CN110956320B - Address selecting and distributing method of sustainable supply chain based on dynamic relaxation intelligent algorithm - Google Patents
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Abstract
The invention discloses a sustainable supply chain address selecting and distributing method based on a dynamic relaxation intelligent algorithm, which comprises the following steps: step 1, based on comprehensive weighted scoring, taking minimized production cost, carbon transaction cost and pollution discharge cost as optimization targets, and establishing a three-level structure sustainable supply chain model integrating supply chain site selection and quantity distribution; and 2, converting the site selection and the quantity distribution of the supply chain into vector forms, and performing iterative updating operation on the solution population by using a dynamic relaxation group intelligent algorithm and combining the fitness function value with the dynamic relaxation factor until the optimal approximate solution of the objective function is obtained, so as to obtain the site selection decision and the quantity distribution scheme of the sustainable supply chain network, and provide a high-quality and high-efficiency solution for designing the complex sustainable supply chain.
Description
Technical Field
The invention belongs to the technical field of sustainable supply chain site selection and collaborative scheduling, and particularly relates to a site selection and allocation method of a sustainable supply chain based on a dynamic relaxation intelligent algorithm.
Background
The supply chain is a network composed of suppliers, manufacturers and clients, and aims to address and distribute the plurality of factories and the plurality of clients in the sustainable supply chain, the suppliers in the sustainable supply chain process raw materials and provide the raw materials for the manufacturers, and the manufacturers optimize the address decision and the quantity distribution of the supply chain in the process of distributing the raw materials to the clients, and simultaneously comprehensively consider environmental factors (carbon emission and sewage emission), so that the influence of the carbon emission in the production of each link on the environment is effectively reduced. In recent years, the problem of site selection and scheduling of a supply chain has become a popular research direction of supply chain management, and research on supply chain scheduling by a plurality of students is concentrated in the directions of logistics management, supply time and the like, and the influence of site selection decision and allocation of processing raw materials and final products on sustainable production is considered, so that a sustainable supply chain network considering economic benefits and environmental benefits is established, the production efficiency of the supply chain is improved, the consumption of resources is reduced, and finally the production cost and the environmental influence of the supply chain are reduced by optimizing the site selection and allocation of the supply chain. In terms of the method, the traditional particle swarm algorithm solving method has the problems of overlong searching time, easiness in sinking into local optimal solution and the like, and an intelligent algorithm combining dynamic relaxation factors is provided for realizing decision making and scheduling optimization of a sustainable supply chain.
Disclosure of Invention
Based on the defects of the prior art, the technical problem solved by the invention is to provide a sustainable supply chain address selecting and distributing method based on a dynamic relaxation intelligent algorithm, so that the optimal supply chain participant combination is effectively selected, the cost of a supply chain network and the influence on the environment are reduced, and a high-quality and high-efficiency solution is provided for the performance balance of the sustainable supply chain on the economic, social and environmental sides.
In order to solve the technical problems, the invention is realized by the following technical scheme:
the invention provides a sustainable supply chain address selecting and distributing method based on a dynamic relaxation intelligent algorithm, which comprises the following steps:
step 1: based on the comprehensive weighted score, taking the minimum production cost, the carbon transaction cost and the pollution discharge cost as optimization targets, and establishing a three-level structure sustainable supply chain model integrating supply chain site selection and quantity distribution;
step 2: converting the supply chain site selection and quantity allocation into vector forms, and using a dynamic relaxation group intelligent algorithm to execute iterative updating operation on the solution population by combining the fitness function value with the dynamic relaxation factor until the optimal approximate solution of the objective function is obtained, so as to obtain the site selection decision and quantity allocation scheme of the sustainable supply chain network.
Further, the specific steps of the step 2 are as follows:
step 2.1: obtaining a supplier set S and a producer set P with high comprehensive scores based on the comprehensive weighted scores;
step 2.2: converting the site selection and the quantity allocation of the supply chain into an x vector representation, initializing all particles in the solution population, using a dynamic relaxation group intelligent algorithm, performing iterative updating operation on the solution population by combining the fitness function value with the dynamic relaxation factor until the optimal approximate solution of the objective function is obtained, obtaining the site selection decision and the quantity allocation scheme of the sustainable supply chain network, and calculating and recording the fitness values of the solution population and the corresponding population.
Optionally, the step 2.1 includes:
step 2.1.1: the comprehensive weighted scoring index of the supplier comprises the production cost of each raw material of the supplier, the transaction cost of carbon quota, the transaction cost of redundant carbon quota, the operation cost and the corresponding cost of pollution discharge generated by each raw material, and the specific calculation method is as follows:
the calculation formula for the composite score of each raw material production cost of the supplier is as follows:
wherein ,αSAm Weighting the production cost of each raw material of the suppliers; PSM (power management module) im The cost of producing a unit of raw material m for supplier i;
the composite score for the carbon quota transaction costs for the supplier is calculated as follows:
WSC i =αSB×(1/CSP i )
wherein αSB is a weight for the carbon quota transaction cost for the provider; CSP (compact size reduction package) i A cost of purchasing a unit carbon quota amount for vendor i;
the composite score for the excess carbon quota transaction costs for the supplier is calculated as follows:
WSCR i =αSC×(1/CSRP i )
where αsc is a weight for the excess carbon quota transaction cost for the provider; CSRP i Purchasing a cost for provider i of excess/sell excess carbon allowance by one unit carbon allowance;
the comprehensive score of the operation cost of the provider is calculated as follows:
WSO i =αSD×(1/OSF i )
wherein αsd is a weight of the operational cost of the provider; OSF (OSF) i The operating cost for vendor i;
the comprehensive score of the cost corresponding to the pollution discharge generated by each raw material of the supplier is calculated as follows:
wherein ,αSEm Weighting the cost of blowdown for each raw material of the supplier; WSM (Wireless sensor module) im Producing a unit of the amount of waste produced by the raw material m for the supplier i;
the comprehensive scores of pollution treatment measures of suppliers are firstly classified, special symbols and Chinese fonts in the scores are replaced by corresponding scoring numbers, and then the treatment scores are calculated, wherein the calculation formula is as follows:
wherein ,αSMm Weight of pollution control measures for raw materials, SCM im Scoring pollution abatement measures for each raw material of each supplier;
the vendor's recoverability composite score is calculated as follows:
wherein ,αSRm Weight of recyclability of each raw material, SR im Scoring recyclability of each raw material for each supplier;
the product quality composite score of the supplier is calculated as follows:
wherein ,αSQm SPQ is a weight for quality of each raw material product of suppliers im Scoring the product quality of each raw material for each supplier;
in summary, for each cost composite weighted score of the provider, the calculation formula is as follows:
step 2.1.2: the comprehensive weighted scoring index of the producer comprises the production cost of each product of the producer, the transaction cost of the carbon quota, the transaction cost of the redundant carbon quota, the operation cost and the corresponding cost of pollution discharge generated by each raw material, and the specific calculation method is as follows:
for the comprehensive score of the production cost of each product of the manufacturer, the calculation formula is as follows:
wherein ,ρPAn The weight of the production cost of each raw material of the producer; PPN (PPN) jn The cost of producing a unit of product n for producer j;
the composite score for the manufacturer's carbon quota transaction costs is calculated as follows:
WPC j =ρPB×(1/CPP j )
wherein ρPB is the weight of the manufacturer's carbon quota transaction costs; CPP (CPP) j A cost of purchasing a unit carbon quota amount for producer j;
the composite score for the excess carbon quota transaction costs for the manufacturer is calculated as follows:
WPCR j =ρPC×(1/CPRP j )
wherein ρpc is a weight for the manufacturer's excess carbon quota transaction costs; CPRP (CPRP) j Purchasing a cost for excess/sell excess carbon allowance by one unit carbon allowance for producer j;
the comprehensive score of the operation cost of the manufacturer is calculated as follows:
WPCR j =ρPD×(1/OPF j )
wherein ρpd is a weight of the operating cost of the manufacturer; OPF (optical fiber) j The operating cost for producer j;
the comprehensive score of the cost corresponding to the pollution discharge generated by each product of the manufacturer is calculated as follows:
wherein ,ρPEn Weighting the pollution discharge cost of each raw material of the manufacturer; WPN (Wireless Power network) jn The sewage discharge capacity generated by a unit of product n is produced for a producer j;
the pollution treatment measures of the manufacturers are comprehensively scored, the scores are classified, special symbols and Chinese fonts in the scores are replaced by corresponding scoring numbers, and then the treatment scores are calculated according to the following calculation formula:
wherein ,ρPNn Weighting pollution control measures of each product, PCN jn Scoring pollution abatement measures for each product of each manufacturer;
the manufacturer's recoverability composite score is calculated as follows:
wherein ,αPRn Weight of recyclability of each product, PR jn Scoring recyclability of each product for each manufacturer;
the product quality comprehensive score of the manufacturer is calculated as follows:
wherein ,αPQn Weight of quality of raw material products of manufacturers, PPQ jn Scoring a product quality of each product for each manufacturer;
in summary, for the cost composite weighted score of each item of the manufacturer, the calculation formula is as follows:
optionally, the specific steps of step 2.2 are as follows:
step 2.2.1: constructing an initial solution population, determining the population scale of the solution population, the space dimension D of particles and the maximum iteration number T, using a Jacobi iteration algorithm according to the order constraint of a customer and the constraint of keeping the proportion of the raw material purchase quantity of a manufacturer to the product production quantity, obtaining a group of rapidly converged values through 10 iterations, and initializing the values to the position of each particle in the solution population, wherein the formula is as follows:
i in the formula is the number of initial groups, D is the space dimension, and T is the maximum update times;
from among solution populationsJudging whether the suppliers and the manufacturers operate or not, and judging the corresponding site selection decision, wherein the formula is as follows:
the address selection decision needs to be updated simultaneously when the solution population is updated each time; adcp ijm Representing the number of raw materials m supplied by supplier i to producer j, adcp jkn Representing the number of products n that manufacturer j provides to customer k;
step 2.2.2: an initial particle movement velocity is constructed, and the calculation formula is as follows:
step 2.2.3: and processing boundary positions of particles and a speed limit of particle updating, and correcting particles which do not meet the condition and the particle updating speed, wherein the calculation formula is as follows:
x in the formula max and xmin For maximum and minimum values of each particle, V max and Vmin A highest moving speed and a lowest moving speed for each particle;
step 2.2.4: according to the individual particles, a corresponding site selection decision is obtained, the fitness value of the individual particles is calculated and compared through a fitness function, the historical best position pbest and the global best position gbest of the particles i are updated and recorded, and the calculation formula is as follows:
in the formulaOptimal particle position for the extremum of the individual, +.>Particle location for a globally optimal solution;
step 2.2.5: particle movement speed: updating individual particle movement speeds of the correction solution population by combining fitness functions with dynamic relaxation factors;
step 2.2.6: vendor layer: for each supplier S i If the number of supply allocations does not meet the upper production limit MQRM of the supplier im ≥∑ j∈J Adcp ijm Then describe provider S i The amount of raw material to be supplied exceeds the supplier S i The upper supply limit that can be provided needs to be reconsidered by the supplier S i Updating each particle in the solution population in combination with the dynamic relaxation factor while obtaining a correspondence according to the new supply allocation number up to the supplier S i Up to the provider S i Until the constraint condition is satisfied;
step 2.2.7: manufacturer layer: for each producer P j If the production allocation quantity does not meet the production upper limit MQRM of the manufacturer jn ≥∑ k∈K Adcp jkn Description of manufacturer P j The number of products to be provided exceeds the manufacturer P j The upper production limit that can be provided requires reconsideration of the manufacturer P j Updating each particle in the solution population in combination with dynamic relaxation factors while obtaining a correspondence according to the new supply allocation number up to the producer P j Up to the manufacturer P j Until the constraint condition is satisfied;
step 2.2.8: calculating the fitness value of the individual particles according to the mathematical model of the objective function;
step 2.2.9: for individual particles in the solution population, comparing the fitness value of the current particle position with the fitness value of the historical optimal position, and if the fitness value of the current particle is better, updating the current particle position into the historical optimal position, wherein the calculation formula is as follows:
step 2.2.10: for individual particles in the solution population, comparing the fitness value of the current particle position with the fitness value of the global optimal position, and if the fitness value of the current particle is better, updating the current particle position into the global optimal position, wherein the calculation formula is as follows:
step 2.2.11: and judging whether the algorithm meets the end condition, if the algorithm does not meet the end condition, returning to the step 2.2.5 to continue iterative updating until the algorithm meets the end condition, stopping calculation, ending the algorithm and outputting the global optimal solution.
By the adoption of the method for selecting and distributing the sustainable supply chain based on the dynamic relaxation intelligent algorithm, the efficiency of the sustainable supply chain for selecting and distributing is improved, the sustainable supply chain collaborative design theory is adopted, the carbon trade market quota cost, the carbon trade cost among enterprises, the sewage discharge cost and the production cost are subjected to collaborative design, the intelligent algorithm based on the dynamic relaxation factor is adopted, the optimal supply chain participant combination is effectively selected, the cost of a supply chain network and the influence on the environment are reduced, and a high-quality and high-efficiency solution is provided for sustainable production of the sustainable supply chain.
The invention relates to a sustainable supply chain addressing and distribution method based on a dynamic relaxation intelligent algorithm, which aims at optimizing minimized production cost, carbon transaction cost and pollution discharge cost and establishes a supply chain mathematical model of a three-level structure for addressing and distribution of integrated manufacturers. Meanwhile, an intelligent solving method based on dynamic relaxation factors is provided, supply chain site selection and quantity distribution are converted into vector forms, correction operation is carried out by combining fitness functions with the dynamic relaxation factors, corresponding site selection decisions are obtained according to the vectors, iterative updating operation is carried out on solution populations by combining fitness function values with the dynamic relaxation factors until optimal approximate solutions of objective functions are obtained, and site selection decisions and quantity distribution schemes of a sustainable supply chain network are obtained. The intelligent algorithm combined with the dynamic relaxation factor adopts the Lagrange relaxation algorithm to obtain the dynamic relaxation factor, optimize particle optimizing speed, strengthen local searching capability of each particle, improve convergence capability of the particles, and have good efficiency in convergence speed and convergence result. The algorithm solves the problem of the addressing and the distribution of the sustainable supply chain, reduces the cost of the sustainable supply chain, reduces the influence on the environment, improves the production efficiency, and can provide a high-quality and high-efficiency solution for the problem of the addressing and the distribution of the sustainable supply chain network.
The foregoing description is only an overview of the present invention, and is intended to be implemented in accordance with the teachings of the present invention, as well as to provide further clarity and understanding of the above and other objects, features and advantages of the present invention, as described in the following detailed description of the preferred embodiments, taken in conjunction with the accompanying drawings.
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In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings of the embodiments will be briefly described below.
FIG. 1 is a flow chart of a method of addressing and assigning a sustainable supply chain based on a dynamic relaxation intelligent algorithm of the present invention.
Detailed Description
The following detailed description of the invention, taken in conjunction with the accompanying drawings, illustrates the principles of the invention by way of example and by way of a further explanation of the principles of the invention, and its features and advantages will be apparent from the detailed description. In the drawings to which reference is made, the same or similar components in different drawings are denoted by the same reference numerals.
Unlike sustainable supply chain networks of general methods, the present invention not only incorporates environmental impact into the supply chain network modeling, but also considers production costs and carbon trade quota costs, sewage costs generated during production, and incorporates the operational costs of suppliers and manufacturers into a mathematical model.
The invention relates to a sustainable supply chain address selecting and distributing method based on a dynamic relaxation intelligent algorithm, which comprises the following steps: the method comprises the following steps:
step 1: based on the comprehensive weighted score, taking the minimum production cost, the carbon transaction cost and the pollution discharge cost as optimization targets, and establishing a three-level structure sustainable supply chain model integrating supply chain site selection and quantity distribution; the mathematical model includes an objective function and a constraint, the objective function having the formula:
wherein I represents the vendor number, I ε I; j represents the manufacturer number, J e J; k represents the customer number, K ε K; m represents the raw material number, M epsilon M; n represents the product number, N ε N; d (D) kn Order total amount of product n for customer k; PSM (power management module) im The cost of producing a unit of raw material m for supplier i; PPN (PPN) jn The cost of producing a unit of product n for producer j; WSM (Wireless sensor module) im Producing a unit of the amount of waste produced by the raw material m for the supplier i; WPN (Wireless Power network) jn The sewage discharge capacity generated by a unit of product n is produced for a producer j; CSQ (common sense amplifier) i A carbon trade quota market unit amount (planning amount) purchased for supplier i; CPQ (CPQ) j Carbon trade quota market units (planning amounts) purchased by producer j; CSPM (common physical distribution System) im Producing a carbon emission amount per unit of raw material m for supplier i; CPPN (CPPN) jn Producing a carbon emission per unit of product n for producer j; CSP (compact size reduction package) i A cost of purchasing a unit carbon quota amount for vendor i; CPP (CPP) j A cost of purchasing a unit carbon quota amount for producer j; CSRP i Purchasing a cost for provider i of excess/sell excess carbon allowance by one unit carbon allowance; CPRP (CPRP) j Purchasing a cost for excess/sell excess carbon allowance by one unit carbon allowance for producer j; MQRM im A maximum production quantity of raw material m that can be produced for supplier i; MQRM jn Maximum production of product n that can be produced for producer jNumber of pieces; OSF (OSF) i The operating cost for vendor i; OPF (optical fiber) j The operating cost for producer j;
Adcp ijm representing the number of raw materials m supplied by supplier i to producer j, adcp jkn Representing the number of products n that manufacturer j provides to customer k;
os i indicating whether or not vendor i is selected as a supply chain partner, 1 representing selection, 0 representing non-selection; op (op) j Indicating whether producer j is selected as a supply chain partner, 1 representing selection, 0 representing non-selection;
the limiting conditions comprise preconditions and constraint conditions, wherein the preconditions are as follows: all customer orders must be satisfied; the supplier has a supply upper limit constraint and the producer has a production upper limit constraint; the operation cost is fixed in the period of each provider and producer; the constraint conditions are as follows:
the customer's order needs must satisfy the constraints:
the raw material purchase quantity is consistent with the product production quantity in proportion:
wherein ,MTN mn representing the quantitative relation proportion between the raw material m and the product n;
vendor supply force constraints:
wherein MQRM im Represents the maximum number of raw materials m that can be provided by supplier i;
manufacturer productivity constraints:
wherein ,MQRM jn representing the maximum production quantity of the product n by the manufacturer j;
non-negative integer and binary constraints:
op i ∈{0,1} (8)
op j ∈{0,1} (9)
step 2: aiming at the problem of addressing and distribution of a sustainable supply chain, the invention converts the addressing and quantity distribution of the supply chain into a vector form, uses a dynamic relaxation group intelligent algorithm to obtain the optimal approximate solution of an objective function by combining a fitness function value with a dynamic relaxation factor, and obtains the addressing decision and quantity distribution scheme of the sustainable supply chain network. The first stage of the dynamic relaxation intelligent algorithm is to comprehensively evaluate a provider layer and a manufacturer layer by using comprehensive weighted scores to obtain a provider and a manufacturer with better evaluation scores, preferentially enumerate all candidate cooperators which can meet the customer order, eliminate the rest of manufacturers which cannot meet the customer order, calculate an objective function approximation value for each of the rest of candidate suppliers, and select the candidate manufacturer with the minimum objective function approximation value as a partner of a final supply chain network; the second stage is to convert the address and quantity distribution of the supply chain into vector form aiming at the address selecting problem and the distribution problem of the sustainable supply chain, obtain the corresponding address selecting decision according to the quantity distribution among different layers of the supply chain, and then use a dynamic relaxation group intelligent algorithm to execute iterative updating operation on the solution population by combining the fitness function value with the dynamic relaxation factor until the optimal approximate solution of the objective function is obtained, so as to obtain the address selecting decision and the quantity distribution scheme of the sustainable supply chain network.
The specific steps of the step 2 are as follows:
step 2.1: obtaining a supplier set S and a producer set P with high comprehensive scores based on the comprehensive weighted scores; the algorithm calculates an evaluation score for candidate manufacturers, and obtains comprehensive weighted scores of the candidate manufacturers by using a weighted average method according to economic cost (production cost, pollution discharge cost, operation cost, carbon cost and the like) of the candidate manufacturers, environmental influence (pollution treatment measures, recoverability), social evaluation (product quality) and other factors, and screens the partner with the lowest cost; adopting an bubbling sequencing algorithm to respectively select the first omega suppliers and manufacturers with high comprehensive scores, and finally obtaining an optimal supplier set S and an optimal manufacturer set P;
the specific steps of the step 2.1 are as follows:
respectively listing scoring indexes when the suppliers and the manufacturers prefer; giving different weights to each index according to different proportions of the index in the value of the objective function;
step 2.1.1: the grading indexes of the suppliers comprise the production cost of each raw material of the suppliers, the transaction cost of carbon quota, the transaction cost of redundant carbon quota, the operation cost and the corresponding cost of pollution discharge generated by each raw material; the specific method comprises the following steps:
the calculation formula for the composite score of each raw material production cost of the supplier is as follows:
wherein ,αSAm Weighting the production cost of each raw material of the suppliers;
the composite score for the carbon quota transaction costs for the supplier is calculated as follows:
WSC i =αSB×(1/CSP i ) (11)
wherein αSB is a weight for the carbon quota transaction cost for the provider;
the composite score for the excess carbon quota transaction costs for the supplier is calculated as follows:
WSCR i =αSC×(1/CSRP i ) (12)
where αsc is a weight for excess carbon quota transaction costs for the provider;
the comprehensive score of the operation cost of the provider is calculated as follows:
WSO i =αSD×(1/OSF i ) (13)
wherein αsd is a weight of the operational cost of the provider;
the comprehensive score of the cost corresponding to the pollution discharge generated by each raw material of the supplier is calculated as follows:
wherein ,αSEm Weighting the cost of blowdown for each raw material of the supplier;
the comprehensive scores of pollution treatment measures of suppliers are firstly classified, special symbols and Chinese fonts in the scores are replaced by corresponding scoring numbers, and then the treatment scores are calculated, wherein the calculation formula is as follows:
wherein ,αSMm Weight of pollution control measures for raw materials, SCM im Scoring pollution abatement measures for each raw material of each supplier;
the vendor's recoverability composite score is calculated as follows:
wherein ,αSRm Weight of recyclability of each raw material, SR im Scoring recyclability of each raw material for each supplier;
the product quality composite score of the supplier is calculated as follows:
wherein ,αSQm For weight of quality of each raw material product, SPQ im Scoring the product quality of each raw material for each supplier;
in summary, for each cost composite score of the provider, the calculation formula is as follows:
step 2.1.2: the grading indexes of the manufacturer comprise the production cost of each product of the manufacturer, the transaction cost of the carbon quota, the transaction cost of the redundant carbon quota, the operation cost and the corresponding cost of pollution discharge generated by each raw material; the specific method comprises the following steps:
for the comprehensive score of the production cost of each product of the manufacturer, the calculation formula is as follows:
wherein ,ρPAn The weight of the production cost of each raw material of the producer;
the composite score for the manufacturer's carbon quota transaction costs is calculated as follows:
WPC j =ρPB×(1/CPP j ) (20)
wherein ρPB is the weight of the manufacturer's carbon quota transaction costs;
the composite score for the excess carbon quota transaction costs for the manufacturer is calculated as follows:
WPCR j =ρPC×(1/CPRP j ) (21)
wherein ρpc is a weight for the manufacturer's excess carbon quota transaction costs;
the comprehensive score of the operation cost of the manufacturer is calculated as follows:
WPCR j =ρPD×(1/OPF j ) (22)
wherein ρpd is a weight of the operating cost of the manufacturer;
the comprehensive score of the cost corresponding to the pollution discharge generated by each product of the manufacturer is calculated as follows:
wherein ,ρPEn Weighting the pollution discharge cost of each raw material of the manufacturer;
the pollution treatment measures of the manufacturers are comprehensively scored, the scores are classified, special symbols and Chinese fonts in the scores are replaced by corresponding scoring numbers, and then the treatment scores are calculated according to the following calculation formula:
wherein ,ρPNn Weighting pollution control measures of each product, PCN jn Scoring pollution abatement measures for each product of each manufacturer;
the manufacturer's recoverability composite score is calculated as follows:
wherein ,αPRn Weight of recyclability of each product, PR jn Scoring recyclability of each product for each manufacturer;
the product quality comprehensive score of the manufacturer is calculated as follows:
wherein ,αPQn Weight of quality of raw material products of manufacturers, PPQ jn Scoring a product quality of each product for each manufacturer;
in summary, for each cost composite score of the manufacturer, the calculation formula is as follows:
step 2.2: the candidate dynamic relaxation intelligent algorithm is a preferred supplier set S, a manufacturer set P and a client set D; converting the site selection and the quantity allocation of a supply chain into an x vector representation, initializing all particles in a solution population according to a Jacobi iteration method, using a dynamic relaxation group intelligent algorithm, carrying out iterative updating operation on the solution population by combining a fitness function value with a dynamic relaxation factor until an optimal approximate solution of an objective function is obtained, obtaining a site selection decision and a quantity allocation scheme of a sustainable supply chain network, calculating and recording fitness values of the solution population and the corresponding population until the intelligent algorithm meets a termination condition, ending the algorithm and outputting a global optimal solution;
the specific steps of the step 2.2 are as follows:
step 2.2.1: constructing an initial solution population, determining the population scale of the solution population, the space dimension D of particles and the maximum iteration number T, using a Jacobi iteration algorithm according to the order constraint of a customer and the constraint of keeping the proportion of the raw material purchase quantity of a manufacturer to the product production quantity, obtaining a group of rapidly converged values through 10 iterations, and initializing the values to the position of each particle in the solution population, wherein the formula is as follows:
i in the formula is the number of initial groups, D is the space dimension, and T is the maximum update times;
from among solution populationsJudging whether the suppliers and the manufacturers operate or not, and judging the corresponding site selection decision, wherein the formula is as follows:
the address selection decision needs to be updated simultaneously when the solution population is updated each time;
step 2.2.2: an initial particle movement velocity is constructed, and the calculation formula is as follows:
step 2.2.3: and processing boundary positions of particles and a speed limit of particle updating, and correcting particles which do not meet the condition and the particle updating speed, wherein the calculation formula is as follows:
x in the formula max and xmin For maximum and minimum values of each particle, V max and Vmin A highest moving speed and a lowest moving speed for each particle;
step 2.2.4: according to the individual particles, a corresponding site selection decision is obtained, the fitness value of the individual particles is calculated and compared through a fitness function, the historical best position pbest and the global best position gbest of the particles i are updated and recorded, and the calculation formula is as follows:
in the formulaOptimal particle position for the extremum of the individual, +.>Particle location for a globally optimal solution;
step 2.2.5: updating individual particle movement speeds of the modified solution population with an fitness function in combination with dynamic relaxation factors, wherein the particle update speeds in the solution population are improved as follows:
step 2.2.5.1: the update speed and position for each particle in the solution population is calculated as follows:
in the formulaFor particle speed, +.>Is the particle position, C 1 and C2 R is the acceleration coefficient 1 and r2 Is [0,1]Random numbers in between;
step 2.2.5.2: the update speed of each particle in the solution population is subjected to relaxation optimization by combining the dynamic relaxation factors, and the calculation formula is as follows:
step 2.2.5.3: the secondary gradient value is updated, and the calculation formula is as follows:
step 2.2.5.4: updating the dynamic Lagrangian relaxation factor by defaultThe values of (2) are all 0, and the calculation formula is as follows:
wherein ,the value of (2) will follow fmin and +.>The value of (2) is continuously changed and is in a monotonically decreasing trend;
step 2.2.5.5: for the updated position of each particle in the solution population, the calculation formula is as follows:
step 2.2.6: vendor layer: for each supplier S i If the number of supply allocations does not meet the upper production limit MQRM of the supplier im ≥∑ j∈J Adcp ijm Then describe provider S i The amount of raw material to be supplied exceeds the supplier S i The upper supply limit that can be provided needs to be reconsidered by the supplier S i Updating each particle in the solution population in combination with the dynamic relaxation factor while obtaining a correspondence according to the new supply allocation number up to the supplier S i Up to the provider S i Until the constraint condition is satisfied;
step 2.2.7: manufacturer layer: for each producer P j If the production allocation quantity does not meet the production upper limit MQRM of the manufacturer jn ≥∑ k∈K Adcp jkn Description of manufacturer P j The number of products to be provided exceeds the manufacturer P j The upper production limit that can be provided requires reconsideration of the manufacturer P j Updating each particle in the solution population in combination with dynamic relaxation factors while obtaining a correspondence according to the new supply allocation number up to the producer P j Up to the manufacturer P j Until the constraint condition is satisfied;
step 2.2.8: calculating the fitness value of the individual particles according to the mathematical model of the objective function;
step 2.2.9: for individual particles in the solution population, comparing the fitness value of the current particle position with the fitness value of the historical optimal position, and if the fitness value of the current particle is better, updating the current particle position into the historical optimal position, wherein the calculation formula is as follows:
step 2.2.10: for individual particles in the solution population, comparing the fitness value of the current particle position with the fitness value of the global optimal position, and if the fitness value of the current particle is better, updating the current particle position into the global optimal position, wherein the calculation formula is as follows:
step 2.2.11: judging whether the algorithm meets the end condition, if not, returning to the step 2.3 (2.2.5) to continue iterative updating until the algorithm meets the end condition, stopping calculation, ending the algorithm and outputting the global optimal solution.
In this embodiment, all codes are implemented by Matlab, and the specific experimental environment configuration is shown in table 1:
table 1 experimental environment configuration
Content | Configuration information |
Operating system | WINDOWS 10 |
Processor and method for controlling the same | 2.7GHz Intel Core i5 |
CPU core number | 4 |
Memory | 8G |
Matlab version | R2016a |
While the invention has been described with respect to the preferred embodiments, it will be understood that the invention is not limited thereto, but is capable of modification and variation without departing from the spirit of the invention, as will be apparent to those skilled in the art.
Claims (1)
1. The method for selecting and distributing the sustainable supply chain based on the dynamic relaxation intelligent algorithm is characterized by comprising the following steps of:
step 1: based on the comprehensive weighted score, taking the minimum production cost, the carbon transaction cost and the pollution discharge cost as optimization targets, and establishing a three-level structure sustainable supply chain model integrating supply chain site selection and quantity distribution;
step 2: converting the supply chain site selection and quantity allocation into vector forms, and using a dynamic relaxation group intelligent algorithm to execute iterative updating operation on the solution population by combining the fitness function value with the dynamic relaxation factor until the optimal approximate solution of the objective function is obtained, so as to obtain a site selection decision and quantity allocation scheme of the sustainable supply chain network;
the specific steps of the step 2 are as follows:
step 2.1: obtaining a supplier set S and a producer set P with high comprehensive scores based on the comprehensive weighted scores by using a weighted average algorithm;
step 2.2: converting the site selection and the quantity allocation of a supply chain into an x vector representation, initializing all particles in a solution population, performing iterative updating operation on the solution population by using a dynamic relaxation group intelligent algorithm and combining a fitness function value with a dynamic relaxation factor until the optimal approximate solution of an objective function is obtained, obtaining a site selection decision and a quantity allocation scheme of a sustainable supply chain network, and calculating and recording fitness values of the solution population and a corresponding population;
the step 2.1 comprises the following steps:
step 2.1.1: the grading index of the supplier comprises the production cost, the carbon quota transaction cost, the redundant carbon quota transaction cost, the operation cost and the corresponding cost of pollution discharge generated by each raw material of the supplier, and the specific calculation method comprises the following steps:
the calculation formula for the composite score of each raw material production cost of the supplier is as follows:
wherein ,αSAm Weighting the production cost of each raw material of the suppliers; PSM (power management module) im The cost of producing a unit of raw material m for supplier i;
the composite score for the carbon quota transaction costs for the supplier is calculated as follows:
WSC i =αSB×(1/CSP i )
wherein αSB is a weight for the carbon quota transaction cost for the provider; CSP (compact size reduction package) i A cost of purchasing a unit carbon quota amount for vendor i;
the composite score for the excess carbon quota transaction costs for the supplier is calculated as follows:
WSCR i =αSC×(1/CSRP i )
where αsc is a weight for the excess carbon quota transaction cost for the provider; CSRP i Purchasing a cost for provider i of excess/sell excess carbon allowance by one unit carbon allowance;
the comprehensive score of the operation cost of the provider is calculated as follows:
WSO i =αSD×(1/OSF i )
wherein αsd is a weight of the operational cost of the provider; OSF (OSF) i The operating cost for vendor i;
the comprehensive score of the cost corresponding to the pollution discharge generated by each raw material of the supplier is calculated as follows:
wherein ,αSEm Weighting the cost of blowdown for each raw material of the supplier; WSM (Wireless sensor module) im Producing a unit of the amount of waste produced by the raw material m for the supplier i;
the comprehensive scores of pollution treatment measures of suppliers are firstly classified, special symbols and Chinese fonts in the scores are replaced by corresponding scoring numbers, and then the treatment scores are calculated, wherein the calculation formula is as follows:
wherein ,αSMm Weight of pollution control measures for raw materials, SCM im Scoring pollution abatement measures for each raw material of the supplier;
the vendor's recoverability composite score is calculated as follows:
wherein ,αSRm Weight of recyclability of each raw material, SR im Scoring recyclability of each raw material of the supplier;
the product quality composite score of the supplier is calculated as follows:
wherein ,αSQm SPQ is a weight for quality of each raw material product of suppliers im Scoring the product quality of each raw material of the supplier;
in summary, for each cost composite score of the provider, the calculation formula is as follows:
step 2.1.2: the grading indexes of the manufacturer comprise the production cost, the carbon quota transaction cost, the redundant carbon quota transaction cost, the operation cost and the pollution discharge corresponding cost generated by the raw materials of the manufacturer, and the specific calculation method comprises the following steps:
for the comprehensive score of the production cost of each product of the manufacturer, the calculation formula is as follows:
wherein ,ρPAn The weight of the production cost of each raw material of the producer; PPN (PPN) jn The cost of producing a unit of product n for producer j;
the composite score for the manufacturer's carbon quota transaction costs is calculated as follows:
WPC j =ρPB×(1/CPP j )
wherein ρPB is the weight of the manufacturer's carbon quota transaction costs; CPP (CPP) j A cost of purchasing a unit carbon quota amount for producer j;
the composite score for the excess carbon quota transaction costs for the manufacturer is calculated as follows:
WPCR j =ρPC×(1/CPRP j )
wherein ρpc is a weight for the manufacturer's excess carbon quota transaction costs; CPRP (CPRP) j Purchasing a cost for excess/sell excess carbon allowance by one unit carbon allowance for producer j;
the comprehensive score of the operation cost of the manufacturer is calculated as follows:
WPCR j =ρPD×(1/OPF j )
wherein pPD is a weight of the operating cost of the manufacturer; OPF (optical fiber) j The operating cost for producer j;
the comprehensive score of the cost corresponding to the pollution discharge generated by each product of the manufacturer is calculated as follows:
wherein ,ρPEn Weighting the pollution discharge cost of each raw material of the manufacturer; WPN (Wireless Power network) jn The sewage discharge capacity generated by a unit of product n is produced for a producer j;
the pollution treatment measures of the manufacturers are comprehensively scored, the scores are classified, special symbols and Chinese fonts in the scores are replaced by corresponding scoring numbers, and then the treatment scores are calculated according to the following calculation formula:
wherein ,pPNn Weighting pollution control measures of each product, PCN jn Scoring pollution abatement measures for each product of the manufacturer;
the manufacturer's recoverability composite score is calculated as follows:
wherein ,αPRn Weight of recyclability of each product, PR jn Scoring recyclability of each product of the manufacturer;
the product quality comprehensive score of the manufacturer is calculated as follows:
wherein ,αpQn Weight of quality of raw material products of manufacturers, PPQ jn Scoring the product quality of each product of the manufacturer;
in summary, for each cost composite score of the manufacturer, the calculation formula is as follows:
the specific steps of step 2.2 are as follows:
step 2.2.1: constructing an initial solution population, determining the population scale of the solution population, the space dimension D of particles and the maximum iteration number T, using a Jacobi iteration algorithm according to the order constraint of a customer and the constraint of keeping the proportion of the raw material purchase quantity of a manufacturer to the product production quantity, obtaining a group of rapidly converged values through 10 iterations, and initializing the values to the position of each particle in the solution population, wherein the formula is as follows:
i in the formula is the number of initial groups, D is the space dimension, and T is the maximum update times;
from among solution populationsJudging whether the suppliers and the manufacturers operate or not, and judging the corresponding site selection decision, wherein the formula is as follows:
the address selection decision needs to be updated simultaneously when the solution population is updated each time; adcp ijm Representing the number of raw materials m supplied by supplier i to producer j, adcp jkn Representing the number of products n that manufacturer j provides to customer k;
step 2.2.2: an initial particle movement velocity is constructed, and the calculation formula is as follows:
step 2.2.3: and processing boundary positions of particles and a speed limit of particle updating, and correcting particles which do not meet the condition and the particle updating speed, wherein the calculation formula is as follows:
x in the formula max and xmin For maximum and minimum values of each particle, V max and Vmin A highest moving speed and a lowest moving speed for each particle;
step 2.2.4: according to the individual particles, a corresponding site selection decision is obtained, the fitness value of the individual particles is calculated and compared through a fitness function, the historical best position and the global best position of the particles i are updated and recorded, and the calculation formula is as follows:
in the formulaOptimal particle position for the extremum of the individual, +.>Particle location for a globally optimal solution;
step 2.2.5: particle movement speed: updating individual particle movement speeds of the correction solution population by combining fitness functions with dynamic relaxation factors;
step 2.2.6: vendor layer: for each supplier S i If the number of supply allocations does not meet the upper production limit MQRM of the supplier im ≥∑ j∈J Adcp ijm Then describe provider S i The amount of raw material to be supplied exceeds the supplier S i The upper supply limit that can be provided needs to be reconsidered by the supplier S i Updating each particle in the solution population in combination with the dynamic relaxation factor while obtaining a correspondence according to the new supply allocation number up to the supplier S i Up to the provider S i Until the constraint condition is satisfied;
step 2.2.7: manufacturer layer: for each producer P j If the production allocation quantity does not meet the production upper limit MQRM of the manufacturer jn ≥∑ k∈K Adcp jkn Description of manufacturer P j The number of products to be provided exceeds the manufacturer P j The upper production limit that can be provided requires reconsideration of the manufacturer P j Is assigned to each of the solution populations in combination with dynamic relaxation factorsThe particles are updated while being corresponding to the new supply distribution quantity up to the producer P j Up to the manufacturer P j Until the constraint condition is satisfied;
step 2.2.8: calculating the fitness value of the individual particles according to the mathematical model of the objective function;
step 2.2.9: for individual particles in the solution population, comparing the fitness value of the current particle position with the fitness value of the historical optimal position, and if the fitness value of the current particle is better, updating the current particle position into the historical optimal position, wherein the calculation formula is as follows:
step 2.2.10: for individual particles in the solution population, comparing the fitness value of the current particle position with the fitness value of the global optimal position, and if the fitness value of the current particle is better, updating the current particle position into the global optimal position, wherein the calculation formula is as follows:
step 2.2.11: and judging whether the algorithm meets the end condition, if the algorithm does not meet the end condition, returning to the step 2.2.5 to continue iterative updating until the algorithm meets the end condition, stopping calculation, ending the algorithm and outputting the global optimal solution.
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