MILP-based nuclear production system economic life design method

Abstract

The invention discloses a nuclear production system economic life design method based on mixed integer linear programming, and relates to the technical field of nuclear production system life and economic affordability design. The method comprises the steps of 1, comprehensively constructing a system-component double-layer framework based on engineering structure decomposition and cost, and positively measuring and calculating the whole life cycle cost and the economic life of a nuclear production system; 2, establishing a nuclear production system economic life design MILP model based on cost forward estimation; and 3, outputting a service life design value of the minimum cost of the whole cycle per hour of the corresponding system as the economic service life of the system through the solving model. According to the method, the life cycle cost of the system under different design life schemes can be measured in the design stage in the forward direction, the optimal economic life of the system is determined, a full-cycle economic quantitative tool is provided for the nuclear production system, the life cycle cost per hour is fully reduced, the service life of the system is scientifically decided, and the economic affordability of the system is improved.

Description

Technical Field

[0001] The present invention provides a nuclear production system economic life design method based on MILP, and particularly relates to the technical field of nuclear production system life and economic affordability design. Background Art

[0002] Due to its characteristics such as long operation cycle, high safety requirements and huge full life cycle investment, the economic affordability of nuclear production systems has become a key bottleneck restricting the large-scale development of the nuclear energy industry and is of great significance to the sustainable development of energy.

[0003] Existing nuclear production system lifecycle design methods typically adopt a long-life design paradigm, aiming to maximize the theoretical service life while satisfying the system's minimum mission reliability constraints. In terms of cost estimation, a cost inversion method based on historical model systems is commonly used, using regression and analogy models to estimate costs based on service life and cost parameters. However, due to factors such as module failures and end-of-life within the system, a lifecycle design approach that maximizes service life may be economically uneconomical. Furthermore, the credibility of the results of existing inverse cost estimates of the system's expected costs is heavily dependent on the accuracy of historical data. A lack of comparable data sources for system modules or low-accuracy data sources can lead to distorted system cost estimates, which in turn affects the scientific nature of the overall system lifecycle and affordability design. Summary of the Invention

[0004] To address the above problems, the present invention proposes a nuclear production system economic life design method based on mixed integer linear programming (MILP). By forward-constructing a nuclear production system full life cycle cost estimation method and a system economic life calculation method through engineering structure decomposition and cost synthesis, the present invention breaks through the data dependence bottleneck of the traditional reverse cost deduction method, quantifies the "design life-hourly cost" relationship, evaluates the system life cycle cost under different design life schemes in the design stage, and determines the optimal design life value that minimizes the system's hourly life cycle cost as the system's economic life.

[0005] A MILP-based economic life design method for a nuclear production system includes the following steps:

[0006] Step 1: Forward estimation of life cycle costs and calculation of economic life;

[0007] Step 1.1: Forward estimation of the life cycle costs of the nuclear production system;

[0008] Specifically, the nuclear production system is decomposed into a "system-module" architecture based on the engineering structure decomposition method. The specific characteristics of the system at each life cycle stage are analyzed to achieve cost synthesis. The system's full life cycle costs mainly include: system development costs, system batch production costs, system operating costs, system maintenance and support costs, and system decommissioning and disposal costs.

[0009] Among them, the system development cost is the ratio of the sum of the development costs of all modules constituting the system to the system production batch; the system batch production cost is the sum of the batch production costs of all modules constituting the system; as a long-term continuous production system, the operating cost of the nuclear production system can be regarded as a constant on an hourly scale; the maintenance and support cost required by the nuclear production system within the system design life is the sum of the fault repair costs and end-of-life replacement costs required by all modules in the system within the system design life; the decommissioning disposal cost required by the nuclear production system within the system design life includes two parts: the periodic product disposal cost required by the system within the design life and the system decommissioning cost at the end of its life.

[0010] Step 1.2: Calculation of economic life of nuclear production system;

[0011] To facilitate the expression of the calculation of the economic life of the nuclear production system, several symbols are introduced in this step: the design life of the nuclear production system is represented by L, the corresponding life cycle cost of the system when the design life is L is represented by LCC(L), the corresponding research and development cost of the system when the design life is L is represented by DC(L), the corresponding batch production cost of the system when the design life is L is represented by PC(L), the corresponding operating cost of the system when the design life is L is represented by OC(L), the corresponding maintenance and support cost of the system when the design life is L is represented by MS(L), the corresponding decommissioning disposal of the system when the design life is L is represented by RD(L), and the economic life of the nuclear production system is represented by EL. The calculation formula is as follows:

[0012]

[0013] When the functional relationship between the various cost items of the nuclear production system and the design life is continuously differentiable, the economic life of the system can be obtained by taking the derivative of the design life and comparing the hourly full life cycle cost values at the extreme points. However, in practice, the functions of the various cost items with respect to the life are not strictly continuously differentiable. Therefore, the subsequent steps of the present invention require the construction of a nuclear production system economic life design MILP model to obtain the optimal value of the system economic life.

[0014] Step 2: Define the parameter representation of the attribute data of the system component modules;

[0015] Specifically, let N be the module type set that makes up the system, i be the module type serial number and i=1,2,…,|N|, the production batch of the system be B, and according to the characteristics of the production system, assume that the hourly usage fee during its service life is a fixed constant k, and the workload operation ratio of the system and the i-th module be θ i , the number of modules of type i installed in the system is A i , the single-unit development cost of the i-th type module is dc i , the production cost of a single machine for the i-th module is pc i , the mean time between failures of the i-th module is mf i , the physical life of the i-th type module is pl i , the fault repair cost of the i-th module is rc i The replacement cost of the i-th module at the end of its service life is ec i , whether the i-th module can be repaired to rw i , whether the i-th module can be replaced by ew i The fixed disposal period for nuclear waste generated by the system is pd, the single disposal cost is fd, the development cost of the entire system is DC, the production cost of the entire system is PC, the decommissioning cost of the entire system is FE, and the planning lower limit of the system design life is L min , the planning upper limit of the system design life is L max , M is a large number such as 9999.

[0016] Step 3: Establish a MILP model for economic lifecycle design of nuclear production systems based on forward cost estimation. Using the system design lifecycle as the decision variable and minimizing the full-cycle cost per unit time as the optimization objective, the system engineering architecture, maintenance requirements, and cost estimation constraints are comprehensively considered to determine the system lifecycle design value that minimizes the full-cycle cost per hour.

[0017] Step 3.1: Define the decision variables for the economic life design of nuclear production systems;

[0018] L: design service life of the nuclear production system;

[0019] HLCC: The hourly life cycle cost of a nuclear production system when its design life is L;

[0020] LCC: the life cycle cost of a nuclear production system when its design life is L;

[0021] OC: The cost of using the nuclear production system to meet the life cycle requirements up to L;

[0022] MS: Maintenance and support costs required for the nuclear production system to meet its life cycle up to L;

[0023] RD: decommissioning costs required for nuclear production systems to meet their lifespan up to L;

[0024] wl i : The workload requirement assigned to the component module i of the nuclear production system when the system design life is L;

[0025] nr i : The expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L;

[0026] mr i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0027] ne i : non-negative integer variable, the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0028] me i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0029] nd: non-negative integer variable, the number of periodic disposals of products required by the nuclear production system when its design life is L;

[0030] Step 3.2: Establish the objective function for “design life-hour cost” optimization;

[0031]

[0032] Among them, HLCC is the established objective function, L is the design life decision variable of the system, LCC is the full life cycle cost required for the nuclear production system to meet the life cycle working requirements of L, DC is the development cost of the nuclear production system, PC is the production cost of the nuclear production system, OC is the operating cost required for the nuclear production system to meet the life cycle working requirements of L, MS is the maintenance and support cost required for the nuclear production system to meet the life cycle working requirements of L, and RD is the decommissioning cost required for the nuclear production system to meet the life cycle working requirements of L;

[0033] Step 3.3: Establish development cost calculation constraints;

[0034]

[0035] Step 3.4: Establish development cost calculation constraints;

[0036]

[0037] Step 3.5: Establish usage fee calculation constraints;

[0038] OC=L·k (5)

[0039] Step 3.6: Establish fault repair cost calculation constraints;

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Among them, wl i The workload requirement assigned to the component module i of the nuclear production system when the system design life is L, nr i is the expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L, mr i is the fault repair cost required for the component module i of the nuclear production system when the system design life is L, ne i is the number of replacement times required for the component module i of the nuclear production system when the system design life is L, me i is the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0048] Step 3.7: Establish decommissioning cost calculation constraints;

[0049]

[0050]

[0051] RD=nd·fd+FE (15)

[0052] Where nd is the number of periodic disposals of products required for the nuclear production system when its design life is L;

[0053] Step 3.8: Variable value constraints;

[0054] L∈[L min ,L max ](16)

[0055] HLCC,LCC,OC,MS,RR≥0 (17)

[0056]

[0057]

[0058] Step 4: Linear modeling of the objective function based on the value range interval segmentation;

[0059] Specifically: According to the planning lower limit value L of the design life of the nuclear production system min With the upper limit value L max , estimate the range of system life cycle cost [LCC min ,LCC max ], construct the possible value range of the objective function LCC / L and divide it into multiple seamless discrete sub-intervals with a maximum absolute error of δ, and use the boundary LCC / L value of each interval to approximate the true value of the objective function.

[0060] Step 4.1: Introduce additional decision parameters and variables;

[0061] SA a : 0 or 1 variable, which is 1 if and only if the objective function value is within the split interval a of its value range, otherwise it is 0;

[0062] SB b : 0 or 1 variable, which is 1 if and only if the objective function value is within the partition interval b of its value range, otherwise it is 0;

[0063] NA: variable SA a The number of parameters;

[0064] NB: variable SB b The number of parameters;

[0065] LCC max : Maximum estimated value of variable LCC;

[0066] LCC min : The minimum estimated value of the variable LCC;

[0067] δ: Maximum acceptable error percentage value of the linearization of the objective function;

[0068] Step 4.2: Use the range interval partitioning method to linearize and approximate the fractional objective function;

[0069]

[0070] Step 4.3: Determine the constraints of the segmentation interval where the objective function is located;

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Step 4.4: Additional parameter and variable value constraints;

[0077]

[0078]

[0079]

[0080] LCC min =DC+PC+FE (29)

[0081]

[0082]

[0083] Step 5: Solve the MILP model for economic life design of nuclear production systems based on forward cost estimation to obtain the system life design value that minimizes the full life cycle cost per unit time.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] The present invention can forward estimate the full life cycle cost of a nuclear production system under any design life based on the engineering structure decomposition and cost synthesis method. It can obtain the economic life value of the nuclear production system with the lowest hourly full life cycle cost in long-term operation in the form of a solvable MILP model as the basis for the system design life. This can fully get rid of the economic uneconomical problems caused by the current long-life design paradigm and the inaccurate results caused by reverse cost estimation, fully reduce system costs, and improve the economic affordability of the system. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 This is a flow chart of a MILP-based economic life design method for a nuclear production system according to the present invention. Figure 2 It is a schematic diagram of the economic life calculation principle of the nuclear production system described in the present invention. Figure 3 It is a schematic diagram of the objective function range interval segmentation linearization method adopted by the present invention. DETAILED DESCRIPTION

[0086] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0087] A MILP-based economic life design method for nuclear production systems, such as Figure 1As shown, it includes the following steps:

[0088] Step 1: Forward estimation of life cycle costs and calculation of economic life;

[0089] Step 1.1: Forward estimation of the life cycle costs of the nuclear production system;

[0090] Specifically, the nuclear production system is decomposed into a "system-module" architecture based on the engineering structure decomposition method. The specific characteristics of the system at each life cycle stage are analyzed to achieve cost synthesis. The system's full life cycle costs mainly include: system development costs, system batch production costs, system operating costs, system maintenance and support costs, and system decommissioning and disposal costs.

[0091] Among them, the system development cost is the ratio of the sum of the development costs of all modules constituting the system to the system production batch; the system batch production cost is the sum of the batch production costs of all modules constituting the system; as a long-term continuous production system, the operating cost of the nuclear production system can be regarded as a constant on an hourly scale; the maintenance and support cost required by the nuclear production system within the system design life is the sum of the fault repair costs and end-of-life replacement costs required by all modules in the system within the system design life; the decommissioning disposal cost required by the nuclear production system within the system design life includes two parts: the periodic product disposal cost required by the system within the design life and the system decommissioning cost at the end of its life.

[0092] Step 1.2: Calculation of economic life of nuclear production system;

[0093] The economic life calculation principle of nuclear production system is as follows Figure 2 As shown, in order to facilitate the expression of the economic life calculation of the nuclear production system, several symbols are introduced in this step: the design life of the nuclear production system is represented by L, the corresponding life cycle cost of the system when the design life is L is represented by LCC(L), the corresponding research and development cost of the system when the design life is L is represented by DC(L), the corresponding batch production cost of the system when the design life is L is represented by PC(L), the corresponding operating cost of the system when the design life is L is represented by OC(L), the corresponding maintenance and support cost of the system when the design life is L is represented by MS(L), the corresponding decommissioning disposal of the system when the design life is L is represented by RD(L), and the economic life of the nuclear production system is represented by EL. The calculation formula is shown below:

[0094]

[0095] When the functional relationship between the various cost items of the nuclear production system and the design life is continuously differentiable, the economic life of the system can be obtained by taking the derivative of the design life and comparing the hourly full life cycle cost values at the extreme points. However, in practice, the functions of the various cost items with respect to the life are not strictly continuously differentiable. Therefore, the subsequent steps of the present invention require the construction of a nuclear production system economic life design MILP model to obtain the optimal value of the system economic life.

[0096] Step 2: Define the parameter representation of the attribute data of the system component modules;

[0097] Specifically, let N be the module type set that makes up the system, i be the module type serial number and i=1,2,…,|N|, the production batch of the system be B, and according to the characteristics of the production system, assume that the hourly usage fee during its service life is a fixed constant k, and the workload operation ratio of the system and the i-th module be θ i , the number of modules of type i installed in the system is A i , the single-unit development cost of the i-th type module is dc i , the production cost of a single machine for the i-th module is pc i , the mean time between failures of the i-th module is mf i , the physical life of the i-th type module is pl i , the fault repair cost of the i-th module is rc i The replacement cost of the i-th module at the end of its service life is ec i , whether the i-th module can be repaired to rw i , whether the i-th module can be replaced by ew i The fixed disposal period for nuclear waste generated by the system is pd, the single disposal cost is fd, the development cost of the entire system is DC, the production cost of the entire system is PC, the decommissioning cost of the entire system is FE, and the planning lower limit of the system design life is L min , the planning upper limit of the system design life is L max , M is a large number such as 9999, NA is the variable SA a NB is the number parameter of the variable SB b The number of parameters, SC max is the maximum estimated value of the sum of variables DC, PC, OC, MS and RD, SC min is the minimum estimated value of the sum of variables DC, PC, OC, MS, and RD, and δ is the maximum acceptable percentage error of the linearization of the objective function.

[0098] Step 3: Establish a MILP model for economic lifecycle design of nuclear production systems based on forward cost estimation. Using the system design lifecycle as the decision variable and minimizing the full-cycle cost per unit time as the optimization objective, the system engineering architecture, maintenance requirements, and cost estimation constraints are comprehensively considered to determine the system lifecycle design value that minimizes the full-cycle cost per hour.

[0099] Step 3.1: Define the decision variables for the economic life design of nuclear production systems;

[0100] L: design service life of the nuclear production system;

[0101] HLCC: The hourly life cycle cost of a nuclear production system when its design life is L;

[0102] LCC: the life cycle cost of a nuclear production system when its design life is L;

[0103] OC: The cost of using the nuclear production system to meet the life cycle requirements up to L;

[0104] MS: Maintenance and support costs required for the nuclear production system to meet its life cycle up to L;

[0105] RD: decommissioning costs required for nuclear production systems to meet their lifespan up to L;

[0106] wl i : The workload requirement assigned to the component module i of the nuclear production system when the system design life is L;

[0107] nr i : The expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L;

[0108] mr i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0109] ne i : non-negative integer variable, the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0110] me i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0111] nd: non-negative integer variable, the number of periodic disposals of products required by the nuclear production system when its design life is L;

[0112] SA a : 0 or 1 variable, which is 1 if and only if the objective function value is within the split interval a of its value range, otherwise it is 0;

[0113] SB b : 0 or 1 variable, which is 1 if and only if the objective function value is within the partition interval b of its value range, otherwise it is 0;

[0114] Step 3.2: Establish the objective function of “design life-hour cost” optimization and use the range interval segmentation method to linearize the fractional objective function. The schematic diagram of the linear approximation method is as follows: Figure 3 As shown;

[0115]

[0116] Among them, HLCC is the established objective function, L is the design life decision variable of the system, DC is the development cost of the nuclear production system, PC is the production cost of the nuclear production system, OC is the use cost required for the nuclear production system to meet the life cycle of L, MS is the maintenance cost required for the nuclear production system to meet the life cycle of L, RD is the decommissioning cost required for the nuclear production system to meet the life cycle of L, SA a and SB b It is the decision variable for locating the objective function value in the range segmentation interval.

[0117] Step 3.3: Constraints on the values of relevant parameters of the objective function linearization;

[0118]

[0119]

[0120] LCC min =DC+PC+FE (36)

[0121]

[0122] Step 3.4: Determine the constraints of the segmentation interval where the objective function is located;

[0123] LCC=DC+PC+OC+MS+RD (38)

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] Step 3.5: Establish development cost calculation constraints;

[0130]

[0131] Step 3.6: Establish development cost calculation constraints;

[0132]

[0133] Step 3.7: Establish usage fee calculation constraints;

[0134] OC=L·k (46)

[0135] Step 3.8: Establish fault repair cost calculation constraints;

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] Among them, wl i The workload requirement assigned to the component module i of the nuclear production system when the system design life is L, nr i is the expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L, mr i is the fault repair cost required for the component module i of the nuclear production system when the system design life is L, ne i is the number of replacement times required for the component module i of the nuclear production system when the system design life is L, me i is the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0144] Step 3.9: Establish decommissioning cost calculation constraints;

[0145]

[0146]

[0147] RD=nd·fd+FE (56)

[0148] Where nd is the number of periodic disposals of products required for the nuclear production system when its design life is L;

[0149] Step 3.10: Variable value constraints;

[0150] L∈[L min ,L max ] (57)

[0151] HLCC,LCC,OC,MS,RR≥0 (58)

[0152]

[0153]

[0154]

[0155]

[0156] Step 4: Solve the MILP model for economic life design of nuclear production systems based on forward cost estimation to obtain the system life design value that minimizes the full life cycle cost per unit time;

[0157] This implementation uses the branch-and-bound algorithm embedded in the commercial MILP solver CPLEX 12.9.0 on the GNU / Linux 4.15.0-142-generic x86_64 operating system to solve the model, with the gap parameter set to 10. -5 , the gap calculation formula is as follows:

[0158]

[0159] In order to reflect the superiority of the economic life design proposed in this invention, this implementation named the MILP model constructed by the invention as the economic life design model, and designed the system life as the planning upper limit value L max It served as a control and was named the long-life design model;

[0160] A nuclear production system test case was selected to test and verify the MILP model constructed by the present invention. The system was assumed to consist of 18 modules, the production batch of the system was 5, and the planning lower limit of the system design life was 4×10 4 hours (about 5 years), the upper limit of the system design life is 44×10 4 hours (about 50 years), the hourly usage cost of the system during its service life is RMB 14,300, the decommissioning cost of the system is RMB 5 million, and the product disposal cycle of the system is 4.38×10 3hours, the single disposal cost is RMB 100,000, M is 9999, the maximum acceptable error percentage of the objective function linearization is 0.1%, the minimum estimated value of the life cycle cost in the planned life interval is RMB 23.8424 million, and the maximum estimated value of the life cycle cost in the planned life interval is RMB 328.2210 million. A total of 9018 objective function segmentation intervals are used. The attribute parameter data of the system component modules are shown in Table 1;

[0161] Table 1 System component module attribute parameters

[0162] The experimental results are shown in Table 2. The economic life design model can determine the design life value that minimizes the hourly life cycle cost of the nuclear production system during the life design period, with a maximum error percentage not exceeding 0.1%, as the economic life design value of the system. From the perspective of the optimal design life value, the economic life of the system is significantly less than the maximum life of the system planning design. From the perspective of the final life cycle cost results, the economic life design model can save a total cost of 45.0748 million yuan over the entire design life cycle compared to the long life design model, and the life cycle cost improvement percentage reaches 13.78%.

[0163] Table 2 Comparison of results between economic life design model and long life design model

[0164] The above comparison results show that the economic life design model outperforms the long life design model in both hourly life cycle costs and total life cycle costs. Therefore, for nuclear production systems, blindly adopting a long design paradigm and extending the system's service life without considering hourly life cycle costs is economically unreliable. From the perspective of minimizing hourly costs, the economic life of the system identified by this invention can provide a reliable basis for calculating the service life of nuclear production systems, thereby improving the economic affordability of the system.

Claims

1. A MILP-based economic life design method for nuclear production systems, comprising the following steps: (1) Forward estimation of life cycle costs and calculation of economic life; (1.1) Forward estimation of the life cycle costs of nuclear production systems: Based on the engineering structure decomposition method, the nuclear production system is decomposed into a "system-module" architecture. The specific characteristics of the system at each life cycle stage are analyzed to achieve cost synthesis. The life cycle costs of the system mainly include: System development costs, system batch production costs, system operating costs, system maintenance and support costs, and system decommissioning and disposal costs; (1.2) Calculation of the economic life of a nuclear production system. Several symbols are introduced: the design life of a nuclear production system is represented by L, the corresponding life cycle cost of the system when the design life is L is represented by LCC(L), the corresponding development cost of the system when the design life is L is represented by DC(L), the corresponding batch production cost of the system when the design life is L is represented by PC(L), the corresponding operating cost of the system when the design life is L is represented by OC(L), the corresponding maintenance and support cost of the system when the design life is L is represented by MS(L), and the corresponding decommissioning disposal of the system when the design life is L is represented by RD(L). The economic life of the nuclear production system is represented by EL, and the calculation formula is as follows: (2) Define the parameter representation of the attribute data of the system components; set the module type set that constitutes the system to N, i is the serial number of the module type and i = 1, 2, ..., |N|, the production batch of the system is B, and according to the characteristics of the production system, assume that the hourly usage fee during its service life is a fixed constant k, and the workload operation ratio of the system and the i-th module is θ i , the number of modules of type i installed in the system is A i , the single-unit development cost of the i-th type module is dc i , the production cost of a single machine for the i-th module is pc i , the mean time between failures of the i-th module is mf i , the physical life of the i-th type module is pl i , the fault repair cost of the i-th module is rc i The replacement cost of the i-th module at the end of its service life is ec i , whether the i-th module can be repaired to rw i , whether the i-th module can be replaced by ew i The fixed disposal period for nuclear waste generated by the system is pd, the single disposal cost is fd, the development cost of the entire system is DC, the production cost of the entire system is PC, the decommissioning cost of the entire system is FE, and the planning lower limit of the system design life is L min , the planning upper limit of the system design life is L max , M is a large number such as 9999, NA is the variable SA a NB is the number parameter of the variable SB b The number of parameters, SC max is the maximum estimated value of the sum of variables DC, PC, OC, MS and RD, SC min is the minimum estimated value of the sum of variables DC, PC, OC, MS, and RD, and δ is the maximum acceptable percentage error of the linearization of the objective function. (3) Establish a MILP model for economic life design of nuclear production systems based on forward cost estimation; (3.1) Define the decision variables for the economic life design of nuclear production systems; Assume that variable L represents the design service life of the nuclear production system; Let the variable HLCC represent the hourly life cycle cost of the nuclear production system when its design life is L; The variable LCC is set to represent the life cycle cost of the nuclear production system when its design life is L; Set the variable OC to represent the cost of using the nuclear production system to meet the life cycle requirements of L; set the variable MS to represent the maintenance cost of the nuclear production system to meet the life cycle requirements of L. Set the variable RD to represent the decommissioning cost required for the nuclear production system to meet its service life L; set the variable wl i represents the workload requirement assigned to the component module i of the nuclear production system when the system design life is L; Set the variable nr i represents the expected number of fault repairs required for component module i of the nuclear production system when the system design life is L; Set the variable mr i represents the fault repair cost required for the component module i of the nuclear production system when the system design life is L; Set the variable ne i represents a non-negative integer variable, the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L; Set the variable me i represents the fault repair cost required for the component module i of the nuclear production system when the system design life is L; Let variable nd represent a non-negative integer variable, the number of periodic disposals of products required by the nuclear production system when its design life is L; Set variable SA a Represents a 0 or 1 variable, which is 1 if and only if the objective function value is within the segmentation interval a of its value range, otherwise it is 0; set the variable SB b Represents a 0 or 1 variable, which is 1 if and only if the objective function value is within the partition interval b of its value range, otherwise it is 0; (3.2) The objective function for optimizing the "design life-hourly cost" is established, and the fractional objective function is linearly approximated using the range interval partitioning method: (3.3) Constraints on the values of the parameters related to the linearization of the objective function: LCC min =DC+PC+FE (3.4) Deterministic constraints on the segmentation interval of the objective function: LCC = DC + PC + OC + MS + RD (3.5) Establishing constraints for development cost calculation: (3.6) Establishing constraints for R&D cost calculation: (3.7) Establish usage fee calculation constraints: OC=L·k (3.8) Establish the fault repair cost calculation constraints: (3.9) Establishing constraints for calculating decommissioning costs: RD=nd·fd+FE (3.10) Variable value constraints: L∈[L min ,L max ] HLCC,LCC,OC,MS,RR≥0 (4) Solve the MILP model for the economic life design of nuclear production systems based on forward cost estimation, forward calculate the life cycle cost of the system under different design life scenarios during the design phase, and determine the economic life that minimizes the hourly life cost of the system as the economic basis for the service life design of the system.

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