Supply chain scheduling method for particle swarm optimization under multi-constraint condition

Abstract

The invention provides a supply chain scheduling method of particle swarm optimization under multi-constraint conditions, and the method searches an optimal supply chain management plan through a particle swarm optimization algorithm and a plurality of constraint conditions, such as inventory constraint, delivery date constraint and the like. The method comprises the specific steps of problem definition and constraint setting, particle initialization and evaluation, iterative optimization, constraint processing, termination condition judgment and the like. First, an objective function is defined, such as minimizing cost, etc. The solutions are then randomly initialized in a search space, and each solution is evaluated by calculating a target function value. And through multiple iterations, the speed and the position of the particles are updated, and finally an optimal solution is found. In the process, if the new solution violates the constraint condition, correction needs to be carried out through a penalty function or a self-adaptive adjustment method. And stopping iteration after the preset maximum number of iterations is reached or the globally optimal solution is stable. And finally, applying the final optimal solution to actual supply chain management.

Description

Technical Field

[0001] The present invention belongs to the field of supply chain scheduling, and more specifically relates to a supply chain scheduling method of particle swarm optimization under multiple constraints. Background Art

[0002] In traditional supply chain management, scheduling is a rather complex problem. The reason is that the supply chain covers all activities from the original supplier to the final consumer, including production, inventory, transportation, distribution and sales, and there are complex dependencies between these links. In order to optimize the supply chain, trade-offs and decisions need to be made in many aspects, such as minimizing costs, maximizing service levels, and meeting various operational constraints.

[0003] One way to solve this problem is to use an optimization algorithm, among which the particle swarm optimization (PSO) algorithm is a very effective global optimization algorithm. The PSO algorithm is an optimization technology based on artificial intelligence and computer simulation, which originated from the simulation research on the behavior of animal groups such as bird flocks and fish schools. Due to its excellent global search ability and visibility in solving practical problems, it has been widely used in many optimization problems.

[0004] However, in most cases, supply chain problems do not have only one optimization goal, but require a trade-off between multiple goals, such as minimum cost, shortest time, etc. At the same time, supply chain operations must meet a series of constraints, such as inventory restrictions, delivery dates, transportation capabilities, etc. In this case, the traditional PSO algorithm may not be able to effectively find the global optimal solution that meets all constraints.

[0005] Therefore, it is very necessary to develop a supply chain scheduling method that can optimize efficiency under multiple constraints, which is also the main background and purpose of the present invention. Summary of the invention

[0006] The technical problem to be solved by the present invention is how to combine multiple constraints in complex supply chain management and use particle swarm optimization algorithm to effectively find the optimal supply chain configuration solution to meet the goals of minimum cost and shortest delivery time. At the same time, actual constraints such as inventory restrictions, delivery deadlines, transportation capacity and production capacity are considered to improve the efficiency and accuracy of supply chain scheduling.

[0007] In order to achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0008] The method includes:

[0009] Problem definition and constraint setting: including objective function and constraint conditions. The objective function includes minimizing the total cost. Preferably, the objective function includes minimizing the total cost, minimizing the delivery time, and maximizing the service level. The constraint conditions include: inventory constraint, delivery time constraint, transportation capacity constraint, production capacity constraint, and demand satisfaction constraint.

[0010] Particle initialization and evaluation: Randomly initialize some solutions in the search space, each solution is regarded as a particle, each particle is evaluated, and the value of the particle fitness function is calculated;

[0011] Iterative optimization: Calculate the new speed and new position of each particle, select the new particle with the best fitness as the global optimal solution, and the calculated new position of the particle is the new candidate solution;

[0012] Constraint processing: During the iterative optimization process, check whether the new candidate solution satisfies the constraints. If not, correct the candidate solution that violates the constraints.

[0013] Termination condition judgment: If the change of the global optimal solution does not exceed the threshold, stop the iteration and take the current global optimal solution as the final solution;

[0014] Supply chain scheduling: Match the final solution with the actual supply chain scheduling.

[0015] In one scheme, the objective function and constraints are defined. The objective function is to minimize the total cost C, which is expressed as:

[0016] C=C 生产 +C 库存 +C 运输 +C 缺货

[0017] Among them, C 生产 is the production cost, C 库存 is the inventory holding cost, C 运输 is the transportation cost, C 缺货 is the stock-out cost;

[0018] Inventory constraint: For each node i, the inventory level I i Must be between the minimum and maximum allowed stock levels:

[0019] I min,i ≤I i ≤I max,i

[0020] Delivery time constraint: The delivery time T of each order delivery Must be within the delivery period required by the customer:

[0021] T order +T production +Ttransport ≤T due

[0022] Transport capacity constraint: The transport volume Q must not exceed the capacity Q of the transport vehicle max :

[0023] Q≤Q max

[0024] Production capacity constraint: For each production node, the production volume P cannot exceed its production capacity P max :

[0025] P≤P max

[0026] Demand satisfaction constraint: The demand D of each retail node must be met, allowing a certain out-of-stock rate α:

[0027] D-α·D≤supply.

[0028] In one embodiment, the particle initialization and evaluation are implemented by randomly generating a set of solutions in the search space, including:

[0029] Particle initialization: There are N particles in the search space, and the position of each particle i is represented by a vector x i =(x i1 ,x i2 ,...,x id ), where d is the dimension of the decision variable; each component x ij It is expressed as:

[0030] x ij =x j,min +rand(0,1)×(x j,max -x j,min )

[0031] Among them, x j,min and x j,max are the minimum and maximum values ​​of the j-th decision variable, respectively. rand(0,1) is a random number uniformly distributed between 0 and 1.

[0032] Calculate the fitness function value of each particle to evaluate the particle: In the supply chain scheduling problem, the objective function is to minimize the total cost C:

[0033] C=C 生产 +C 库存 +C 运输 +C 缺货

[0034] The fitness f(x i ) is the corresponding objective function value C(x i ):

[0035] f(x i )=C(x i ).

[0036] In one embodiment, the iterative optimization includes:

[0037] The speed update formula is:

[0038] v ij (t+1)=ωv ij (t)+c1r1(p ij -x ij (t))+c2r2(g j -x ij (t))

[0039] The position update formula is:

[0040] x ij (t+1)=x ij (t)+v ij (t+1)

[0041] Where: v ij (t) is the current velocity of particle i in the jth dimension; ω is the inertia weight, which controls the influence of the current velocity of the particle on the next step velocity; c1 and c2 are learning factors; r1 and r2 are random numbers between [0,1]; p ij is the individual historical optimal position of particle i in the jth dimension; g j is the global historical optimal position of the group in the jth dimension; x ij Represents the component of the particle's position vector.

[0042] In one embodiment, the constraint processing adopts a penalty function method, including:

[0043] The objective function is f(x) and the constraint is g k (x)≤0 and h l (x) = 0, then the fitness function after penalty is expressed as:

[0044]

[0045] Among them, λ k and μ l is the penalty factor, which is used to control the degree of penalty for constraint violation; g k (x) is an inequality constraint. Constraints include inventory constraints, delivery time constraints, computing power constraints, and production capacity constraints. l (x) is an equality constraint, including a demand satisfaction constraint.

[0046] In one embodiment, the termination condition determination includes:

[0047] Initialize a counter n stable =0;

[0048] After each iteration, the difference Δg between the current global optimal solution g(t) and the global optimal solution g(t-1) of the previous iteration is calculated:

[0049] Δg=|f(g(t))-f(g(t-1))|

[0050] If Δg<ò, increase the stability counter: n stable =n stable +1; otherwise, reset the counter: n stable =0; where ò represents the maximum change value allowed for the global optimal solution in continuous iterations;

[0051] If n stable ≥N stable , then stop the iteration and output the current global optimal solution.

[0052] In one embodiment, the supply chain scheduling includes:

[0053] Production scheduling: Arrange production activities according to the production sequence in the optimal solution, including making detailed production plans, determining the production time and sequence of each product, and coordinating resource allocation for different production lines;

[0054] Logistics and distribution: Arrange the transportation and distribution of goods according to the flow of goods at logistics nodes in the optimal solution, including selecting the optimal transportation route, determining transportation batches and schedules, and coordinating the scheduling of warehouses and transportation vehicles.

[0055] Beneficial effects of the present invention:

[0056] Improve supply chain scheduling efficiency and optimization effect: The particle swarm optimization algorithm can search globally through information sharing among groups, better handle complex and large-scale optimization problems, deeply explore and optimize the potential in the supply chain, and improve supply chain scheduling efficiency.

[0057] Scalability and strong adaptability: The model of the present invention can handle various complex manufacturing and distribution environments, and still performs well under more constraints, and has good scalability and adaptability.

[0058] The adaptive iterative strategy can adjust the parameters of the penalty function according to different constraints, so that the algorithm can find the global optimal solution while satisfying all constraints without the need for complex manual adjustments.

[0059] This method is applicable to a variety of supply chain scheduling environments, including but not limited to production and manufacturing, logistics and distribution, and has wide practicality and application value.

[0060] In summary, the present invention provides an effective, efficient, easy-to-implement and general particle swarm optimization supply chain scheduling method under multiple constraints, which can find the optimal solution that satisfies the objective function while satisfying the constraints, and has important reference value and practical significance for enterprise decision-making and supply chain management. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flow chart of the method of the present invention;

[0062] Figure 2 Iterative optimization flow chart for the present invention;

[0063] Figure 3 This is a termination condition judgment flow chart of the present invention. DETAILED DESCRIPTION

[0064] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. Typical embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in the present invention. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0065] Unless otherwise defined, all technical and scientific terms used in the present invention have the same meaning as those commonly understood by those skilled in the art to which the present invention belongs. The terms used in the present invention in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. Typical embodiments of the present invention are shown in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in the present invention. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0066] This paper proposes a particle swarm optimization algorithm for processing multiple constraints in supply chain scheduling. Supply chain scheduling is a typical NP-hard problem, and it is not easy to find a suitable optimization algorithm to deal with it. By using the particle swarm optimization algorithm and determining the appropriate objective function and constraints, such problems can be effectively solved.

[0067] Constraints: In supply chain scheduling problems, there are multiple constraints, including inventory, transportation, production, demand satisfaction, etc. This paper proposes a method to integrate these constraints, using a penalty function to penalize solutions that violate the constraints, so that infeasible solutions can be left out during the search process, further improving the solution efficiency.

[0068] The implementation process of the present invention is as follows:

[0069] S1. Problem definition and constraint setting: Understand all relevant elements in the supply chain and the relationships between them, and then use this information to build a mathematical model. This model will include an objective function (such as minimum cost, shortest time, etc.) and a series of constraints (such as inventory restrictions, delivery time, transportation capacity, etc.).

[0070] In the definition and constraint setting of supply chain scheduling problems, it is first necessary to clarify the various components of the supply chain and their interrelationships. Supply chains usually include suppliers, manufacturers, distributors, retailers, and end consumers. There are interactions between logistics and information flows between each node, and these interactions need to be modeled to optimize the performance of the entire supply chain.

[0071] First, define an objective function, including minimizing total cost, minimizing delivery time, maximizing service level, etc. Service level generally refers to the ability to meet customer needs in supply chain management. It is processed through constraints, such as taking order satisfaction as a demand satisfaction constraint. The objective function is to minimize the total cost C, which can be expressed as:

[0072] C=C 生产 +C 库存 +C 运输 +C 缺货

[0073] Among them, C 生产 is the production cost, C 库存 is the inventory holding cost, C 运输 is the transportation cost, C 缺货 is the stock-out cost.

[0074] Next, we need to define a series of constraints that ensure the feasibility of the solution:

[0075] Inventory constraint: For each node i, the inventory level I i Must be between the minimum and maximum allowed stock levels:

[0076] I min,i ≤I i ≤I max,i

[0077] Delivery time constraint: The delivery time T of each orderdelivery Must be within the delivery period required by the customer:

[0078] T order +T production +T transport ≤T due

[0079] Transport capacity constraint: The transport volume Q must not exceed the capacity Q of the transport vehicle max :

[0080] Q≤Q max

[0081] Production capacity constraint: For each production node, the production volume P cannot exceed its production capacity P max :

[0082] P≤P max

[0083] Demand satisfaction constraint: The demand D of each retail node must be satisfied, allowing a certain out-of-stock rate α:

[0084] D-α·D≤Supply

[0085] By establishing the above objective function and constraints, a mathematical model can be formed, which is used to guide the particle swarm optimization algorithm to find the optimal solution in the search space. This process requires comprehensive consideration of the mutual influence of each link in the supply chain to ensure that all constraints are met while achieving the optimal goal.

[0086] S2, particle initialization and evaluation: Randomly initialize some solutions in the search space, each of which is regarded as a particle. Then, each particle is evaluated, usually by calculating the value of its fitness function (i.e., objective function).

[0087] In the supply chain scheduling problem, the particle initialization and evaluation steps of the particle swarm optimization (PSO) algorithm are the key starting processes. First, it is necessary to define the search space, which consists of all possible combinations of supply chain decision variables, such as production plans, inventory levels, transportation arrangements, etc. Each particle represents a potential solution in this multidimensional space.

[0088] Particle initialization

[0089] The particle initialization is achieved by randomly generating a set of solutions in the search space. Assuming there are N particles, the position of each particle i can be represented by a vector x i =(x i1 ,x i2 ,...,x id ), where d is the dimension of the decision variable. Each component x ij It can be expressed as:

[0090] x ij =x j,min +rand(0,1)×(x j,max -x j,min )

[0091] Among them, x j,min and x j,max are the minimum and maximum values ​​of the j-th decision variable, respectively, and rand(0,1) is a random number uniformly distributed between 0 and 1.

[0092] Particle evaluation

[0093] Once the particles are initialized, they need to be evaluated. This is done by calculating the fitness function value for each particle, which is usually the objective function defined earlier. In the supply chain scheduling problem, the objective function may be to minimize the total cost C, as described earlier:

[0094] C=C 生产 +C 库存 +C 运输 +C 缺货

[0095] The fitness f(x i ) is the corresponding objective function value:

[0096] f(x i )=C(x i )

[0097] In this process, it is necessary to ensure that the solution of each particle meets all constraints, such as inventory restrictions, delivery time, transportation capacity, etc. If a particle violates the constraints, its fitness value can be adjusted through the penalty function to reduce its relative superiority in the group.

[0098] Through the particle initialization and evaluation steps, a set of initial solutions are obtained in the search space, which provides a basis for subsequent iterative optimization. The fitness value of each particle will be used to guide the movement of the particle in the search space to gradually approach the global optimal solution.

[0099] S3, iterative optimization: In each iteration, the new speed and position of each particle are first calculated, which is calculated based on the particle's current speed, current position, and its individual and global historical optimal position. Then, the one with the best fitness among these new particles is selected as the global optimal solution.

[0100] like Figure 2As shown in Figure 1, in the supply chain scheduling problem, the iterative optimization process of the particle swarm optimization (PSO) algorithm is achieved by updating the speed and position of each particle. This process allows the particles to gradually approach the optimal solution in the search space. Each iteration consists of the following steps:

[0101] S301, speed and position update

[0102] In each iteration, the speed and position of each particle i are updated. The speed update formula combines the particle's current speed, the individual historical best position (i.e. the best position found by the particle itself), and the global historical best position (i.e. the best position found by the entire group). The speed update formula is:

[0103] v ij (t+1)=ωv ij (t)+c1r1(p ij -x ij (t))+c2r2(g j -x ij (t))

[0104] in:

[0105] v ij (t) is the current velocity of particle i in the jth dimension.

[0106] ω is the inertia weight, which controls the influence of the particle's current velocity on the next step's velocity.

[0107] c1 and c2 are learning factors, usually with values ​​between [0,2].

[0108] r1 and r2 are random numbers between [0,1].

[0109] p ij is the individual historical optimal position of particle i in the jth dimension.

[0110] g j is the global historical optimal position of the group in the jth dimension.

[0111] The position update formula is:

[0112] x ij (t+1)=x ij (t)+v ij (t+1)

[0113] S302, individual and global optimal update

[0114] After updating the speed and position, it is necessary to recalculate the fitness value f(x i (t+1)), and update the individual and global optimal positions according to the fitness values.

[0115] Individual optimal update: If the fitness of the new position of particle i is better than its historical optimal position, the individual optimal position is updated:

[0116] if f(x i (t+1))<f(p i )then p i =x i (t+1)

[0117] Global optimal update: If the fitness of the new position of particle i is better than the current global optimal position, the global optimal position is updated:

[0118] if f(x i (t+1))<f(g)then g=x i (t+1)

[0119] S303, iterative process

[0120] Through the above steps, each iteration will adjust the position of the particle so that it gradually approaches the optimal solution. During the entire iteration process, it is necessary to ensure that the new solution of each particle satisfies all constraints. If a particle violates a constraint, its fitness value can be adjusted through a penalty mechanism to limit its impact on the global optimal solution.

[0121] This iterative optimization process continues until a preset stopping condition is reached, such as the maximum number of iterations or the global optimal solution has not been significantly improved in several iterations. In this way, the PSO algorithm effectively explores the search space in the supply chain scheduling problem and finds the optimal supply chain configuration solution.

[0122] S4. Constraint processing: During the iterative optimization process, the newly calculated solutions may sometimes violate the constraints. It is necessary to adopt penalty function methods and adaptive adjustment methods to correct these solutions so that they meet all the constraints.

[0123] The newly calculated solution is the new particle position calculated in each iteration of the particle swarm optimization algorithm according to the particle speed and position update rules, that is, the new candidate solution.

[0124] The position of each particle corresponds to a possible supply chain scheduling solution, and the fitness value of the particle evaluates the quality of this scheduling solution. In the iterative optimization process, new particle positions, that is, new scheduling solutions, can be found by updating the speed and position.

[0125] The newly calculated solution here refers to the new scheduling plan. During each iteration, the new candidate solution will be checked to see if it meets the constraints. If the constraints are violated, it needs to be corrected using the predetermined constraint processing method.

[0126] In the iterative optimization process of the particle swarm optimization (PSO) algorithm, handling constraints is a key step to ensure the feasibility and effectiveness of the solution. Supply chain scheduling problems usually involve multiple constraints, such as inventory capacity, production capacity, delivery time, etc. When updating the position and speed of particles, the new solution may violate these constraints, so an effective strategy needs to be adopted to correct them.

[0127] Penalty function method: The penalty function method reduces the fitness value of infeasible solutions by adding a penalty term to the fitness function. The objective function is f(x) and the constraint is g k (x)≤0 and h l (x) = 0, then the fitness function after penalty can be expressed as:

[0128]

[0129] Among them, λ k and μ l is a penalty factor that controls the degree of penalty for constraint violation. In this way, solutions that violate the constraints will be given higher penalty values ​​and thus eliminated in the selection process. l (x) generally represents an equality constraint. In supply chain scheduling problems, this includes demand satisfaction constraints. k (x) generally represents an inequality constraint. In supply chain scheduling problems, it includes inventory constraints, delivery constraints, computing power constraints, and production capacity constraints.

[0130] In the iterative optimization process of PSO, constraint processing is usually performed after updating the particle position, that is, after calculating the new position, it is immediately checked whether all constraints are met. If not, they are corrected according to the selected constraint processing method.

[0131] By combining the penalty function method and the adaptive adjustment method, various types of constraints can be effectively handled to ensure that the solution of the particle swarm optimization algorithm in the supply chain scheduling problem is feasible and gradually approaches the optimal solution. This combination strategy improves the robustness and adaptability of the algorithm, enabling it to operate effectively in a complex constraint environment.

[0132] S5. Termination condition judgment: If the global optimal solution does not change significantly after a certain number of iterations, then the iteration is stopped and the current global optimal solution is the final solution.

[0133] In the particle swarm optimization (PSO) algorithm, the determination of the termination condition is a key step to ensure that the algorithm ends its operation in a reasonable time and outputs the optimal solution. The global optimal solution has no significant changes in several iterations.

[0134] In order to improve the quality of the solution, a stability condition can be set: if the global optimal solution is found in several consecutive iterations (such as N stable If there is no significant change in the time interval (times), the algorithm is considered to have converged and the iteration is stopped. The “significant change” here can be determined by setting a threshold value ò.

[0135] like Figure 3 As shown, the implementation steps are:

[0136] S501, initialize a counter n stable =0.

[0137] S502. After each iteration, the difference between the current global optimal solution g(t) and the global optimal solution g(t-1) of the previous iteration is calculated:

[0138] Δg=|f(g(t))-f(g(t-1))|

[0139] S503, if Δg<ò, increase the stability counter: n stable =n stable +1; otherwise, reset the counter: n stable =0. ε is a very small positive number here, which represents the maximum change value allowed for the global optimal solution in continuous iterations. In other words, if the change of the global optimal solution is less than ε, which is a threshold of 0.00001, then the global optimal solution is considered to be close enough to the true optimal solution, and the algorithm can stop iterating. This is a method to judge the convergence of the algorithm. The size of the ε value will affect the convergence speed of the algorithm and the accuracy of the solution.

[0140] S504, if n stable ≥N stable , then stop the iteration and output the current global optimal solution.

[0141] In practical applications, these two termination conditions are usually used at the same time to ensure that the algorithm can end in a reasonable time and obtain a satisfactory solution.

[0142] The present invention applies the PSO algorithm to supply chain scheduling, which can avoid unnecessary computational overhead while ensuring the quality of the solution, thereby improving the efficiency and practicability of the algorithm.

[0143] S6. Supply chain scheduling: Let the optimal solution (a set of decision variables) finally found correspond to the actual supply chain management. For example, if the decision variable is the production sequence of each production node, then the production activities should be scheduled according to this sequence. If the decision variable is the flow of goods between each logistics node, then the goods should be distributed according to this result.

[0144] In the supply chain scheduling problem, the particle swarm optimization (PSO) algorithm is used to find the optimal solution, that is, a set of decision variables that can optimize the performance of the entire supply chain. In the iterative process, the PSO algorithm explores the solution space by updating the positions of particles and finally converges to a global optimal solution. The following is a detailed implementation process of how to apply the optimal solution finally found to actual supply chain management:

[0145] Once the PSO algorithm finds the optimal solution, the next step is to map these decision variables to actual supply chain operations:

[0146] Production scheduling: Arrange production activities according to the production sequence in the optimal solution. This includes making a detailed production plan, determining the production time and sequence of each product, and coordinating the resource allocation of different production lines.

[0147] Logistics and distribution: Arrange the transportation and distribution of goods according to the flow of goods at logistics nodes in the optimal solution. This involves selecting the optimal transportation route, determining transportation batches and schedules, and coordinating the scheduling of warehouses and transportation vehicles.

[0148] Implementation and monitoring: During the implementation phase, actual operations are performed according to the optimized production and logistics plans. At the same time, a real-time monitoring system needs to be established to track key performance indicators (KPIs), such as production efficiency, inventory levels, and transportation costs. Through monitoring, deviations can be discovered in a timely manner and corrective measures can be taken.

[0149] Feedback and Adjustment: As market demand and supply chain environment change, the optimal solution may need to be adjusted. Therefore, establish a feedback mechanism to regularly re-evaluate and optimize the supply chain scheduling plan to maintain a competitive advantage.

[0150] Through the above steps, the PSO algorithm not only provides a theoretical optimal solution for the supply chain scheduling problem, but also effectively applies it to actual operations through specific implementation steps, thereby improving the overall efficiency and responsiveness of the supply chain.

[0151] Example:

[0152] The following is a specific example of a supply chain scheduling problem to illustrate the specific implementation process of this method.

[0153] Assume that the supply chain we are concerned with contains one production node and three retail nodes, and the demand of each retail node changes over time. The production node can choose different production strategies to meet the demand. Production cost, inventory cost, transportation cost, and out-of-stock cost all affect the total cost. We need to find a supply chain scheduling strategy to minimize the total cost. The following are the relevant parameters and constraints:

[0154] The production capacity of the production node is 100 units / day, and the production cost is $5 / unit;

[0155] The daily inventory holding cost is $0.1 / unit;

[0156] The capacity of the transport vehicle is 80 units and the transport cost is $1 / unit;

[0157] The demand at each retail node is [30, 40, 50] units, the maximum allowed out-of-stock rate is 0.1, and the cost of out-of-stock is $10 / unit.

[0158] First, we initialize a set of particles (solutions), such as coefficient particles. Each particle contains a set of parameters, such as production strategy, inventory level, transportation arrangement, etc., representing a possible supply chain scheduling solution.

[0159] Then, we execute the main loop of the particle swarm optimization algorithm to find the optimal solution. In each iteration:

[0160] Update the speed and position of each particle using the speed and position update formula.

[0161] After the update, the fitness (i.e., total cost) of the particle is evaluated and checked to see if all constraints are met. If a particle does not meet the constraints, we adjust it using a penalty function.

[0162] Update the individual optimal solution of each particle. If the fitness is better than the historical optimal solution, replace the historical optimal solution.

[0163] Update the global optimal solution. If the fitness of a particle is better than the existing global optimal solution, replace the global optimal solution with the position of this particle.

[0164] When the termination condition is met (for example, the preset maximum number of iterations is reached, or the global optimal solution does not change significantly in several consecutive iterations), the algorithm ends and outputs the optimal solution.

[0165] Finally, we apply this optimal solution to actual supply chain operations, such as adjusting production behavior according to the optimal production strategy found, managing inventory according to the set inventory level, and arranging goods distribution according to the determined transportation arrangement.

[0166] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0167] It should be understood that the detailed description of the technical solutions of the present invention by means of the preferred embodiments is illustrative rather than restrictive. A person skilled in the art may modify the technical solutions described in the embodiments, or replace some of the technical features by equivalents, based on reading the specification of the present invention; and these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A particle swarm optimization supply chain scheduling method under multiple constraints, characterized by: The method includes: Problem definition and constraint setting: including objective function and constraint conditions. The objective function includes minimizing total cost. Constraint conditions include inventory constraints, delivery time constraints, transportation capacity constraints, production capacity constraints, and demand satisfaction constraints. Particle initialization and evaluation: Randomly initialize some solutions in the search space, each solution is regarded as a particle, each particle is evaluated, and the value of the particle fitness function is calculated; Iterative optimization: Calculate the new speed and new position of each particle, select the new particle with the best fitness as the global optimal solution, and the calculated new position of the particle is the new candidate solution; Constraint processing: During the iterative optimization process, check whether the new candidate solution satisfies the constraints. If not, correct the candidate solution that violates the constraints. Termination condition judgment: If the change of the global optimal solution does not exceed the threshold, stop the iteration and take the current global optimal solution as the final solution; Supply chain scheduling: Match the final solution with the actual supply chain scheduling.

2. The supply chain scheduling method based on particle swarm optimization under multiple constraints according to claim 1, characterized in that: The objective function is to minimize the total cost C, expressed as: C=C 生产 +C 库存 +C 运输 +C 缺货 Among them, C 生产 is the production cost, C 库存 is the inventory holding cost, C 运输 is the transportation cost, C 缺货 is the stock-out cost; Inventory constraint: For each node i, the inventory level I i Must be between the minimum and maximum allowed stock levels: I min,i ≤I i ≤I max,i Delivery time constraint: The delivery time T of each order delivery Must be within the delivery period required by the customer: T order +T production +T transport ≤T due Transport capacity constraint: The transport volume Q must not exceed the capacity Q of the transport vehicle max : Q≤Q max Production capacity constraint: For each production node, the production volume P cannot exceed its production capacity P max : P≤P max Demand satisfaction constraint: The demand D of each retail node must be satisfied, allowing a certain out-of-stock rate α: D-α·D≤supply.

3. The supply chain scheduling method based on particle swarm optimization under multiple constraints according to claim 1, characterized in that: The particle initialization and evaluation are implemented by randomly generating a set of solutions in the search space, including: Particle initialization: There are N particles in the search space, and the position of each particle i is represented by a vector x i =(x i1 ,x i2 ,...,x id ), where d is the dimension of the decision variable; each component x ij It is expressed as: x ij =x j,min +rand(0,1)×(x j,max -x j,min ) Among them, x j,min and x j,max are the minimum and maximum values ​​of the j-th decision variable, respectively. rand(0,1) is a random number uniformly distributed between 0 and 1. Calculate the fitness function value of each particle to evaluate the particle: In the supply chain scheduling problem, the objective function is to minimize the total cost C: C=C 生产 +C 库存 +C 运输 +C 缺货 The fitness f(x i ) is the corresponding objective function value C(x i ): f(x i )=C(x i )。 4. The supply chain scheduling method based on particle swarm optimization under multiple constraints according to claim 1, characterized in that: The iterative optimization includes: The speed update formula is: v ij (t+1)=ωv ij (t)+c1r1(p ij -x ij (t))+c2r2(g j -x ij (t)) The position update formula is: x ij (t+1)=x ij (t)+v ij (t+1) Where: v ij (t) is the current velocity of particle i in the jth dimension; ω is the inertia weight, which controls the influence of the current velocity of the particle on the next step velocity; c1 and c2 are learning factors; r1 and r2 are random numbers between [0,1]; p ij is the individual historical optimal position of particle i in the jth dimension; g j is the global historical optimal position of the group in the jth dimension; x ij Represents the component of the particle's position vector.

5. The supply chain scheduling method based on particle swarm optimization under multiple constraints according to claim 1, characterized in that: The constraint processing adopts a penalty function method, including: The objective function is f(x) and the constraint is g k (x)≤0 and h l (x) = 0, then the fitness function after penalty is expressed as: Among them, λ k and μ l is the penalty factor, which is used to control the degree of penalty for constraint violation; g k (x) is an inequality constraint. Constraints include inventory constraints, delivery time constraints, computing power constraints, and production capacity constraints. l (x) is an equality constraint, including a demand satisfaction constraint.

6. The supply chain scheduling method based on particle swarm optimization under multiple constraints according to claim 1, characterized in that: The termination condition judgment includes: Initialize a counter n stable =0; After each iteration, the difference Δg between the current global optimal solution g(t) and the global optimal solution g(t-1) of the previous iteration is calculated: Δg=|f(g(t))-f(g(t-1))| If Δg < ò, increase the stability counter: n stable =n stable +1; otherwise, reset the counter: n stable =0; where ò represents the maximum change value allowed for the global optimal solution in continuous iterations; If n stable ≥N stable , then stop the iteration and output the current global optimal solution.

7. The supply chain scheduling method based on particle swarm optimization under multiple constraints according to claim 1, characterized in that: The supply chain scheduling includes: Production scheduling: Arrange production activities according to the production sequence in the optimal solution, including making detailed production plans, determining the production time and sequence of each product, and coordinating resource allocation for different production lines; Logistics and distribution: Arrange the transportation and distribution of goods according to the flow of goods at logistics nodes in the optimal solution, including selecting the optimal transportation route, determining transportation batches and schedules, and coordinating the scheduling of warehouses and transportation vehicles.

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