Batch planning optimization method for mixed-model assembly processing system based on material set consistency

Abstract

The present application belongs to the technical field of production scheduling optimization, and discloses a mixed flow assembly processing system batch plan optimization method based on material matching, which comprises the following steps: establishing a mixed flow assembly processing plan integrated optimization model with the minimum finished product inventory and work-in-process inventory cost as the target; setting total cost confidence and external demand satisfaction confidence constraints to re-describe the mixed flow assembly processing plan integrated optimization model as a two-level fuzzy chance-constrained programming model; rewriting the two-level fuzzy chance-constrained programming model into a multi-level programming model; and solving the multi-level programming model based on a hybrid algorithm of a radial basis function network, a particle swarm algorithm and a cross-entropy method. The present application can maintain the lowest work-in-process inventory and finished product inventory cost, and maximally reduce product delivery delay cost.

Description

Technical Field

[0001] This invention belongs to the technical field of production scheduling optimization, and more specifically, relates to a batch planning optimization method for a mixed-flow assembly processing system based on material kitting. Background Technology

[0002] In mixed-flow assembly-processing systems, determining the batch size for assembly production often requires full consideration of the capacity constraints of the parts processing line. An inappropriate batch size may result in the parts processing line being unable to supply enough parts to the assembly line within the specified time, making the batch plan infeasible. It may also lead to excessively frequent product switching or excessively large batch sizes on the processing line, resulting in increased production preparation costs or inventory costs in work-in-process, thus making the batch plan uneconomical.

[0003] Early MRP systems did not consider the production capacity of component processing lines when processing related demands, and the feasibility of the output production plan in the actual production system was not guaranteed. Closed-loop MRP systems, which emerged in the 1970s, combined production planning with capacity planning, considering capacity constraints when formulating production plans, greatly enhancing the feasibility of the generated plans. However, for production systems consisting of product assembly lines and component processing lines, this approach of first formulating the master production schedule and then generating the component processing batch plan is a hierarchical strategy of solving sub-problems separately, and the resulting plan cannot guarantee a superior overall production cost. Considering that the uncertainty of external demand should not be simply ignored, in-depth research on the integrated optimization problem of production planning in mixed-flow assembly-processing systems under such circumstances is of great theoretical and practical significance. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a batch planning optimization method for mixed-flow assembly and processing systems based on material kitting. The aim is to determine the production batch size of each production line (product assembly line and parts processing line) in various time periods through efficient solution optimization while meeting production needs, and to maintain the lowest possible work-in-process inventory and finished goods inventory costs, thereby minimizing product delay delivery costs.

[0005] To achieve the above objectives, according to one aspect of the present invention, a batch planning optimization method for a mixed-flow assembly and processing system based on material kitting is provided. The method includes: S1: establishing an integrated optimization model for mixed-flow assembly and processing planning based on material kitting, with the goal of minimizing the cost of finished goods inventory and work-in-process inventory; S2: re-describing the integrated optimization model for mixed-flow assembly and processing planning as a two-level fuzzy chance-constrained programming model by setting total cost confidence and external demand satisfaction confidence constraints; S3: rewriting the two-level fuzzy chance-constrained programming model into a multi-level programming model based on an iterative strategy; S4: solving the sub-models in the multi-level programming model using radial basis function networks and cross-entropy methods, and solving the optimal solution of the multi-level programming model using particle swarm optimization, evaluating the fitness of the particle swarm optimization results using the uncertainty function and nonlinear function, thereby obtaining the target optimal solution of the multi-level programming model.

[0006] Preferably, the integrated optimization model for the mixed-flow assembly process planning is as follows:

[0007]

[0008] The constraints are:

[0009]

[0010]

[0011] Y l，j，t ≥0,

[0012] Y 0，k，T ≥0,

[0013]

[0014] Q l，k，t ≥0,

[0015] Q 0，k，t ≥0,

[0016] t∈{1,...,T}, k∈{1,...,K0}, l∈{1,...,L}, j∈{1,...,K l}

[0017] Where Z(Q, Y0) is the total cost corresponding to the batch plan, Q is the batch plan, Y0 is the safety stock of the processing line products, L is the number of production lines, l = 0 represents the assembly line, and T is the time period involved in the planning period; K l The number of different models of finished products / parts produced by production line l, α lkt γ represents the unit inventory holding cost of product l or component k on production line l during time period t. lktY represents the unit stockout cost of product l or component k on production line during time period t; l，k，t Y represents the net inventory of product l or component k at the end of period t on production line l. l，k，0 (l≥1) represents the safety stock of components, denoted as Y. l，0 =(Y l，1，0 , ..., Y l，k，0 ), Y0=(Y 1，0 , ..., Y L，0 ), Y 0，k，t Y represents the net inventory of product k on the assembly line at the end of period t. 0，k，0 For product safety stock, Let k be the batch size of product k that is put into production on the assembly line during time period t. The demand for product k during time period t ranges from [(1-η)]. k )d k ,(1+η k )d k ],0≤η k <1; Y l，j，t Y represents the net inventory of component j on production line l at the end of period t. l，j，0 For the safety stock of component j, For the production batch size of component j in production line l during time period t, a k，l，j Y represents the number of parts j that need to be produced by processing line l for a unit product k, and Y represents the number of finished products of each model produced by the assembly line. 0，k，T The net inventory of assembly line product k throughout the entire planning period; σ l Q is the comprehensive coefficient for the production line, and its value is determined empirically. lt =(Q 11t Q 1Kt ) T Let F be the production batch vector of production line l during time period t. l NEH (Q lt To complete Q lt The assembly / processing time, C, is obtained using the NEH algorithm. lt Q represents the available capacity of production line l during time period t; σ0 is the overall assembly line coefficient, which is determined empirically; Q 0t Let be the batch size vector of the assembly line during time period t. To complete Q 0t The assembly time C is obtained using the NEH algorithm. 0t Q represents the available capacity of the assembly line during time period t. l，k，t Q represents the production batch size of product / component k that production line l starts producing during time period t. 0，k，t Let k be the batch size of product k that is put into production on the assembly line during time period t.

[0018] Preferably, the two-level fuzzy chance-constrained programming model is as follows:

[0019]

[0020] Constraints:

[0021]

[0022]

[0023]

[0024] Cr{Y 0，k，T ≥0}≥θ,

[0025] Y l，j，t ≥0,

[0026]

[0027] Q l，k，t ≥0, Q 0，k，t ≥0,

[0028] t∈{1,...,T}, k∈{1,...,K0}, l∈{1,...,L}, j∈{1,...,K l}

[0029] in, Let Cr be the supremum of cost in the sense of a credibility measure, ε be the credibility measure, and θ be a given confidence level. This means "total cost not exceeding" The credibility of "" is no less than ε, that is It is the upper bound of the total cost in terms of credibility (not less than ε); taking the supremum means minimizing it within the objective. The preferred multilevel programming model is:

[0030]

[0031]

[0032] Constraints:

[0033]

[0034]

[0035]

[0036] Cr{Y 0，k，T ≥0}≥θ,

[0037]

[0038] Q 0，k，t ≥0,

[0039] t∈{1,...,T}, k∈{1,...,K0}, l∈{1,...,L},

[0040] in, To define the upper bound of the total cost of the assembly line in the sense of reliability measurement. For the work-in-process inventory cost of processing line l, α ljt Let Z0(Q0) be the unit inventory holding cost of component j on production line l during time period t, and let Q be the work-in-process inventory cost on the assembly line. l，j，t For the batch size of component j produced by processing line l during time period t, α 0kt γ represents the unit inventory holding cost of assembly line product k during time period t. 0kt This represents the unit stockout cost for product k on the assembly line during time period t.

[0041] Preferably, step S4 specifically includes: S41: Randomly generating an initial particle swarm corresponding to the assembly line batch in the first layer model; S42: Solving multiple sub-models using radial basis function networks and cross-entropy methods to calculate the optimal solution corresponding to the particles; S43: Evaluating particle fitness using radial basis function networks and updating particle positions; S44: Improving the PSO algorithm by combining the inertia weight descent method and considering the strategy of accepting unimproved algebras; S45: Evaluating the updated particle fitness again using radial basis function networks and updating particle positions; S46: Determining whether the maximum number of iterations has been reached; if yes, proceed to S48; if no, proceed to S47; S47: Determining whether the swarm optimal solution has been improved; if no, proceed to S42; S48: Outputting the swarm optimal particle position and the corresponding target optimal solution.

[0042] Preferably, step S42 specifically includes:

[0043] S421: The steps for solving using a radial basis function network are as follows:

[0044] Introducing helper functions First, generate a certain number of Q values ​​randomly and uniformly. t As sample inputs to the RBF network, f is calculated using the fuzzy random algorithm and the NEH algorithm. l (Q l，t The value of ) is used as the sample output, and then the RBF network is trained using a clustering method with this set of samples; the output value of the trained RBFN is then used. To replace the actual function value;

[0045] S4222: Problem of estimating the correlation between sub-models:

[0046] Define the performance function of the sub-model:

[0047]

[0048]

[0049] The operator ζ(·) is defined as:

[0050]

[0051] When there is no risk of confusion, T l，j，0 Let it be Q l，j，0 and use Q l Replace (Q) l Y l，0 (Adding a row with t=0 indicates Y) l，0 If the sub-model under consideration is: Max S(Q), then the sub-model under consideration can be written as: l )

[0052] The following estimation problem is relevant:

[0053]

[0054] Among them, S(Q) l Y l，0 W is the performance function of the sub-model. l (Q l Y l，0 Q is the reciprocal of the performance function. l ={Q l1 Q lT} represents the batch plan for processing line l, Y l，0 =(Y l，1，0 , ..., Y l，k，0 ) represents the safety stock of products / parts on the processing line, M is a sufficiently large positive number, ζ is an operator, and f l (Q l，t Let ) represent the auxiliary function value mentioned above, l(γ) represent the estimation problem, γ be a set value, and I be the indicator function. E P This means calculating the expected value based on the distribution P, where P = (P... l，j，t，q ) for Q l The discrete distribution of Y, when t=0, represents Y. l，j，0 Distribution:

[0055]

[0056] M l，j，t F represents the maximum feasible batch size for production line l when it only produces model j during time period t. l，j The maximum permissible safety stock level;

[0057] S423: Based on the estimation problem, a solution algorithm is obtained, and the solution algorithm is solved using radial basis function networks and cross-entropy method.

[0058] Step 1: Set P0 = P, s = 1;

[0059] Step 2: and according to distribution P s Randomly generate N samples Q (1) ,…,Q (N) And calculate the performance of each sample according to the performance function of the sub-model;

[0060] Step 3: Arrange the N performance values ​​in ascending order, denoted as S. (1) ≤…≤S (N) ,Pick

[0061] Step 4: Solving for the result:

[0062]

[0063] Update by pressing

[0064]

[0065] Step 5: Let s = s + 1;

[0066] Step 6: Repeat steps 2-5 until... No longer change, output

[0067]

[0068] in: This represents the performance value of the (1-ρ)Nth sample, where ρ is a parameter in the algorithm used to determine the "ρ quantile" in the sample. The "Q" estimated by the algorithm in the s-th iteration * l，k，t The probability of taking the value "q". For indicator functions, Q (i) For the i-th randomly generated sample, For indicator functions, Q (i) l，k，t Let q represent the amount of production line l in the i-th sample out of N samples, with production k in time period t. Let q be a parameter in the expression for the discrete distribution P, and α be a smoothing parameter in the algorithm, 0 ≤ α ≤ 1. * l，k，t，q；s-1 The "Q" estimated by the algorithm in the (s-1)th iteration * l，k，tThe probability that the value is "q", Q * l，k，t To take Q from the currently estimated probability distribution P. l，k，t The value with the highest probability.

[0069] Preferably, the fitness calculation in step S43 is specifically performed as follows:

[0070] Based on the currently estimated probability distribution Corresponding target value Substitute into the following formula:

[0071]

[0072] in:

[0073]

[0074]

[0075] f(Q 0t )=σ0F NEH (Q 0t )-C 0t

[0076]

[0077] Fit0(x) is the fitness function, where x represents the particle position of the solution, expressed as x = (Q 01 Q 0T ), For the introduced uncertain function, Let δ be the work-in-process inventory cost corresponding to the particle position on the processing line, and let δ be the operator, defined as follows: For the introduced uncertain function, f(Q) 0t ) is the nonlinear function introduced.

[0078] Preferably, the particle position update operation in step S43 is as follows:

[0079]

[0080]

[0081]

[0082] For a particle i in d-dimensional space, its position is denoted as x. i ={x i1 x i2 , ..., x id The flight speed is denoted as v. i ={vi1 v i2 , ..., v id Let p be the optimal position that the user has flown to. i ={p i1 p i2 , ..., p id The best position for a companion to fly over is g = {g1, g2, ..., g}. d}; ω is the inertia weight; c1 is the "cognitive acceleration coefficient"; c2 is the "social acceleration coefficient"; rand() and Rand() are two random values ​​that vary in the range [0, 1].

[0083] Preferably, step S44 specifically includes:

[0084] S441: Perform a preset number of neighborhood samplings on the updated solution, and accept the sampled solutions as solutions in the population according to the following formula:

[0085]

[0086] Where Prob(x←x′) is the probability that the sampled solution is accepted, x is the original solution, x′ is the sampled solution, Fit0(x) is the fitness function value substituted into x, Fit0(x′) is the fitness function value substituted into x′, and Γ T N is a constant. NI The algebra in which the population optimal solution has not improved continuously up to the current generation;

[0087] S442: Inertia weight ω * Update according to the following formula:

[0088]

[0089] Where ω0 is the initial inertia weight coefficient, and N is the current algebra. max For the total algebra.

[0090] Preferably, the sampling method is to take any two components of the current solution x and swap their values, or take any one component of the current solution x and randomly increase or decrease it by 1.

[0091] In summary, compared with the prior art, the batch planning optimization method for mixed-flow assembly processing systems based on material kitting provided by this invention has the following beneficial effects:

[0092] 1. After establishing a mixed-flow assembly-processing plan integrated optimization model based on material kitting, this application, considering the uncertainty of actual work requirements, reformulates the model into a two-level fuzzy chance-constrained programming model, and rewrites the planning problem into a multi-level programming form for solution. The planning is more reasonable and has stronger engineering practical significance.

[0093] 2. The hybrid algorithm proposed in this application, based on radial basis function network (RBFN), particle swarm optimization (PSO) and cross-entropy method (CE), has high efficiency in solving batch optimization problems of processing lines under relevant requirements, and at the same time, it significantly reduces the work-in-process inventory cost and the total cost. Attached Figure Description

[0094] Figure 1 This is a flowchart illustrating the steps of the batch planning optimization method for a mixed-flow assembly and processing system based on material kitting in this application embodiment;

[0095] Figure 2 This is a flowchart of a batch planning optimization method for a mixed-flow assembly and processing system based on material kitting, according to an embodiment of this application.

[0096] Figure 3 This is a flowchart of a hybrid algorithm based on radial basis function networks, particle swarm optimization, and cross-entropy method according to an embodiment of this application.

[0097] Figure 4 In the table, (a) represents the projected daily demand during the week, and (b) represents the optimal batch plan.

[0098] Figure 5 This is the final production plan calculated by the hybrid algorithm in the embodiments of this application. Detailed Implementation

[0099] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0100] The batch planning optimization method for mixed-flow assembly and processing systems based on material kitting provided by this invention, such as... Figure 1 and Figure 2 As shown, the main steps include S1 to S4.

[0101] S1: With the goal of minimizing the cost of finished goods inventory and work-in-process inventory, an integrated optimization model for mixed-flow assembly and processing planning is established based on material availability.

[0102] Material completeness refers to the following: for a single processing line, when it has completed the processing of all the parts of a certain type required for a certain assembly operation, it can be considered to be in a "complete" state; however, if the parts required for the assembly operation are not completed on other processing lines, the assembly operation obviously has to wait, and the parts required for the operation are in a "discomplete" state.

[0103] As a further preferred embodiment, the integrated optimization model for the mixed-flow assembly process planning is as follows:

[0104]

[0105] The constraints are:

[0106]

[0107]

[0108] Y l，j，t ≥0, (4)

[0109] Y 0，k，T ≥0, (5)

[0110]

[0111] Q l，k，t ≥0, Q 0，k，t ≥0, (7)

[0112] t∈{1,...,T}, k∈{1,...,k0}, l∈{1,...,L}, j∈{1,...,K l} (8)

[0113] Where Z(Q, Y0) is the total cost corresponding to the batch plan, Q is the batch plan, Y0 is the safety stock of the processing line products, L is the number of production lines, l = 0 represents the assembly line, and T is the time period involved in the planning period; K l The number of different models of finished products / parts produced by production line l, α lkt γ represents the unit inventory holding cost of product l or component k on production line l during time period t. lkt Y represents the unit stockout cost of product l or component k on production line during time period t; l，k，t Y represents the net inventory of product l or component k at the end of period t on production line l. l，k，0 (l≥1) represents the safety stock of components, denoted as Y. l，0 =(Y l，1，0 , ..., Y l，k，0 ), Y0=(Y 1，0 , ..., Y L，0 ), Y 0，k，tY represents the net inventory of product k on the assembly line at the end of period t. 0，k，0 For product safety stock, Let k be the batch size of product k that is put into production on the assembly line during time period t. The demand for product k during time period t ranges from [(1-η)]. k )d k , (1+η k )d k ],0≤η k <1; Y l，j，t Y represents the net inventory of component j on production line l at the end of period t. l，j，0 For the safety stock of component j, For the production batch size of component j in production line l during time period t, a k，l，j Y represents the number of parts j that need to be produced by processing line l for a unit product k, and Y represents the number of finished products of each model produced by the assembly line. 0，k，T The net inventory of assembly line product k throughout the entire planning period; σ l Q is the comprehensive coefficient for the production line, and its value is determined empirically. lt =(Q l1t Q lKt ) T Let F be the production batch vector of production line l during time period t. l NEH (Q lt To complete Q lt The assembly / processing time, C, is obtained using the NEH algorithm. lt Q represents the available capacity of production line l during time period t; σ0 is the overall assembly line coefficient, which is determined empirically; Q 0t Let be the batch size vector of the assembly line during time period t. To complete Q 0t The assembly time C is obtained using the NEH algorithm. 0t Q represents the available capacity of the assembly line during time period t. l，k，t Q represents the production batch size of product / component k that production line l starts producing during time period t. 0，k，t Let be the batch size of product k that the assembly line puts into production during time period t. Equation (1) represents the objective of minimizing the total finished goods inventory cost, finished goods delayed delivery cost, and work-in-process inventory cost corresponding to the batch plan. The first term on the right side represents the inventory holding cost, and the second term on the right side represents the delayed delivery cost. Constraint (2) is the material conservation constraint for the assembly line; constraint (3) is the material conservation constraint for the processing line; constraint (4) indicates that there should be no shortage of parts required for assembly; constraint (5) indicates that all demand during the planning period will eventually be met; constraint (6) is the capacity constraint; constraint (7) is the non-negativity constraint; and equation (8) represents the range of each indicator in the above constraints.

[0114] S2: Set the total cost confidence level and the confidence level that all external requirements are met to re-describe the mixed-flow assembly processing plan integrated optimization model as a two-level fuzzy chance-constrained programming model.

[0115] Since the above model contains uncertainties, as a further preferred option, the restated two-level fuzzy chance-constrained programming model is as follows:

[0116]

[0117] Constraints:

[0118]

[0119]

[0120]

[0121] Cr{Y 0，k，T ≥0}≥θ,

[0122] Y l，j，t ≥0, (11)

[0123]

[0124] Q l，k，t ≥0, Q 0,k，t ≥0,

[0125] t∈{1,...,T}, k∈{1,...,K0}, l∈{1,...,L}, j∈{1,...,K l}

[0126] in, Let Cr be the supremum of cost in the sense of a credibility measure, ε be the credibility measure, and θ be a given confidence level. This means "total cost not exceeding" The credibility of "" is no less than ε, that is It is the upper bound of the total cost in the sense of credibility (not less than ε); taking the supremum means minimizing it in the objective.

[0127] S3: Based on the iterative strategy, the two-level fuzzy chance-constrained programming model is rewritten into a multi-level programming model.

[0128] Since the integrated optimization model of the mixed-flow assembly-processing system production plan involves multiple production lines and there is a dependency between the processing line and the assembly line (see the third term in equation (3)), it belongs to a two-level batch problem. Therefore, the model cannot be decomposed into several independent single-level models for separate solutions. The solution strategies for multi-level batch problems can be divided into three categories: (1) hierarchical method, (2) iterative method, and (3) full-space method. The iterative method has higher efficiency and better quality. This invention uses the iterative strategy to solve this multi-level batch optimization problem.

[0129] As a further preferred option, the rewritten multi-level programming form is as follows:

[0130]

[0131]

[0132] Constraints:

[0133]

[0134]

[0135]

[0136] Cr{Y 0，k，T ≥0}≥θ, (16)

[0137]

[0138] Q 0，k，t ≥0, (18)

[0139] t∈{1,...,T}, k∈{1,...,K0}, l∈{1,...,L},

[0140] in, To define the upper bound of the total cost of the assembly line in the sense of reliability measurement. For the work-in-process inventory cost of processing line l, α ljt Let Z0(Q0) be the unit inventory holding cost of component j on production line l during time period t, and let Q be the work-in-process inventory cost on the assembly line. l，j，t For the batch size of component j produced by processing line l during time period t, α 0kt γ represents the unit inventory holding cost of assembly line product k during time period t. 0kt This represents the unit stockout cost for product k on the assembly line during time period t.

[0141] Equation (12) decomposes the objective function into two parts, where the second part on the right is the optimal solution of L sub-models, and the sub-models aim to minimize the work-in-process inventory cost of each processing line; Equation (13) is the objective function of the assembly line, and Equation (14) represents the confidence constraint on the total cost of the assembly line.

[0142] S4: The sub-models in the multi-level programming model are solved using radial basis function networks and cross-entropy method, and the optimal solution of the multi-level programming model is solved using particle swarm optimization algorithm. The fitness of the particle swarm optimization algorithm result is evaluated using the uncertainty function and nonlinear function, thereby obtaining the target optimal solution of the multi-level programming model.

[0143] like Figure 3 As shown, step S4 specifically includes:

[0144] S41: Randomly generate the initial particle swarm corresponding to the assembly line batch in the first layer model.

[0145] S42: For multiple sub-models, radial basis function networks and cross-entropy methods are used to solve the problem and calculate the optimal solution for each particle.

[0146] Step S42 specifically includes:

[0147] S421: The steps for solving using a radial basis function network are as follows:

[0148] For L sub-models, an algorithm based on RFBN and CE is used for solution, where an auxiliary function is introduced to account for capacity constraints:

[0149]

[0150] First, generate a certain number of Q values ​​randomly and uniformly. t As sample inputs to the RBF network, f is calculated using the fuzzy random algorithm and the NEH algorithm. l (Q l，t The value of ) is used as the sample output, and then the RBF network is trained using a clustering method with this set of samples; the output value of the trained RBFN is then used. To replace the actual function value.

[0151] S422: Problem of estimating sub-model associations:

[0152] Define the performance function of the sub-model:

[0153]

[0154]

[0155] The operator ζ(·) is defined as:

[0156]

[0157] When there is no risk of confusion, Y l，j，0 Let it be Q l，j，0 and use Q l Replace (Q) l Y l，0 (Adding a row with t=0 indicates Y) l，0 If ), then the sub-model under consideration can be written as:

[0158] MaxS(Q l ) (twenty two)

[0159] The following estimation problem is relevant:

[0160]

[0161] Among them, S(Q) l Y l，0 W is the performance function of the sub-model. l (Q l Y l，0 Q is the reciprocal of the performance function. l ={Q l1 Q lT} represents the batch plan for processing line l, Y l，0 =(Y l，1，0 , ..., Y l，k，0 ) represents the safety stock of products / parts on the processing line, M is a sufficiently large positive number, ζ is an operator, and f l (Q l，t Let ) represent the auxiliary function value mentioned above, l(γ) represent the estimation problem, γ be a set value, and I be the indicator function. E P This means calculating the expected value based on the distribution P, where P = (P... l，j，t，q ) for Q l The discrete distribution of Y, when t=0, represents Y. l，j，0 Distribution:

[0162]

[0163] M l，j，t F represents the maximum feasible batch size for production line l when it only produces model j during time period t. l，j The maximum permissible safety stock level;

[0164] S423: Based on the estimation problem, a solution algorithm is obtained, and the solution algorithm is solved using radial basis function networks and cross-entropy method.

[0165] Step 1: Set P0 = P, s = 1;

[0166] Step 2: and according to distribution P s Randomly generate N samples Q (1) ,…,Q (N) And calculate the performance of each sample according to the performance function of the sub-model;

[0167] Step 3: Arrange the N performance values ​​in ascending order, denoted as S. (1) ≤…≤S (N) ,Pick

[0168] Step 4: Solving for the result:

[0169]

[0170] renew

[0171]

[0172] Step 5: Let s = s + 1;

[0173] Step 6: Repeat steps 2-5 until... No longer change, output

[0174]

[0175] in: This represents the performance value of the (1-ρ)Nth sample, where ρ is a parameter in the algorithm used to determine the "ρ quantile" in the sample. The "Q" estimated by the algorithm in the s-th iteration * l，k，t The probability of taking the value "q". For indicator functions, Q (i) For the i-th randomly generated sample, For indicator functions, Q (i) l，k，t Let q represent the amount of production line l in the i-th sample out of N samples, with production k in time period t. Let q be a parameter in the expression for the discrete distribution P, and α be a smoothing parameter in the algorithm, 0 ≤ α ≤ 1. * l，k，t，q；s-1 The "Q" estimated by the algorithm in the (s-1)th iteration * l，k，t The probability that the value is "q", Q * l，k，t To take Q from the currently estimated probability distribution P. l，k，t The value with the highest probability.

[0176] S43: Use radial basis function networks to evaluate particle fitness and update particle positions.

[0177] The specific operation for solving the fitness problem is to calculate the fitness based on the currently estimated probability distribution. Corresponding target value Substitute into the following formula:

[0178]

[0179] in:

[0180]

[0181]

[0182] f(Q 0t )=σ0F NEH (Q 0t )-C 0t (28)

[0183]

[0184] Fit0(x) is the fitness function, where x represents the particle position of the solution, expressed as x = (Q 01 Q 0T ), For the introduced uncertain function, Let δ be the work-in-process inventory cost corresponding to the particle position on the processing line, and let δ be the operator, defined as follows: For the introduced uncertain function, f(Q) 0t ) represents the introduced nonlinear function;

[0185] To prevent excessive speed from causing slow algorithm convergence, the speed is generally limited to a certain range. The particle position update process in the algorithm is as follows:

[0186]

[0187]

[0188] x i * =[(x i +v i * (32)

[0189] Here, for a particle i in d-dimensional space, its position is denoted as x. i ={x i1 x i2 , ..., x id The flight speed is denoted as v.i ={v i1 v i2 , ..., v id Let p be the optimal position that the user has flown to. i =[p i1 p i2 , ..., p id The best position for a companion to fly over is g = {g1, g2, ..., g}. d}; ω is the inertia weight; c1 is the "cognitive acceleration coefficient"; c2 is the "social acceleration coefficient"; rand() and Rand() are two random values ​​that vary in the range [0, 1].

[0190] S44: Improve the PSO algorithm by combining the inertia weight descent method with a strategy that considers accepting the unimproved algebra.

[0191] Step S44 specifically includes:

[0192] S441: Perform a preset number of neighborhood samplings on the updated solution, and accept the sampled solutions as solutions in the population according to the following formula:

[0193]

[0194] Where Prob(x←x′) is the probability that the sampled solution is accepted, x is the original solution, x′ is the sampled solution, Fit0(x) is the fitness function value substituted into x, Fit0(x′) is the fitness function value substituted into x′, and Γ T N is a constant. NI The algebra in which the population optimal solution has not improved continuously up to the current generation;

[0195] The sampling method is to take any two components of the current solution x and swap their values, or take any one component of the current solution x and randomly increase or decrease it by 1.

[0196] S442: Inertia weight ω * Update according to the following formula:

[0197]

[0198] Where ω0 is the initial inertia weight coefficient, and N is the current algebra. max For the total algebra.

[0199] S45: The updated ion fitness is re-evaluated using a radial basis function network, and the particle positions are updated. After updating the particle positions, the neighborhood of the updated particles is searched according to the improved method described above. During the search process, the cross-entropy method is still used to solve the sub-model.

[0200] S46: Determine if the maximum number of iterations has been reached. If yes, go to S48; otherwise, go to S47.

[0201] S47: Determine whether the group optimal solution has been improved. If not, go to S42.

[0202] S48: Output the optimal particle position of the swarm and the corresponding optimal solution for the objective.

[0203] Example

[0204] The daily demand for engines produced by Chery's Second Engine Company is typically determined by the demand plan formulated at the end of the previous week, but actual demand fluctuates. An accurate daily production plan is only available near the end of the previous day. To avoid drastic fluctuations in demand, the difference between actual demand and the weekly plan is limited to an agreed-upon range. In addition to the assembly line, five processing lines for key components such as cylinder heads, cylinder blocks, connecting rods, crankshafts, and camshafts ("5C lines") must also be considered. The assembly line needs to comprehensively consider finished goods inventory information to determine its batch planning, and each processing line needs to comprehensively determine its corresponding production batch plan based on assembly line information and its own work-in-process inventory data to ensure sufficient supply to the assembly line.

[0205] Taking the finished product demand for a certain week as an example, the estimated daily demand d during that week. kt like Figure 4 (a).

[0206] On the assembly line, the unit inventory holding cost and the unit stockout cost are respectively α k = 8.5 yuan / (piece·day) and γ k = 19.0 yuan / (piece·day) As agreed, the actual demand fluctuation will not exceed 5% of the expected amount (η = 0.05). The membership function of the fuzzy variable used to characterize this uncertainty is (x ∈ N):

[0207]

[0208] The workshop must refer to this demand plan to formulate batch production plans for each working day next week. Considering the relatively stable operation of this assembly workshop, we take σ = 1.

[0209] Based on the above data, randomly generated sample inputs are used, and corresponding results are obtained through fuzzy simulation technology and the NEH algorithm. The values ​​of f were used as training samples for the RBFN, and the training and approximation effects were statistically analyzed when the network contained different numbers of hidden neurons. The results showed that the average relative error rate was [missing information - likely a percentage] when the sample size was 4000 and the number of hidden neurons was 400. The minimum is 0.82. The value is 0.80, and f is 0.79.

[0210] Taking finished goods inventory and overtime costs into account in conjunction with the above requirements, the assembly line batch plan was optimized. Algorithm parameters were selected through trial and error: particle swarm size 600, maximum iterations 800, v max Take 5, C0=8000, κ=1.0, Γ T =10 -3 The neighborhood search length is 50. The resulting optimal batch plan is as follows: Figure 4 (b)

[0211] On the processing line, taking into account all kinds of disturbances that objectively exist in the workshop, the comprehensive coefficients σ0 and σ1 in formula (6) are set as follows: σ0 = 1.05 for assembly line, and σ for cylinder block line, cylinder head line, crankshaft axis, camshaft axis and connecting rod line are 1.11, 1.09, 1.11, 1.11 and 1.05 respectively.

[0212] The parameters of the RBFN in the sub-model were determined through trial and error, including the sample size, number of hidden layer neurons, and average relative error rate for each processing line. The smoothing coefficient in the cross-entropy algorithm for solving the sub-model is set to 0.7. Figure 2 Based on the assembly line batch plan, an iterative strategy is applied using a hybrid algorithm based on RBFN, CE, and PSO to solve the problem. The basic process is as follows: Figure 2 The particle swarm size is 800, the maximum number of iterations is 1200, and v max Take 5, Γ T =10 -3 The neighborhood search length is 100, and the output obtained from training the RBF network is used. And f is applied to Equation (25) to calculate particle fitness; particle position update refers to Equation (30); sampling acceptance probability refers to Equation (33); inertia weight is updated according to Equation (34). The resulting optimal batch plan is as follows: Figure 5 .

[0213] The company's original optimal batch planning critical cost for finished goods was 3245.20 yuan, and the cost of work-in-process inventory was 5663.20 yuan. In comparison, the method adopted in this invention reduces the cost of work-in-process inventory by 54.21% and the total cost by 33.39%. It is evident that this method can further reduce costs.

[0214] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A batch planning optimization method for a mixed-flow assembly and processing system based on material kitting, characterized in that, The method includes: S1: To minimize the cost of finished goods inventory and work-in-process inventory, an integrated optimization model for mixed-flow assembly and processing planning is established based on material availability. S2: Set the total cost confidence level and the confidence level that all external demands are met to re-describe the mixed-flow assembly processing plan integrated optimization model as a two-level fuzzy chance-constrained programming model; S3: Based on the iterative strategy, the two-level fuzzy chance-constrained programming model is rewritten into a multi-level programming model; S4: The sub-models in the multi-level programming model are solved using radial basis function networks and cross-entropy methods, and the optimal solution of the multi-level programming model is solved using particle swarm optimization. The fitness of the particle swarm optimization results is evaluated using uncertainty functions and nonlinear functions, thereby obtaining the target optimal solution of the multi-level programming model. The integrated optimization model for the mixed-flow assembly process planning is as follows: The constraints are: in, This represents the total cost corresponding to the batch plan. For batch planning, The safety stock of products on the processing line, where L is the number of production lines. This indicates the assembly line, where T represents the time period involved in the planning period; For production line The number and model of finished products / parts produced. For production line Product or component k exist t Unit inventory holding cost for a period of time For production line Product or component k exist t Unit out-of-stock cost during the period For production line Products / Components k exist t Net inventory at the end of the period; For safety stock of spare parts, record , , For assembly line products k exist t Net inventory at the end of the period, For product safety stock, For the assembly line t Products put into production during specific periods k Production volume For products k During the period t The requirement is that the value range is [(1-η k )d k ,(1+η k )d k ],0≤η k < 1; For production line Components j exist t Net inventory at the end of the period, For parts j Safety stock, For production line During the period t Parts put into production j Production volume For unit products k Processing line required manufactured parts j The quantity refers to the number of finished product models produced on the assembly line. For assembly line products k Net inventory for the entire planning period; For production line The comprehensive coefficient is determined based on experience. For production line exist t Production batch vector within a time period To complete Assembly / processing time obtained using the NEH algorithm For production line During the period t Available capabilities; This is the overall coefficient for the assembly line, and its value is determined based on experience. For the assembly line t Production batch vector within a time period To complete Assembly time obtained using the NEH algorithm For the assembly line t Available capabilities during the time period; For production line exist t Products / components put into production during specific periods k Production volume Let k be the batch size of product k that is put into production on the assembly line during time period t.

2. The method according to claim 1, characterized in that, The two-level fuzzy chance-constrained programming model is as follows: Constraints: in, To define the upper bound of cost in the sense of credibility measurement, As a measure of credibility, and For a given confidence level; This means "total cost not exceeding" The credibility of "" is no less than ε, that is It is the upper bound of the total cost in the sense of credibility; taking the supremum means minimizing it in the objective.

3. The method according to claim 2, characterized in that, The multi-level programming model is as follows: Constraints: in, To define the upper bound of the total cost of the assembly line in the sense of reliability measurement. For processing line Work-in-process inventory costs For production line Components j The unit inventory holding cost in time period t, This refers to the cost of work-in-process inventory on the assembly line. For processing line Parts production will begin during time period t. j Production volume For assembly line products k exist t Unit inventory holding cost for a period of time For assembly line products k exist t Unit out-of-stock cost for a given period.

4. The method according to claim 1, characterized in that, Step S4 specifically includes: S41: Randomly generate the initial particle swarm corresponding to the assembly line batch in the first layer model; S42: For multiple sub-models, radial basis function networks and cross-entropy methods are used to solve the problem and calculate the optimal solution for each particle. S43: Use radial basis function networks to evaluate particle fitness and update particle positions; S44: Improve the PSO algorithm by combining the inertia weight descent method and considering the strategy of accepting the continuous unimproved algebra; S45: The updated ion fitness is re-evaluated using a radial basis function network, and the particle positions are updated. S46: Determine if the maximum number of iterations has been reached. If yes, go to S48; otherwise, go to S47. S47: Determine whether the group optimal solution has been improved. If not, go to S42. S48: Output the optimal particle position of the swarm and the corresponding optimal solution for the objective.

5. The method according to claim 4, characterized in that, Step S42 specifically includes: S421: The steps for solving using a radial basis function network are as follows: Introducing helper functions First, a certain number of uniformly and randomly generated... As sample inputs to the RBF network, fuzzy random algorithms and the NEH algorithm are used to compute... The values ​​of these samples are used as the output samples, and then the RBF network is trained using a clustering method based on these samples; the output values ​​of the trained RBFN are then used. To replace the actual function value; S4222: Problem of estimating the correlation between sub-models: Define the performance function of the sub-model: The operator ζ(·) is defined as: When there is no risk of confusion, Recorded as and use replace Add rows where t = 0. Then the sub-model under consideration can be written as: Max The following estimation problem is relevant: in, This is the performance function of the sub-model. The reciprocal of the performance function. For processing line Batch planning, For processing line Safety stock of products / components For sufficiently large positive numbers, For operators, The auxiliary function value mentioned above, To estimate the problem, For a set value, For indicator functions, , This means calculating the expected value based on the distribution P. for The discrete distribution, when t = 0, represents Distribution: ， For production line During the period t Only models put into production j The maximum feasible batch size at that time. The maximum permissible safety stock level; S423: Based on the estimation problem, a solution algorithm is obtained, and the solution algorithm is solved using radial basis function networks and cross-entropy method. Step 1: Set P0 = P, s = 1; Step 2: According to distribution P s Randomly generate N samples Q (1) ,…,Q (N) And calculate the performance of each sample according to the performance function of the sub-model; Step 3: Arrange the N performance values ​​in ascending order, denoted as S. (1) ≤…≤S (N) ,Pick ; Step 4: Solving for the result: Update by pressing : Step 5: Let s = s+1; Step 6: Repeat steps 2-5 until... No longer change, output : in: , indicating the (1- N performance values, This is a parameter in the algorithm used to extract "from the sample" quantile", The algorithm estimates " in the s-th iteration" Values The probability of " For indicator functions, , For the randomly generated number i One sample, For indicator functions, , Represents the Nth sample i Production lines in the sample exist t Production in a specific period k The amount, Let be the parameter in the expression for the discrete distribution P. For smoothing parameters in the algorithm, , The algorithm estimates " in the (s-1)th iteration" Values The probability of " Based on the currently estimated probability distribution Take the distribution The value with the highest probability.

6. The method according to claim 5, characterized in that, The specific steps for solving the fitness problem in step S43 are as follows: Based on the currently estimated probability distribution Corresponding target value Substitute into the following formula: in: For the fitness function, Let represent the particle position of the solution, denoted as , For the introduced uncertain function, This represents the work-in-process inventory cost corresponding to the particle's position on the processing line. For an operator, it is defined as follows: , For the introduced uncertain function, This is the nonlinear function introduced.

7. The method according to claim 4, characterized in that, The particle position update operation in step S43 is as follows: For a particle in d-dimensional space Its position is recorded as Flight speed is denoted as Record the best position that you have ever flown over as The best position for your companion to fly over is ω represents the inertia weight. c 1 represents the "cognitive acceleration coefficient"; c 2 represents the "social acceleration coefficient"; rand() and Rand() are two random values ​​that vary in the range [0, 1].

8. The method according to claim 4, characterized in that, Step S44 specifically includes: S441: Perform a preset number of neighborhood samplings on the updated solution. The sampled solutions are accepted as solutions in the population according to the following probability: in, Let be the probability that the sampled solution is accepted. The original solution, The solution obtained from sampling, To substitute the fitness function value of x, For substitution The fitness function value, It is a constant. The algebra in which the population optimal solution has not improved continuously up to the current generation; S442: Inertia Weight Update according to the following formula: Where ω0 is the initial inertia weight coefficient, and N is the current algebra. max For the total algebra.

9. The method according to claim 8, characterized in that, The sampling method is to take any two components of the current solution x and swap their values, or take any one component of the current solution x and randomly increase or decrease it by 1.

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