Multi-objective production plan optimization method with uncertain demand and tardiness cost

Abstract

The invention discloses a multi-objective production plan optimization method with uncertain demand and tardiness cost, which analyzes uncertain factors caused by the interior and exterior of a system on the basis of an existing production plan, considers uncertain factors including product demand and tardiness delivery penalty cost coefficients, and optimizes the production plan. According to the method, multiple constraints such as inventory, materials and productivity are constructed, a demand and tardiness cost uncertain production plan model with minimization of tardiness cost and minimization of inventory cost as targets is established, a multi-target optimization problem is effectively solved by using a quantum behavior particle swarm optimization algorithm, and the accuracy and robustness of a production plan are improved. In order to solve the problem that main production plan making is affected by uncertain factors and is limited by materials and production capacity and thus an optimization mechanism is lacked, compared with an original method, the method has the advantages of being high in solving precision, high in robustness and the like, and is very suitable for solving the complex function optimization problem under the uncertain condition.

Description

Technical Field

[0001] The present invention relates to the technical field of production planning and control of manufacturing enterprises, and in particular to a multi-objective production planning optimization method with uncertain demand and delay cost. Background Art

[0002] Master production planning plays a vital role in modern manufacturing enterprises. It is not only a core component of the enterprise resource planning (ERP) system, but also serves as a bridge between market demand and production capacity, effectively coordinating production processes and resource allocation. With the ever-changing market demand, traditional master production planning methods face many challenges, such as demand fluctuations, insufficient production capacity, and material shortages. Therefore, proposing an efficient and flexible master production planning method is of great significance to improve production response speed, optimize resource utilization, and enhance the competitiveness of enterprises.

[0003] The traditional master production plan formulation method has two main deficiencies in planning: First, most master production plans are formulated for production in a deterministic environment, mostly based on experience or mathematical methods, and through repeated experiments or "trial and error" to formulate production plans, ignoring some uncertain factors that may exist in the production process. In the actual production process, the manufacturing system must consider the impact of external uncertain factors from product demand and raw material supply, and the fluctuation of production conditions within the manufacturing system. Second, the constraints of production capacity are not considered. The planning process is first based on the assumption of infinite capacity. In the planning process, it is necessary to repeatedly coordinate and balance between production plans and production capacity. There is a lack of optimization means. When there are many production tasks and serious conflicts in production capacity, it is impossible to fully solve the capacity conflict problem. Summary of the invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a multi-objective production planning optimization method with uncertain demand and delay cost. This method not only considers the impact of uncertainty factors caused by the system internal and external on the production plan formulation, but also takes materials and production capacity as constraints of the production planning model, and delay cost and inventory cost as the objectives of the model, which helps to improve the accuracy and robustness of the production plan.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a multi-objective production plan optimization method with uncertain demand and delay cost, which specifically includes the following steps:

[0006] Step 1: Construct a multi-objective production planning model based on uncertain product demand and delay cost, specifically:

[0007] Step 1.1: Define uncertain variables;

[0008] Product demand and delay cost are set as uncertain variables, product demand is defined as an uncertain set, and the delay penalty cost coefficient is expressed as a random variable and obeys a normal distribution;

[0009] Step 1.2: Define the objective function:

[0010] Define the minimum total cost in the production process as the model objective, and the total cost includes delay cost and inventory cost;

[0011] Step 1.3: Set model constraints;

[0012] Step 1.3a: Set the material constraints as follows: neither the intermediate materials nor the raw materials can be out of stock;

[0013] Step 1.3b: Set the capacity constraint as follows: the planned output of the product in each period cannot exceed the normal production capacity available in that period;

[0014] Step 1.3c: Set the product inventory constraint as follows: the end-of-period inventory quantity of the product must not be less than the safety stock quantity and must not exceed the maximum allowable inventory quantity;

[0015] Step 1.3d: Set non-negative and integer constraints on variables;

[0016] Step 1.4: Analyze the uncertain factors caused by the system internally and externally, consider the uncertain factors including product demand, penalty cost coefficient of delayed delivery, etc., and obtain the multi-objective production planning model with uncertain demand and delayed cost under the conditions of non-negative and integer multiple constraints of product materials, production capacity, inventory and planned output, with the goal of minimizing delayed cost and minimizing inventory cost;

[0017] Step 2: Convert the uncertain multi-objective production planning model into a deterministic model. The uncertain part defined as the uncertain set adopts the robust optimization method, and the part defined as the random variable uses the chance constrained programming method. The model constructed in step 1 is converted into an equivalent deterministic model through the integration method.

[0018] Step 3: Solve the determined model based on the quantum behavior particle swarm algorithm to obtain an optimized production plan, specifically: set the encoding method, use one particle to represent a production operation plan, the dimension represents the number of planning cycles, the position information of each dimension represents the planned output of each cycle, and use the delay cost and inventory cost as the fitness function of the quantum behavior particle swarm algorithm to solve the multi-objective production planning model.

[0019] Step 3.1: Set the number of particles and dimensions, initialize the population according to the set number of particles and dimensions, set the number of iterations G, and set the upper and lower limits of the search space;

[0020] Step 3.2: Calculate the fitness value of each particle, that is, the objective function value Z. The best individual position Pn is the individual with the best fitness value in the initialization position X. The best group position Gn is the individual with the best fitness value among all particles.

[0021] Step 3.3: Use quantum random walk to update the position and velocity of the particle. The updated position needs to meet the upper and lower limit constraints of the search space.

[0022] Step 3.4: Calculate the fitness value Z of each particle after update i ′, update the individual best position and the group best position;

[0023] Step 3.5: Iterative optimization, determine whether this iteration is the maximum number of iterations, if so, output the optimal solution set and obtain the optimized individuals; otherwise, continue to iterate and repeat steps 3.2 to 3.4 for the new population.

[0024] Step 3.6: Output the optimized individuals and obtain the optimal production plan.

[0025] Specifically, in step 1.1

[0026] Define uncertain variables:

[0027] Step 1.1a: For uncertain product demand Assumptions Belongs to the following uncertain set U t

[0028]

[0029] in, is the median of the product demand interval in period t, R is the product demand set; θ t is the demand uncertainty level, i.e., the maximum percentage of the median deviation of actual demand, θ t The larger it is, the higher the level of demand uncertainty.

[0030] Step 1.1b: Delay Penalty Cost Coefficient is expressed as a random variable and follows a normal distribution, where is the penalty cost coefficient for the failure to meet the demand per unit quantity of product per unit period. Parameters with the symbol “~” indicate uncertain parameters.

[0031] In step 1.2

[0032] The objective function of the model is

[0033] min z=(z1,z2)

[0034] The goal of the model is to minimize the total cost z, which includes the delay cost z1 and the inventory cost z2. The calculation formulas for each are as follows:

[0035]

[0036] Among them: t is the planning period, T is the total planning period set, is the penalty cost coefficient for unsatisfied demand per unit quantity of product per unit period, S t is the number of unmet demands for the product in period t;

[0037]

[0038] Where: H is the inventory cost coefficient of unit quantity per unit cycle, GI t is the average inventory quantity of the product in period t, and its value is equal to the initial inventory quantity BI of the product in period t t EI t half of the sum;

[0039] In step 1.3;

[0040] Step 1.3a: Establish material constraints: During the production process, both intermediate materials and raw materials cannot be out of stock:

[0041]

[0042] Among them, BI mt is the initial inventory quantity of intermediate material m in period t, R mt is the demand quantity of intermediate material m in period t, BI nt is the initial inventory quantity of raw material n in period t, R nt is the demand quantity of raw material n in period t, M is the set of intermediate materials, and RM is the set of raw materials;

[0043] Step 1.3b: Establish capacity constraints. The planned output in each period cannot exceed the available normal production capacity, that is, the planned output Q for period t t Must be less than or equal to the current available normal production capacity C t .

[0044] Step 1.3c: Establish product inventory constraints. The ending inventory quantity of each period must be greater than or equal to the safety stock quantity and less than or equal to the maximum allowable inventory quantity:

[0045]

[0046] Among them, SS t is the safety inventory quantity of the product in period t, EI t is the ending inventory quantity of the product in period t, MI tis the maximum allowable inventory quantity of the product in period t;

[0047] In the above formula: For the ending inventory quantity EI t :When t=1, EI t = Initial inventory quantity of the product OI + planned production quantity of the product Q t - Quantity of product demanded When the value is less than or equal to zero, the ending inventory quantity is zero; t>1, EI t = Initial inventory quantity BI of the current product t + Planned production quantity Q of the current product t -The quantity of product demanded in the current period - The cumulative number of products that did not meet demand in the previous period S t-1 , when the value is less than or equal to zero, the ending inventory quantity is zero.

[0048] Among them, the initial inventory quantity BI for the product in period t is t , t = 1, BI t = equal to the given initial inventory quantity OI, when t>1, BI t = Ending inventory quantity EI of the previous period's product t-1 ;

[0049] Step 1.3d: Establish non-negative and integer constraints: The planned output Q t 、The number of unmet needs of the product S t , Initial inventory quantity BI t , Ending inventory quantity EI t , the demand quantity R of intermediate material m mt , the demand quantity R of raw material n nt All must satisfy non-negative and integer constraints.

[0050] Compared with the prior art, the advantages of the present invention are that, based on the existing production plan, the uncertainty factors caused by the system inside and outside are analyzed, the uncertainty factors including product demand and penalty cost coefficient for delayed delivery are considered, and the material, production capacity, inventory, etc. are constrained. Through multiple constraints, a production plan model with uncertain demand and delayed cost is established with the goal of minimizing delayed cost and minimizing inventory cost, and the quantum behavior particle swarm algorithm is used to effectively solve the multi-objective optimization problem, thereby improving the accuracy and robustness of the production plan. In order to overcome the problem that the formulation of the master production plan is affected by uncertain factors and lacks an optimization mechanism due to the limitation of materials and production capacity, compared with the original method, the method of the present invention has the advantages of high solution accuracy and strong robustness, and is very suitable for solving complex function optimization problems under uncertain conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a flowchart of a multi-objective production plan optimization method in an embodiment of this specification;

[0052] Figure 2 This is a flow chart of the quantum behavior particle swarm algorithm in the embodiments of this specification. DETAILED DESCRIPTION

[0053] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0054] like Figure 1 As shown, the present invention proposes a multi-objective production planning optimization method with uncertain demand and delay cost, which mainly includes the following steps:

[0055] Step 1: Construct a multi-objective production planning model based on uncertain product demand and delay cost, specifically:

[0056] Step 1.1: Define uncertain variables;

[0057] Step 1.1a: For uncertain product demand Assumptions Belongs to the following uncertain set U t

[0058]

[0059] is the median of the product demand interval in period t, R is the product demand set; θ t is the demand uncertainty level, i.e., the maximum percentage of the median deviation of actual demand, θ t The larger it is, the higher the level of demand uncertainty.

[0060] Step 1.1b: Delay Penalty Cost Coefficient It is expressed as a random variable and follows a normal distribution; The penalty cost coefficient for not meeting demand per unit quantity of product per unit period. Parameters with the symbol “~” are uncertain parameters.

[0061] Step 1.2: Define the model objective as minimizing the total cost, including delay cost and inventory cost:

[0062] The objective function of the model is

[0063] min z=(z1,z2)

[0064] The goal of the model is to minimize the total cost z, which includes the delay cost z1 and the inventory cost z2

[0065] in,

[0066]

[0067] Among them: t is the planning period, T is the total planning period set, is the penalty cost coefficient for unsatisfied demand per unit quantity of product per unit period, S t is the number of unmet demands for the product in period t;

[0068]

[0069] Where: H is the inventory cost coefficient of unit quantity per unit cycle, GI t is the average inventory quantity of the product in period t, and its value is equal to the initial inventory quantity BI of the product in period t t EI t half of the sum;

[0070] Step 1.3: Set constraints;

[0071] Step 1.3a: Establish material constraints: During the production process, both intermediate materials and raw materials cannot be out of stock:

[0072]

[0073] Among them, BI mt is the initial inventory quantity of intermediate material m in period t, R mt is the demand quantity of intermediate material m in period t, BI nt is the initial inventory quantity of raw material n in period t, R nt is the demand quantity of raw material n in period t, M is the set of intermediate materials, and RM is the set of raw materials;

[0074] Where: The demand quantity R of intermediate material m in period t mt = All intermediate materials at t+LT m The planned completion quantity for the period The quantity B of intermediate material m required to produce a unit of product m The sum of the products; LT m The minimum production lead time of intermediate material m required to produce the product.

[0075] The demand quantity R of raw material n in period t nt = All raw materials at t+LT n The planned completion quantity for the period The quantity B of raw materials n required to produce a unit of product n The sum of the products of

[0076] Step 1.3b: Establish capacity constraints. The planned output in each period cannot exceed the available normal production capacity, that is, the planned output Q for period t t ≤Current available normal production capacityt .

[0077] Step 1.3c: Establish product inventory constraints. The ending inventory quantity of each period must be greater than or equal to the safety stock quantity and less than or equal to the maximum allowable inventory quantity:

[0078]

[0079] Among them, SS t is the safety inventory quantity of the product in period t, EI t is the ending inventory quantity of the product in period t, MI t is the maximum allowable inventory quantity of the product in period t;

[0080] In the above formula: For the ending inventory quantity EI t :When t=1, EI t = Initial inventory quantity of the product OI + planned production quantity of the product Q t - Quantity of product demanded When the value is less than or equal to zero, the ending inventory quantity is zero; t>1, EI t = Initial inventory quantity BI of the current product t + Planned production quantity Q of the current product t -The quantity of product demanded in the current period - The cumulative number of products that did not meet demand in the previous period S t-1 , when the value is less than or equal to zero, the ending inventory quantity EI t is zero.

[0081] For the cumulative number of products that do not meet demand in period t, S t The calculation is as follows:

[0082] At t = 1, the cumulative number of products that do not meet demand is S t = Product demand quantity -Product planned production quantity Q t -The initial inventory quantity OI of the product. When this value is less than or equal to zero, the cumulative number of products that do not meet demand at the beginning of the planning period is zero, indicating that there are no products that do not meet demand; when t>1, the cumulative number of products that do not meet demand S t = The cumulative number of products that did not meet demand in the previous period S t-1 +Product demand quantity for this period -The planned production quantity of this product is Q t - Initial inventory quantity of this product BI t , when the value is less than or equal to zero, the cumulative number of products with unmet demand is zero, indicating that there are no products with unmet demand;

[0083] Among them, the initial inventory quantity BI for the product in period t is t, t = 1, BI t = equal to the given initial inventory quantity OI, when t>1, BI, = the ending inventory quantity EI of the previous period's product t-1 ;

[0084] Step 1.3d: Establish non-negative and integer constraints: The planned output Q t 、The number of unmet needs of the product S t , Initial inventory quantity BI t , Ending inventory quantity EI t , the demand quantity R of intermediate material m mt , the demand quantity R of raw material n nt All must satisfy non-negative and integer constraints.

[0085] Step 1.4: Analyze the uncertain factors caused by the system internally and externally, consider the uncertain factors including product demand and penalty cost coefficient of delayed delivery, and obtain a multi-objective production planning model with uncertain demand and delayed cost under the conditions of non-negative and integer multiple constraints of product materials, production capacity, inventory and planned output, with the goal of minimizing delayed cost and minimizing inventory cost;

[0086] Step 2: Convert the uncertain multi-objective production planning model into a deterministic model. The model constructed in step 1 is converted into a deterministic model by using a robust optimization method for the uncertain part defined as an uncertain set and a chance constrained programming method for the part defined as a random variable.

[0087] Step 2.1: Opportunity Constrained Planning Transformation: In the production planning model constructed above, the uncertain variables It is expressed as a random variable and obeys the normal distribution, and is included in z1 in the objective function. The chance constrained programming method is used to express the model as a stochastic programming model, and it is further transformed into an equivalent deterministic model through the integration method, that is, the random variable is transformed into a deterministic variable.

[0088] In the optimization model, the deterministic part of the objective function remains unchanged, and the part containing uncertain coefficients It is expressed in the following chance-constrained programming form:

[0089]

[0090] Among them, Pr{·} is the probability calculation function, α1∈[0,1] represents the confidence level of the objective function z1. The larger its value is, the smaller the risk of violation is. Correspondingly, a larger value of z1 is required, which increases the cost, but the optimization result will be more reliable.

[0091] Assuming that the random variables in the model obey normal distribution, the opportunity constrained programming model is transformed into a deterministic model by using the integral method. According to the probability distribution function of each random variable, the corresponding equivalent deterministic variable is obtained and processed by indirect integral. Through model conversion, it can be equivalently converted to:

[0092]

[0093] Where E() and σ() represent the expectation and standard deviation of the random variable, respectively. represents the inverse function of the probability distribution function of a random variable, represents the confidence level of the above inequality constraints.

[0094] Step 2.2: Robust Optimization Conversion: For Uncertain Product Demand The original optimization problem is transformed into a robust equivalence model. In order to satisfy the constraints in the worst case, the ending inventory quantity EI of the product in period t is t Converted to robust form:

[0095]

[0096] Out of stock quantity t Converted to robust form:

[0097]

[0098] Step 3: Solve the determined model based on the quantum behavior particle swarm algorithm to obtain an optimized production plan, specifically: set the encoding method, use one particle to represent a production operation plan, the dimension represents the number of planning cycles, the position information of each dimension represents the planned output of each cycle, and use the delay cost and inventory cost as the fitness function of the quantum behavior particle swarm algorithm to solve the multi-objective production planning model, specifically as follows Figure 2 shown.

[0099] Step 3.1: Set the number of particles and dimensions, initialize the population according to the set number of particles and dimensions, set the number of iterations G, and set the upper and lower limits of the search space;

[0100] Step 3.2: Calculate the fitness value of each particle, that is, the objective function value Z. The best individual position Pn is the individual with the best fitness value in the initialization position X. The best group position Gn is the individual with the best fitness value among all particles.

[0101] Step 3.3: Use quantum random walk to update the position and velocity of the particle. The updated position needs to meet the upper and lower limit constraints of the search space.

[0102] Step 3.4: Calculate the fitness value Z of each particle after update i ’ , update the individual best position and the group best position;

[0103] Step 3.5: Iterative optimization, determine whether this iteration is the maximum number of iterations, if so, output the optimal solution set and obtain the optimized individuals; otherwise, continue to iterate and repeat steps 3.2 to 3.4 for the new population.

[0104] Step 3.6: Output the optimized individuals and obtain the optimal production plan.

[0105] Compared with the prior art, the advantages of the present invention are that, based on the existing production plan, the uncertainty factors caused by the system inside and outside are analyzed, the uncertainty factors including product demand and penalty cost coefficient for delayed delivery are considered, and the material, production capacity, inventory, etc. are constrained. Through multiple constraints, a production plan model with uncertain demand and delayed cost is established with the goal of minimizing delayed cost and minimizing inventory cost, and the quantum behavior particle swarm algorithm is used to effectively solve the multi-objective optimization problem, thereby improving the accuracy and robustness of the production plan. In order to overcome the problem that the formulation of the master production plan is affected by uncertain factors and lacks an optimization mechanism due to the limitation of materials and production capacity, compared with the original method, the method of the present invention has the advantages of high solution accuracy and strong robustness, and is very suitable for solving complex function optimization problems under uncertain conditions.

[0106] Those skilled in the art will readily appreciate other embodiments of the present invention after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses or adaptations of the present invention, which follow the general principles of the present invention and include common knowledge or customary techniques in the art that are not disclosed by the present invention. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present invention are indicated by the claims of the present application.

[0107] The above is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A multi-objective production planning optimization method with uncertain demand and delay cost, characterized in that: The specific steps include: Step 1: Construct a multi-objective production planning model based on uncertain product demand and delay cost; Step 2: converting the uncertain multi-objective production planning model into a deterministic model; Step 3: Solve the determination model based on the quantum behavior particle swarm algorithm to obtain an optimized production plan.

2. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 1, characterized in that: The step 1 comprises the following steps: Step 1.1: Define uncertain variables, including the set of uncertain product requirements and the penalty cost coefficient for delay Step 1.2: defining the objective function of the uncertain multi-objective production planning model; Step 1.3: Set model constraints; Step 1.4: Based on the uncertain variables, objective function and constraints, a multi-objective production planning model with uncertain demand and tardiness cost is obtained with the goal of minimizing tardiness cost and minimizing inventory cost under the non-negative and integer multiple constraints of product materials, production capacity, inventory and planned output.

3. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 2, characterized in that: Defining uncertain variables in step 1.1 includes the following steps: Step 1.1a: The uncertain product demand set Belongs to the following uncertain set U t : in, is the median of the product demand interval in period t, R is the product demand set; θ t is the demand uncertainty level, i.e., the maximum percentage of the median deviation of actual demand, θ t The larger it is, the higher the level of demand uncertainty; Step 1.1b: The delay penalty cost coefficient is expressed as a random variable and follows a normal distribution, where is the penalty cost coefficient for unsatisfied demand per unit quantity of product per unit period. Parameters with the symbol "~" indicate uncertain parameters.

4. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 3, characterized in that: The objective function of the model in step 1.2 is: minz=(z1,z2) The goal of the model is to minimize the total cost z, which includes the delay cost z1 and the inventory cost z2; in, Where: t is the planning period, T is the total planning period set, is the penalty cost coefficient for unsatisfied demand per unit quantity of product per unit period, S t is the number of unmet demands for the product in period t; Where: H is the inventory cost coefficient of unit quantity per unit cycle, GI t is the average inventory quantity of the product in period t, and its value is equal to the initial inventory quantity BI of the product in period t t EI t Half of the sum.

5. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 4, characterized in that: The step 1.3 specifically includes: Step 1.3a: Set the material constraints as follows: neither the intermediate materials nor the raw materials can be out of stock; Step 1.3b: Set the capacity constraint as follows: the planned output of the product in each period cannot exceed the normal production capacity available in that period; Step 1.3c: Set the product inventory constraint as follows: the end-of-period inventory quantity of the product must not be less than the safety stock quantity and must not exceed the maximum allowable inventory quantity; Step 1.3d: Set non-negative and integer constraints on variables.

6. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 5, characterized in that: The step 1.3a specifically includes: Among them, BI mt is the initial inventory quantity of intermediate material m in period t, R mt is the demand quantity of intermediate material m in period t, BI nt is the initial inventory quantity of raw material n in period t, R nt is the demand quantity of raw material n in period t, M is the set of intermediate materials, and RM is the set of raw materials.

7. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 6, characterized in that: The step 1.3c specifically includes: Among them, SS t is the safety inventory quantity of the product in period t, EI t is the ending inventory quantity of the product in period t, MI t is the maximum allowable inventory quantity of the product in period t; In the above formula: For the ending inventory quantity EI t :When t=1, EI t = Initial inventory quantity of the product OI + planned production quantity of the product Q t - Quantity of product demanded When the value is less than or equal to zero, the ending inventory quantity is zero; t>1, EI t = Initial inventory quantity BI of the current product t + Planned production quantity Q of the current product t - The quantity of products demanded in the current period - The cumulative number of products that did not meet demand in the previous period S t-1 , when the value is less than or equal to zero, the ending inventory quantity is zero; Among them, the initial inventory quantity BI of the product in period t is t The value of is: when t=1, BI t Equal to the given initial value OI; when t>1, BI t Equal to the ending inventory quantity EI of the previous period's product t-1 .

8. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 7, characterized in that: The step 2 specifically includes: Step 2.1: Opportunity Constrained Planning Transformation: In the production planning model constructed in step 1 above, the delay penalty cost coefficient It is expressed as a random variable and obeys the normal distribution, and is included in z1 in the objective function. The model is expressed as a random programming model using the chance constrained programming method, and is further transformed into an equivalent deterministic model through the integration method, that is, the random variable is transformed into a deterministic variable; In the optimization model, the deterministic part of the objective function remains unchanged, and the part containing uncertain coefficients It is expressed in the following chance-constrained programming form: Among them, Pr{·} is the probability calculation function, α1∈[0,1] represents the confidence level of the objective function z1. The larger its value is, the smaller the risk of violation is. Correspondingly, a larger value of z1 is required, which increases the cost, but the optimization result will be more reliable. Assuming that the random variables in the model obey normal distribution, the opportunity constrained programming model is transformed into a deterministic model by using the integral method; according to the probability distribution function of each random variable, the corresponding equivalent deterministic variable is obtained and processed by indirect integration; through model conversion, it can be equivalently converted into: Where E() and σ() represent the expectation and standard deviation of the random variable, respectively. represents the inverse function of the probability distribution function of a random variable, represents the confidence level of the above inequality constraints; Step 2.2: Robust Optimization Conversion: For Uncertain Product Demand The original optimization problem is transformed into a robust equivalence model. In order to satisfy the constraints in the worst case, the ending inventory quantity EI of the product in period t is t Converted to robust form: Out of stock quantity t Converted to robust form:

9. A multi-objective production planning optimization method with uncertain demand and delay cost as claimed in claim 1, characterized in that: The step 3 specifically includes the following steps: Step 3.1: Set the number of particles and dimensions, initialize the population according to the set number of particles and dimensions, set the number of iterations G, and set the upper and lower limits of the search space; Step 3.2: Calculate the fitness value of each particle, that is, the objective function value Z. The best individual position Pn is the individual with the best fitness value in the initialization position X; the best group position Gn is the individual with the best fitness value among all particles; Step 3.3: Use quantum random walk to update the position and velocity of the particle. The updated position needs to meet the upper and lower limit constraints of the search space. Step 3.4: Calculate the fitness value Z of each particle after update i ', update the individual best position and the group best position; Step 3.5: Iterative optimization, determine whether this iteration is the maximum number of iterations, if so, output the optimal solution set and obtain the optimized individual; Otherwise, continue the iteration and repeat steps 3.2 to 3.4 for the new population; Step 3.6: Output the optimized individuals and obtain the optimal production plan.

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