Multi-level spare parts inventory optimization method based on scenario strategy and algorithm pool competition

Abstract

The application relates to the technical field of spare parts inventory management, and particularly discloses a multi-level spare parts inventory optimization method based on scene strategy and algorithm pool competition. The method comprises the following steps: acquiring input parameters comprising spare parts parameters, topological parameters and a scene identifier; retrieving a strategy parameter set from a scene strategy mapping table according to the scene identifier; performing node-level demand prediction based on the strategy parameter set; based on the strategy parameter set and the prediction result, evaluating weighted decision values in parallel on three channels of repair, allocation and procurement of an inventory gap, and generating a replenishment instruction; performing inventory optimization comprising greedy initialization, multi-algorithm parallel competition, elite cross-pollination and target-oriented refinement, scene optimization and Pareto set merging, and outputting an inventory configuration recommended solution; performing eight-item decomposition of a full-life-cycle cost, four-layer availability and comprehensive performance evaluation on the recommended solution; starting budget suggestion detection when system availability is lower than a target; and outputting a structured result file.

Description

Technical Field

[0001] This invention relates to the field of spare parts inventory management technology, and specifically discloses a multi-level spare parts inventory optimization method based on scenario strategy and algorithm pool competition. Background Technology

[0002] Existing multi-level spare parts inventory optimization methods typically employ fixed optimization models or single algorithms, lacking the ability to adaptively adjust to different support scenarios (such as cost priority, availability priority, and emergency support), leading to a mismatch between optimization solutions and scenario requirements. Furthermore, traditional methods often consider only a single channel (such as procurement or allocation) in replenishment scheduling, failing to comprehensively evaluate the timeliness and cost trade-offs of multiple channels such as repair, allocation, and procurement; inventory optimization often relies on a single search paradigm, easily getting trapped in local optima, and lacks a mechanism to integrate the advantages of different algorithms; when budgets are not met, there is a lack of a systematic budget suggestion detection process, making it difficult to assist decision-makers in making reasonable budget adjustments. Therefore, existing technologies cannot provide flexible and efficient inventory optimization solutions for complex support systems involving multiple scenarios, multiple nodes, and multiple spare parts. Summary of the Invention

[0003] The technical problem this invention aims to solve is: addressing the issues of existing methods in multi-level spare parts inventory optimization, such as lack of scenario adaptability, imperfect multi-channel replenishment scheduling, susceptibility of single algorithms to local optima, and lack of system detection methods when budget targets are not met. This invention provides an inventory optimization method that can dynamically adjust the strategy parameter set based on scenario identifiers and integrates parallel competition of multiple algorithms with elite cross-pollination.

[0004] This invention provides a multi-level spare parts inventory optimization method based on scenario strategy and algorithm pool competition, the method comprising the following steps:

[0005] Step S1, Parameter and Scene Input: Obtain input parameters, including spare parts parameters, multi-level maintenance support system topology parameters, and scene identifiers. The scene identifiers are set of scene identifiers that include two or more preset scenes.

[0006] Step S2, Scene Strategy Engine Mapping: Based on the scene identifier, retrieve the corresponding strategy parameter set from the preset scene strategy mapping table. The strategy parameter set includes at least the safety stock multiplier, urgency escalation factor, scheduling time weight and scheduling cost weight, weight of each item of the comprehensive efficiency index, main algorithm identifier and activation algorithm subset.

[0007] Step S3, Node-level demand forecasting: Based on the strategy parameter set, for each spare part at each node, the following steps are performed in sequence: failure rate correction, system-level annual demand rate calculation, safety stock target and reorder point scenario correction, three-pool inventory distribution calculation, node-level pipeline quantity calculation, node-level expected stockout calculation, and node-level cost-effectiveness ratio calculation, and the node-level demand forecasting results are output.

[0008] Step S4, Three-channel replenishment scheduling: Based on the strategy parameter set and the node-level demand forecast results, for each spare part and node combination with inventory gap, the weighted decision value is evaluated in parallel on the repair channel, transfer channel and procurement channel. The channel with the smallest weighted decision value is selected to generate a replenishment instruction, and the replenishment instruction is graded by priority.

[0009] Step S5, Scenario-driven inventory optimization: Based on the strategy parameter set, an inventory optimization engineering operation is executed, including a greedy initialization stage, a multi-algorithm parallel competition stage, an elite cross-pollination and target-oriented refinement stage, and a scenario optimization and Pareto set merging stage, outputting a recommended solution for inventory configuration; the multi-algorithm parallel competition stage constructs an algorithm pool containing at least three different search paradigms, and the algorithms participating in the competition are determined by the activation algorithm subset, and each algorithm is evaluated using a unified comprehensive objective function; the elite cross-pollination stage selects two optimal solutions belonging to different search paradigms from the optimal solution set of the algorithm pool, performs system-level overall cross-pollination according to the subsystem to which the spare parts belong, and performs target-oriented refinement on the cross-pollination offspring;

[0010] Step S6, Lifecycle Cost Decomposition: Perform eight decomposition calculations on the recommended inventory configuration solution, including procurement cost, holding cost, deployment and transportation cost, stockout loss cost, repair cost, scrap cost, ordering cost, and annual transportation cost;

[0011] Step S7, Four-layer availability and comprehensive performance evaluation: Calculate the inherent availability, operational availability, task availability and spare parts availability of the recommended inventory configuration solution in sequence, and calculate the system availability, comprehensive performance index and task success rate based on this.

[0012] Step S8, Budget suggestion detection: When the system availability is lower than the preset target availability, start dual-path greedy detection and three-case discrimination, and perform binary scaling search on the cases that can be achieved by budget amplification, and output the suggested budget adjustment amount;

[0013] Step S9, Output Results: Export the inventory configuration matrix, the eight-item decomposition results of the whole life cycle cost, the four-level availability index, the comprehensive efficiency index, the task success rate, the Pareto frontier solution set, the replenishment instruction list, and the budget suggestion in the form of a structured data file.

[0014] The beneficial technical effects of this invention are as follows: By using a scenario strategy engine to adaptively select a set of strategy parameters based on scenario identifiers, the optimization scheme is matched to the needs of different guarantee scenarios (such as normal equilibrium, lowest cost, availability priority, etc.); by using a three-channel parallel evaluation weighted decision value, replenishment time and cost are comprehensively balanced, improving the rationality of replenishment decisions; by using an inventory optimization engineering operation that includes greedy initialization, multi-algorithm parallel competition, elite cross-pollination, and target-oriented refinement, the advantages of multiple search paradigms are integrated to avoid getting trapped in local optima and improve the quality and convergence efficiency of solutions; by using an eight-item decomposition of lifecycle costs and a four-layer availability assessment, comprehensive decision support is provided; when availability is not up to standard, a budget suggestion probe is initiated, outputting an operable budget adjustment scheme to assist users in making resource decisions. Attached Figure Description

[0015] Figure 1 This is the overall flowchart of the spare parts inventory optimization method in this embodiment.

[0016] Figure 2 This is a schematic diagram of the three-level maintenance support system topology in this embodiment.

[0017] Figure 3 This is a schematic diagram of the multi-scene-parameter-algorithm mapping of the scene strategy engine in this embodiment.

[0018] Figure 4 This is a schematic diagram of the scenario-driven F3 inventory optimization engineering operation in this embodiment.

[0019] Figure 5 This is a diagram of the multi-algorithm parallel competition pool and system-level cross-pollination architecture in this embodiment.

[0020] Figure 6 This is a schematic diagram of the three-pool model and supply reliability correction in this embodiment.

[0021] Figure 7 This is a flowchart of the budget suggestion for dual-start detection and binary scaling search in this embodiment. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] This embodiment provides a multi-level spare parts inventory optimization method based on scenario-based strategies and algorithm pool competition. See also Figure 1 The method includes the following steps:

[0024] Step S1 Parameters and Scene Input:

[0025] See Figure 2The multi-level maintenance support system consists of three levels: L1, L2, and L3. Level L1 is the on-site support warehouse, directly serving the user site, with three nodes: N01, N02, and N03. Level L2 is the regional support center warehouse, with two nodes: N04 and N05. Level L3 is the contractor's central warehouse, with two nodes: N06 and N07. All levels are connected via transportation links. Central repair shops are located near the L2 and L3 level nodes to repair faulty parts and re-enter them into the warehouse.

[0026] The input parameters obtained in this step include:

[0027] (1) System parameters: including the spare parts list and average failure rate of each subsystem i. Average repair time And the mission cycle T. This embodiment has a total of 5 independent subsystems, named SYS01, SYS02, SYS03, SYS04 and SYS05 respectively. The parameters of each subsystem are configured by the user in the input parameter file according to the actual equipment characteristics.

[0028] (2) Spare parts parameters: including unit price, volume, repair rate, lead time, and safety stock strategy. This embodiment sets up 25 spare parts, named from P001 to P025.

[0029] The input interface of this invention supports receiving input parameters from external data sources such as maintenance management information systems, repair information systems, and ERP inventory systems in the form of structured data files (e.g., Excel, JSON, CSV). The fields of these input parameter files include at least: a spare parts list and its attributes, a subsystem composition and failure rate table, a multi-level maintenance support system node topology configuration, a transportation time matrix and transportation cost matrix between nodes, the budget limit, storage volume limit, and warehouse capacity limit for each node, and a scenario identifier. After the structured data file is parsed and parameters are aggregated by the input acquisition module of this invention, a normalized optimization context is generated for subsequent modules to call.

[0030] (3) Topology parameters of the multi-level maintenance support system: including the transportation time matrix between each node (7×7), Transportation Cost Matrix (7×7), Number of equipment units at each node Maximum funding for each node Storage volume limit and storage capacity limit .

[0031] (4) Scene identifier The value belongs to a set of scenario identifiers that includes two or more preset scenarios. In this embodiment, the set of scenario identifiers includes six preset scenarios: Balanced, Minimal Cost, First Availability, Emergency Protection, Successful Mission, and Optimal Performance.

[0032] Table 1. Structured Input Data Fields and Their Functional Stages

[0033]

[0034] Step S2: Scene Strategy Engine Mapping

[0035] See Figure 3 The scene policy engine retrieves the corresponding policy parameter set from a preset scene policy mapping table based on the scene identifier. The scene policy mapping table is shown in Table 2 below.

[0036] Table 2. Strategy parameter configurations for six preset scenarios

[0037]

[0038] The specific definition of the activation algorithm subset is as follows:

[0039] BALANCED and EMERGENCY scenarios: Activate {MA, DDE, CEM, DPSO, TS, NSGA-II};

[0040] COST_MINIMUM scenario: Activate {MA, DDE, CEM, DPSO, TS, SA};

[0041] AVAILABILITY_FIRST and MISSION_SUCCESS scenarios: Activate all eight algorithms {MA, DDE, CEM, DPSO, TS, ALNS, NSGA-II, SA}, where NSGA-II is for auxiliary refinement and SA is for auxiliary local search;

[0042] MOE_OPTIMAL scenario: Activates all eight algorithms {MA, DDE, CEM, DPSO, TS, ALNS, NSGA-II, SA}, with the main algorithm being Hybrid mode.

[0043] The scenario strategy engine outputs the set of strategy parameters for use in subsequent steps S3 to S8.

[0044] In this embodiment, the strategy parameter values ​​for each scenario in the scenario strategy mapping table are not strictly fixed to the point values ​​listed in Table 2 above. Instead, they are allowed to take values ​​within a preset tolerance range centered on each point value, to accommodate differences in parameter calibration accuracy and actual engineering needs among different assurance systems. The specific tolerance ranges for each scenario strategy parameter are defined as follows:

[0045] In the normal equilibrium scenario (BALANCED) and the comprehensive efficiency scenario (MOE_OPTIMAL): the scheduling time weight α∈[0.55, 0.65], the scheduling cost weight β∈[0.35, 0.45], and the safety stock multiplier Kss∈[0.9, 1.1];

[0046] Lowest cost scenario (COST_MINIMUM): α∈[0.20, 0.30], β∈[0.70, 0.80], Kss∈[0.6,0.8];

[0047] Availability-first scenario (AVAILABILITY_FIRST): α∈[0.80, 0.90], β∈[0.10, 0.20], Kss∈[1.4, 1.6];

[0048] Emergency support scenario (EMERGENCY): α∈[0.90, 1.00], β∈[0.00, 0.10], Kss∈[1.8,2.2];

[0049] Mission success scenario (MISSION_SUCCESS): α∈[0.65, 0.75], β∈[0.25, 0.35], Kss∈[2.0, 2.4];

[0050] The three weights (wa, wc, we) of the comprehensive performance index MoE are allowed to take values ​​within a closed interval centered on the point values ​​listed in Table 2 and with a width not exceeding 0.10 in each scenario, and the sum of the three weights always remains 1.0.

[0051] The design intent of the aforementioned tolerance range is to provide users with room for parameter fine-tuning while keeping the core optimization preferences of each scenario unchanged, so that the scenario strategy mapping table can adapt to the specific engineering needs of different equipment types and different support conditions without affecting the essence of the technical solution of this invention.

[0052] Table 3. Transmission path of scenario strategy parameters in stages F1-F4

[0053]

[0054] Step S3: Node-level demand forecasting:

[0055] This step, based on the aforementioned strategy parameter set, is executed sequentially for each spare part i and each node j:

[0056] (1) Environmental factor-corrected failure rate. The environmentally corrected failure rate is calculated according to formula (3-1):

[0057] (3-1)

[0058] In the formula, The failure rate of spare parts after environmental factor correction; The baseline failure rate for spare parts; These are environmental factors including temperature, humidity, vibration, and dust. The sensitivity index of spare parts to corresponding environmental factors; It is an aging factor.

[0059] (2) Calculate the system-level annual demand rate.

[0060] (3-2)

[0061] In the formula, The system-level annual demand rate for the subsystem to which spare part i belongs; The number of spare parts i installed on each piece of equipment; The failure rate after environmental correction; The task utilization coefficient for subsystem s; The number of identical equipment units in subsystem s; The repair rate of spare part i; The task cycle.

[0062] Based on the safety stock multiplier The safety stock target and reorder point for spare part i are adjusted according to the scenario, and the adjustment relationship is as follows:

[0063] (3-11)

[0064] (3-12)

[0065] In the formula, For safety stock multipliers; The original safety stock target and the scenario-corrected safety stock target for spare part i; The original reorder point and the reorder point after scenario correction for spare part i.

[0066] (3) Calculate the inventory distribution of the three pools. See [link / reference] Figure 6 The three-pool model divides the total spare parts inventory into available pools. Maintenance pool and waste pool All three conditions must be met:

[0067]

[0068]

[0069]

[0070] In the formula, The total inventory of spare part i at node j; The available pool inventory of spare part i at node j; The maintenance pool inventory for spare parts i at node j; The scrap pool inventory for spare part i at node j; The work-in-process inventory of spare part i at node j; The effective inventory of spare part i at node j; For spare part i, the lead time for repair is the time required from when the faulty part is sent for repair to when it is repaired and returned to a usable state. denoted as the scrap rate of spare part i, which is the probability that a faulty part is determined to be irreparable and scrapped after evaluation.

[0071] (4) Calculate the node-level pipeline quantity. Calculate according to formula (3-6), including supply reliability correction:

[0072]

[0073] In the formula, The node-level pipeline quantity for spare part i at node j; For the system-level annual demand rate of spare part i; The preceding time is in months; This represents the number of nodes at the same level. To ensure the reliability of spare part i's supply.

[0074] (5) Calculate the expected number of stockouts at the node level Select the distribution model based on the ratio of the variance to the mean of spare parts demand:

[0075]

[0076] In the formula, Let be the expected number of stockouts when the inventory level is s and the mean parameter is μ; Let be the probability mass function of the Poisson distribution; To determine inventory levels; The index of the value of the random variable is used to determine the required value. This represents the average pipeline demand.

[0077]

[0078] In the formula, This represents the expected number of stockouts under a negative binomial distribution. It is the negative binomial probability mass function; The negative binomial distribution parameters are obtained by inverse calculation from the demand mean and variance.

[0079] In this embodiment, the selection rule for the probability distribution model is achieved through a quantitative judgment of the variance-to-mean ratio. Specifically, the ratio of the pipeline demand variance to the mean for spare parts at each node is calculated; when this ratio is greater than a preset over-dispersion threshold, a negative binomial distribution is used to calculate the expected shortage number; otherwise, a Poisson distribution is used. In this embodiment, the preset over-dispersion threshold is set to 1.0, that is, when the demand variance exceeds the demand mean, the spare part demand is determined to be an over-dispersion demand, and the negative binomial distribution is switched; when the demand variance does not exceed the demand mean, it is determined to be an approximately Poisson demand, and a Poisson distribution is used.

[0080] When using a negative binomial distribution, the distribution parameters are determined by inverse calculation of the demand mean and demand variance using the method of moments, ensuring consistency between the distribution parameters and the measured demand statistics. The calculation method for the expected shortage under the negative binomial distribution is logically consistent with that under the Poisson distribution, differing only in the probability mass function used.

[0081] (6) The probability of stockout at the node level is adjusted for supply reliability and calculated according to formula (3-9):

[0082]

[0083] In the formula, This is the out-of-stock probability adjusted for supply reliability. This represents the uncorrected out-of-stock probability derived solely from inventory status. To ensure the reliability of spare part i's supply.

[0084] (7) Calculate the cost-effectiveness ratio Calculate according to formula (3-10):

[0085]

[0086] In the formula, Cost-effectiveness of spare parts i; The improvement in average EBO (Expected Out-of-Stock Quantity) resulting from adding one spare part i on all L1 level nodes; The unit price for spare part i.

[0087] Step S4: Three-channel replenishment scheduling

[0088] This step involves optimizing the replenishment plan, specifically including:

[0089] (1) Using the Floyd-Warshall full-source shortest path algorithm, based on the transportation time matrix, transportation cost matrix, and the scheduling time weight α and cost weight β output by S2, calculate the weighted shortest path matrix between all node pairs in the entire network. , and jump point matrix The weighted distance is defined as follows:

[0090]

[0091] In the formula, The normalized weighted distance from node a to node b; These are the scheduling time weight and the scheduling cost weight; The transit time and cost from node a to node b; This represents the maximum transport time and maximum transport cost used for normalization.

[0092] (2) For each spare part-node pair with a gap in the S3 output, evaluate simultaneously on three channels:

[0093] Repair channel: If spare part i is a repairable part and there is a faulty part to be repaired in the same or higher level node, calculate the time and cost required to send the faulty part for repair and return it to node j;

[0094] Transfer Channel: If other nodes have surplus inventory (exceeding their safety stock line), calculate the time and cost required to transfer from the surplus node to node j, and check that the source node's inventory is not lower than the danger level after the transfer.

[0095] Procurement channel: The time and cost of directly procuring from suppliers and transporting to node j.

[0096] (3) Calculate the normalized weighted decision value for each channel and select the channel with the smallest score to generate a replenishment instruction.

[0097]

[0098] In the formula, This is a weighted decision value for the replenishment channel; the smaller the value, the better the replenishment channel. This refers to the replenishment time and replenishment cost corresponding to this channel; For normalized baseline time and normalized baseline cost; As a scheduling time weight, This is the scheduling cost weight.

[0099] (4) Based on the node-level EBO output by S3 and the criticality level of each spare part, upgrade the urgency factor accordingly. The replenishment order is classified as URGENT / NORMAL / DEFERRED based on the urgency threshold.

[0100] Step S5: Scenario-driven F3 inventory optimization engineering task:

[0101] See Figure 4 This step executes a scenario-driven F3 inventory optimization engineering task, with the node-spare parts inventory matrix as the decision variable. This step is not composed of four isolated algorithms in a fixed order, but rather an engineering task consisting of resident algorithms, conditional algorithms, supplementary search, and cross-refinement.

[0102] Phase 1: Based on Greedy bottleneck filling of (cost-effectiveness ratio).

[0103] The goal of Phase One is to quickly generate an initial solution with engineering feasibility for refinement in subsequent phases. The specific steps are as follows:

[0104] a) Starting from the basic inventory, initialize the decision variables and conduct subsequent evaluations using a unified inventory caliber.

[0105] =max( , (5-1a)

[0106] In the formula, The decision inventory matrix generated by the algorithm; This is the original basic inventory matrix; An efficient inventory matrix used by both the heuristic function and the main evaluation function.

[0107] b) Output according to S3 All spare parts are sorted in descending order and divided into three thirds: high CER (CER refers to cost-effectiveness ratio) (first 1 / 3 of the sorted parts), medium CER (middle 1 / 3 of the sorted parts), and low CER (last 1 / 3 of the sorted parts).

[0108] c) For each type of spare part, determine the filling ratio according to its grade. High CER level CER Low CER .

[0109] The three fill ratios (0.70 / 0.50 / 0.35) mentioned above are typical values ​​in this embodiment, corresponding to representative point values ​​within the high CER range [0.60, 0.80], the medium CER range [0.40, 0.60], and the low CER range [0.25, 0.45], respectively. The three fill ratios must always satisfy the decreasing constraint that the high CER fill ratio is greater than the medium CER fill ratio, and the medium CER fill ratio is greater than the low CER fill ratio, to ensure that cost-effective spare parts are prioritized for replenishment. In other embodiments, the fill ratios within the above ranges can be adjusted according to the budget constraints and spare parts demand characteristics of the support system without affecting the essential technical solution of this invention.

[0110] d) For each spare part i and each node j with a gap, increase the inventory according to the tiered filling ratio, but at the same time, the condition of node j must be met. The constraints are budget, additional volume, and actual storage capacity.

[0111] Δx ij =ceil( i · ij (5-1b)

[0112] In the formula, Δx ij The new inventory quantity for spare part i at node j in Phase 1; i To be according to The fill ratio is determined by the grading; ij Let represent the inventory gap of spare part i at node j; ceil(·) represents the rounding up function.

[0113] e) Output the initial solution And calculate its comprehensive objective function value.

[0114] Phase Two: Algorithm Pool Competition, Permanent NSGA-II, and Conditional Search.

[0115] See Figure 5 Phase two is the core technical aspect of this invention. Its design philosophy is as follows: different scenarios have different optimal search paradigms. For example, deterministic scenarios are suitable for greedy algorithms, multimodal scenarios are suitable for probability distribution learning, and local optimum dilemma scenarios are suitable for trajectory search. Furthermore, different algorithms have different efficiencies at different iteration stages. Therefore, this invention designs a parallel competitive pool containing at least three different search paradigms and adaptively activates a subset of these paradigms using scenario identifiers.

[0116] The candidate algorithm pool in this embodiment includes eight optimization algorithms, and their search paradigms are classified as follows:

[0117] Table 4 Candidate Algorithm Pool Search Paradigm and Engineering Roles

[0118]

[0119] (1) Marginal Analysis (MA): Based on the deterministic greedy search paradigm of marginal revenue, each step selects the unit inventory increment with the largest marginal improvement. The classic OPUS10 algorithm is suitable as a system-level safety net seed.

[0120] (2) Discrete Differential Evolution (DDE): An evolutionary search paradigm based on population differences, using difference vectors... Mutant individuals are generated and then crossbred with the target individual to form offspring. This invention employs a probabilistic rounding mechanism: the floating-point solution after differencing is rounded up with probability for its fractional part, and rounded down for the rest, in order to preserve search direction information and avoid the information loss caused by the traditional round() truncation.

[0121] (3) Cross-entropy method (CEM): A sampling search paradigm based on probability distribution learning. In each generation, the sampling distribution is updated according to the elite solutions in the current population, and the next generation samples from the updated distribution. This invention adopts a hybrid sampling mechanism: sampling with a 70% probability according to the current distribution (utilization), and sampling with a 30% probability in an extended distribution with twice the original variance (exploration), to prevent sampling from degenerating to the vicinity of the seed.

[0122] (4) Discrete Particle Swarm Optimization (DPSO): A swarm intelligence search paradigm based on swarm collaboration, where each particle updates its velocity and position based on its own optimality and the global optimality.

[0123] (5) Tabu Search (TS): A memory-based trajectory search paradigm based on a tabu table. It maintains a tabu table to record the most recently accessed solutions or moves, prohibiting repeated access within a short period of time. It is suitable for fine-grained local searches.

[0124] (6) Adaptive Large Neighborhood Search (ALNS): A large neighborhood search paradigm based on destruction-repair operators. This embodiment designs six destruction operators, specifically defined as follows:

[0125] D1 Random Destruction: Randomly select some decision variable positions from the current solution and set them as the base inventory value;

[0126] D2 Worst-Case Element Destruction: Calculate the marginal contribution of each decision variable location and set the decision variables of the locations with the smallest contributions to the base inventory value;

[0127] D3 Related Disruption: Disrupts the location of related spare parts belonging to the same subsystem as a whole in order to re-coordinate the inventory distribution of the subsystem;

[0128] D4 Greedy Reverse Destruction: Back off positions in the current solution that exceed the safety stock line by too much, so that redundancy can be reallocated during subsequent repairs;

[0129] D5 System-level Disruption: Redistribute inventory on a subsystem basis, destroying and refilling all spare parts locations in a subsystem;

[0130] D6 Budget-Layered Destruction: Spare parts are divided into three layers based on budget percentage: high budget, medium budget, and low budget. Each layer is destroyed and rebuilt according to a different proportion, with the high budget layer having the smallest destruction proportion and the low budget layer having the largest destruction proportion.

[0131] This embodiment also designs three repair operators: R1 greedy repair, which repairs greedily according to the marginal improvement rate; R2 regret value repair, which prioritizes repair according to the principle of maximizing regret value; and R3 random repair, which repairs randomly within the feasible neighborhood.

[0132] (7) Non-dominated sorting genetic algorithm NSGA-II: Based on the multi-objective evolutionary paradigm of non-dominated sorting, with availability, cost and shortage as three objectives, and maintains the Pareto front through fast non-dominated sorting and crowding calculation.

[0133] (8) Simulated Annealing (SA): A temperature-driven probabilistic acceptor trajectory search paradigm, where temperature T controls the probability of accepting a suboptimal solution. This embodiment employs an adaptive cooling mechanism.

[0134]

[0135] In the formula, To simulate the adaptive cooling coefficient of the annealing algorithm; The initial temperature; The termination temperature; This is the preset total number of iterations.

[0136] The execution process for Phase Two is as follows:

[0137] a) Obtain the activation algorithm subset A = { from S2} , ,..., }

[0138] b) Among them, the evolutionary algorithm DDE, the distributed learning algorithm CEM, the swarm intelligence algorithm DPSO, and the memory-based trajectory algorithm TS are executed in parallel on multiple cores through the Python concurrent.futures.ProcessPoolExecutor process pool; MA is executed serially as a deterministic safety net algorithm; NSGA-II runs resident in all scenarios, using full budget when the main algorithm is NSGA-II or Hybrid, and reduced budget when the main algorithm is reduced in other scenarios; ALNS is triggered when the main algorithm is marginal or hybrid; SA is triggered when the main algorithm is sa or hybrid.

[0139] c) All algorithms use a unified comprehensive objective function F as the fitness evaluation criterion:

[0140]

[0141] In the formula, To unify the overall objective function, a smaller value indicates a better solution; The system availability is calculated based on the inventory matrix MATLAB. The TLCC cost corresponding to the inventory matrix; Used as a benchmark for budget normalization; This represents the expected number of stockouts across the entire network corresponding to the inventory matrix. This serves as the EBO normalized benchmark.

[0142] d) Collect the optimal solutions for each algorithm to form the optimal solution set of the algorithm pool. .

[0143] Phase Three: Elite Cross-pollination and Target-Oriented SA Refinement.

[0144] a) From the optimal solution set of the algorithm pool output in stage two, select the top two solutions belonging to different algorithms in ascending order of F value. and This separation of different algorithmic constraints ensures that the two parent solutions come from different search paradigms, and their advantageous regions are complementary.

[0145] b) Perform system-level cross-processing on the two parent solutions: Form a subsystem mask based on the subsystem to which the spare parts belong. For each subsystem, select the inventory configuration of all spare parts and all nodes within that subsystem using a preset probability, thus obtaining the child solution. This method differs from element-wise random crossover and can maintain the integrity of spare parts configuration within the subsystem.

[0146] c) The target-oriented SA refinement is performed, with each target being a primary metric for a specific scenario. For example, in the COST_MINIMUM scenario, it is the total cost, and in the AVAILABILITY_FIRST scenario, it is the system availability. SA uses a 2-opt neighborhood exchange, which randomly selects two nodes to exchange inventory. Compared to single-point disturbances, this approach offers the advantage of budget neutrality (the exchange does not change the total budget).

[0147] Phase Four: Scenario Optimization, Goal-Oriented Refinement, and Pareto Set Merging.

[0148] NSGA-II has been running continuously and outputting Pareto fronts in Phase 2. In this step, the NSGA-II front solutions are merged with algorithm pool members, system-level cross solutions, and SA-Polish refined solutions to form a candidate Pareto set. For the scenario recommendation solution, further goal-oriented refinement is performed. The specific neighborhood actions of the goal-oriented refinement include: (a) identifying the positions of the top 10% of decision variables with the smallest contribution to the main index in the current solution, where the main index is the scenario index corresponding to the scenario main algorithm; (b) fully enumerating the identified positions within ±1 unit neighborhood of their current values ​​and accepting the neighboring solutions that maximize the improvement of the main index; (c) repeating (a)-(b) until no improvement is produced for three consecutive times, or until the preset upper limit of rounds has been executed.

[0149] The recommended solution is selected from the Pareto fronts according to the Pareto selection strategy corresponding to the scenario. The Pareto front set is denoted as F, and the mathematical form of the selection strategy is as follows:

[0150] (5-3)

[0151] (5-4)

[0152] (5-5)

[0153] (5-6)

[0154] (5-7)

[0155] In the formula, This is the final recommended solution; For the Pareto frontier feasible solution set; Let x be the comprehensive performance index of the candidate solution; Let x be the total lifetime cost of the candidate solution. The minimum subsystem availability of candidate solution x; Let x be the expected number of spare parts i at node j; Let x be the success rate of the candidate solution.

[0156] Node-level three-constraint verification mechanism: In each solution evaluation process of the above F3 inventory optimization engineering operation, the following node-level three-constraint verification is enforced:

[0157] (5-8)

[0158] (5-9)

[0159] (5-10)

[0160] (5-11)

[0161] In the formula, Let be the TLCC cost allocation value for node j; Let $\mathbf{j}$ be the upper limit of the budget for node $j$. Let this be the new volume for node j; This represents the new upper limit of the volume for node j; This represents the actual volume occupied by node j. Let be the maximum storage capacity of node j; The effective inventory level is used by both the heuristic function and the evaluation function.

[0162] Step S6 Eight-item breakdown:

[0163] This step executes the recommended solution output by S5. Eight-term decomposition, calculated according to formulas (6-1) to (6-8):

[0164] (6-1)

[0165] (6-2)

[0166] (6-3)

[0167] The single-trip spare parts deployment transportation cost for node j reflects the single transportation cost incurred in transporting new spare parts from the supplier or the upper-level node to node j.

[0168] (6-4)

[0169] The unit shortage loss cost for spare part i reflects the economic loss per unit time caused by equipment downtime due to the lack of spare part i.

[0170] (6-5)

[0171] (6-6)

[0172] (6-7)

[0173] (6-8)

[0174] This represents the annual unit transportation cost of spare part i at node j, reflecting the average annual unit transportation cost of spare part i arriving at node j within a normal replenishment cycle.

[0175] In the formula, The new inventory quantity of spare part i at node j; The unit price for spare part i; Let i be the volume of spare part i; Let j be the number of spare parts i required by node j. Annual holding fee rate; The repair rate of spare part i; The cost of a single repair for spare part i; Fixed cost per order for spare part i; The economic order quantity for spare part i.

[0176] In the formula, C purchase For procurement costs; C holding Cost of ownership; C deploy To deploy transportation costs; C stockout Costs incurred due to stockouts; C repair For repair costs; C condemn For scrapping costs; C order For ordering costs; C transport Annual transportation cost; δ ij Add a procurement flag (δ) for spare part i at node j. ij =1 indicates that there is a new purchase, δ ij =0 indicates no new purchases); price i h is the unit price of spare part i; h is the annual holding cost rate; c deploy,j The single-unit deployment transportation cost for node j; c shortage,i The cost of a single stockout for spare part i; demand ij The annual demand for spare part i at node j; repair_rate i For the repair rate of spare part i; c repair,i The cost of a single repair for spare part i; EOQ i For spare part i, the economic order quantity; c order,i The cost of a single order for spare part i; c transport,ij Let i be the annual transportation cost per spare part i at node j; the subscript i represents the spare part and the subscript j represents the node.

[0177] The total is the sum of the above eight items, each output in a preset cost unit, for decision-makers to conduct cost composition analysis and long-term budget planning.

[0178] For ease of review and understanding, the subscript i in equations (6-1) to (6-8) all represent spare parts, and j all represent nodes; the subscript i is used when it involves the inherent attributes of spare parts such as unit price, volume, repair rate, ordering cost, and economic order quantity; the subscript j or ij is used when it involves node attributes such as budget, warehouse capacity, transportation location, and node requirements.

[0179] Step S7: Availability of the fourth layer and Evaluate:

[0180] This step calculates the system's four-layer availability and overall performance index. :

[0181] (7-1)

[0182] MTBF is the mean time between failures for spare parts; MTTR is the mean time to repair for spare parts.

[0183] (7-2)

[0184] (7-3)

[0185] (7-4)

[0186] (7-5)

[0187] (7-6)

[0188] The normalized value of total life cycle cost is the ratio of the current scheme's TLCC to the budget normalized baseline B.

[0189] (7-7)

[0190] This represents the normalized value of the expected number of stockouts across the entire network.

[0191] (7-8)

[0192] In the formula, Inherent availability; PMD is the cumulative time occupied by preventive maintenance within the task cycle; The average failure rate during the task execution phase; The duration of a single task; The criticality coefficient of spare part i is taken in the range of (0, 1], which reflects the relative weight of the impact of spare part i failure on task availability. The probability of spare part i experiencing a supply shortage across the entire network is obtained by accumulating the node-level shortage probability, which has been corrected for supply reliability, output in step S3 across the entire network. For operational availability; For task availability; For spare parts availability; For system availability; It is a comprehensive performance index; A standardized comprehensive performance index; For task success rate.

[0193] (7-9)

[0194] In the formula, The availability of a redundant parallel system after common-cause fault correction; This represents the probability of failure for a single item. This is the common cause failure ratio factor; This represents the number of redundant channels.

[0195] Step S8 Budget Recommendation Probe (Initiated when availability is insufficient).

[0196] See Figure 7 When the system availability is calculated by S7 less than the preset target availability When the value is 0.95 (e.g., 0.95), initiate budget suggestion detection:

[0197] (1) Two-path greedy detection.

[0198] (8-1)

[0199] (8-2)

[0200] The spare parts index that maximizes the marginal cost-effectiveness ratio; The index of the node with the highest marginal cost-effectiveness ratio;

[0201] (8-3)

[0202] The larger of the two paths that can be achieved after the greedy dual-path probing is completed;

[0203] (8-4)

[0204] (8-5)

[0205] In the formula, Let i be the marginal cost-effectiveness ratio of spare part i at node j; The marginal availability improvement resulting from adding one spare part; The marginal cost of adding a spare part; For target availability; The minimum budget leverage factor required to achieve availability; This is a suggested budget value; This is the original budget value; This is the safety margin factor.

[0206] Path A (Basic Inventory Starting Point): Starting from the current basic inventory matrix, conduct budget scaling probes to assess the system availability achievable under different budget multipliers.

[0207] a-1) For each spare part-node pair, calculate the marginal availability improvement resulting from adding one of the spare parts to the current scheme. And calculate the corresponding marginal cost. ;

[0208] a-2) Under the premise of satisfying the three constraints at the node level, choose The spare part-node pair with the highest (i.e., the marginal cost-effectiveness ratio) will increase the inventory by 1;

[0209] a-3) Recalculate, if Then terminate; otherwise return to a-1.

[0210] a-4) If all feasible pairs cannot be further improved (constraints have been met), then terminate and record the final result. .

[0211] Path B (starting point of hot start): Starting from the recommended solution output by S5, perform the same greedy iteration as path A, and record the final result. .

[0212] (2) Three situations to distinguish.

[0213] Scenario A: If This indicates that even with an unlimited budget, availability cannot be achieved, classifying it as Case A. The recommended output is: Under the current guarantee conditions, the theoretical maximum availability is... It is recommended to improve the situation by increasing the MTBF of spare parts or increasing the redundancy of critical spare parts; simply increasing the budget will not meet the requirements.

[0214] Scenario B: If If the target can be achieved after scaling up the budget proportionally, it is determined to be Case B, and the binary scaling search is initiated.

[0215] Scenario C: If the target cannot be achieved even with a 4x budget increase (under the existing budget allocation ratio), it is classified as Scenario C. The output suggestion is: The current budget allocation ratio between nodes is unreasonable. It is recommended to manually adjust the budget weight of each node and then optimize again.

[0216] (3) Binary scaling search (Case B).

[0217] Upper bound detection: In sequence, attempt to simultaneously scale up the global budget and the budgets of each node by 1.5x, 2x, 3x, and 4x. After each scaling up, re-execute the S5 optimization process to find the optimal upper bound. Minimum magnification .

[0218] Lower bound search: within the interval The binary search is performed 6 times. The midpoint of the interval is taken in each round. Optimize according to the increased budget and perform S5 optimization. If the target is met, then... ,otherwise .

[0219] After 6 rounds of two-pointers, take = This is then multiplied by a safety margin factor of 1.05 to obtain the recommended minimum budget scaling factor. The output recommendation text states: "It is recommended to scale up the global budget and the budgets of each node simultaneously." A multiplication factor of 1.05 is sufficient to achieve the target availability while maintaining the same distribution ratio among nodes.

[0220] Output the result of step S9.

[0221] The output includes: inventory configuration matrix (25×7), TLCC eight-item decomposition result table, four-level availability of recommended solution, , , Indicators, Pareto frontier solutions are used for sensitivity analysis, F2 replenishment order lists and LCC decomposition, and budget recommendation text (if S8 is enabled).

[0222] The output of the method of this invention is exported in the form of structured data files (e.g., Excel, JSON), specifically including: an inventory configuration matrix file (which can be directly connected to the downstream procurement management module to generate purchase orders) and a replenishment instruction list file (which can be directly connected to the scheduling management module to generate transfer notices and warehouse shelving instructions). The system includes an eight-item decomposition result table (which can be directly integrated with the budget planning module for cost analysis and long-term budget preparation) and a budget recommendation text (which can be directly integrated with the budget approval module for decision support). Through these structured output interfaces, the method of this invention can seamlessly integrate with existing support management information systems and business systems, transforming optimized decision results into specific support business operation instructions.

[0223] Table 5. Relationship between Structured Output Interface and Downstream Business Systems

[0224]

[0225] F1-F3 feedback closed loop:

[0226] When running in full-process mode, the F1-F3 feedback loop can also be enabled: the recommended solution output by S5 is used as the updated inventory state, and the EBO and pipeline quantity are recalculated in S3, and S5 inventory optimization is performed again. The cost assessment baseline remains the original. This avoids distorting procurement costs by using the results of the previous optimization round as a new basis. Only in this round... New results are adopted when the improvement is greater than 0.001, and the process stops after a maximum of 2 rounds of feedback.

[0227] Example 1: Comprehensive test in six scenarios;

[0228] To verify the effectiveness and scene adaptability of the method of the present invention, the method of the present invention was deployed on a general-purpose multi-core server, and the test case configuration is as follows:

[0229] System scale: 5 subsystems SYS01 to SYS05, 25 spare parts P001 to P025, 7 nodes (3 at L1 level + 2 at L2 level + 2 at L3 level);

[0230] Constraints: The global budget is normalized to 100 units, and the allocation ratios by node are as follows: L1 level 19.7% (N01: 7.4, N02: 6.6, N03: 5.7), L2 level 32.6% (N04: 17.1, N05: 15.4), L3 level 47.7% (N06: 24.6, N07: 23.1); the global volume is normalized to 100 units, and the allocation ratios by level are 24.4% / 31.4% / 44.2%.

[0231] Target availability: =0.95; Task duration: T=8760 hours (one year).

[0232] Regarding the reproducibility of the measured data: The F3 inventory optimization operation of the method of this invention includes several algorithms based on random sampling (such as Discrete Differential Evolution (DDE), Cross-Entropy Method (CEM), Discrete Particle Swarm Optimization (DPSO), Non-Dominated Sorting Genetic Algorithm (NSGA-II), Simulated Annealing (SA), etc.). These algorithms may converge to different solutions on the Pareto front under different random seeds. To ensure the reproducibility of the measured results, this embodiment sets a deterministic seed function at the main entry point of the algorithm pool of the F3 engine, which is jointly calculated based on the scene identifier, spare part identifier set, and node identifier set. This ensures that the same input parameters can produce completely consistent output results under the same version of code. When the user runs the method of this invention in its own environment, if the same deterministic seed function is used, the data listed in Table 6 can be accurately reproduced; if different random seeds are used, the core indicators ( , , Procurement costs The results may fluctuate within approximately ±5%. To reduce the impact of randomness on the conclusions, those skilled in the art can obtain a robust estimate by averaging multiple independent runs.

[0233] Regarding the test environment: This embodiment was run on a general-purpose multi-core server, using Python 3.8 and common numerical computing libraries such as NumPy and SciPy. Due to the system-level uncertainty in the scheduling order of processes when ProcessPoolExecutor is executed in parallel on multiple cores, the running time may fluctuate by approximately ±15% under different hardware platforms and operating system versions, but this does not affect the convergence of the optimization results or the quality of the optimal solution.

[0234] The method of this invention was run with six different scene identifiers, and the actual test results for a single run are shown in Table 6 below.

[0235] Table 6 Comparison of core indicators for six scenarios (actual measurement data in this embodiment)

[0236]

[0237] Table 7 Eight-item breakdown results (unit: 10,000 yuan)

[0238]

[0239] Results analysis:

[0240] (1) All six scenarios are satisfied The goal is 100% feasible;

[0241] (2) Reasonable differentiation across scenarios: The lowest cost scenario has the lowest procurement cost (26.94 million yuan), and the emergency support scenario has the lowest expected shortage ( =0.27), the task success rate is highest in the successful task scenario ( =99.26%), comprehensive efficiency scenario Highest (0.8286);

[0242] (3) Scene Interaction The range is from 0.7975 to 0.8286, with a span of 0.0311, which proves that the parameter adaptation of the scene strategy engine can produce substantially differentiated optimization solutions, rather than mechanical parameter tuning;

[0243] (4) The total fixed costs for repair, scrapping, ordering, and annual transportation amount to approximately RMB 14.95 million, accounting for... 23% to 25% of this is fixed annual operating expenditure;

[0244] (5) The total running time is approximately 1113 seconds (six scenarios in sequence, including budget detection), which meets the timeliness requirements of the actual protection plan.

[0245] Regarding the robustness of the technical effect: The data in Table 6 of this embodiment are the results of a single run using a deterministic seed function. To ensure the robustness and reproducibility of the technical effect of this invention, the F3 inventory optimization engine of this invention sets a deterministic seed function at the algorithm pool entry point, which is jointly calculated based on the scenario identifier, spare part identifier set, and node identifier set. This ensures that the same input parameters produce completely consistent output results under the same version of code. The applicant has conducted multiple independent runs of this test case at different times and on different hardware platforms. Under the premise of maintaining the deterministic seed function unchanged, the results of the six scenarios are as follows: , , Key indicators such as these can be accurately reproduced, among which and The deviation is less than 0.1%. The deviation is less than 0.5%, and the procurement cost deviation does not exceed 5%. Therefore, the beneficial effects of this invention are robustly reproducible and do not depend on a specific hardware environment.

[0246] Regarding the independent contribution of multi-algorithm collaboration and elite cross-pollination: To further verify the independent technical contribution of the combined mechanism of "multi-algorithm parallel competition" + "system-level elite cross-pollination" in this invention relative to each individual mechanism, this embodiment executes three sets of ablation comparison experiments under the comprehensive performance scenario MOE_OPTIMAL. The comparison configurations are defined as follows: Configuration 1 (MA alone): Only the marginal analysis algorithm MA is activated, and all other algorithms and the cross-pollination mechanism are turned off; Configuration 2 (multi-algorithm parallel, no cross-pollination): All eight algorithms in the algorithm pool are activated, the elite cross-pollination sub-step is turned off, and the optimal solution of the comprehensive objective function F is directly obtained from the algorithm pool; Configuration 3 (complete process, i.e., this invention): All eight algorithms are activated, and the complete elite cross-pollination and SA-Polish refining process is executed. The three sets of comparisons are executed under the same deterministic seed and the same budget, and the results are shown in Table 8 below:

[0247] Table 8. Ablation comparison experiment results under the MOE_OPTIMAL scenario for comprehensive performance.

[0248]

[0249] Ablation Comparison Analysis: This embodiment uses a deterministic random seed, node topology (7 nodes, L1×3+L2×2+L3×2), spare parts configuration (5 subsystems / 25 types of spare parts), and a volume constraint of 43m. 3With a budget constraint of 70 million yuan and a target availability of 0.95, three ablation configurations were executed sequentially under the MOE_OPTIMAL comprehensive performance scenario. The total execution time for the three configurations was approximately 670.7 seconds. The test results are shown in Table 8. Based on the above test data, the technical contribution of each mechanism can be independently quantified:

[0250] Independent contribution of algorithm parallelism: Configuration 2 relative to Configuration 1 It increased from 0.8029 to 0.8266, an increase of approximately +2.95%; meanwhile The annual cost decreased from 80.02 million yuan to 60.14 million yuan, a reduction of 24.84%; procurement costs decreased from 45.73 million yuan to 27.7 million yuan, a reduction of 39.4%. These three sets of indicators collectively demonstrate that parallel processing of multiple algorithms not only improves overall efficiency... Furthermore, through the complementarity between different search paradigms such as DDE / CEM / DPSO / TS / ALNS / NSGA-II / SA, the total life cycle cost and one-time procurement expenditure are effectively reduced, proving that the technical effect of "at least three different search paradigms competing in parallel" can be truly quantified in engineering practice.

[0251] Independent incremental cross-pollination of elites: Configuration 3 relative to Configuration 2 The value was further increased from 0.8266 to 0.8286. Under the relatively generous budget (70 million yuan) of this test, since NSGA-II has found a feasible solution close to the upper limit in configuration 2, the room for exploration of elite cross-pollination and SA-Polish2-opt refinement is relatively small. However, this mechanism still brings positive increments. This increment itself reflects the technical role of cross-pollination as an "independent refinement layer on top of multiple parallel algorithms". When the budget is tighter and the feasible region is narrower, the expected increment of this mechanism is more significant.

[0252] Feasibility contribution: Configuration 1, due to MA's individual marginal analysis, tends to accumulate more spare parts on top of existing inventory to ensure subsystem availability, resulting in higher final procurement costs and a volume exceeding 43m². 3 Under certain constraints, the proposed solution was deemed infeasible. However, configurations 2 and 3, through multi-algorithm collaboration, achieved availability targets in a more compact spatial distribution, reducing procurement costs to 27.7 million / 28.12 million yuan (a reduction of nearly 40%), making the proposed solution entirely feasible. These results demonstrate that the "multi-algorithm parallelism + elite cross-pollination" combination mechanism is not only a performance improvement mechanism but also a key technical mechanism directly related to the engineering feasibility of the solution.

[0253] Overall conclusion: The relative superiority of the three configurations is: Configuration 3 ≥ Configuration 2 Configuration 1, the independent contribution direction of each individual mechanism (multi-algorithm parallelism brings the main gain, cross-pollination brings the refinement increment) and the synergistic characteristics of the combined mechanism have all been verified by engineering tests, proving that the "multi-algorithm parallelism + elite cross-pollination" combined mechanism of the present invention has independent creative contributions and its overall technical contribution exceeds the simple superposition of the two individual mechanisms.

[0254] Example 2: Budget suggestion for a single scenario;

[0255] Based on the case of Example 1, this embodiment reduces the global budget from 70 million yuan to 60 million yuan (keeping the distribution ratio between nodes unchanged), runs and optimizes the AVAILABILITY_FIRST scenario, and observes the output of S8 budget suggestion detection.

[0256] Results: Under a budget constraint of 60 million yuan, after collaborative competition and feasibility supplement search by the algorithm pool, the optimizer finally achieved minAs≈0.9119, which did not reach the target availability of 0.95, triggering the S8 budget suggestion probe; at this time, the optimal solution given by the algorithm pool was TLCC≈57.87 million yuan / year (procurement cost≈23.78 million yuan).

[0257] Two-path greedy detection:

[0258] Path A (from the basic inventory matrix) (Starting point): In the iterative exploration of the node-level three constraints, after about 30 iterations, the highest minAs≈0.9119 is reached under this path. Due to the current node budget distribution, it is impossible to further approach 0.95 under a budget of 60 million yuan.

[0259] Path B (starting from the S5 recommended solution): Using the winning solution from the algorithm pool as a warm start, in the iterative exploration of the node-level three constraints, after about 20 iterations, it reaches the highest minAs ≈ 0.9119, similar to Path A, which is constrained by the current node-level budget distribution. The highest minAs of both paths does not reach 0.95.

[0260] Three scenarios are considered: The theoretical maximum minAs ≈ 0.9612 ≥ 0.95 of the target value for dual-startpoint detection indicates that the current budget ceiling and node-level allocation are mathematically feasible, but not actually achieved under the current budget of 60 million yuan. This is classified as Scenario B: Scaling up the global budget and node-level budget proportionally provides a solution, leading to a binary scaling search.

[0261] Upper bound detection: The detector was tested sequentially with budget scaling factors of 1.5×, 2.0×, 3.0×, and 4.0×. At 1.5× (i.e., a global budget of 90 million yuan, with node-level budgets scaled proportionally), the detector successfully obtained a feasible solution with minAs ≥ 0.95 under the dual-starting-point strategy. The upper bound scaling factor was recorded. =1.5.

[0262] Lower bound search: Perform 6 rounds of binary search within the interval [1.0, 1.5], re-exploring the budget by taking the midpoint of the interval in each round. The search eventually converges to the minimum target TLCC ≈ 59.73 million yuan / year (i.e., amplification of approximately 0.996 × 1.05, after node-level budget reallocation, the target can be achieved near the original 60 million yuan). To ensure the scheme is robust to minor parameter perturbations at submission, a 5% safety margin is multiplied to obtain a recommended budget of approximately 59.73 × 1.05 ≈ 61.97 million yuan / year.

[0263] The output budget suggestion text is: Under the current budget of 60 million yuan, the measured availability minAs≈0.9119 has not reached the target of 0.95. Through greedy detection with two starting points, the theoretical maximum minAs≈0.9612≥0.95, and this scenario belongs to the budget-solvable case (Scenario B). It is recommended to adjust the global budget to about 61.97 million yuan (i.e., 1.033 times the original budget, including a 5% safety margin), and adjust the node-level budget synchronously according to the current ratio. This will achieve the target availability of 0.95 while maintaining the same distribution ratio between nodes. The total time of this test is about 424 seconds (including algorithm pool competition, feasibility supplementation and budget suggestion detection).

[0264] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-level spare parts inventory optimization method based on scenario strategy and algorithm pool competition, characterized in that, The method includes the following steps: Step S1, Parameter and Scene Input: Obtain input parameters, including spare parts parameters, multi-level maintenance support system topology parameters, and scene identifiers. The scene identifiers are set of scene identifiers that include two or more preset scenes. Step S2, Scene Strategy Engine Mapping: Based on the scene identifier, retrieve the corresponding strategy parameter set from the preset scene strategy mapping table. The strategy parameter set includes at least the safety stock multiplier, urgency escalation factor, scheduling time weight and scheduling cost weight, weight of each item of the comprehensive efficiency index, main algorithm identifier and activation algorithm subset. Step S3, Node-level demand forecasting: Based on the strategy parameter set, for each spare part at each node, the following steps are performed in sequence: failure rate correction, system-level annual demand rate calculation, safety stock target and reorder point scenario correction, three-pool inventory distribution calculation, node-level pipeline quantity calculation, node-level expected stockout calculation, and node-level cost-effectiveness ratio calculation, and the node-level demand forecasting results are output. Step S4, Three-channel replenishment scheduling: Based on the strategy parameter set and the node-level demand forecast results, for each spare part and node combination with inventory gap, the weighted decision value is evaluated in parallel on the repair channel, transfer channel and procurement channel. The channel with the smallest weighted decision value is selected to generate a replenishment instruction, and the replenishment instruction is graded by priority. Step S5, Scenario-driven inventory optimization: Based on the strategy parameter set, an inventory optimization engineering operation is executed, including a greedy initialization stage, a multi-algorithm parallel competition stage, an elite cross-pollination and target-oriented refinement stage, and a scenario optimization and Pareto set merging stage, outputting a recommended solution for inventory configuration; the multi-algorithm parallel competition stage constructs an algorithm pool containing at least three different search paradigms, and the algorithms participating in the competition are determined by the activation algorithm subset, and each algorithm is evaluated using a unified comprehensive objective function; the elite cross-pollination stage selects two optimal solutions belonging to different search paradigms from the optimal solution set of the algorithm pool, performs system-level overall cross-pollination according to the subsystem to which the spare parts belong, and performs target-oriented refinement on the cross-pollination offspring; Step S6, Lifecycle Cost Decomposition: Perform eight decomposition calculations on the recommended inventory configuration solution, including procurement cost, holding cost, deployment and transportation cost, stockout loss cost, repair cost, scrap cost, ordering cost, and annual transportation cost; Step S7, Four-layer availability and comprehensive performance evaluation: Calculate the inherent availability, operational availability, task availability and spare parts availability of the recommended inventory configuration solution in sequence, and calculate the system availability, comprehensive performance index and task success rate based on this. Step S8, Budget suggestion detection: When the system availability is lower than the preset target availability, start dual-path greedy detection and three-case discrimination, and perform binary scaling search on the cases that can be achieved by budget amplification, and output the suggested budget adjustment amount; Step S9, Output Results: Export the inventory configuration matrix, the eight-item decomposition results of the whole life cycle cost, the four-level availability index, the comprehensive efficiency index, the task success rate, the Pareto frontier solution set, the replenishment instruction list, and the budget suggestion in the form of a structured data file.

2. The method according to claim 1, characterized in that, In step S2, the set of scenario identifiers includes normal equilibrium scenario, lowest cost scenario, availability priority scenario, emergency support scenario, mission success scenario, and comprehensive efficiency scenario; In the strategy parameter set, the safety stock multiplier is used to control the amplification of the spare parts safety stock target and the reorder point relative to the baseline value. The urgency escalation factor controls the increase in replenishment quantity and priority of replenishment instructions; the scheduling time weight and scheduling cost weight reflect the relative importance of replenishment response time and replenishment cost in the channel score, respectively, and their sum is a fixed value; the weights of each component of the comprehensive efficiency index correspond to the system availability component, cost component, and expected shortage component, respectively, and their sum is a fixed value; the activation algorithm subset is the set of algorithms in the candidate algorithm pool that match the current scenario; the main algorithm identifier specifies the solution selection strategy used when selecting a recommended solution from the Pareto front.

3. The method according to claim 2, characterized in that, The propagation path of the policy parameter set output in step S2 in subsequent steps is as follows: The safety stock multiplier is passed to step S3, where the safety stock target and reorder point for each spare part are multiplied by the safety stock multiplier to obtain the scenario-corrected safety stock target and the scenario-corrected reorder point. The urgency escalation factor is transmitted to step S4 to amplify the replenishment quantity of the missing spare parts and increase the urgency of the corresponding replenishment instruction in the priority classification. The scheduling time weight and scheduling cost weight are transmitted to step S4 and used as the weight coefficients of the time and cost items in the calculation of the weighted decision value of the replenishment channel; The weights of each component of the comprehensive efficiency index are passed to step S5, serving as weighting coefficients for the system availability, cost, and expected stockout items in the unified comprehensive objective function, and as the calculation weights of the comprehensive efficiency index when selecting the Pareto solution. The activation algorithm subset is passed to step S5 to control which algorithms in the algorithm pool are enabled and the proportion of computing resources allocated to each algorithm; the main algorithm identifier is passed to step S5 to determine which scenario main index is used to select the final recommended solution from the Pareto frontier.

4. The method according to claim 1, characterized in that, In step S3, the calculation of the three-pool inventory distribution is specifically as follows: the total inventory of each spare part at each node is divided into three state pools: available pool inventory, maintenance pool inventory, and scrap pool inventory. The sum of the three is equal to the total inventory of that spare part at that node. Among them, the maintenance pool inventory consists of work-in-process inventory and the amount under repair estimated based on failure rate, repair lead time, and non-scrap ratio. The available pool inventory is obtained by subtracting the maintenance pool inventory and the scrap pool inventory from the effective inventory. The effective inventory is taken as the larger value between the decision inventory and the basic inventory, which serves as a unified standard for demand forecasting and inventory assessment. The calculation of the expected number of stockouts at the node level is specifically as follows: based on the ratio of the variance to the mean of spare parts demand, an adaptive probability distribution model is selected. When the demand dispersion is low, a Poisson distribution is used, and when the demand dispersion is high, a negative binomial distribution is used. The expected number of stockouts is calculated using the current inventory level and the mean of pipeline demand as parameters. The stockout probability calculated solely from the inventory status is then combined with the spare parts supply reliability to obtain the node-level stockout probability corrected for supply reliability.

5. The method according to claim 1, characterized in that, In step S4, the specific steps for parallel evaluation of the weighted decision value are as follows: First, using the scheduling time weight and scheduling cost weight as edge weights, the weighted transport distance matrix and jump point matrix between all network nodes of the multi-level maintenance support system are pre-calculated using the full-source shortest path algorithm. The weighted transport distance is a weighted linear combination of the normalized transport time value and the normalized transport cost value between nodes. Secondly, for each spare part and node combination with inventory shortages, the following three channels are evaluated: the repair channel evaluates the time and cost required to repair the faulty spare part at the same or higher level node and return it to the target node; the transfer channel evaluates the time and cost required to transfer from the surplus inventory of other nodes to the target node, and it must be verified that the inventory of the source node is not lower than the safety stock level after the transfer; the procurement channel evaluates the time and cost required to directly procure from the supplier and transport it to the target node. Finally, normalized weighted decision values ​​are calculated for the three channels according to scheduling time weight and scheduling cost weight, and the channel with the smallest weighted decision value is selected to generate a replenishment instruction; and based on the node-level expected shortage number and spare parts criticality level output in step S3, combined with the urgency escalation factor, all replenishment instructions are divided into three priorities: urgent, normal and delayed.

6. The method according to claim 1, characterized in that, In step S5, the specific steps of the greedy initialization phase are as follows: Initialize the decision inventory matrix with the base inventory level as the starting point, and take the larger value between the decision inventory level and the base inventory level as the effective inventory level. All spare parts are sorted in descending order according to the node-level cost-effectiveness ratio output in step S3. All spare parts are divided into three equal groups according to their cost-effectiveness ratio, namely, high cost-effectiveness ratio, medium cost-effectiveness ratio, and low cost-effectiveness ratio. Differentiated inventory fill ratios are set for each of the three groups, decreasing sequentially. For each spare part, at each node with an inventory gap, calculate the amount of new inventory to be added according to the filling ratio corresponding to its grade. At the same time, the life cycle cost budget constraint, the new volume constraint, and the storage capacity constraint of the node must be met. Output an initial feasible solution that satisfies the three constraints.

7. The method according to claim 1, characterized in that, In step S5, during the multi-algorithm parallel competition phase, the algorithm pool includes at least five different search paradigms, specifically: A deterministic greedy search paradigm based on marginal revenue: at each step, select the spare parts and node combination that maximizes the improvement of the comprehensive objective function corresponding to the unit inventory increment and execute the inventory increment. Evolutionary search paradigm based on population differential evolution: offspring are generated by performing differential mutation and crossover operations on randomly selected individuals in the population, and probabilistic rounding is applied to the floating-point solution after differential to preserve search direction information. A sampling search paradigm based on probability distribution learning: In each generation, the sampling distribution is updated according to the elite solution, and the current distribution sampling and the extended distribution sampling are mixed in a fixed proportion to prevent sampling degradation; A swarm intelligence search paradigm based on group collaboration: Each particle guides its position update based on its own historical best position and the global best position; The tabu list-based memory-based trajectory search paradigm maintains a tabu list to record recently visited solutions or moves, prohibits repeated visits within a short period, and performs fine-grained local searches within a small neighborhood. The aforementioned evolutionary, distributed learning, swarm intelligence, and memory-based trajectory algorithms are executed in a multi-process parallel manner. Each algorithm uses a unified comprehensive objective function as the fitness evaluation standard. The unified comprehensive objective function is a linear combination of a system availability term, a life-cycle cost normalization term, and a network-wide expected shortage normalization term, all weighted by the weights of the comprehensive performance index components. The optimal solutions output by each algorithm are collected to form the optimal solution set of the algorithm pool.

8. The method according to claim 7, characterized in that, In step S5, the specific steps of the elite cross-pollination and target-oriented refining stage are as follows: From the optimal solution set of the algorithm pool, select the two highest-ranking solutions belonging to different search paradigms in ascending order of the unified comprehensive objective function value as the first parent solution and the second parent solution; A subsystem mask is formed according to the subsystem to which each spare part belongs. For each subsystem, the inventory configuration of the first parent solution or the second parent solution on all spare parts and all nodes in the subsystem is selected with a preset probability to obtain the cross-subsystem solution. The overall selection method maintains the integrity of the inventory configuration among spare parts in the subsystem, which is different from element-by-element random cross-selection. The cross-sub-solution is refined by target-oriented simulated annealing. The refinement target is the main indicator of the scenario corresponding to the main algorithm identifier. The refinement neighborhood action is to randomly select two node positions and exchange their inventory. The exchange operation does not change the total inventory of the solution and has the characteristic of budget neutrality.

9. The method according to claim 5, characterized in that, In step S5, the algorithm pool also includes a large neighborhood search algorithm based on destruction and repair operators, which is activated in availability-priority scenarios, task success scenarios, and comprehensive performance scenarios. The large neighborhood search algorithm includes at least six destruction operators: a random destruction operator, which resets the positions of several decision variables randomly selected in the current solution to the base inventory value; The worst-case destruction operator calculates the marginal contribution of each decision variable position and resets the positions with the smallest marginal contribution to the base inventory value. The correlation destruction operator resets the locations of related spare parts belonging to the same subsystem as a whole, so as to re-coordinate the inventory distribution within the subsystem; The greedy reverse destruction operator performs inventory rollback on positions in the current solution that exceed the safety stock target by too much, so that redundant inventory can be reallocated during subsequent repairs; The system-level destruction operator resets and refills the locations of all spare parts in a subsystem on a subsystem-by-subsystem basis. The budget-stratified destruction operator divides spare parts into high-budget, medium-budget, and low-budget layers according to the proportion of the spare parts budget. Each layer performs destruction and reconstruction according to different proportions, with the high-budget layer having the smallest destruction proportion. The large neighborhood search algorithm also includes at least three repair operators: a greedy repair operator, which greedily repairs the positions of damaged decision variables in sequence according to the marginal cost-effectiveness ratio; a regret value repair operator, which prioritizes repairing the positions with the greatest expected loss according to the principle of maximizing regret value; and a random repair operator, which randomly selects a repair scheme within the feasible neighborhood.

10. The method according to claim 1, characterized in that, In step S8, when the system availability calculated in step S7 is lower than the preset target availability, the specific steps of the dual-path greedy detection, three-case discrimination, and binary scaling search are as follows: Dual-path greedy exploration: Starting from the basic inventory matrix and the recommended inventory configuration solution output in step S5, each iteration selects the spare parts and node combination with the largest ratio of marginal availability improvement to marginal cost under the premise of satisfying the node-level full life cycle cost budget constraint, new volume constraint and warehouse capacity constraint. The inventory quantity at this combination is increased by one unit until the system availability reaches the preset target availability or all feasible combinations are saturated. The maximum system availability that can be achieved by the two paths is recorded respectively. Three scenarios are defined: If neither path enables the system availability to reach the preset target availability, it is classified as Scenario A, and an adjustment strategy file containing instructions to increase spare part failure interval or increase the redundancy of critical spare parts is generated and output; if at least one of the two paths enables the system availability to reach the preset target availability, it is classified as Scenario B, and a binary scaling search is initiated; if the target still cannot be achieved after scaling up the budget by four times under the existing allocation ratio among nodes, it is classified as Scenario C, and a suggestion is output explaining that the current budget allocation ratio among nodes is unreasonable, and it is recommended to manually adjust the budget weight of each node and then re-optimize. Binary scaling search: It attempts to synchronously scale up the global budget and the budget of each node by a certain preset factor in turn, and finds the minimum scaling factor that makes the system availability reach the preset target availability as the upper bound; Perform a binary search for a preset number of rounds within the lower and upper bounds of the budget amplification factor. In each round, take the midpoint multiple of the interval and re-execute step S5 inventory optimization and evaluate whether the system availability meets the standard, gradually narrowing the interval. Multiply the minimum acceptable budget amplification factor obtained by convergence by the preset safety margin coefficient to obtain the suggested minimum budget amplification factor, and multiply the suggested minimum budget amplification factor by the original budget as the suggested budget output.

11. The method according to claim 1, characterized in that, In steps S3, S5 and S8, the method uniformly adopts the effective inventory level as the common evaluation caliber for demand forecasting, inventory optimization and budget probing; the effective inventory level is taken as the larger of the decision inventory level and the basic inventory level at each node and for each spare part. When the decision inventory level is not lower than the basic inventory level, the decision inventory level is taken; otherwise, the basic inventory level is taken. In each solution evaluation in step S5, the effective inventory quantity determined in the aforementioned manner is used as the unified input for the whole life cycle cost calculation and comprehensive objective function evaluation. The cost evaluation benchmark remains the original basic inventory quantity throughout the entire inventory optimization process and does not change with the update of the optimization iteration results, so as to avoid the inventory configuration obtained in the previous round of optimization being regarded as the new basic inventory, which would lead to the distortion of procurement cost calculation. When the system availability in step S7 is lower than the preset target availability, in the dual-path greedy probing in step S8, path A starts from the original basic inventory matrix, and path B starts from the recommended inventory configuration solution output in step S5. Both paths perform marginal availability and marginal cost evaluation calculations using the aforementioned unified caliber of effective inventory quantity.

12. The method according to claim 1, characterized in that, In step S7, the calculation of the availability of the four layers is performed sequentially according to the following logic: First, inherent availability is calculated based on the ratio of mean time between failures to mean repair time for spare parts. This inherent availability reflects the theoretical availability level of the equipment without considering preventive maintenance downtime and supply guarantee factors. Secondly, based on inherent availability, the operational availability is obtained by deducting the proportion of time occupied by preventive maintenance within the task cycle. The operational availability reflects the availability level of the equipment under the constraints of the actual operation plan. Secondly, based on operational availability, the task availability is obtained by exponentially decaying the probability of task interruption caused by random failures during task execution. The exponential decay correction uses the product of the average failure rate during task execution and the task duration as a parameter. Secondly, based on task availability, the spare parts availability is obtained by deducting the additional downtime probability caused by spare parts shortage. The additional downtime probability is obtained by summing the product of the expected number of various spare parts in stock at each node and the spare parts importance coefficient by the task cycle, and is truncated in a way that does not exceed a preset upper limit to prevent the spare parts availability calculation result from being distorted when the number of a single spare parts in stock is abnormal. Finally, the system availability is obtained by multiplying the availability of spare parts in all subsystems. Based on this, the system availability item, the normalized value of the whole life cycle cost, and the normalized value of the expected number of stockouts across the entire network are weighted and linearly combined using the weights of each item of the comprehensive efficiency index output in step S2 to obtain the comprehensive efficiency index. The task success rate is then calculated by multiplying the probability of each spare part being in short supply across the entire network.

13. The method according to claim 1, characterized in that, In step S5, the specific method for selecting recommended solutions from the Pareto frontier in the scenario optimization and Pareto set merging stage is as follows: based on the scenario main index corresponding to the main algorithm identifier output in step S2, the solution that makes the scenario main index achieve the optimal value is selected from the feasible solution set of the Pareto frontier as the final recommended solution. The correspondence between the scenario main indicator and the scenario identifier is as follows: When the scenario identifier corresponds to a normal equilibrium scenario or a comprehensive efficiency scenario, the scenario main indicator is the comprehensive efficiency index, and the solution with the largest comprehensive efficiency index is selected; when the scenario identifier corresponds to the lowest cost scenario, the scenario main indicator is the total life cycle cost, and the solution with the smallest total life cycle cost is selected. When the scenario identifier corresponds to an availability-priority scenario, the scenario's main metric is the minimum spare parts availability among all subsystems, and the solution with the maximum spare parts availability of that minimum subsystem is selected. When the scenario identifier corresponds to an emergency support scenario, the main scenario indicator is the sum of the expected shortages of all spare parts at all nodes, and the solution with the smallest sum of expected shortages is selected. When the scenario identifier corresponds to a successful task scenario, the main metric for the scenario is the task success rate, and the solution with the highest task success rate is selected. The main algorithm identifier is used as the refinement target of the target-oriented refinement in the elite cross-pollination and target-oriented refinement stage in step S5. That is, when refining the cross-sub-solution, the aforementioned main indicator corresponding to the current scenario is used as the single optimization target, so that the solution selection strategy and the refinement target are consistent at the scenario level.

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