Multi-target integrated production planning and scheduling method based on improved NSGA-II

Abstract

The invention discloses a multi-target integrated production plan scheduling method based on improved NSGA-II, which considers multiple constraints such as materials, productivity and inventory on the basis of the existing production plan, and constructs a multi-target integrated production plan scheduling method based on the multiple constraints by taking the materials, the productivity and the inventory as the constraints. According to the method, an integrated production plan model with minimization of tardiness cost, minimization of inventory cost and maximization of balanced production as targets is established, an improved non-dominated sorting genetic algorithm is designed to effectively solve a multi-target optimization problem, the accuracy of a production plan is improved, and compared with an original solving method, the method has the advantages that the cost is reduced, and the production efficiency is improved. The improved NSGA-II algorithm has the advantages of being high in solving precision, high in convergence speed and the like, and is very suitable for solving the problem of complex function optimization under the multi-constraint condition.

Description

Technical Field

[0001] The invention relates to a production planning and scheduling method, and in particular to a multi-objective integrated production planning and scheduling method based on an improved NSGA-II. Background Art

[0002] Modern manufacturing enterprises often use enterprise resource planning systems to achieve unified planning and management of resources. Through product demand planning, on the basis of balancing and coordinating production demand and available capacity, the master production plan of the product is formulated, and the execution of the material requirement plan is driven by this plan. As the core and hub of the enterprise resource planning system, the master production plan is a bridge between market demand and enterprise product production. It can not only balance demand and available capacity, but also is an effective tool for coordinating the production process. Researching efficient and optimized master production plan formulation methods is of great significance to manufacturing enterprises.

[0003] The traditional master production planning method has two main deficiencies in planning: First, it does not consider the constraints of production capacity. The planning process is first based on the infinite capacity assumption, which needs to be tested by the rough capacity plan (RCCP), and then decomposed to obtain the material requirement plan. All work-in-progress must also be tested by the capacity requirement plan (CRP). This planning method relies on a closed-loop feedback mechanism. During the planning process, it is necessary to repeatedly coordinate and balance between the production plan and production capacity. It lacks optimization means. When there are many production tasks and serious conflicts in production capacity, it is impossible to fully solve the capacity conflict problem. On the other hand, it cannot achieve balanced utilization of production capacity. Some optimization methods often take production capacity as a constraint and optimize it with production cost, customer service level, etc. as the goal, but often ignore the balanced utilization and optimization of production capacity. These methods cannot adapt well to the production environment with uneven distribution of production capacity and high requirements for production management. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a multi-objective integrated production planning and scheduling method based on an improved NSGA-II which can improve the accuracy of production planning.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a multi-objective integrated production planning and scheduling method based on improved NSGA-II, which specifically includes the following steps:

[0006] Step (1): Construct a multi-objective integrated production planning model based on balanced production, specifically:

[0007] Step (1-1): Set constraints:

[0008] a) Set product inventory constraints as follows: the initial inventory quantity and the final inventory quantity of each period of the product must not be less than the safety stock quantity and not exceed the maximum allowable inventory quantity;

[0009] b) Set the material constraints as follows: intermediate materials and raw materials cannot be out of stock:

[0010] c) 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;

[0011] d) Set the planned output non-negative and integer constraints as follows: the planned output of the product in each period must be non-negative and integer;

[0012] Step (1-2): Based on the above-mentioned constrained spare parts, define the minimization of delay cost, minimization of inventory cost and maximization of balanced production indicators in the production process;

[0013] Step (1-3): Obtain a multi-objective integrated production planning model based on balanced production with the objectives of minimizing tardiness cost, minimizing inventory cost and maximizing balanced production index under the non-negative and integer multiple constraints of product inventory, materials, production capacity and planned output;

[0014] Step (2): Based on the multi-objective integrated production planning process of the improved NSGA-II, the actual production plan and production scheduling Gantt chart are obtained, specifically: the encoding method of NSGA-II is set, an individual is used to represent a production operation plan, the individual dimension represents the number of planning cycles, the position information of each dimension represents the planned output of each cycle, the delay cost, inventory cost, and penalty cost for not meeting the balanced production are used as the fitness function of the improved NSGA-II, and the multi-objective integrated production planning model of the balanced production is solved.

[0015] Step (2-1): Set the algorithm parameters, including individual population size, maximum number of iterations, mutation scaling factor and crossover probability;

[0016] Step (2-2): Set the number of individuals in the initial population;

[0017] Step (2-3): sort the individuals into different non-dominant levels according to their dominance relationship;

[0018] Step (2-4): Evaluate the quality of individuals in the same non-dominated level by their crowding distance;

[0019] Step (2-5): Select operation, using the binary tournament strategy, randomly select two individuals from the population. If the two individuals have different non-dominated ranks, the individual with the smaller non-dominated rank is selected as the parent. If the two individuals have the same non-dominated rank, the individual with the larger crowding distance is selected as the parent.

[0020] Step (2-6): Genetic operation, performing mutation operation and crossover operation in sequence to generate offspring population;

[0021] Step (2-7): merge the parent and the offspring, merge the parent population and the offspring population, perform non-dominated sorting on the merged population, and then prune to obtain a new generation population through the elite strategy;

[0022] Step (2-8): 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 to iterate and repeat steps 2-3 to 2-8 for the new population;

[0023] Step (2-9): Output the optimized individuals and obtain the production plan and scheduling Gantt chart.

[0024] Compared with the prior art, the advantages of the present invention are that, based on the existing production operation plan, factors such as materials, production capacity, and inventory are considered, and a production plan model with materials, production capacity, and inventory as constraints is constructed. Through multiple constraints, an integrated production plan model with the goals of minimizing delay costs, minimizing inventory costs, and maximizing balanced production is established, and an improved non-dominated sorting genetic algorithm is designed to effectively solve multi-objective optimization problems. When formulating a production plan, the material and production capacity of the product can be considered at the same time to avoid problems such as material shortages or capacity conflicts, thereby improving the accuracy of the production plan. In order to overcome the problem that the main production plan formulation is limited by materials and production capacity and lacks an optimization mechanism, compared with the original method, the method of the present invention has the advantages of high solution accuracy and fast convergence speed, and is very suitable for solving complex function optimization problems under multiple constraints.

[0025] Specifically, in step (1-2)

[0026] Minimize the delay cost

[0027]

[0028] Where: t is the planning period, T is the total planning period set, P is the penalty cost coefficient for unsatisfied demand per unit period and per unit quantity of product, S t is the number of unmet demands for products in period t, and its calculation formula is:

[0029]

[0030] Among them: GR t is the demand quantity of the product in period t, Q t is the planned production quantity of the product in period t, OI is the initial inventory quantity of the product at the beginning of the planning period, BI t The initial inventory quantity of the product in period t;

[0031] Minimize inventory cost

[0032]

[0033] Where: H is the inventory occupancy cost coefficient of unit quantity per unit cycle, AI t is the average inventory quantity of the product in period t, and its calculation formula is as follows:

[0034]

[0035] Among them, EI t is the ending inventory quantity of the product in period t;

[0036] The maximum equilibrium production index is

[0037]

[0038] Where: Q t is the planned production quantity of the product in period t, is the average planned production quantity of each product, and its calculation formula is as follows:

[0039]

[0040] The product inventory constraints are:

[0041]

[0042]

[0043] Among them, SS t is the safety inventory quantity of the product in period t, MI t is the maximum allowable inventory quantity of the product in period t;

[0044] Where, the initial inventory quantity of the product in period t is:

[0045]

[0046] At the beginning of the planning period, i.e., t=1, the initial inventory quantity of the product is equal to the given initial value OI. In subsequent periods, i.e., when t>1, the initial inventory quantity of the product is equal to the ending inventory quantity of the previous period's product.

[0047] Ending inventory quantity of product in period t:

[0048]

[0049] At the beginning of the planning period, i.e., t=1, the ending inventory quantity of the product = the initial inventory quantity of the product + the planned production quantity of the product - the demand quantity of the product. When the value is less than or equal to zero, the ending inventory quantity is zero;

[0050] In subsequent periods, that is, when t>1, the ending inventory quantity of the product = the initial inventory quantity of the current product + the planned production quantity of the current product - the demand quantity of the current product - the cumulative number of products that did not meet the demand in the previous period. When the value is less than or equal to zero, the ending inventory quantity is zero;

[0051] The material constraints are:

[0052]

[0053]

[0054] Among them, BI mt is the initial inventory quantity of intermediate material m in period t, GR 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, GR nt is the demand quantity of raw material n in period t;

[0055] The capacity constraints are:

[0056]

[0057] Among them, C t is the available normal production capacity in period t, expressed in production quantity;

[0058] The non-negative and integer constraints of planned output are:

[0059] Q t ≥0, Q t ∈Z

[0060] Z is an integer. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is the flow chart of the improved NSGA-II algorithm of the present invention. DETAILED DESCRIPTION

[0062] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0063] like Figure 1 As shown, the present invention proposes a multi-objective integrated production planning and scheduling method based on improved NSGA-II, which mainly includes the following steps:

[0064] Step (1): Construct a multi-objective integrated production planning model based on balanced production, specifically:

[0065] Step (1-1): Set constraints;

[0066] a) Set the product inventory constraint as follows: the beginning and ending inventory quantities of each period must not be less than the safety stock quantity and not exceed the maximum allowable inventory quantity, expressed as the following formula:

[0067]

[0068]

[0069] Among them, BI t The initial inventory quantity of the product in period t, EI t is the ending inventory quantity of the product in period t, SS t is the safety inventory quantity of the product in period t, MI t is the maximum allowable inventory quantity of the product in period t;

[0070] Where, the initial inventory quantity of the product in period t is:

[0071]

[0072] Among them: OI is the initial inventory quantity of the product at the beginning of the planning period, EI t＝1 The ending inventory quantity of the previous period's product;

[0073] At the beginning of the planning period, i.e., t=1, the initial inventory quantity of the product is equal to the given initial value OI. In subsequent periods, i.e., when t>1, the initial inventory quantity of the product is equal to the ending inventory quantity of the previous period's product.

[0074] Ending inventory quantity of product in period t:

[0075]

[0076] Among them: GR t is the demand quantity of the product in period t, Q t is the planned production quantity of the product in period t, S (t-1) The cumulative number of products that did not meet demand in the previous period;

[0077] At the beginning of the planning period, i.e., t=1, the ending inventory quantity of the product = the initial inventory quantity of the product + the planned completion quantity of the product - the demand quantity of the product. When the value is less than or equal to zero, the ending inventory quantity is zero;

[0078] Due to the unmet product demand, the ending inventory quantity of the product in subsequent periods, that is, when t>1 = the initial inventory quantity of the current product + the planned production quantity of the current product - the demand quantity of the current product - the cumulative quantity of the unmet demand products in the previous period. When the value is less than or equal to zero, the ending inventory quantity is zero;

[0079] The calculation formula for the cumulative number of products that have not met demand in period t is:

[0080]

[0081] At the beginning of the planning period, that is, t = 1, the cumulative number of products with unmet demand = product demand quantity - product planned production quantity - product initial inventory quantity. When this value is less than or equal to zero, the cumulative number of products with unmet demand at the beginning of the planning period is zero, indicating that there are no products with unmet demand.

[0082] The cumulative number of products with unmet demand in subsequent periods (when t>1) = the cumulative number of products with unmet demand in the previous period + the product demand quantity in this period - the planned production quantity of the product in this period - the inventory quantity of the product in this period. When this 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] b) Set the material constraint condition as follows: intermediate materials and raw materials cannot be out of stock, which can be expressed as follows:

[0084]

[0085]

[0086] Among them, BI mt is the initial inventory quantity of intermediate material m in period t, GR 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, GR nt is the demand quantity of raw material n in period t;

[0087] Among them: The demand quantity of intermediate material m in period t:

[0088]

[0089] Among them, m is the intermediate material, M is the intermediate material set, LT m The minimum production lead time for intermediate material m required to produce the product, B m The quantity of intermediate material m required to produce the product;

[0090] Where GR mt The demand quantity of intermediate materials in period t = the demand quantity of all intermediate materials in period t + LT mThe sum of the planned completion quantity during the period and the product of the quantity of intermediate material m required to produce each unit of product;

[0091] Initial inventory quantity of intermediate material m in period t:

[0092]

[0093] Among them, OI m N is the initial inventory quantity of intermediate material m at the beginning of the planning period; t is the normal working time of period t, PR m is the production rate of intermediate material m (production quantity per shift), SR m is the production loss rate of intermediate material m;

[0094] The demand quantity of raw material n in period t is:

[0095]

[0096] Among them, n is the raw material, RM is the raw material set, B n The amount of raw material n required to produce a product, GR mt is the demand quantity of intermediate material m in period t;

[0097] Where GR nt The demand quantity of raw materials in period t = the total demand quantity of raw materials in period t + LT n The sum of the planned completion quantity during the period and the product of the quantity of raw materials n required to produce a unit of product;

[0098] Initial inventory quantity of raw material n in period t:

[0099]

[0100] Among them, OI n is the initial inventory quantity of raw material n at the beginning of the planning period;

[0101] c) 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, expressed as:

[0102]

[0103] Among them, C t is the available normal production capacity in period t, expressed in production quantity;

[0104] d) Set the planned output non-negative and integer constraints as follows: the planned output of the product in each period must be non-negative and integer, expressed as:

[0105] Q t ≥0, Q t ∈Z

[0106] Z is an integer;

[0107] Step (1-2): Based on the above-mentioned constrained spare parts, define the minimum delay cost, minimum inventory cost and maximum equilibrium production indicators in the production process as follows:

[0108] Minimize the delay cost

[0109]

[0110] Where: t is the planning period, T is the total planning period set, and P is the penalty cost coefficient for unsatisfied demand per unit quantity of product per unit period;

[0111] Minimizing inventory cost is

[0112]

[0113] Where: H is the inventory occupancy cost coefficient of unit quantity per unit cycle, AI t is the average inventory quantity of the product in period t, and its calculation formula is as follows:

[0114]

[0115] The maximum equilibrium production index is

[0116]

[0117] in: is the average planned production quantity of each product, and its calculation formula is as follows:

[0118]

[0119] Step (1-3): Taking into account the non-negative and integer constraints of product inventory, materials, production capacity and planned output, a multi-objective integrated production planning model based on balanced production is obtained with the goals of minimizing tardiness cost, minimizing inventory cost and maximizing balanced production index;

[0120] Step (2): Based on the multi-objective integrated production planning process of the improved NSGA-II, the actual production plan and production scheduling Gantt chart are obtained, specifically: the encoding method of NSGA-II is set, and individuals are used to represent a production operation plan scheme, the individual dimension represents the number of planning cycles, and the position information of each dimension represents the planned output of each cycle. The delay cost, inventory cost, and penalty cost for not satisfying balanced production are used as the fitness function of the improved NSGA-II. Assuming that the number of individuals in the initial population is N, the multi-objective integrated production planning model of balanced production is solved.

[0121] Step (2-1): Set the algorithm parameters, including the number of individuals N in the initial population, the maximum number of iterations GEN, the mutation scaling factor F and the crossover probability CR;

[0122] Step (2-2): Use the reverse learning strategy to generate the number of individuals N of the initial population. The specific steps are as follows:

[0123] Step (2-2-1) Randomly initialize N individual positions Z in the search space i (i=1,2,…,N) as the initial population RP;

[0124] Step (2-2-2) According to the definition, each individual Z in the initial population RP i The reverse individual Z′ i Constitute the reverse population OP;

[0125] Step (2-2-3) merges the initial population RP and the reverse population OP, sorts the 2N individuals in ascending order according to their fitness values, and selects the top N individuals as the individuals of the initial population;

[0126] Step (2-3): sort the individuals into different non-dominant levels according to their dominance relationship;

[0127] Step (2-4): The crowding distance of individuals is obtained by summing up the distance differences between adjacent individuals in the same non-dominated level on each sub-goal. The crowding distance of each individual in the same non-dominated level is used to evaluate the quality of individuals in the same non-dominated level, and solutions with smaller crowding distances are removed to improve the diversity of the solution set.

[0128] Step (2-5): Select operation, using the binary tournament strategy, randomly select two individuals from the population. If the two individuals have different non-dominated ranks, the individual with the smaller non-dominated rank is selected as the parent. If the two individuals have the same non-dominated rank, the individual with the larger crowding distance is selected as the parent.

[0129] Step (2-6): Genetic operation, performing mutation operation and crossover operation in sequence to generate offspring population;

[0130] Step (2-7): merge the parent and the offspring, merge the parent population and the offspring population, perform non-dominated sorting on the merged population, and then prune to obtain a new generation population through the elite strategy;

[0131] Step (2-8): 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 to iterate and repeat steps 2-3 to 2-8 for the new population;

[0132] Step (2-9): Output the optimized individuals and obtain the production plan and scheduling Gantt chart.

Claims

1. A multi-objective integrated production planning and scheduling method based on improved NSGA-II, characterized in that: The specific steps include: Step (1): Construct a multi-objective integrated production planning model based on balanced production, specifically: Step (1-1): Set constraints; a) Set product inventory constraints as follows: the initial inventory quantity and the final inventory quantity of each period of the product must not be less than the safety stock quantity and not exceed the maximum allowable inventory quantity; b) Set the material constraints as follows: intermediate materials and raw materials cannot be out of stock: c) 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; d) Set the planned output non-negative and integer constraints as follows: the planned output of the product in each period must be non-negative and integer; Step (1-2): Based on the above-mentioned constrained spare parts, define the minimization of delay cost, minimization of inventory cost and maximization of balanced production indicators in the production process; Step (1-3): Obtain a multi-objective integrated production planning model based on balanced production with the objectives of minimizing tardiness cost, minimizing inventory cost and maximizing balanced production index under the non-negative and integer multiple constraints of product inventory, materials, production capacity and planned output; Step (2): Based on the multi-objective integrated production planning process of the improved NSGA-II, the actual production plan and scheduling Gantt chart are obtained, specifically: The encoding method of NSGA-II is set, and individuals are used to represent a production operation plan. The individual dimension represents the number of planning cycles. The position information of each dimension represents the planned output of each cycle. The delay cost, inventory cost, and penalty cost of not satisfying balanced production are used as the fitness function of the improved NSGA-II. The multi-objective integrated production planning model of balanced production is solved. Step (2-1): Set the algorithm parameters, including individual population size, maximum number of iterations, mutation scaling factor and crossover probability; Step (2-2): Set the number of individuals in the initial population; Step (2-3): sort the individuals into different non-dominant levels according to their dominance relationship; Step (2-4): Evaluate the quality of individuals in the same non-dominated level by their crowding distance; Step (2-5): Select operation, using the binary tournament strategy, randomly select two individuals from the population. If the two individuals have different non-dominated ranks, the individual with the smaller non-dominated rank is selected as the parent. If the two individuals have the same non-dominated rank, the individual with the larger crowding distance is selected as the parent. Step (2-6): Genetic operation, performing mutation operation and crossover operation in sequence to generate offspring population; Step (2-7): merge the parent and the offspring, merge the parent population and the offspring population, perform non-dominated sorting on the merged population, and then prune to obtain a new generation population through the elite strategy; Step (2-8): Iterative optimization, determine whether this iteration is the maximum number of iterations, if so, output the optimal solution set to obtain the optimized individual; Otherwise, continue the iteration and repeat steps 2-3 to 2-8 for the new population; Step (2-9): Output the optimized individuals and obtain the production plan and scheduling Gantt chart.

2. A multi-objective integrated production planning and scheduling method based on improved NSGA-II as claimed in claim 1, characterized in that: In step (1-2) Minimize the delay cost Where: t is the planning period, T is the total planning period set, P is the penalty cost coefficient for unsatisfied demand per unit period and per unit quantity of product, S t is the number of unmet demands for products in period t, and its calculation formula is: Among them: GR t is the demand quantity of the product in period t, Q t is the planned production quantity of the product in period t, OI is the initial inventory quantity of the product at the beginning of the planning period, BI t The initial inventory quantity of the product in period t; Minimizing inventory cost is Where: H is the inventory occupancy cost coefficient of unit quantity per unit cycle, AI t is the average inventory quantity of the product in period t, and its calculation formula is as follows: Among them, EI t is the ending inventory quantity of the product in period t; The maximum equilibrium production index is Where: Q t is the planned production quantity of the product in period t, is the average planned production quantity of each product, and its calculation formula is as follows:

3. A multi-objective integrated production planning and scheduling method based on improved NSGA-II as claimed in claim 2, characterized in that: The product inventory constraints are: Among them, SS t is the safety inventory quantity of the product in period t, MI t is the maximum allowable inventory quantity of the product in period t; Where, the initial inventory quantity of the product in period t is: At the beginning of the planning period, i.e., t=1, the initial inventory quantity of the product is equal to the given initial value OI. In subsequent periods, i.e., when t>1, the initial inventory quantity of the product is equal to the ending inventory quantity of the previous period's product. Ending inventory quantity of product in period t: At the beginning of the planning period, i.e., t=1, the ending inventory quantity of the product = the initial inventory quantity of the product + the planned production quantity of the product - the demand quantity of the product. When the value is less than or equal to zero, the ending inventory quantity is zero; In subsequent periods, that is, when t>1, the ending inventory quantity of the product = the initial inventory quantity of the current product + the planned production quantity of the current product - the demand quantity of the current product - the cumulative number of products that did not meet the demand in the previous period. When the value is less than or equal to zero, the ending inventory quantity is zero; The material constraints are: Among them, BIm t is the initial inventory quantity of intermediate material m in period t, GRm t is the demand quantity of intermediate material m in period t, BIn t is the initial inventory quantity of raw material n in period t, GRn t is the demand quantity of raw material n in period t; The capacity constraints are: Among them, C t为 The normal production capacity available in period t, expressed in production quantity; The non-negative and integer constraints of planned output are: Q∈Z Z is an integer.

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