Robust optimization method for risk prediction of waste household appliance recovery supply chain

Abstract

The invention provides a waste household electrical appliance recovery supply chain risk prediction robust optimization method, which establishes a robust optimization target model of demand loss and operation energy consumption, constructs a cascade risk prediction evolution mechanism, designs a feedforward self-adjustment variation strategy, and improves the risk prediction accuracy under the influence of the demand uncertainty of a waste household electrical appliance recovery supply chain. The robust optimal scheduling scheme of the waste household appliance recovery supply chain is reliably obtained, the cascade risk amplification effect caused by demand fluctuation is effectively inhibited, and the stability and operation efficiency of the supply chain are improved.

Description

Technical Field

[0001] This invention addresses the robust optimization requirements of the waste household appliance (WBO) recycling supply chain and the cascading risk amplification problem caused by demand uncertainty during the recycling process. It proposes a robust optimization method for predicting risks in the WBO recycling supply chain. This method establishes a robust optimization objective model for demand loss and operating energy consumption, constructs a cascading risk prediction evolution mechanism, designs a feedforward self-adjusting mutation strategy, and obtains a robust optimal scheduling scheme for the WBO recycling supply chain. This suppresses the cascading risk amplification effect caused by demand uncertainty, improving the stability and economy of the recycling system. It falls under both the fields of supply chain risk management and optimization, and the field of electronic solid waste resource utilization. Background Technology

[0002] With the rapid pace of product upgrades and replacements in the home appliance industry, the number of discarded appliances has increased dramatically. Their standardized recycling and resource utilization have become crucial aspects of the circular economy and environmental protection. my country's "Regulations on the Management of Recycling and Disposal of Waste Electrical and Electronic Products" and other policy documents explicitly require strengthening the construction of a waste appliance recycling system to promote green and circular development. The waste appliance recycling supply chain involves multiple stages, including collection, transportation, dismantling, and processing. This complex system is significantly affected by factors such as market demand fluctuations and uncertain recycling volumes. Improper scheduling can easily lead to a chain of risks, including inventory backlog, insufficient processing capacity, and increased energy consumption, severely impacting recycling efficiency. Therefore, optimizing the demand loss and energy consumption of the waste appliance recycling supply chain is of paramount importance.

[0003] Currently, research on optimizing the waste appliance recycling supply chain largely focuses on minimizing energy consumption or optimizing service, with common scheduling methods including linear programming, dynamic programming, and intelligent optimization algorithms. However, these methods often assume that demand is fixed or follows a fixed distribution, failing to fully consider the high degree of uncertainty in demand during the actual recycling process and the cascading effects of risk transmission across multiple stages. In practice, demand fluctuations are easily amplified through each stage of the supply chain, causing scheduling schemes to deviate significantly from expectations, resulting in resource waste, soaring energy consumption, and even system paralysis. Therefore, how to achieve robust scheduling and risk mitigation of the recycling supply chain under uncertain demand conditions is a critical issue that urgently needs to be addressed in this field.

[0004] This invention proposes a robust optimization method for risk prediction in the waste home appliance recycling supply chain. It establishes a robust optimization objective model for demand loss and operating energy consumption, constructs a cascaded risk prediction evolution mechanism, designs a feedforward self-adjusting mutation strategy, and obtains a robust optimal scheduling scheme for the waste home appliance recycling supply chain. This method suppresses the cascaded risk amplification effect caused by demand uncertainty, improves the operational stability and economy of the waste home appliance recycling supply chain, and has important practical significance for promoting the sustainable development of the waste home appliance recycling industry. Summary of the Invention

[0005] This invention designs a robust optimization method for risk prediction in the waste home appliance recycling supply chain. The method establishes a robust optimization objective model for demand loss and operating energy consumption, constructs a cascaded risk prediction evolution mechanism, designs a feedforward self-adjusting mutation strategy, obtains a robust optimal scheduling scheme for the waste home appliance recycling supply chain, suppresses the cascaded risk amplification effect caused by demand uncertainty, and ensures the efficient and stable operation of the waste home appliance recycling supply chain.

[0006] The present invention adopts the following technical solution and implementation steps:

[0007] A robust optimization method for risk prediction in the waste household appliance recycling supply chain includes the following steps:

[0008] (1) Establish a robust optimization objective model for demand loss and operating energy consumption:

[0009] (1)

[0010] Among them, f c s (x(t)), f l s (x(t)) represent the demand loss and operating energy consumption of waste appliance recycling at time t in scenario s, respectively, and E[•] represents the expectation of the objective function under different scenarios, x(t) = [x r,s (t), y d,s [(t)] represents the decision variable for the optimization objective, x r,s (t), y d,s (t) are all binary variables, x r,s (t)=[x 1,r,s , x 2,r,s ,…, x o,r,s Let y be the decision variable for whether recycling station r processes o orders in scenario s at time t. d,s (t)=[y 1,d,s , y 2,d,s ,…, y o,d,s Let f be the decision variable for whether dismantling plant d processes o orders in scenario s at time t. c s (x(t)) and f l s The calculation method for (x(t)) is as follows:

[0011] (2)

[0012] (3)

[0013] Among them, c r p , c dp The processing energy consumption of the r-th recycling station and the d-th dismantling plant are respectively, c r b , c d b B represents the accumulated energy consumption of the r-th recycling station and the d-th dismantling plant, respectively. r (t), B d (t) represents the backlog at the r-th recycling station and the d-th dismantling plant, respectively. o The demand loss for the 0th order represents the number of orders that did not respond to user requests within a given time window, and is calculated as follows:

[0014] (4)

[0015] Where, t p d t represents the order completion time. c T represents the order arrival time. max Given a time window, since the number of orders effectively allocated cannot exceed the total demand, the order constraint is expressed as follows:

[0016] (5)

[0017] Where O represents the total number of orders, the number of orders for recycling station r should be within its processing capacity, and the processing capacity constraint is:

[0018] (6)

[0019] Among them, C r (t) represents the processing capacity of recycling station r at time t, B r max B is the maximum accumulation of recycling station r. r (t) represents the return at time t.

[0020] The amount of waste collected by merchant r, and the utilization rate ρ of recycling station r in scenario s. r, s The calculation method is as follows:

[0021] (7)

[0022] Its value range is [0.2, 0.8], and the inventory update formula for the recycling station r is:

[0023] (8)

[0024] Similarly, the processing capacity constraint of dismantling plant d is:

[0025] (9)

[0026] Among them, Cd (t) represents the processing capacity of dismantling plant d at time t, B d max B is the maximum volume of dismantling plant d. d (t) represents the backlog of dismantling plant d at time t, and ρ represents the utilization rate of dismantling plant d under scenario s. d,s for:

[0027] (10)

[0028] Its value range is [0.2, 0.8]. The inventory balance update formula for dismantling plant d is:

[0029] (11)

[0030] (2) Constructing a cascaded risk prediction evolution mechanism

[0031] ① Initialize population evolution parameters: Set the maximum number of population iterations It max =100, population size N=100, the nth decision variable is initialized as:

[0032] (12)

[0033] Where, x t n (λ) is the decision variable of the nth individual in generation λ at time t. Under the premise of satisfying the processing capacity, utilization rate, inventory and order constraints of the dismantling plant and recycling station, the decision variables for order processing of the recycling station and dismantling plant are randomly generated.

[0034] ② Scenario-cascading risk prediction:

[0035] (13)

[0036] Where S(t,t-1) represents the similarity between time t and (t-1), j represents the number of scene attributes, S1(t) is the total demand at time t, S2(t) represents the maximum backlog at the recycling station at time t, and S2(t) represents the maximum backlog at the dismantling plant at time t. The similarity between time t and the previous time t-1 is calculated sequentially, and the scene s corresponding to the minimum similarity value is selected. m ;

[0037] ③ Individual crossover operations within the population:

[0038] (14)

[0039] Where, x t,new (λ) represents the offspring decision variable of the λ-generation population at time t, x t,sm n(best) represents scenario s m The optimal solution, the U(•) function represents the uniform crossover operation, corresponding to each pair of parent individuals x t,new (λ) and x t,sm n (best) Generates a random mask array with the same number of variables, with each element randomly set to 0 or 1. Offspring variables inherit their values ​​from their corresponding parents based on the mask; when the mask is 1, the values ​​are inherited from x. t,new (λ) Inheritance, when λ is 0, it is inherited from x. t,sm n (best) inheritance, repeating this method to generate N individuals to form a new population;

[0040] ④ Assess the fitness of individuals in the new population. The method for comparing the Pareto dominance of the nth and n-1th individuals is as follows:

[0041] Among them, f c s (x t n (λ)), f c s (x t n-1 (λ)) represent the energy consumption of the nth and (n-1th)th individuals in scenario s, respectively, f l s (x t n (λ)), f l s (x t n-1 (λ)) represent the demand loss of the nth and n-1th individuals in scenario s, respectively. The Pareto dominance relationship of each individual in the population is compared pairwise, and all individuals not dominated by any other individual are classified as elite individuals of the λ+1th generation.

[0042] (3) Design a feedforward self-adjusting mutation strategy

[0043] Based on the real-time operational status of integrated recycling stations and dismantling plants, a risk indicator (CRI) is defined. r+τ as follows:

[0044] (16)

[0045] Where α and β are the time lag impact factors of the recycling station and dismantling plant, respectively, with values ​​ranging from [0,1] to [0,1]. u (t) represents the demand of user u at time t, τ r , τ d These represent the propagation time lags at recycling centers and dismantling plants, respectively. When the risk index exceeds the threshold CRI... maxAt that time, according to probability p v Randomly select individuals in the population for mutation operations, and the decision variable x r,s t,n The mutation strategy of (λ) reduces risk by transferring orders to underutilized recycling stations. The specific mutation operations are as follows:

[0046] (17)

[0047] Where, γ r B is the balance coefficient of the recycling station r. r (0) represents the amount of waste accumulated at recycling station r at a historical time, y d,s t,n The variation strategy of (λ) reduces risk by transferring orders to underutilized dismantling plants, as follows:

[0048] (18)

[0049] Where, γ d B is the balance coefficient of dismantling plant d. d (0) represents the backlog at dismantling plant d at a historical moment;

[0050] (4) Obtain a robust optimal scheduling scheme for the waste home appliance recycling supply chain.

[0051] Check if the number of iterations λ has reached It max If λ <It max Then the iteration number λ is increased by 1 and the process jumps to step ②; otherwise, it starts from step It. max A solution x is randomly selected from the elite individuals of the generation. * (t)=[x r,s (t), y d,s [(t)], as a task allocation scheme for the waste home appliance recycling supply chain, suppresses the cascading risk amplification effect caused by demand uncertainty, and reduces operating energy consumption and demand loss; Attached Figure Description

[0052] Figure 1 This is the energy consumption curve of the waste household appliance recycling supply chain operation of the present invention.

[0053] Figure 2 This is the iterative convergence curve of demand loss in the waste household appliance recycling supply chain of this invention. Detailed Implementation

[0054] A robust optimization method for risk prediction in the waste household appliance recycling supply chain includes the following steps:

[0055] (1) Establish a robust optimization objective model for demand loss and operating energy consumption:

[0056] (19)

[0057] Among them, f c s (x(t)), f l s (x(t)) represent the demand loss and operating energy consumption of waste appliance recycling at time t in scenario s, respectively, and E[•] represents the expectation of the objective function under different scenarios, x(t) = [x r,s (t), y d,s [(t)] represents the decision variable for the optimization objective, x r,s (t), y d,s (t) are all binary variables, x r,s (t)=[x 1,r,s , x 2,r,s ,…, x o,r,s Let y be the decision variable for whether recycling station r processes o orders in scenario s at time t. d,s (t)=[y 1,d,s , y 2,d,s ,…, y o,d,s Let f be the decision variable for whether dismantling plant d processes o orders in scenario s at time t. c s (x(t)) and f l s The calculation method for (x(t)) is as follows:

[0058] (20)

[0059] (twenty one)

[0060] Among them, c r p , c d p The processing energy consumption of the r-th recycling station and the d-th dismantling plant are respectively, c r b , c d b B represents the accumulated energy consumption of the r-th recycling station and the d-th dismantling plant, respectively. r (t), B d (t) represents the backlog at the r-th recycling station and the d-th dismantling plant, respectively. o The demand loss for the 0th order represents the number of orders that did not respond to user requests within a given time window, and is calculated as follows:

[0061] (twenty two)

[0062] Where, t pd t represents the order completion time. c T represents the order arrival time. max Given a time window, since the number of orders effectively allocated cannot exceed the total demand, the order constraint is expressed as follows:

[0063] (twenty three)

[0064] Where O represents the total number of orders, the number of orders for recycling station r should be within its processing capacity, and the processing capacity constraint is:

[0065] (twenty four)

[0066] Among them, C r (t) represents the processing capacity of recycling station r at time t, B r max B is the maximum accumulation of recycling station r. r (t) represents the return at time t.

[0067] The amount of waste collected by merchant r, and the utilization rate ρ of recycling station r in scenario s. r, s The calculation method is as follows:

[0068] (25)

[0069] Its value range is [0.2, 0.8], and the inventory update formula for the recycling station r is:

[0070] (26)

[0071] Similarly, the processing capacity constraint of dismantling plant d is:

[0072] (27)

[0073] Among them, C d (t) represents the processing capacity of dismantling plant d at time t, B d max B is the maximum volume of dismantling plant d. d (t) represents the backlog of dismantling plant d at time t, and ρ represents the utilization rate of dismantling plant d under scenario s. d,s for:

[0074] (28)

[0075] Its value range is [0.2, 0.8]. The inventory balance update formula for dismantling plant d is:

[0076] (29)

[0077] (2) Constructing a cascaded risk prediction evolution mechanism:

[0078] ① Initialize population evolution parameters: Set the maximum number of population iterations It max =100, population size N=100, the nth decision variable is initialized as:

[0079] (30)

[0080] Where, x t n (λ) is the decision variable of the nth individual in generation λ at time t. Under the premise of satisfying the processing capacity, utilization rate, inventory and order constraints of the dismantling plant and recycling station, the decision variables for order processing of the recycling station and dismantling plant are randomly generated.

[0081] ② Scenario-cascading risk prediction:

[0082] (31)

[0083] Where S(t,t-1) represents the similarity between time t and (t-1), j represents the number of scene attributes, S1(t) is the total demand at time t, S2(t) represents the maximum backlog at the recycling station at time t, and S2(t) represents the maximum backlog at the dismantling plant at time t. The similarity between time t and the previous time t-1 is calculated sequentially, and the scene s corresponding to the minimum similarity value is selected. m ;

[0084] ③ Individual crossover operations within the population:

[0085] (32)

[0086] Where, x t,new (λ) represents the offspring decision variable of the λ-generation population at time t, x t,sm n (best) represents scenario s m The optimal solution, the U(•) function represents the uniform crossover operation, corresponding to each pair of parent individuals x t,new (λ) and x t,sm n (best) Generates a random mask array with the same number of variables, with each element randomly set to 0 or 1. Offspring variables inherit their values ​​from their corresponding parents based on the mask; when the mask is 1, the values ​​are inherited from x. t,new (λ) Inheritance, when λ is 0, it is inherited from x. t,sm n (best) inheritance, repeating this method to generate N individuals to form a new population;

[0087] ④ Assess the fitness of individuals in the new population. The method for comparing the Pareto dominance of the nth and n-1th individuals is as follows:

[0088] (33)

[0089] Among them, f c s (x t n (λ)), f c s (x t n-1 (λ)) represent the energy consumption of the nth and (n-1th)th individuals in scenario s, respectively, f l s (x t n (λ)), f l s (x t n-1 (λ)) represent the demand loss of the nth and n-1th individuals in scenario s, respectively. The Pareto dominance relationship of each individual in the population is compared pairwise, and all individuals not dominated by any other individual are classified as elite individuals of the λ+1th generation.

[0090] (3) Design a feedforward self-adjusting mutation strategy:

[0091] Based on the real-time operational status of integrated recycling stations and dismantling plants, a risk indicator (CRI) is defined. r+τ as follows:

[0092] (34)

[0093] Where α and β are the time lag impact factors of the recycling station and dismantling plant, respectively, with values ​​ranging from [0,1] to [0,1]. u (t) represents the demand of user u at time t, τ r , τ d These represent the propagation time lags at recycling centers and dismantling plants, respectively. When the risk index exceeds the threshold CRI... max At that time, according to probability p v Randomly select individuals in the population for mutation operations, and the decision variable x r,s t,n The mutation strategy of (λ) reduces risk by transferring orders to underutilized recycling stations. The specific mutation operations are as follows:

[0094] (35)

[0095] Where, γ r B is the balance coefficient of the recycling station r. r (0) represents the amount of waste accumulated at recycling station r at a historical time, y d,s t,nThe variation strategy of (λ) reduces risk by transferring orders to underutilized dismantling plants, as follows:

[0096] (36)

[0097] Where, γ d B is the balance coefficient of dismantling plant d. d (0) represents the backlog at dismantling plant d at a historical moment;

[0098] (4) Obtain a robust optimal scheduling scheme for the waste home appliance recycling supply chain.

[0099] Check if the number of iterations λ has reached It max If λ <It max Then the iteration number λ is increased by 1 and the process jumps to step ②; otherwise, it starts from step It. max A solution x is randomly selected from the elite individuals of the generation. * (t)=[x r,s (t), y d,s [(t)], as a task allocation scheme in the waste home appliance recycling supply chain, suppresses the cascading risk amplification effect caused by demand uncertainty, and reduces operating energy consumption and demand loss.

Claims

1. A robust optimization method for risk prediction in the waste household appliance recycling supply chain, characterized in that: A robust optimization objective model for demand loss and operating energy consumption is established, a cascading risk prediction evolution mechanism is constructed, a feedforward self-adjusting mutation strategy is designed, and a robust optimal scheduling scheme for the waste household appliance recycling supply chain is obtained to suppress the cascading risk amplification effect caused by demand uncertainty. Specifically, the following steps are included: (1) Establish a robust optimization objective model for demand loss and operating energy consumption: (1) Among them, f c s (x(t)), f l s (x(t)) represent the demand loss and operating energy consumption of waste appliance recycling at time t in scenario s, respectively, and E[•] represents the expectation of the objective function under different scenarios, x(t) = [x r,s (t), y d,s [(t)] represents the decision variable for the optimization objective, x r,s (t), y d,s (t) are all binary variables, x r,s (t)=[x 1,r,s , x 2,r,s ,…, x o,r,s Let y be the decision variable for whether recycling station r processes o orders in scenario s at time t. d,s (t)=[y 1,d,s , y 2,d,s ,…, y o,d,s Let f be the decision variable for whether dismantling plant d processes o orders in scenario s at time t. c s (x(t)) and f l s The calculation method for (x(t)) is as follows: (2) (3) Among them, c r p , c d p The processing energy consumption of the r-th recycling station and the d-th dismantling plant are respectively, c r b , c d b B represents the accumulated energy consumption of the r-th recycling station and the d-th dismantling plant, respectively. r (t), B d (t) represents the backlog at the r-th recycling station and the d-th dismantling plant, respectively, L o The demand loss for the 0th order represents the number of orders that did not respond to user requests within a given time window, and is calculated as follows: (4) Where, t p d t represents the order completion time. c T represents the order arrival time. max Given a time window, since the number of orders effectively allocated cannot exceed the total demand, the order constraint is expressed as follows: (5) Where O represents the total number of orders, the number of orders for recycling station r should be within its processing capacity, and the processing capacity constraint is: (6) Among them, C r (t) represents the processing capacity of the recycling station r at time t, B r max B is the maximum accumulation of recycling station r. r (t) represents the return at time t. The amount of waste collected by merchant r, and the utilization rate ρ of recycling station r in scenario s. r, s The calculation method is as follows: (7) Its value range is [0.2, 0.8], and the inventory update formula for the recycling station r is: (8) The processing capacity constraint of dismantling plant d is: (9) Among them, C d (t) represents the processing capacity of dismantling plant d at time t, B d max B is the maximum volume of dismantling plant d. d (t) represents the backlog of dismantling plant d at time t, and ρ represents the utilization rate of dismantling plant d under scenario s. d,s for: (10) Its value range is [0.2, 0.8]. The inventory balance update formula for dismantling plant d is: (11) (2) Constructing a cascaded risk prediction evolution mechanism: ① Initialize population evolution parameters: Set the maximum number of population iterations It max =100, population size N=100, the nth decision variable is initialized as: (12) Where, x t n (λ) is the decision variable of the nth individual in generation λ at time t. Under the premise of satisfying the processing capacity, utilization rate, inventory and order constraints of the dismantling plant and the recycling station, the decision variables for order processing of the recycling station and the dismantling plant are randomly generated. ② Scenario-cascading risk prediction: (13) Where S(t,t-1) represents the similarity between time t and (t-1), j represents the number of scene attributes, S1(t) is the total demand at time t, S2(t) represents the maximum backlog at the recycling station at time t, and S2(t) represents the maximum backlog at the dismantling plant at time t. The similarity between time t and the previous time t-1 is calculated sequentially, and the scene s corresponding to the minimum similarity value is selected. m ; ③ Individual crossover operations within the population: (14) Where, x t,new (λ) represents the offspring decision variable of the λ-generation population at time t, x t,sm n (best) represents scenario s m The optimal solution, the U(•) function represents the uniform crossover operation, corresponding to each pair of parent individuals x t,new (λ) and x t,sm n (best) Generates a random mask array with the same number of variables, with each element randomly set to 0 or 1. Offspring variables inherit their values ​​from their corresponding parents based on the mask; when the mask is 1, the values ​​are inherited from x. t,new (λ) Inheritance, when λ is 0, it is inherited from x. t,sm n (best) inheritance, repeating this method to generate N individuals to form a new population; ④ Assess the fitness of individuals in the new population. The method for comparing the Pareto dominance of the nth and n-1th individuals is as follows:

2. Among them, f c s (x t n (λ)), f c s (x t n-1 (λ)) represent the energy consumption of the nth and (n-1th)th individuals in scenario s, respectively, f l s (x t n (λ)), f l s (x t n-1 (λ)) represent the demand loss of the nth and n-1th individuals in scenario s, respectively. The Pareto dominance relationship of each individual in the population is compared pairwise, and all individuals not dominated by any other individual are classified as elite individuals of the λ+1th generation. (3) Design a feedforward self-adjusting mutation strategy: Based on the real-time operational status of integrated recycling stations and dismantling plants, a risk indicator (CRI) is defined. r+τ as follows: (16) Where α and β are the time lag impact factors of the recycling station and dismantling plant, respectively, with values ​​ranging from [0,1] to [0,1]. u (t) represents the demand of user u at time t, τ r , τ d These represent the propagation time lags at recycling centers and dismantling plants, respectively. When the risk index exceeds the threshold CRI... max When, according to probability p v Randomly select individuals in the population for mutation operations, and the decision variable x r,s t,n The mutation strategy of (λ) reduces risk by transferring orders to underutilized recycling stations. The specific mutation operations are as follows: (17) Where, γ r B is the balance coefficient of the recycling station r. r (0) represents the amount of waste accumulated at recycling station r at a historical time, y d,s t,n The variation strategy of (λ) reduces risk by transferring orders to underutilized dismantling plants, as follows: (18) Where, γ d B is the balance coefficient of dismantling plant d. d (0) represents the backlog at dismantling plant d at a historical moment; (4) Obtain a robust optimal scheduling scheme for the waste home appliance recycling supply chain. Check if the number of iterations λ has reached It max If λ <It max Then the iteration number λ is increased by 1 and the process jumps to step ②; otherwise, it starts from step It. max A solution x is randomly selected from the elite individuals of the generation. * (t)=[x r,s (t), y d,s [(t)], as a task allocation scheme in the waste home appliance recycling supply chain, suppresses the cascading risk amplification effect caused by demand uncertainty, and reduces operating energy consumption and demand loss.

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