owing to respectively planning and scheduling is used alternatingly two tabu search and calculates its performance index with high-speed simulation, so be called alternative expression tabu search simulation method.

The alternative expression tabu search simulation method of the integrated optimization problem of algorithm 3 production schedules, scheduling and emulation

Step 1 initialization

(1) reads various data and parameter in formula (9)-(10).

(2) read algorithm parameter, comprise production schedule taboo table length PT_size, the mobile number of times PM-max of given plan, scheduling taboo table length ST_size and the given mobile number of times SM_max of scheduling.

(3) G_best=M_big is set, PM_ctr=0, PT_list={ φ }, P_best=φ, S_best={ φ }.

Step 2 initial feasible scheme of search and scheduling

(1) initial production plan p is set ₀=x.

(2) current planning p=p is set ₀, and call algorithm 2 is given the p that works out a scheme with search feasible schedule.

(3) if SC_flag=1 and G be (p, S ^{* *})＜G_best then is provided with p ^*← p, P_best ← p, S_best ← S ^{* *}, G_best ← G (p, S ^{* *}).Change Step 3 then.

(4) generate p ₀An adjacent plan p, p is set ₀=p.Change Step 2 (2) then.

The best planning and scheduling of Step 3 search

(1) generates one adjacent to p ^*Institute might plan collection, and put G (p ^*, S ^{* *})=M_big.

(2) for a plan p in this set, if p is not in PT_list, then by corresponding p of fast dispatch simulation calculation and S ^{* *}Performance index G (p, S ^{* *}), and upgrade preferably plan in the current Neighbor Set: p ^*← p, G (p ^*, S ^{* *}) ← G (p, S ^{* *}), if SC_flag=1 and G be (p, S ^{* *})＜G (p ^*, S ^{* *}); Otherwise abandon p.If the plan number among the plan taboo table PT_list is less than PT_size, p is added to the top of PT_list.So repeat, until finishing p ^*All adjacent plans.

(3) call algorithm 2 to search for for given p ^*Preferably scheduling S ^{* *}

(4) doing once plan moves: p is set ^*← p ^*, G (p ^*, S ^{* *}) ← G (p ^*, S ^{* *}If) and p ^*Not in PT_list then with p ^*Be added to the top of PT_list; If the plan number＞PT_size among the PT_list then deletes a plan the oldest from the bottom of PT_list.

(5) if plan has improvement, if i.e. G (p ^*, S ^{* *})＜G_best then upgrades and preferably separates: P_best ← p ^*, S_best ← S ^{* *}, G_best ← G (p ^*, S ^{* *}).

(6) the mobile number of times of plan that is updated to so far to be done: PM_ctr ← PM_ctr+1.If PM_ctr＞PM_max then stops iteration and changes Step 4, otherwise (1) of changeing Step 3.

Step 4 output results

Output P_best, S_best and G_best.

The program flow diagram of algorithm 3 as shown in Figure 6.Like this, according to algorithm 3 and program flow diagram thereof, the present inventor has adopted MicrosoftVisual C ⁺⁺5.0 programming has realized finding the solution the above-mentioned batch assembly line production schedule and the alternative expression tabu search simulation method of dispatching the integrated optimization problem of mixing.

The computational complexity of algorithm 3 is o ((n ²+ n+0.5n (n-1) SM_max) inferior emulation PM_max).If n is enough big, then the complicacy of algorithm 1 is o (n ⁴), and algorithm 3 is o (n ²).So algorithm 3 is more faster than algorithm 1, but the latter often obtains better to separate than the former.If n is very big, even algorithm 3 also can't obtain optimum or suboptimal solution in acceptable time.For this reason, we will propose string type tabu search simulation method and find the solution formula (9)-(11).

3.3 string type tabu search simulation method and realization thereof

Undoubtedly, a kind of effective ways that quicken solution procedure are the computational complexities that reduce algorithm, just are reduced to and obtain the emulation total degree that best dispatching office is done.For this reason, the basic thought of string type tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as original plan and with the rule-based scheduling simulation method; (2), seek rule-based scheduling and pass through the plan that high-speed simulation calculating has the top performance index with tabu search from feasible scheme; (3), use another tabu search to seek and calculate scheduling with top performance index through high-speed simulation for best plan.Owing to plan and scheduling are used tabu search successively and are calculated its performance index with high-speed simulation, so be called string type tabu search simulation method.

The string type tabu search simulation method of the integrated optimization problem of algorithm 4 production schedules, scheduling and emulation

Step 1 initialization

(1) reads various data and parameter in formula (9)-(10).

(2) read algorithm parameter, comprise production schedule taboo table length PT_size, the mobile number of times PM-max of given plan, scheduling taboo table length ST_size and the given mobile number of times SM_max of scheduling.

(3) G_best=M_big is set, PM_ctr=0, PT_list={ φ }, P_best=φ, S_best={ φ }.

Step 2 search feasible schemes

(1) initial production plan p is set ₀=x.

(2) current planning p=p is set ₀, and call algorithm 5 to determine scheduling corresponding to p.

(3) if (p S)＜G_best, then is provided with p for SC_flag=1 and G ^*← p, P_best ← p, S_best ← S, G_best ← G (p, S).Change Step 3 then.

(4) generate p ₀An adjacent plan p, p is set ₀=p.Change Step2 (2) then.

Preferably plan of Step 3 search

(1) generates one adjacent to p ^*Institute might plan collection, and put G (p ^*, S)=M_big.

(2),, and upgrade the preferably plan in the current Neighbor Set: P if p not in PT_list, then calls algorithm 5 with definite scheduling corresponding to p for a plan p in this set ^*← p, G (p ^*, S) ← G (p, S), if SC_flag=1 and G (p, S)＜G (p ^*, S); Otherwise abandon p.If the plan number among the plan taboo table PT_list is less than PT_size, p is added to the top of PT_list.So repeat, until finishing p ^*All adjacent plans.

(3) doing once plan moves: p is set ^*← p ^*, G (p ^*, S) ← G (p ^*If, S) and p ^*Not in PT_list then with p ^*Be added to the top of PT_list; If the plan number＞PT_size among the PT_list then deletes a plan the oldest from the bottom of PT_list.

(4) if plan has improvement, if i.e. G (p ^*, S)＜and G_best, then upgrade and preferably separate: P_best ← p ^*, S_best ← S, G_best ← G (p ^*, S).

(5) the mobile number of times of plan that is updated to so far to be done: PM_ctr ← PM_ctr+1.If PM_ctr＞PM_max then changes Step 4, otherwise (1) of changeing Step 3.

Preferably scheduling of Step 4 search

(1) p=P_best is set, and calls algorithm 2 with the preferably scheduling of search corresponding to p.

(2) if scheduling has improvement, i.e. G (p, S ^{* *})＜G_best then upgrades and preferably separates: S_best ← S ^{* *}, G_best ← G (p, S ^{* *}).

Step 5 output results

Output P_best, S_best and G_best.

Here, S is a scheduling of being determined by algorithm 5.

Algorithm 5 is corresponding to determining algorithm for the scheduling of working out a scheme

Step 1 determines scheduling

(1), according to delivery period, minimum isopreference rule in batches the earliest, determines scheduling S successively for giving the p that works out a scheme.

(2) by fast dispatch emulation, calculate G corresponding to p and S (p, S).

(3), then put SC_flag=0, otherwise put SC_flag=1 if S is infeasible.

Step 2 returns

The computational complexity of algorithm 4 is o ((n ²+ n) PM_max+0.5n (n-1) SM_max) inferior emulation.If n is enough big, the complicacy of algorithm 4 is the same with algorithm 3 all to be o (n ²).But be to use algorithm 4 to begin to search best planning and scheduling and do [1+0.5n (n-1) SM_max] (PM_max-1) inferior emulation than using algorithm 3 to lack from initial feasible scheme.Therefore, algorithm 4 is faster than algorithm 3, but the latter often obtains better to separate than the former.

The program flow diagram of algorithm 4 and algorithm 5 is respectively shown in Fig. 7 and 8.Like this, according to algorithm 4 and algorithm 5 and program flow diagram thereof, the present inventor has adopted Microsoft Visual C ⁺⁺5.0 programming has realized finding the solution the above-mentioned batch assembly line production schedule and the string type tabu search simulation method of dispatching the integrated optimization problem of mixing.

In the integrated optimization of the production schedule, scheduling and emulation, the function of plan be determine every kind of product assembling in batches, the function of scheduling is to determine every kind of product by which type of assembling of reaching the standard grade in proper order, the function of emulation is the performance index of the given scheduling of calculating.

4, the rapid simulation method of production scheduling and realization thereof

The fast dispatch emulation of above-mentioned embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method is all by setting up the scheduling simulation model and OO technology realizes with the senior at random judgement Petri net of expansion, and controls simulation process with variable time stream.Implication is that no literal and dynamic figures show fast herein, only calculates the performance index of given scheduling by high-speed simulation.

4.1 expand senior at random judgement Petri net

Because the fast changing requirement of the market demand can mix on batch assembly line order of in time finishing kind, constantly changing in batches at one, therefore how working out and optimizing the production schedule of mixing batch assembly line is very important with scheduling.Must calculate the performance index of each scheduling of each feasible scheme for the planning and scheduling that obtains integrated optimization, yet owing to mix batch complicacy of assembly line scheduling, be difficult to consider with the way of resolving the various factors of assembly line, comparatively feasible method is emulation.For this reason, need set up realistic model, promptly need a kind of can the description to mix the modeling tool of criticizing assembly line structure and running status.The present invention adopt that the present inventor proposes and in flexible manufacturing system (FMS) modeling, scheduling, emulation the senior at random judgement of achieving success Application Expansion Petri net (ESHLEP-N) carry out modeling to mixing batch assembly line, to solve the scheduling simulation problem of mixing batch assembly line.

The major advantage of ESHLEP-N is: (1) for make the storehouse in token both be convenient to that the user observes and performance evaluation, be convenient to the FMS scheduling simulation again, in ESHLEP-N, defined dual token and dual sign; (2) rule such as will dispatch and be incorporated among the ESHLEP-N, with reasoning and the decision-making capability that improves it.But the original definition of ESHLEP-N is at the FMS modeling, thereby need make amendment to this and perfect, makes it be fit to mix the modeling of batch assembly line.Amended Petri net still is called ESHLEP-N, and it is defined as follows:

Define 1 ESHLEP-N and may be defined as one 16 tuple:

ESHLEP-N={P, T (R), F, A _p, C, I _-, I ₊, I _a, I _s, I _r, DI _a, DI _s, DI _r, K, M ₀, CM ₀Wherein:

P={P _g, R}={p ₁, p ₂..., p _h, r ₁, r ₂..., r _kBe that a limited storehouse collects p _i∈ P _g, r _j∈ R, P _gBe that common storehouse collects, R is the decision-making point set.

T (R)={ t ₁(r ₁), t ₂(r ₂) ..., t _k(r _k) be a limited transition collection T (R) ∩ P=φ, φ is an empty set.

F P * T (R) ∪ T (R) * P is a flow relation.

A _p∶P _g→A _p(P _g)，R→A _p(R)。A _p(P _g) be P _gOn the parameter list collection.A _p(R)=S={S ₁, S ₂..., S _kRepresent that the rule (decision logic) on the R collects.S _jBe control transition t _j(r _j) rule set that enables and trigger.A _p(P _g) ∪ A _p(R) be the token collection of ESHLEP-N.

C: A _p(P) power set of ∪ T (R) → known color makes p ∈ P, C (A _p(p)) be the set that a p goes up all possible token look: t (r) ∈ T (R), C (t (r)) be on the t (r) the set of look might appear.

I _-Be a negative function, make

(p, t (r)) ∈ P _g* T (R): I _-(p, t (r)) ∈ [C (t (r)) _MS→ C (A _p(p)) _MS] _LAnd I _-The adequate condition of (p, t (r))=0 is $(p,t\left(r\right))\∉F.$ Here, C (...) _MSBe multiset, C (A _p(p)) _MSBe the coloured token collection on the p, [...] _LIt is the linear function collection.

I ₊Be a positive function, make

(t (r), p) ∈ T (R) * P _g: I ₊(p, t (r)) ∈ [C (t (r)) _MS→ C (A _p(p)) _MS] _LAnd I ₊The adequate condition of (p, t (r))=O is $(t\left(r\right),p)\∉F.$

I _a: A _p(P _g) → φ ∪ R _a ⁺, R _a ⁺Be non-negative set of real numbers, represent the installation time collection of all products at each assembly station.If r ∈ R _a ⁺, then r represents the installation time of a certain product at a certain assembly station.

I _s∶A _p(P _g)→φ∪R _s ⁺。R _s ⁺Be non-negative set of real numbers, non-fault collection service time of expression information desk (assembly station, assembly robot, equipment, instrument etc.).

I _r∶A _p(P _g)→φ∪R _r ⁺。R _r ⁺Be non-negative set of real numbers, collection servicing time of expression information desk.

DI _a∶A _p(P _g)→φ∪{N(μ ₁₁，σ ₁₁ ²)，N(μ ₁₂，σ ₁₂ ²)，…，N(μ ₂₁，σ ₂₁ ²)，…}。N (μ wherein _Ij, σ _Ij ²) be the normal distyribution function that product i obeys in the installation time of j assembly station, μ _IjBe average, σ _Ij ²It is variance.

DI _s∶A _p(P _g)→φ∪{exp(λ ₁)，exp(λ ₂)，…，exp(λ _m)}。Wherein, exp (λ _j) be the negative index distribution function that the between-failures of information desk j is obeyed, λ _jIt is failure rate.

DI _r∶A _p(P _g)→φ∪{exp(θ ₁)，exp(θ ₂)，…，exp(θ _m)}。Wherein, exp (θ _j) be the negative index distribution function of obeying servicing time of information desk j, θ _jIt is maintenance rate.

K: P _g→ N ⁺∪ { ω }, N here ⁺Be the positive integer collection, ω represents positive infinity, and K is positive capacity function. p ∈ P _g, K (p) is N ⁺The subclass of ∪ { ω }, its each element is all represented the upper bound of corresponding coloured token number among the p.Obviously, the dimension of K (p) and C (A _p(p)) identical.If it is a certain element of K (p) is ω, then unrestricted among the p with the number of the corresponding coloured token of this element.

M ₀Be the initial marking that initial token constituted of ESHLEP-N, satisfy p ∈ P: M ₀∈ A _p(p).

CM ₀Be to be used for initial coloured sign that the user observes the ESHLEP-N of coloured token distribution and performance statistics, satisfy

p∈P _g∶M ₀(p)∈A _p(p)→CM ₀(p)∈C(A _p(p)) _MS

What it may be noted that a bit is, the triggering of transition is exactly the corresponding coloured token that takes out some token and equivalent amount according to the rule in the decision point relevant with these transition from a certain storehouse institute subclass, and it is added to other storehouse institute subclass.No matter when, as long as when a certain input magazine institute's subclass of transition and the token in a certain output storehouse institute subclass and some rule in its decision point are complementary, these transition just are enabled.This means: enough suitable tokens are held in (1) these input magazines; (2) upper bound of certain token (can be mapped to coloured token of color of the same race) number can not be exceeded because these transition trigger the increase of back this token in these output storehouses institutes; (3) these tokens will stop time enough in input magazine institute.Transition just are triggered once enabling.

4.2 batch assembly line modeling that mixes based on ESHLEP-N

Article one, mix the total individual assembly station of m (=33) of batch assembly line.Because the assembling many assembly parts of product needed (part, parts and assembly etc.), therefore for simplifying modeling, we represent the assembly parts assembling process of each assembly station with product in the installation time of each assembly station, and each concrete assembly parts are not carried out modeling.Because product can not wait in the installation time of each assembly station, can be zero for individual product even in the installation time of some assembly station, promptly only specifically do not assemble by these assembly stations.Product,, is delivered to next station successively and is continued assembling after a last station has assembled successively by each assembly station according to scheduling given in advance (in proper order).Because product assembling is finished by the workman, so if the fittage of a last station is finished, and also finish in the fittage of this station, then limit in the workman interval that can freely cross over assembly station, directly assembles next product.Equally, if the product on certain station is not finished assembling, and this product has moved on to outside the boundary of this station with assembly line, then allows the workman of this station that task is postponed to next station and continues to finish, thereby logically form virtual buffering region.But it should be noted that the workman can not unrestrictedly cross over station, each assembly station also may break down.Each station at any time can only be adorned a product at the most.The station that product sum on the line at any time equals on the line is at the most counted m, just, if at a time each station all has a product, after a product such as then having only in the end station m installing and rolls off the production line, could be at station 1 product to be installed of reaching the standard grade.The synchronous translational speed of assembly line is variable, is not determined by the assembling speed of its last station when having full buffer zone on line, and is determined by the assembling speed of its bottleneck station when full buffer zone is arranged.Because the different product of each station assembling may need the different time, so the bottleneck station may shift when product category, mixed wholesale changing.

According to the front to the description that mixes batch assembly line and the definition of ESHLEP-N, we at first determine the common storehouse of ESHLEP-N number, position and implication.Arc between transition, decision point and the node then successively draws.Obtain the ESHLEP-N graphical model that mixes batch assembly line as shown in Figure 9 at last.Among Fig. 9, the implication of common storehouse institute, decision point and transition is explained as follows:

p ₁It is " assembly station free time " storehouse institute.As the p of storehouse institute ₁When only holding coloured token, corresponding assembly station is in idle condition.

p ₂It is " product to be installed storehouse " storehouse institute.As the p of storehouse institute ₂When holding coloured token, the product to be installed of waiting for the assembling of reaching the standard grade are arranged in the product to be installed storehouse.

p ₃It is " queuing " storehouse institute.As the p of storehouse institute ₃When holding coloured token, there have corresponding product waiting in the buffer zone of corresponding assembly station to be to be assembled.

p ₄It is " assembling " storehouse institute.As the p of storehouse institute ₄When holding coloured token, corresponding assembly station assembles (containing preparations) product accordingly.

p ₅It is " fault " storehouse institute.As the p of storehouse institute ₅When holding coloured token, corresponding assembly station is in malfunction, Under Repair.

p ₆It is " warehouse for finished product " storehouse institute.As the p of storehouse institute ₆When holding coloured token, there is the finished product that assembles in the warehouse for finished product.

r _1-5It is decision point.These nodes have stipulated to need among the ESHLEP-N figure to introduce the position of making a strategic decision.Decision point r _j(j=1-5) the rule set S in _jBe control transition t _j(r _j) rule set that enables and trigger.

t ₁Be t ₁(r ₁), be " assembly line on the product to be installed " transition.Buffer zone that its triggering is represented to have product to be installed to enter first station in the product to be installed storehouse etc. is to be assembled.

t ₂Be t ₂(r ₂), be " beginning assembling " transition.Its triggering represents that corresponding assembly station begins corresponding product is specified assembling (containing preparation).

t ₃Be t ₃(r ₃), be " finishing assembling " transition.Its triggering represents that corresponding assembly station finishes the appointment assembling of corresponding product.

t ₄Be t ₄(r ₄), be " fault generation " transition.Its triggering represents that the corresponding station that is in confined state or idle condition is out of order.

t ₅Be t ₅(r ₅), be " fault end " transition.Its triggering means that corresponding assembly station or idle station finish malfunction.

For making ESHLEP-N more can reflect the characteristics of finishing assembling by the workman, below above ESHLEP-N graph model is done necessary explanation:

(1) p ₃Be " queuing " storehouse institute, for the realization workman strides the station assembled product, and do not make the station quantity of leap surpass certain limit, we are provided with maximum queuing quantity that each station allows, the i.e. virtual buffering region of each station in database.If the workman on certain station reach or after the station number that moves surpass this restriction, then explanation is carved assembly line at this moment and is blocked.

(2) p ₂It is " product to be installed storehouse " storehouse institute.In mixing batch assembly line, the reaching the standard grade of product to be installed by line traffic control under the finished product.After in program, being reflected as each last station of finished product off line, require " queuing " storehouse in first station formation in adding one product to be installed, promptly trigger t ₁Transition.Therefore, after all product to be installed that require were in the works reached the standard grade, wired product of going up can both be finished remaining assembling in order to guarantee, can " product to be installed storehouse " storehouse in the virtual product to be installed of adding guarantee that emulation carries out smoothly.

Because ESHLEP-N figure is user oriented, is mainly used in and analyzes the performance of mixing batch assembly line, so in the institute of the common storehouse of Fig. 9, only show the color ream board.This is because represent that by coloured token the state of ESHLEP-N graph model can reduce status number.For example, the p of Fig. 9 storehouse institute ₁Coloured token 5w represent to have 5 assembly stations to be in idle condition.But these 5 assembly stations can be respectively any one in the individual assembly station of m (=33), and are just corresponding $C_m^5=237336$ Plant the station combination.If each assembly station all uses a token to represent, then these 5 coloured token correspondences 237336 kinds of token combinations (promptly taking out 5 number of combinations from 33 different tokens).Although the common storehouse of Fig. 9 in token do not show, exist really, just implicit.When a coloured token moved, the user should imagine that a token moves thereupon.Like this, just can according to common storehouse in the distribution of coloured token roughly determine the distribution of corresponding token.Below main the problem relevant with coloured token be discussed.

According to the definition of 1 couple of ESHLEP-N of definition, if represent an assembly station with w, b represents a product (product to be installed, formal dress product or finished product), q _i(i=1,2 ..., m) product of i station assembling is waited in one of expression,＜the expression tertiary colour, the common storehouse of Fig. 9 in the color set of all possible coloured token can be expressed as follows:

C (A _p(p ₁))={ w}, expression has station to be in idle condition.

C(A _p(p ₂))＝{b}。Representing has product to be installed in the product to be installed storehouse.

C (A _p(p ₃))={ q ₁, q ₂..., q _m, the expression have product i (i=1,2 ..., m) wait in line assembling on the individual station.

C (A _p(p ₄))=＜w, b〉}, expression has product in assembling.

C (A _p(p ₅))=w,＜w, b〉}, w represents to have a station that is in idle condition to break down.＜w, b〉represent have a station that is in confined state to break down.

C (A _p(p ₆))={ b} has the finished product that assembles in the expression warehouse for finished product.

Token in the decision point is more special, and they can be reused and but can not move on to other storehouse institute, that is to say, the triggering of the transition relevant with a certain decision point will make token shift out from this decision point to lay equal stress on and move into this decision point.

The transition of ESHLEP-N trigger with common Petri net different, it is not to shift out token from all input magazine institutes, then it is added to all output storehouse institutes, but according to the rule in the decision point, from part or all of input magazine institute, move mountain token and corresponding coloured token, it is joined part and whole output storehouse institutes.For example, transition t ₂A kind of possible coloured token moves and is during triggering:

From the p of input magazine institute ₁, p ₃In shift out a coloured token w respectively, q _j, (j=1,2 ..., m), be merged into one and be compounded with color ream board＜w, b 〉, it is added to the output storehouse p of institute ₄

In case all transition among Fig. 9 determined trigger the mobile relation of its corresponding coloured token, just can determine the dynamic process of this model in view of the above.

Among Fig. 9 all transition all possible look as follows occurs:

C(t ₁)＝{q ₁)， C(t ₂)＝{<w，b>}，

C(t ₃)＝{w，b，q ₂，q ₃，…，q _m}，C(t ₄)＝{w，<w，b>}

C(t ₅)＝{w，<w，b>}

The ESHLEP-N graph model of contrast Fig. 9 is dynamically described below.If:

(q ₁← b) represent a kind of linear mapping promptly to be mapped to q from b ₁, represent the formation of product to be installed to station 1.

p _r1, p _rThe 2nd, projection, promptly get tertiary colour＜in first kind of look or the mapping of second kind of look.

ID is identical mapping.

X (t ₂) represent because transition t ₂Triggering and the moving of coloured token of causing and satisfied

X(t ₂)∈C(t ₂) _MS

Like this, the dynamic description of ESHLEP-N model is exemplified below:

1) original state

The common storehouse of Fig. 9 in initial coloured sign can be expressed as follows:

CM ₀(p ₁)=5w, expression has 5 assembly station free time.

CM ₀(p ₂)=10b, representing has 10 product to be installed in the product to be installed storehouse.

CM ₀(p ₃)=q ₁+ q ₅+ 2q ₁₀+ 2q ₂₅, represent No. 1 and No. 5 stations respectively have one, No. 10 and No. 25 stations respectively have two products etc. to be assembled that all the other station product-frees etc. are to be assembled.

CM ₀(p ₄)=26＜w, b 〉, expression has 26 stations just at assembled product.

CM ₀(P ₅)=w+＜w, b 〉, expression respectively has a station that is in idle and confined state to be out of order.

CM ₀(p ₆)=20b has 20 finished products that assemble in the expression warehouse for finished product.

As then with vector representation

CM ₀＝(5w，10b，q ₁+q ₅+2q ₁₀+2q ₂₅，26<w，b>，w+<w，b>，20b)

2) establish CM ₀(p ₁One of idle station among the)=5w is No. 1.Like this, by decision point r ₂In rule, t ₂Can trigger, a coloured token also promptly respectively be arranged from p ₁And p ₃In shift out, be merged into one and be compounded with color ream board＜w, b〉move into p ₄In (establish this moment non-fault take place).

Establish I again _-(p ₁, t ₂)=p _r1;

$I\_(p_3,t_2)=\left({\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20031010600600282.png"\; state="\{\{state\}\}">q</figure-callout>}}_1\stackrel{L}{\&LeftArrow;}b\right)(P,2);$

I ₊(p ₄，t ₂)＝ID；

X(t ₂)＝<w，b>

Like this:

CM ₁(p ₁)＝CM ₀(p ₁)-I _-(p ₁，t ₂)X(t ₂)＝5w-(P _r1)<w，b>＝5w-w＝4w

$C{M}_1\left(p_3\right)=C{M}_0\left(p_3\right)-I\_(p_3,t_2)X\left(t_2\right)$

$={\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20031010600600282.png"\; state="\{\{state\}\}">q</figure-callout>}}_1+q_5+2q_{10}+2q_{25}-\left({\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20031010600600282.png"\; state="\{\{state\}\}">q</figure-callout>}}_1\stackrel{L}{\&LeftArrow;}b\right)\left(p_{r}2\right)<w,b>$

$={\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20031010600600282.png"\; state="\{\{state\}\}">q</figure-callout>}}_1+q_5+2q_{10}+2q_{25}-{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A20031010600600282.png"\; state="\{\{state\}\}">q</figure-callout>}}_1=q_5+2q_{10}+2q_{25}$

CM ₁(p ₄)＝CM ₀(p ₄)+I ₊(p ₄，t ₂)<w，b>＝26<w，b>+<w，b>

＝27<w，b>

Be CM ₁=(4w, 10b, q ₅+ 2q ₁₀+ 2q ₂₅, 27＜w, b 〉, w+＜w, b 〉, 20b)

3) establish station 33 again and finish fittage, then according to decision point r ₃In rule, transition t ₃Trigger.Be compounded with color ream board＜w, b with one for this reason〉from p ₄In shift out, and resolve into coloured token w and b moves into p respectively ₁And p ₆At this moment, coloured sign becomes:

CM ₂＝(5w，10b，q ₅+2q ₁₀+2q ₂₅，26<w，b>，w+<w，b>，21b)。

4) for other transition too, if its I/O storehouse in token and the rule in coloured token and the corresponding decision point be complementary with regard to the triggering.Therefore, though it is complicated to mix batch assembly line, can clearly be described its dynamic process with ESHLEP-N figure.

4.3 mix the OO realization of the ESHLEP-N model of batch assembly line

The Simula language that object-oriented (Object-Oriented) speech was released from the sixties, the basic thought of Object-oriented Technique are the structure objects, by the method for modeling, data structure and behavior are all merged in the single entity.It comes organize models round extension things, the common approach of some object and model and behavior extracted encapsulate the formation class, object in the class has identical attribute and behavior pattern, instantiation by class produces object again, this group objects also has universal relation, general behavior and general semantic.Certainly, inhomogeneous object also may have identical property value and relation.

Object-oriented method emphasizes that object properties can only be changed by the object factum, is undertaken alternately by the message transmission between the object, can realize the refinement of object class by inheritance mechanism, by the replacement of object behavior then being brought out the polymorphism notion of object.Encapsulation, succession, polymorphism are OO key characters.

The present invention adopts the Visual C of Microsoft company ⁺⁺5.0 realize mixing the ESHELP-N model of batch assembly line as developing instrument.Visual C ⁺⁺5.0 since being born, be topmost application development system under the Windows environment always.It provides easily that classwizard makes the developer can handle self-designed class easily, and provides packaged MFC to make the developer can realize various operations easily.In the present invention, also mainly be designed for the class that realizes emulation, utilize MFC to come the extraction of fundamental simulation data in the fulfillment database, the operations such as structure of transition chained list with its classwizard.The OO realization of ESHELP-N model is discussed below.

4.3.1 storehouse institute and transition are represented

In the implementation procedure of ESHLEP-N, we with basic class realize common storehouse in token, represent with wherein attribute which storehouse institute concrete token is in, for this reason, at Microsoft Visual C ⁺⁺5.0 in, utilize the following class of Microsoft MFC design:

Class CWorkstation:public CObject { public:stationstate priorstate; ∥ state double surplus_needtime before the record trouble when breaking down; ∥ is used for writing down the residue installation time long buffer of corresponding assembly station this product when the process of assembling corresponding product is bumped ∥ to fault; The size of the corresponding assembly station buffer zone of ∥, promptly the deposit position number＜!--SIPO＜DP n=" 18 "〉--〉＜dp n=" d18 "/Cprodnode waitingprod; The product that ∥ waits in line to assemble in corresponding station buffer zone, the double needtime of p3 storehouse institute; This product of ∥ is total to the installation time stationstate state that needs on the position at this; ∥ station state double sum_emptytime, sum_processtime, sum_readytime; ∥ adds up free time, and the accumulative total station is handled (assembling) time, accumulative total setup time int current_prodno, current-prodtype; The numbering of the product that the corresponding station of ∥ is assembling and kind double begintime, planfinishtime; The beginning installation time of this product of ∥ on this station and plan deadline int GetProdNumber (); ∥ obtains the numbering double getplanfinishtime () of the product that corresponding station assembling; ∥ obtains the plan deadline int getcurrentprodtype () of this product on this station; ∥ obtains the kind CWorkstation () of the product that corresponding station assembling; Virtual～CWorkstation (); Void init (); ;

The attribute record that in such, encapsulates the state of corresponding station in the whole piece assembly line course of work, the method in such then realizes the operation to this station attribute.Attribute state belongs to typedef enum{empty=1, wrong, and working, waiting, ready, sleep}stationstate, it is worth empty, and the corresponding station of ready and sleep (represent this corresponding station also do not start working) expression is in the p of storehouse institute ₁, working represents that corresponding station is in the p of storehouse institute ₄, wrong represents that corresponding station is in the p of storehouse institute ₅

For " the product to be installed storehouse " p of storehouse institute among the ESHLEP-N ₂, we have designed product to be installed storehouse institute class in program:

Class Cbodysimu ∥ sets up the class { public:Cbodysimu () of initial product chained list to be installed; Virtual～Cbodysimu (); Public:int prodnum; ∥ product numbering to be installed int prodtype; ∥ product kind to be installed Cbodysimu * next; ∥ points to the pointer of next product to be installed };

And realize p with following class ₂In token (product to be installed) sort by the dispatching sequence:

The chained list of the initial product to be installed of class Cprodnode ∥, also as the chained list of the product in corresponding station buffer zone ∥, waiting in line to assemble public:＜!--SIPO＜DP n=" 19 "〉--〉＜dp n=" d19 "/Cprodnode (); Virtual～Cprodnode (); Public:void delhead (); Cbodysimu * GetPointNow (); Cbodysimu * head, * now, * end; Int count; Void add (int prodnum, int prodtype); ∥ adds new node void deleteall (); ∥ deletes whole chained lists };

When ESHLEP-N started, available above-mentioned data structure realized " product to be installed storehouse " p of storehouse institute ₂Initialization.Equally, for " queuing " storehouse p of institute on each station ₃, also available above-mentioned data structure realizes.

For " warehouse for finished product " storehouse p of institute among the ESHLEP-N ₆, in emulation, being recorded in and having assembled the finished product of finishing on the assembly line with a variable overprods, the value of overprods is represented p ₆Middle token quantity.

Owing to there are the mapping relations of one-to-many between coloured token and the token, coloured token can be regarded as " view " of token, so in the implementation procedure of ESHLEP-N model, do not design special data structure and preserve the color ream board, just in performance statistics and the demonstration of ESHLEP-N graph model, define number, demonstration and the distribution of color ream board by token according to the mapping relations of one-to-many between coloured token and the token.

As for, the transition class can be defined as follows:

Transition class { public:CTransition () among the class CTransition:public CObject ∥ ESHLEP-N; CTransition (int transition, double begin, int sta) { transitiontype=transition; Begintime=begin; Station=sta; ∥ transition constructed fuction public:int transitiontype; ∥ transition kind, 1:t1,2:t2,3:t3,4:t4,5:t5 double begintime; The time int station that these transition of ∥ trigger; The station 0-m that the ∥ transition trigger };

Defined transition attribute transitiontype in the CTransition class, its value is 1,2,3,4, represents the transition t among the ESHLEP-N at 5 o'clock respectively ₁, t ₂, t ₃, t ₄, t ₅Buffer zone that transitiontype=1 represents to have product to be installed or virtual product to be installed to enter first station in the product to be installed storehouse etc. is to be assembled.

Define transition attribute begin and attribute sta in the CTransition class, represented these transition time of taking place and the station that these transition take place respectively.

In the realization of program, utilize the CtypedPtrArray＜CObArray of MFC encapsulation, CTransition ^*Transitions realizes the list structure (formation) of transition.The CTypedPtrArray that encapsulates in MFC provides Add (), Remove (), and InsertInto methods such as () can be with CTransition ^*Insert among the pointer array transitions, and easy to maintenance.So, each as long as take out the transition that according to time sequence take place at first in the program implementation process, the function that execution is relevant, deletion is just passable in pointer array then.

In addition, in OO emulation, also must solve the simulation time problem.In discrete events simulation, simulation time be one with the different logical timer of yardstick actual time, it is all relevant with the activity of all entities and all scheduling.The yardstick of simulation time is choosing arbitrarily, and is independent of actual time.Each incident is associated with logical timer by the event time that is scheduled, and when the corresponding physical incident took place, this event time was just corresponding to actual time of physical system.In the design of program, we have defined attribute simulationclock in the CsimulationDoc:public of master routine CDocument class, be used for writing down simulation time.

4.3.2 transition triggering rule

The transition triggering rule has 12 of 5 classes, the triggering of the corresponding a kind of transition of each rule-like.Specific as follows, wherein R adds digital watch and shows that the first digit behind the R is represented the kind of transition regular number.

R101; If (1) assembly line does not block, last station on (2) assembly line has a product to finish assembling, (3) storehouse p of institute ₂In token b is arranged; Transition t then ₁Trigger, promptly from p ₂In shift out a token b, and at p ₃Token q of middle increase ₁

R201: if (1) assembly line does not block, (2) p ₁In have the expression station i free time token w, (3) p ₃In token q is arranged _i(expression waiting for station i assembling at the dress product), then transition t ₂Trigger, promptly from p ₁In shift out a token w, from p ₃In shift out a token q _i, be merged into a compound token＜w, b〉and be added to p ₄In.

R202: if (1) assembly line blocks (2) p ₁In have the expression station i free time token w, (3) p ₃In token q is arranged _i, that (4) are blocked now is station i; Transition t then ₂Trigger, promptly from p ₁In shift out a token w, from p ₃In shift out a token q _i, be merged into a compound token＜w, b〉and be added to p ₄In.If be no more than load quantity at dress product sum in the buffer zone of the buffer zone of station i and station i+1, then remove the blocked state of assembly line and station i.

R301: if (1) assembly line does not block, (2) p ₄In have an expression station i just to finish compound token＜w of assembling, b at dress product b, (3) station i is not last station on the assembly line; Transition t then ₃Trigger, promptly from p ₄In shift out a compound token＜w, b, resolve into a token w and a token q _I+1Be added to p respectively ₁And p ₃In.

R302: if (1) assembly line does not block, (2) p ₄In have an expression station i just to finish compound token＜w of assembling, b at dress product b, (3) station i is last station on the assembly line; Transition t then ₃Trigger, promptly from p ₄In shift out a compound token＜w, b, resolve into a token w and a token b is added to p respectively ₁And p ₆In.

R303: if p ₃In the number of token q transfinite (promptly represent in the buffer zone of the buffer zone of station i and station i+1 at dress product sum above load quantity, the buffer zone of station i is full); Then the whole piece assembly line enters blocked state.

R304: if (1) assembly line blocks (2) p ₄In have an expression station i just to finish compound token＜w of assembling, b at dress product b, (3) station i is not last station on the assembly line, (4) station i is present obstruction station; Transition t then ₃Trigger, promptly from p ₄In shift out a compound token＜w, b, resolve into a token w and a token q _I+1Be added to p respectively ₁And p ₃In.

R305: if (1) assembly line blocks (2) p ₄In have an expression station i just to finish compound token＜w of assembling, b at dress product b, (3) station i is last station on the assembly line, (4) station i is present obstruction station; Transition t then ₃Trigger, promptly from p ₄In shift out a compound token＜w, b, resolve into a token w and a token b is added to p respectively ₁And p ₆In.

R401: if p ₁In have a represented idle station of token w to break down; Transition t then ₄Trigger, promptly from p ₁In shift out a token w and be added to p ₅In.

R402: if p ₄In a compound token＜w is arranged, b the represented station i that is assembling breaks down; Transition t then ₄Trigger, promptly from p ₄In shift out a compound token＜w, b be added to p ₅In.

R501: if p ₅In have the malfunction of the represented station i of token w to eliminate; Transition t then ₅Trigger, promptly from p ₅In shift out a token w and be added to p ₁In.

R502: if p ₅In a compound token＜w is arranged, b the malfunction of represented station i eliminates; Transition t then ₅Trigger, promptly from p ₅In shift out a compound token＜w, b be added to p ₄In.

4.3.3 transition treatment scheme

In The Realization of Simulation based on the ESHLEP-N model, we at first get a transition incident that takes place at first and handle from the transition formation, step is to judge whether assembly line blocks earlier, just enter the obstruction handling procedure if block, if do not block, just read the kind of transition and the station that transition trigger, enter corresponding transition handling procedure.The triggering of transition will be followed above-mentioned transition triggering rule, below with its implementation procedure of flow chart description.

(1) main flow of system's transition processing

If one mix on batch assembly line and have 33 assembly stations, and 20 products of a collection of production schedule requirement assembling, then initial coloured sign of ESHLEP-N model can be expressed as:

CM ₀(p ₁)=33w represents that all assembly stations are all idle.

CM ₀(p ₂)=20b, representing has 20 product to be installed in the product to be installed storehouse.

CM ₀(p ₃)=φ, all product-free etc. is to be assembled to represent all stations.

CM ₀(p ₄)=φ, expression does not have station just at assembled product.

CM ₀(p ₅)=φ, expression does not have station to be out of order.

CM ₀(p ₆)=φ, the finished product that does not assemble in the expression warehouse for finished product.

According to top initial coloured sign, can get main flow (being the main program block diagram of simulation software) that system transition handle as shown in figure 10.

(2) transition t ₁Treatment scheme

Transition t ₁Effect be make " product to be installed storehouse " storehouse in product to be installed enter assembly line.The station that these transition take place must be the minimum station of assembly line, the station of promptly reaching the standard grade.Handling transition t ₁The time, judge earlier in the institute of product to be installed storehouse whether also have token; If have, then in the institute of the queuing storehouse of minimum station, add product to be installed; If no, then " queuing " storehouse of this station in to add type be-1 product virtual to be installed.Its treatment scheme as shown in figure 11.

(3) transition t ₂Treatment scheme

Transition t ₂Be " begin assembling " transition, promptly from the queuing storehouse institute of transition generation station, get a product, as then this station state not being set to working and producing the transition t of this station for virtual product to be installed ₃Insert the transition formation, finish tasks such as blocking judgement then, its treatment scheme as shown in figure 12.What deserves to be mentioned is, in this treatment scheme, produce transition t ₃The time, consider whether this product needs to assemble the situation of preparation at this station, prepares if desired, must be added that then its installation time is as transition t the setup time of product ₃Triggered time, otherwise with the installation time of product as transition t ₃Triggered time.Owing to making assembly line, the artificial treatment assembling work has flexibility, permission in the virtual buffering region of each station, be provided with some at dress product (the just product in assembling process) deposit position, promptly allow the workman under the situation that task is finished, suitably to move forward rigging position, suitably mobile backward rigging position under the situation that task has little time to finish, but be subjected to the restriction of assembly parts position, the position that the workman moves forward and backward can not surpass the regulation boundary, being no more than load quantity at dress product sum and limiting in the buffer zone that this can be by stipulating each station and the buffer zone of next station thereof.Therefore, be provided with according to the station parameter in the database, just determine the buffer zone load quantity of each station at first in emulation, when in this station buffer zone and the next station buffer zone thereof at dress product sum during above load quantity, the buffer zone that defines this station is full, and assembly line blocks.

(4) transition t ₃Treatment scheme

Transition t ₃Be " finishing assembling " transition, the fittage of promptly a certain station corresponding product is finished transition, mainly handles the state of this station and next station, and its treatment scheme as shown in figure 13.Among the figure, the corresponding station of ready state representation of station is ready, can begin assembling (containing preparation).

(5) transition t ₄Treatment scheme

Transition t ₄Be " fault generation " transition, its treatment scheme is simple relatively, as shown in figure 14.In this treatment scheme, need at first to judge whether whether station promptly station on have at dress product in work when fault takes place, if having, then needs the transition t of this station of deletion in the transition formation ₃Preserve then fault take place before the status information of this station and the state of putting this station be wrong.

(6) transition t ₅Treatment scheme

Transition t ₅Be " fault end " transition, its treatment scheme as shown in figure 15.Whether in this treatment scheme, at first needing to judge has on this station at the dress product, if do not have, then only need are changed to empty with the state of this station simply.Otherwise need further to judge that whether this station is at assembled product, if then need recover the transition t that triggers before this before fault takes place ₄Treatment scheme in the transition t of this station of deleting ₃And with t ₃Triggered time originally adds that the duration of this fault is as t ₃The new triggered time, if not, the transition t of this station then generated ₂

(7) block treatment scheme

Top transition t _1-5Treatment scheme takes place under the assembly line normal condition.Under congestion situations, total treatment principle is slightly had any different, as shown in figure 16: as transition t under blocked state with under normal circumstances roughly the same ₂During triggering, need at first to judge whether station that transition trigger is in the station of blocked state, if then remove the obstruction sign of assembly line and this station, and handle this transition by normal condition; Otherwise do not handle these transition.Equally, handling transition t ₃The time, to judge earlier that also the station that transition trigger is current obstruction station, if then handle this transition, otherwise do not handle these transition by normal condition.So blocking the transition that trigger on the station by handling these, just can eliminate the obstruction of assembly line.After block eliminating, handle in the transition formation all transition triggered times again less than the transition of current simulation time (current simulation time is to eliminate the transition triggered time that assembly line blocks).Do like this and be equivalent to when assembly line blocks, " the beginning assembling " on all the other stations reach " finishing assembling " incident and " assembly line on the product to be installed " incident all can not take place, and only after the elimination of assembly line obstruction, these incidents could take place.

4.4 mix the realization of batch assembly line production scheduling emulation

The realization that mixes batch assembly line production scheduling emulation is the basis that is embodied as with the senior at random judgement of expansion Petri net (ESHLEP-N) model.In front, we have set up and have mixed the model of the ESHLEP-N of batch assembly line, and have introduced its OO realization, comprise the class based on Microsoft MFC (class) expression of storehouse institute, token and transition, transition formation, transition triggering rule and transition treatment scheme.On this basis, we adopt Microsoft Visual C ⁺⁺5.0 write the production scheduling simulation software that mixes batch assembly line.

Simulation process is as follows: at first, come initialization " product to be installed storehouse " storehouse institute according to plan (product category and quantity) given in above-mentioned embedded tabu search simulation method, alternative expression tabu search simulation method or the string type tabu search simulation method and scheduling (assemble sequence), promptly determine the order of kind, the quantity of product to be installed and the assembling of reaching the standard grade, then according to First Come First Served rule and above-mentioned transition triggering rule, successively will " product to be installed storehouse " storehouse in product to be installed serve assembly line and assemble; Product to be installed become at the dress product after the station assembling of reaching the standard grade, and assemble at each station successively along assembly line; After each station is finished assembling, enter " queuing " storehouse institute of next station at the dress product; All constant volumes of " queuing " storehouse of each station, when certain station " queuing " storehouse in dress product quantity during above this capacity, assembly line enters blocked state; Become finished product and enter " warehouse for finished product " storehouse institute after last station (station rolls off the production line) assembling at the dress product; In whole simulation process, allow station to break down; After all automobiles rolled off the production line, emulation finished.For shortening simulation time, adopt variable time stream to control simulation process and no literal and dynamic figures demonstration in simulation process, only calculate the performance index of given scheduling by high-speed simulation.

Owing to need a lot of parameters in emulation, the versatility for software is placed on parameter in the database, and reads these parameters when starting emulation.Like this, after the situation of assembly line changes, only need to revise parameter, just can adapt to news and need not to revise scheduling simulation software according to the database interface that provides.Owing to use Microsoft Visual C ⁺⁺5.0 as the developing instrument of scheduling simulation software, so the MFC class libraries that can utilize Microsoft to provide is easily finished reading of data in the database.Simultaneously, we also provide the modification interface of database in VC, mainly realize reading and revising of data with activex control DBGrid and RemoteDataControl.

In sum, ESHLEP-N has visual in image, and is simple in structure, and node is few, and descriptive good, decision-making capability is strong, and advantages such as dual token and dual sign are fit to mix modeling and the scheduling simulation of criticizing assembly line very much.This scheduling simulation software has two main applications: one, as fast dispatch emulator (promptly not having literal and dynamic figures shows), in order to calculate the performance index of given scheduling; Its two, after obtaining Optimal Production plan and scheduling, the scheduling simulation software setting is become animation display (or ESHLEP-N graphic presentation) mode, in order to observe the optimal scheduling process of mixing batch assembly line, obtain the optimal scheduling performance index.

5, mix the integration optimizing software of the production schedule, scheduling and the emulation of batch assembly line

According to above-mentioned algorithm 1-5 and program flow diagram and mixed model and the OO implementation method thereof of criticizing the ESHLEP-N of assembly line, the present inventor has adopted Microsoft Visual C ⁺⁺5.0 programming has realized finding the solution the above-mentioned batch assembly line production schedule and embedded tabu search simulation method, alternative expression tabu search simulation method and the string type tabu search simulation method of dispatching the integrated optimization problem of mixing, developed the integration optimizing software that mixes the production schedule, scheduling and the emulation of batch assembly line, its software configuration as shown in figure 17.This software is made up of 8 modules such as level and smooth, the thick production schedule of order, embedded tabu search, alternative expression tabu search, string type tabu search, animation scheduling simulation, parameter management and optimization result queries, and wherein embedded tabu search, alternative expression tabu search and string type tabu search module are called the fast dispatch emulation module again jointly.Among the figure, the level and smooth module of order is used for level and smooth client's demand; Thick production schedule module adopts MILP (Mixed Integer Linear Programming) model that branch and bound method finds the solution formula (4)-(8) to obtain the setting up cost that makes each assembly station and free time is the least possible and the thick production schedule of As soon as possible Promising Policy product demand; The key distinction of animation scheduling simulation module and fast dispatch emulation module is to have or not in the simulation process animation display; Cost of products coefficient in the parameter management module management MILP (Mixed Integer Linear Programming) model, product is in installation time, setup time and the setting up cost of each station, station free time and fault, and algorithm parameter; Optimize the result queries module and be used to inquire about the production schedule and the result who dispatches integrated optimization.

Claims (4)

1, a kind of integrated optimization control method of mixing batch assembly line is characterized in that this method may further comprise the steps:

(1) level and smooth client's product demand;

(2), find the solution the mixed-integer programming model that mixes batch assembly line with branch-bound algorithm, to obtain the making setting up cost of each assembly station and free time is the least possible and the thick production schedule of As soon as possible Promising Policy product demand according to the product demand after level and smooth;

(3) on the integrated optimization model based of the production schedule of mixing batch assembly line and scheduling, at product category and quantity less, in, many etc. three in various degree, obtaining with the thick production schedule with embedded tabu search simulation method, alternative expression tabu search simulation method and string type tabu search simulation method respectively is that product category and quantity and scheduling are assemble sequence as the best production schedule of mixing batch assembly line of initial solution;

(4) observe the optimal scheduling process of mixing batch assembly line by the animation scheduling simulation;

(5) judge whether to satisfy client's product demand;

(6) if, think and do not satisfy product demand through the animation scheduling simulation, emulation again after then can doing suitably to revise to best planning and scheduling;

(7) if, think and satisfy product demand through the animation scheduling simulation, then can be with it as formal plan and the scheduling of preparing to assign execution;

(8), arrange production and control reaching the standard grade of product to be installed, and the assembly line translational speed control of determining during according to the animation scheduling simulation mixes the operation of batch assembly line according to formal plan and scheduling.

2, integrated optimization control method of mixing batch assembly line according to claim 1, the key step that it is characterized in that embedded tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as the initial production plan, (2) seek best plan in plan layer with tabu search then, (3) and to each adjacent plan that plan layer generates seek the scheduling that has the top performance index through high-speed simulation calculating with another tabu search, until making the production schedule and scheduling reach optimization simultaneously.

3, integrated optimization control method of mixing batch assembly line according to claim 1, it is characterized in that the key step of alternative expression tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as the initial production plan; (2) plan that has the top performance index through high-speed simulation calculating is sought in given scheduling with tabu search; (3) worked out a scheme conversely, seek through high-speed simulation with another tabu search again and calculate scheduling with top performance index; (4) be used alternatingly (2), (3) two steps until finding best planning and scheduling.

4, integrated optimization control method of mixing batch assembly line according to claim 1 is characterized in that the key step of string type tabu search simulation method is: (1) seeks a feasible scheme and scheduling with the thick production schedule as the initial production plan and with the rule-based scheduling simulation method; (2), seek rule-based scheduling and pass through the plan that high-speed simulation calculating has the top performance index with tabu search from feasible scheme; (3), use another tabu search to seek and calculate scheduling with top performance index through high-speed simulation for best plan.

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