A hybrid uncertain batch decision method for material requirement planning in smart factories

Abstract

The present invention discloses a mixed uncertain intelligent factory material requirement planning batch decision method. Combining the uncertainty of the external environment and production system in actual production, aiming at the uncertainty of MRP batch decision in the intelligent factory, an MRP model with mixed uncertain parameters is constructed. The credibility and probability are used to measure the uncertain parameters, and a mixed chance constraint programming model is constructed, and then the MRP model with mixed uncertain parameters is reconstructed. By converting the objective function, fuzzy chance constraints and random chance constraints in the model into equivalent deterministic forms, a deterministic equivalent mixed integer programming model is formed, and the solution is obtained by conventional methods. The method introduces mixed chance constraint programming into the material requirement planning in the intelligent factory, fully considers the actual production situation of the factory, meets the actual requirements of the factory production, and helps to solve the actual material requirement planning batch decision problem.

Description

Technical Field

[0001] The present invention relates to the technical field of batch decision-making for material requirement planning, and in particular to a mixed uncertain intelligent factory material requirement planning batch decision-making method. Background Art

[0002] Material Requirements Planning (MRP) is the core of the production planning system, which determines the production batches and start times of all intermediate products that will be used in the production of final products to ensure the completion of the master production plan. Most of the previous studies on MRP were aimed at deterministic situations, while in actual production systems, especially in Industry 4.0 and smart manufacturing environments, some input parameters, such as market demand, cost coefficients, time coefficients, and machine capabilities, are often imprecise or changing. Because uncertainty is widely present in the external environment and production systems, imprecise parameters often manifest themselves in different forms, that is, decision makers may encounter a mixed uncertain environment where ambiguity and randomness coexist in the decision-making process. In smart factories, customer demand and production status change over time, which increases the uncertainty of MRP batch decisions. Summary of the invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a hybrid uncertain intelligent factory material requirement planning batch decision method, which develops a hybrid chance constraint programming (HCCP) model, takes into account the fuzziness and randomness in the decision-making process, minimizes the total production cost, and is used for intelligent factory material requirement planning batch decision. In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0004] A mixed uncertain intelligent factory material requirement planning batch decision method includes the following steps:

[0005] Step 1: Construct an original material requirement planning (MRP) model with mixed uncertain parameters;

[0006] Step 2: Construct a hybrid chance-constrained programming (HCCP) model;

[0007] Step 3: Defuzzify the HCCP model and transform it into a deterministic equivalent mixed integer programming (MIP) model. Solve the MIP model to obtain the batch decision of each material.

[0008] The symbol definition in the MRP model with mixed uncertain parameters in step 1; according to the characteristics of batch decision of material requirement planning with mixed uncertain parameters, establishing constraint conditions and objective function;

[0009] Step 1, the MRP problem is described as a multi-product, multi-level and multi-period capacity batch decision model, whose goal is to meet time-varying demand by balancing production quantity or batch, inventory level and other manufacturing parameters within a limited planning range in an uncertain environment;

[0010] Step 2, symbol definition in the MRP model with mixed uncertain parameters (parameters with "~" symbol are uncertain parameters):

[0011] i: material type number (i=1, .., N);

[0012] t: planning cycle number (t=1, .., T);

[0013] k: machine number;

[0014] G i : The direct successor set of material i;

[0015] κ k : The set of materials produced on resource k;

[0016] N: Quantity of material type, including final product, subassembly, components, and parts;

[0017] F: the quantity of the final product;

[0018] T: planning cycle;

[0019] The demand for final products within the planning period t;

[0020] The manufacturing cost per unit of material i in planning period t;

[0021] Unit inventory holding cost of material i during planning period t;

[0022] The preparation cost of producing material i within planning period t;

[0023] C kt : The available processing time of resource k in planning period t;

[0024] r ij : The quantity of material i directly required to produce a unit of material j;

[0025] The production time required to produce a unit of material i on resource k;

[0026] The preparation time for producing material i on resource k;

[0027] M: preset large number;

[0028] Q it : The production quantity of material i in the planning period t;

[0029] I it : Inventory level of material i in planning period t;

[0030] Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t;

[0031] Step 3, establish constraints based on the characteristics of material requirement planning:

[0032] Constraint 1: Inventory balance constraint for final products

[0033]

[0034] Constraint 2: Inventory balance constraint for components or parts that meet the relevant requirements of material j

[0035]

[0036] Constraint 3: The capacity consumption of production activities and the preparation time of resource k will never exceed the available capacity within the planning period t

[0037]

[0038] Constraint 4: If material i is produced within planning period t, then variable Y is guaranteed to be prepared it Equal to 1

[0039]

[0040] Constraint 5: Decision variable Q it , I it The value is not negative

[0041]

[0042] Constraint 6: Variable Y it Value is binary

[0043]

[0044] Step 4, establish the objective function of the model, the expression is as follows:

[0045]

[0046] In the step 2, according to the type of uncertain parameters, a hybrid chance constraint programming model is constructed by using the method of credibility measurement fuzzy variables and probability measurement random variables to reconstruct the MRP model with hybrid uncertain parameters;

[0047] Step 1, reconstruct the symbol definition in the MRP model with mixed uncertain parameters according to the hybrid chance constraint programming model (the parameters with the "~" symbol are uncertain parameters):

[0048] i: material type number (i=1, .., N);

[0049] t: planning cycle number (t=1, .., T);

[0050] k: machine number;

[0051] G i : The direct successor set of material i;

[0052] κ k : The set of materials produced on resource k;

[0053] N: Quantity of material type, including final product, subassembly, components, and parts;

[0054] F: the quantity of the final product;

[0055] T: planning cycle;

[0056] The demand for final products within the planning period t;

[0057] The manufacturing cost per unit of material i in planning period t;

[0058] Unit inventory holding cost of material i during planning period t;

[0059] The preparation cost of producing material i within planning period t;

[0060] C kt : The available processing time of resource k in planning period t;

[0061] r ij : The quantity of material i directly required to produce a unit of material j;

[0062] The production time required to produce a unit of material i on resource k;

[0063] The preparation time for producing material i on resource k;

[0064] M: preset large number;

[0065] Q it : The production quantity of material i in the planning period t;

[0066] I it : Inventory level of material i in planning period t;

[0067] Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t;

[0068] x: decision variable;

[0069] ξ: fuzzy variable;

[0070] η: random variable;

[0071] α: the predetermined confidence level of the fuzzy chance constraint (0≤α≤1);

[0072] γ, γ kt : The predetermined confidence level of the fuzzy chance constraint (0≤γ, γ kt ≤1);

[0073] β, β it : The predetermined confidence level of the random chance constraint (0≤β, β it ≤1);

[0074] Step 2, using the method of credibility measurement fuzzy variables and probability measurement random variables, construct the fuzzy chance constraints and random chance constraints in the hybrid chance constraint programming (HCCP) model. The objective function of the general HCCP model is as follows:

[0075] min f(x,ξ) (8)

[0076] Its constraints are

[0077] Cr{g i (x,ξ)≤0,i=1,2,…,s}≥α (9)

[0078] Pr{h j (x, η)≤0,j=1,2,…,t}≥β (10)

[0079] Where f is the objective function, and the constraint (9) Cr{g i (x,ξ)≤0,i=1,2,…,s} represents the fuzzy chance constraint based on credibility measure. Constraint (10)Pr{h j (x,η)≤0,j=1,2,…,t} represents a random chance constraint based on a probability metric. If α=1 or β=1, the corresponding chance constraint is equivalent to a deterministic one;

[0080] Since there are uncertain parameters in the objective function, it needs to be converted into its equivalent clear form to find its minimum optimal solution. The original objective function can be replaced by the following equivalent objectives and fuzzy constraints:

[0081]

[0082]

[0083] in is the equivalent optimization objective, and γ is the confidence of constraint (12).

[0084] Step 3, reconstruct the MRP model equation of mixed uncertain parameters:

[0085] As mentioned above, the objective function (7) and constraints (3) is assumed to be a fuzzy variable, and the requirement in constraint (1) It is defined as a random variable with a known probability distribution. Due to mixed uncertainty, the original model cannot be solved by traditional mathematical programming methods. In order to deal with mixed uncertainty, the HCCP method is to construct an optimization model for the MRP problem with mixed uncertainty. According to the general form of the HCCP model, the MRP model with mixed uncertain parameters can be restated as the following HCCP model:

[0086] The objective function of reconstructing the MRP model with mixed uncertain parameters is:

[0087]

[0088] Its constraints are

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] Among them, constraints (14) and (16) are fuzzy chance constraints based on credibility measurement, and constraint (15) is a random chance constraint based on probability measurement.

[0097] In step 3, the objective function, fuzzy chance constraints and random chance constraints in the model are converted into equivalent deterministic forms to form a deterministic equivalent mixed integer programming model, which is solved using conventional methods;

[0098] Step 1, symbolic definition in the deterministic equivalent mixed integer programming model (parameters with the "~" symbol are uncertain parameters):

[0099] i: material type number (i=1, .., N);

[0100] t: planning cycle number (t=1, .., T);

[0101] k: machine number;

[0102] G i : The direct successor set of material i;

[0103] κ k : The set of materials produced on resource k;

[0104] N: Quantity of material type, including final product, subassembly, components, and parts;

[0105] F: the quantity of the final product;

[0106] T: planning cycle;

[0107] C kt : The available processing time of resource k in planning period t;

[0108] r ij : The quantity of material i directly required to produce a unit of material j;

[0109] The production time required to produce a unit of material i on resource k;

[0110] The preparation time for producing material i on resource k;

[0111] M: preset large number;

[0112] Q it : The production quantity of material i in the planning period t;

[0113] I it : Inventory level of material i in planning period t;

[0114] Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t;

[0115] x: decision variable;

[0116] ξ: fuzzy variable;

[0117] η: random variable;

[0118] α: the predetermined confidence level of the fuzzy chance constraint (0≤α≤1);

[0119] γ, γ kt : The predetermined confidence level of the fuzzy chance constraint (0≤γ, γ kt ≤1);

[0120] β, β it : The predetermined confidence level of the random chance constraint (0≤β, β it ≤1);

[0121] Φ: The probability distribution of

[0122] Φ -1 : inverse function of Φ;

[0123] μ it : The mathematical expectation of

[0124] σ it : The standard deviation of

[0125] f 1 : The lower bound of triangular fuzzy numbers;

[0126] f 2 : The most likely estimate of a triangular fuzzy number;

[0127] f 3 : The upper bound of triangular fuzzy numbers;

[0128] Step 2, deterministic processing of the objective function:

[0129] The objective function is a linear non-negative function whose value is a triangular fuzzy number, which is expressed by a triangular fuzzy number, that is, f(x, ξ) = (f 1 , f 2 , f 3 ), let f 1 <f 2 <f 3 , where x and ξ represent the decision vector and fuzzy vector respectively. In actual production planning decisions, the credibility value greater than or equal to 0.5 is of great significance to decision makers. This means that the acceptable confidence range is greater than or equal to 0.5, and the constraint equation (14) can be transformed into the following clear equivalent form: The confidence level is set to α ≥ 0.5.

[0130] Step 3, convert the fuzzy chance constraints into clear equivalent constraints:

[0131] Similarly, the confidence γ in constraint equation (16) kt It should also be greater than or equal to 0.5. The constraint equation (16) can be transformed into the following clear equivalent form:

[0132]

[0133] Step 4, convert the random chance constraint into a clear equivalent constraint:

[0134] Constraint equation (15) is a probability-based chance constraint. Here, it is assumed that it is a random variable with a normal probability distribution. Constraint equation (15) can be converted into its deterministic equivalent form: i(t-1) +Q it -I it ≥μ it +Φ -1 (β it )*σ it ;

[0135] Step 5, transform the HCCP model into a deterministic single-objective equivalent MIP model:

[0136] The objective function of the deterministic single-objective equivalent MIP model transformed from the HCCP model is:

[0137]

[0138] Its constraints are

[0139]

[0140] I i(t-1) +Q it -I it ≥μ it +Φ -1 (β it )*σ it i=1 to F,t=1 to T (23)

[0141]

[0142]

[0143]

[0144]

[0145]

[0146] Beneficial effects of the present invention:

[0147] For the batch decision problem of material requirement planning, the MRP model with mixed uncertain parameters is established through step 1, and the MRP problem with mixed uncertain parameters is represented by a mathematical model, in which the product demand, cost and time in constraints (1), (2), (3) and objective function (7) are treated as uncertain parameters, making the batch decision problem of material requirement planning clearer and more specific;

[0148] Through step 2, a hybrid chance constraint programming model is introduced for the MRP problem with random demand and fuzzy time / cost parameters. The fuzzy variables and random variables are constructed as fuzzy chance constraints and random chance constraints. The fuzzy variables in the objective function (7) are and the fuzzy variables in constraint (3) Construct fuzzy chance constraints to form constraints (14) and (16), where is the random variable in constraint (1) Construct random chance constraints to form constraints (15) to transform uncertain parameters into a clearer form;

[0149] Through step 3, the confidence-based constraints and probability-based constraints are converted into their corresponding deterministic equivalent forms, wherein the confidence is set to be greater than or equal to 0.5, so that constraint (14) is converted into constraint (22) and constraint (16) is converted into constraint (24), and the random variable is assumed to obey the normal distribution, so that constraint (15) is converted into constraint (23), so that the uncertain constraints can be converted into a deterministic form, which is conducive to solving the problem model;

[0150] The established model is applicable to multi-level, multi-project, and multi-period MRP problems with a general product structure, and different confidence levels can be set according to the risk preferences of decision makers to obtain different calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0151] Figure 1 This is a schematic diagram of the general product structure of a transmission.

[0152] Figure 2 For different confidence levels β it The cost comparison diagram is shown below.

[0153] Figure 3 For different confidence levels γ 12 The cost comparison diagram is shown below. DETAILED DESCRIPTION

[0154] The following is a further explanation with reference to the embodiments.

[0155] Step 1: Construct an original material requirement planning (MRP) model with mixed uncertain parameters;

[0156] Step 1, the MRP problem is described as a multi-product, multi-level and multi-period capacity batch decision model, whose goal is to meet time-varying demand by balancing production quantity or batch, inventory level and other manufacturing parameters within a limited planning range in an uncertain environment;

[0157] Step 2, symbol definition in the MRP model with mixed uncertain parameters (parameters with "~" symbol are uncertain parameters):

[0158] i: material type number (i=1,..,N);

[0159] t: planning cycle number (t=1, .., T);

[0160] k: machine number;

[0161] G i : The direct successor set of material i;

[0162] κ k : The set of materials produced on resource k;

[0163] N: Quantity of material type, including final product, subassembly, components, and parts;

[0164] F: the quantity of the final product;

[0165] T: planning cycle;

[0166] The demand for final products within the planning period t;

[0167] The manufacturing cost per unit of material i in planning period t;

[0168] Unit inventory holding cost of material i during planning period t;

[0169] The preparation cost of producing material i within planning period t;

[0170] C kt : The available processing time of resource k in planning period t;

[0171] r ij : The quantity of material i directly required to produce a unit of material j;

[0172] The production time required to produce a unit of material i on resource k;

[0173] The preparation time for producing material i on resource k;

[0174] M: preset large number;

[0175] Q it : The production quantity of material i in the planning period t;

[0176] I it : Inventory level of material i in planning period t;

[0177] Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t;

[0178] Step 3, establish constraints based on the characteristics of material requirement planning:

[0179] Constraint 1: Inventory balance constraint for final products

[0180]

[0181] Constraint 2: Inventory balance constraint for components or parts that meet the relevant requirements of material j

[0182]

[0183] Constraint 3: The capacity consumption of production activities and the preparation time of resource k will never exceed the available capacity within the planning period t

[0184]

[0185] Constraint 4: If material i is produced within planning period t, then variable Y is guaranteed to be prepared it Equal to 1

[0186]

[0187] Constraint 5: Decision variable Q it , I it The value is not negative

[0188]

[0189] Constraint 6: Variable Y it Value is binary

[0190]

[0191] Step 4, establish the objective function of the model, the expression is as follows:

[0192]

[0193] This method establishes an objective function with cost as the optimization target to obtain the minimum value of the sum of production cost, subcontracting cost, inventory cost and preparation cost.

[0194] Through step 1, the MRP problem with mixed uncertain parameters is transformed into a specific mathematical model, and the corresponding constraint relationship and objective function are established.

[0195] Step 2: Construct a hybrid chance-constrained programming (HCCP) model;

[0196] Step 1, reconstruct the symbol definition in the MRP model with mixed uncertain parameters according to the hybrid chance constraint programming model (the parameters with the "~" symbol are uncertain parameters):

[0197] i: material type number (i=1, .., N);

[0198] t: planning cycle number (t=1, .., T);

[0199] k: machine number;

[0200] G i : The direct successor set of material i;

[0201] κ k : The set of materials produced on resource k;

[0202] N: Quantity of material type, including final product, subassembly, components, and parts;

[0203] F: the quantity of the final product;

[0204] T: planning cycle;

[0205] The demand for final products within the planning period t;

[0206] The manufacturing cost per unit of material i in planning period t;

[0207] Unit inventory holding cost of material i during planning period t;

[0208] The preparation cost of producing material i within planning period t;

[0209] C kt : The available processing time of resource k in planning period t;

[0210] r ij : The quantity of material i directly required to produce a unit of material j;

[0211] The production time required to produce a unit of material i on resource k;

[0212] The preparation time for producing material i on resource k;

[0213] M: preset large number;

[0214] Q it : The production quantity of material i in the planning period t;

[0215] I it : Inventory level of material i in planning period t;

[0216] Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t;

[0217] x: decision variable;

[0218] ξ: fuzzy variable;

[0219] η: random variable;

[0220] α: the predetermined confidence level of the fuzzy chance constraint (0≤α≤1);

[0221] γ, γ kt : The predetermined confidence level of the fuzzy chance constraint (0≤γ, γ kt ≤1);

[0222] β, β it : The predetermined confidence level of the random chance constraint (0≤β, β it ≤1);

[0223] Step 2, using the method of credibility measurement fuzzy variables and probability measurement random variables, construct the fuzzy chance constraints and random chance constraints in the hybrid chance constraint programming (HCCP) model. The objective function of the general HCCP model is as follows:

[0224] min f(x,ξ) (8)

[0225] Its constraints are

[0226] Cr{g i (x,ξ)≤0,i=1,2,…,s}≥α (9)

[0227] Pr{h j (x, η) ≤ 0, j = 1, 2,…, t}≥β (10)

[0228] Where f is the objective function, and the constraint (9) Cr{g i (x, ξ)≤0, i=1, 2, …, s} represents a fuzzy chance constraint based on credibility measure. Constraint (10) Pr{h j (x, η) ≤ 0, j = 1, 2, …, t} represents a random chance constraint based on a probability metric. If α = 1 or β = 1, the corresponding chance constraint is equivalent to a deterministic one;

[0229] Since there are uncertain parameters in the objective function, it needs to be converted into its equivalent clear form to find its minimum optimal solution. The original objective function can be replaced by the following equivalent objectives and fuzzy constraints:

[0230]

[0231]

[0232] in is the equivalent optimization objective, and γ is the confidence of constraint (12).

[0233] Step 3, reconstruct the MRP model equation of mixed uncertain parameters:

[0234] As mentioned above, the objective function (7) and constraints (3) is assumed to be a fuzzy variable, and the requirement in constraint (1) It is defined as a random variable with a known probability distribution. Due to mixed uncertainty, the original model cannot be solved by traditional mathematical programming methods. In order to deal with mixed uncertainty, the HCCP method is to construct an optimization model for the MRP problem with mixed uncertainty. According to the general form of the HCCP model, the MRP model with mixed uncertain parameters can be restated as the following HCCP model:

[0235] The objective function of reconstructing the MRP model with mixed uncertain parameters is:

[0236]

[0237] Its constraints are

[0238]

[0239]

[0240]

[0241]

[0242]

[0243]

[0244]

[0245] Among them, constraints (14) and (16) are fuzzy chance constraints based on credibility measurement, and constraint (15) is a random chance constraint based on probability measurement.

[0246] Through step 2, the HCCP model is used to reconstruct the MRP model with mixed uncertain parameters and establish the corresponding constraint relationship and objective function.

[0247] Step 3: Defuzzify the HCCP model and transform it into a deterministic equivalent mixed integer programming (MIP) model;

[0248] Step 1, symbolic definition in the deterministic equivalent mixed integer programming model (parameters with the "~" symbol are uncertain parameters):

[0249] i: material type number (i=1, .., N);

[0250] t: planning cycle number (t=1, .., T);

[0251] k: machine number;

[0252] G i : The direct successor set of material i;

[0253] κ k : The set of materials produced on resource k;

[0254] N: Quantity of material type, including final product, subassembly, components, and parts;

[0255] F: the quantity of the final product;

[0256] T: planning cycle;

[0257] C kt : The available processing time of resource k in planning period t;

[0258] r ij : The quantity of material i directly required to produce a unit of material j;

[0259] The production time required to produce a unit of material i on resource k;

[0260] The preparation time for producing material i on resource k;

[0261] M: preset large number;

[0262] Q it : The production quantity of material i in the planning period t;

[0263] I it : Inventory level of material i in planning period t;

[0264] Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t;

[0265] x: decision variable;

[0266] ξ: fuzzy variable;

[0267] η: random variable;

[0268] α: the predetermined confidence level of the fuzzy chance constraint (0≤α≤1);

[0269] γ, γ kt : The predetermined confidence level of the fuzzy chance constraint (0≤γ, γ kt ≤1);

[0270] β, β it : The predetermined confidence level of the random chance constraint (0≤β, β it ≤1);

[0271] Φ: The probability distribution of

[0272] Φ -1 : inverse function of Φ;

[0273] μ it : The mathematical expectation of

[0274] σ it : The standard deviation of

[0275] f 1 : The lower bound of triangular fuzzy numbers;

[0276] f 2 : The most likely estimate of a triangular fuzzy number;

[0277] f 3 : The upper bound of triangular fuzzy numbers;

[0278] Step 2, deterministic processing of the objective function:

[0279] The objective function is a linear non-negative function whose value is a triangular fuzzy number, which is expressed by a triangular fuzzy number, that is, f(x, ξ) = (f 1 , f 2 , f 3 ), let f 1 <f 2 <f 3 , where x and ξ represent the decision vector and fuzzy vector respectively. In actual production planning decisions, the credibility value greater than or equal to 0.5 is of great significance to decision makers. This means that the acceptable confidence range is greater than or equal to 0.5, and the constraint equation (14) can be transformed into the following clear equivalent form: The confidence level is set to α ≥ 0.5.

[0280] Step 3, convert the fuzzy chance constraints into clear equivalent constraints:

[0281] Similarly, the confidence γ in constraint equation (16) kt It should also be greater than or equal to 0.5. The constraint equation (16) can be transformed into the following clear equivalent form:

[0282]

[0283] Step 4, convert the random chance constraint into a clear equivalent constraint:

[0284] Constraint equation (15) is a probability-based chance constraint. Here, it is assumed that it is a random variable with a normal probability distribution. Constraint equation (15) can be converted into its deterministic equivalent form: i(t-1) +Q it -I it ≥μ it +Φ -1 (β it )*σ it ;

[0285] Step 5, transform the HCCP model into a deterministic single-objective equivalent MIP model:

[0286] The objective function of the deterministic single-objective equivalent MIP model transformed from the HCCP model is:

[0287]

[0288] Its constraints are

[0289]

[0290] I i(t-1) +Q it -I it ≥μ it +Φ -1 (β it )*σ it i=1 to F,t=1 to T (23)

[0291]

[0292]

[0293]

[0294]

[0295]

[0296] Through step 3, the MRP model with mixed uncertain parameters using the HCCP model is defuzzified and converted into an equivalent MIP model with a deterministic single objective, and the model is solved using a conventional MIP algorithm.

[0297] A specific example of batch decision-making in material requirement planning is used to illustrate the practicability and effectiveness of the present invention. Figure 1 The simplified product structure of the transmission is shown. The symbols P1 and P2 represent two different types of transmissions, A and B represent one of the subassemblies of P1 and P2 respectively, C and D represent different gears, and gear D is a common component of A and B. Figure 1 The numbers in represent the Gozinto factor, which is the quantity required to produce higher-level components. According to the company's production layout, the final production process of the final product includes multiple stages, namely, final products P1 and P2 are assembled in production line 1, subcomponents A and B are assembled in production line 2, and C and D are arranged to be manufactured in production lines 3 and 4, respectively. Other input data are listed in Tables 1-5. Table 1 shows the demand for final products P1 and P2 in each cycle. Cycle 6 is a rest cycle, but since the demand is continuous, there is also demand in cycle 6. Table 2 lists the available resource capacity of each production line. Tables 3 and 4 give the preparation time and production time respectively, where the symbol "-" indicates that the material is not manufactured on the corresponding production line. Table 5 shows other relevant input data, in which it is assumed that inventory, preparation and production costs are triangular fuzzy numbers. Table 6 shows the corresponding calculation results, in which all confidence levels are assumed to be 0.8. Table 7 lists the results when the confidence level β it 0.6, 0.7, 0.8 and 0.9, α and γ kt When set to 0.8, planned orders are issued every period. Figure 2 The change of cost (unit: RMB) under the same conditions is shown in Table 8. 12 =0.6-1.0 and other confidence levels of 0.8, the total production quantity of materials P1 and P2 produced by production line 1 in each period at different confidence levels, Figure 3 Shown as γ 12 When changes, the corresponding cost changes, and Table 9 gives the corresponding total cost.

[0298] Table 1 External requirements

[0299]

[0300] Table 2 Resource capacity

[0301]

[0302] Table 3 Preparation time

[0303]

[0304] Table 4 Production time

[0305]

[0306] Table 5 Other relevant data

[0307]

[0308] Table 6 Calculation results

[0309]

[0310] Table 7 Planned input amount (when β it = 0.6, 0.7, 0.8, 0.9 and other confidence levels are 0.8)

[0311]

[0312] Table 8 Material P 1 and P 2 Production quantity

[0313]

[0314]

[0315] Table 9 Total cost

[0316]

Claims

1. A hybrid uncertain intelligent factory material requirement planning batch decision method, characterized in that: The following steps are involved: Step 1: Construct an original material requirement planning (MRP) model with mixed uncertain parameters; Step 2: Construct a hybrid chance-constrained programming (HCCP) model; Step 3: Defuzzify the HCCP model and transform it into a deterministic equivalent mixed integer programming (MIP) model. Solve the MIP model to obtain the batch decision of each material. The symbol definition in the MRP model with mixed uncertain parameters in step 1; establishing constraints and establishing an objective function according to the characteristics of batch decision-making of material requirement planning with mixed uncertain parameters, including the following steps: Step 1, the MRP problem is described as a multi-product, multi-level and multi-period capacity batch decision model, whose goal is to meet time-varying demand by balancing production quantity or batch, inventory level and other manufacturing parameters within a limited planning range in an uncertain environment; Step 2, symbol definition in the MRP model with mixed uncertain parameters, where the parameters with the "~" symbol are uncertain parameters: i: material type number (i=1,..,N); t: planning cycle number (t=1, .., T); k: machine number; G i : The direct successor set of material i; κ k : The set of materials produced on resource k; N: Quantity of material type, including final product, subassembly, components and parts; F: the quantity of the final product; T: planning cycle; The demand for final products within the planning period t; The manufacturing cost per unit of material i in planning period t; Unit inventory holding cost of material i during planning period t; The preparation cost of producing material i within planning period t; C kt : Available processing time of resource k in planning period r; r ij : The quantity of material i directly required to produce a unit of material j; The production time required to produce a unit of material i on resource k; The preparation time for producing material i on resource k; M: preset large number; Q it : The production quantity of material i in planning period t; I it : Inventory level of material i in planning period t; Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t; Step 3, establish constraints based on the characteristics of material requirement planning: Constraint 1: Inventory balance constraint of final product Constraint 2: Inventory balance constraint for components or parts that meet the relevant requirements of material j Constraint 3: The capacity consumption of production activities and the preparation time of resource k will never exceed the available capacity within the planning period t Constraint 4: If material i is produced within planning period t, then variable Y is guaranteed to be prepared it Equal to 1 Constraint 5: Decision variable Q it ,I it The value is not negative Constraint 6: Variable Y it Value is binary Step 4, establish the objective function of the model, the expression is as follows: This method establishes an objective function with cost as the optimization target to obtain the minimum value of the sum of production cost, subcontracting cost, inventory cost and preparation cost. In step 2, according to the type of uncertain parameters, a hybrid chance constraint programming model is constructed by using the method of credibility measurement fuzzy variables and probability measurement random variables, and the MRP model with hybrid uncertain parameters is reconstructed, which includes the following steps: Step 1, reconstruct the symbolic definition in the MRP model with mixed uncertain parameters according to the hybrid chance constraint programming model. The parameters with the "~" symbol are uncertain parameters: i: material type number (i=1,..,N); t: planning cycle number (t=1, .., T); k: machine number; G i : The direct successor set of material i; κ k : The set of materials produced on resource k; N: Quantity of material type, including final product, subassembly, components and parts; F: the quantity of the final product; T: planning cycle; The demand for final products within the planning period t; The manufacturing cost per unit of material i in planning period t; Unit inventory holding cost of material i during planning period t; The preparation cost of producing material i within planning period t; C kt : Available processing time of resource k in planning period t; r ij : The quantity of material i directly required to produce a unit of material j; The production time required to produce a unit of material i on resource k; The preparation time for producing material i on resource k; M: preset large number; Q it : The production quantity of material i in planning period t; I it : Inventory level of material i in planning period t; Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t; x: decision variable; ξ: fuzzy variable; η: random variable; α: the predetermined confidence level of the fuzzy chance constraint (0≤α≤1); γ,γ kt : The predetermined confidence level of fuzzy chance constraints (0≤γ,γ kt ≤1); β,β it : The predetermined confidence level of random chance constraints (0≤β,β it ≤1); Step 2, using the method of credibility measurement fuzzy variables and probability measurement random variables, construct the fuzzy chance constraints and random chance constraints in the hybrid chance constraint programming (HCCP) model. The objective function of the HCCP model is as follows: minf(x,ξ)(8) Its constraints are Cr{g i (x,ξ)≤0,i=1,2,…,s}≥α (9) Pr{h j (x,η)≤0,j=1,2,…,t}≥β (10) Where f is the objective function, and the constraint (9) Cr{g i (x,ξ)≤0,i=1,2,…,s} represents the fuzzy chance constraint based on credibility measure. Constraint (10)Pr{h j (x,η)≤0,j=1,2,…,t} represents a random chance constraint based on a probability metric. If α=1 or β=1, the corresponding chance constraint is equivalent to a deterministic one; Since there are uncertain parameters in the objective function, it needs to be converted into its equivalent clear form to find its minimum optimal solution. The original objective function can be replaced by the following equivalent objectives and fuzzy constraints: in is the equivalent optimization objective, γ is the confidence of constraint (12); Step 3, reconstruct the MRP model equation of mixed uncertain parameters: As mentioned above, the objective function (7) and constraints (3) is assumed to be a fuzzy variable, and the requirement in constraint (1) Defined as a random variable with a known probability distribution, according to the general form of the HCCP model, the MRP model with mixed uncertain parameters can be reformulated as the following HCCP model: The objective function of reconstructing the MRP model with mixed uncertain parameters is: Its constraints are Among them, constraints (14) and (16) are fuzzy chance constraints based on credibility measurement, and constraint (15) is a random chance constraint based on probability measurement; In step 3, the objective function, fuzzy chance constraints and random chance constraints in the model are converted into equivalent deterministic forms to form a deterministic equivalent mixed integer programming model, which is solved using conventional methods, including the following steps: Step 1, symbolic definition in the deterministic equivalent mixed integer programming model. The parameters with the "~" symbol are uncertain parameters: i: material type number (i=1,..,N); t: planning cycle number (t=1, .., T); k: machine number; G i : The direct successor set of material i; κ k : The set of materials produced on resource k; N: Quantity of material type, including final product, subassembly, components and parts; F: the quantity of the final product; T: planning cycle; C kt : Available processing time of resource k in planning period t; r ij : The quantity of material i directly required to produce a unit of material j; The production time required to produce a unit of material i on resource k; The preparation time for producing material i on resource k; M: preset large number; Q it : The production quantity of material i in planning period t; I it : Inventory level of material i in planning period t; Y it : A binary preparation variable indicating whether the preparation of material i has changed in period t; x: decision variable; ξ: fuzzy variable; η: random variable; α: the predetermined confidence level of the fuzzy chance constraint (0≤α≤1); γ,γ kt : The predetermined confidence level of fuzzy chance constraints (0≤γ,γ kt ≤1); β,β it : The predetermined confidence level of random chance constraints (0≤β,β it ≤1); Φ: The probability distribution of Φ -1 : Inverse function of Φ; μ it : The mathematical expectation of σ it : The standard deviation of f1: lower bound of triangular fuzzy number; f2: the most likely estimate of the triangular fuzzy number; f3: upper bound of triangular fuzzy number; Step 2, deterministic processing of the objective function: The objective function is a linear non-negative function, and its value is a triangular fuzzy number, which is expressed by triangular fuzzy numbers, that is, f(x,ξ)=(f1,f2,f3), let f1<f2<f3, where x and ξ represent the decision vector and fuzzy vector respectively. In the actual production planning decision, the credibility value greater than or equal to 0.5 is of great significance to the decision maker. The acceptable confidence range is greater than or equal to 0.

5. The constraint equation (14) can be transformed into the following clear equivalent form: Set the confidence level to α ≥ 0.5; Step 3, convert the fuzzy chance constraints into clear equivalent constraints: Similarly, the confidence γ in constraint equation (16) kt should also be greater than or equal to 0.5, and the constraint equation (16) is transformed into the following clear equivalent form: Step 4, convert the random chance constraint into a clear equivalent constraint: Constraint equation (15) is a probability-based chance constraint. Assuming that it is a random variable with a normal probability distribution, constraint equation (15) can be converted into its deterministic equivalent form: I i(t-1) +Q it -I it ≥μ it +F -1 (b it )*s it ; Step 5, transform the HCCP model into a deterministic single-objective equivalent MIP model: The objective function of the deterministic single-objective equivalent MIP model transformed from the HCCP model is: Its constraints are I i(t-1) +Q it -I it ≥μ it +Φ -1 (β it )*σ it i=1 to F,t=1 to T (23) The MRP model with mixed uncertain parameters using the HCCP model is defuzzified and transformed into an equivalent MIP model with a deterministic single objective, which is then solved using the conventional MIP algorithm.

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