Multi-device maintenance and spare part ordering joint decision-making method and system based on probability threshold

Abstract

The invention provides a multi-device maintenance and spare part ordering joint decision-making method and system based on a probability threshold, and the method comprises the steps: a model building step: enabling the defined related parameters to be integrated, and building a complete Markov decision-making process model; the parameters comprise a state space, an action space, a state transition probability matrix and a cost function; and a solving and decision-making step: solving the Markov decision-making process model by applying an optimization algorithm to obtain an equipment maintenance and spare part ordering combined strategy. Compared with strategies such as a single component, the method has the advantages that the system is more intelligent and efficient in multi-project purchase by integrating equipment maintenance and spare part ordering joint optimization strategies based on probability thresholds; compared with strategies such as (s, S) inventory, dynamic changes of projects and equipment are comprehensively considered, so that the system can more comprehensively meet actual requirements, and more accurate and comprehensive decision support is provided for decision makers.

Description

Technical Field

[0001] This invention relates to the technical field of mathematical programming methods for equipment maintenance and spare parts ordering, specifically to a joint decision-making method and system for multi-equipment maintenance and spare parts ordering based on probability thresholds. Background Technology

[0002] In today's fiercely competitive and ever-changing manufacturing market, businesses face increasingly complex challenges. Globalization and informatization are leading to greater supply chain complexity, while consumers are demanding higher product quality and faster delivery times. Against this backdrop, manufacturing companies need more flexible and intelligent management strategies to adapt to dynamic market changes.

[0003] In this environment, equipment management is particularly critical. As core assets in manufacturing, the operational status and maintenance of equipment are crucial to production efficiency and product quality. Traditional scheduled maintenance models often fail to maximize equipment lifespan, while over-maintenance can lead to unnecessary cost increases. Therefore, modern manufacturing enterprises are increasingly focusing on predictive maintenance based on equipment condition to improve equipment reliability and utilization.

[0004] Meanwhile, inventory management, a critical aspect of manufacturing operations, has also faced challenges. Traditional inventory management methods, often based on fixed ordering rules and safety stock levels, struggle to adapt to rapid changes in market demand. Modern enterprises require smarter, real-time data-driven inventory management systems to reduce inventory holding costs, improve inventory turnover, and ensure timely fulfillment of order demands.

[0005] Regarding maintenance decisions, many types of maintenance policies have been used in practice and extensively studied in various situations, such as corrective maintenance, periodic maintenance, age-based maintenance, and condition-based maintenance (CBM). Furthermore, inventory strategies have also been extensively studied, as reviewed by Kennedy, W., Wayne Patterson, J., and Fredendall, L. in their high-profile international paper "An overview of recent literature on spare parts inventories" (International Journal of Production Economics, 2002, Vol. 76, pp. 201-215), and by van Houtun and Krannburg in their high-profile international paper "A new partial pooling structure for spareparts networks" (European Journal of Operational Research, 2009, Vol. 199, pp. 908-921). Spare parts inventory literature often treats demand as a given requirement, thus ignoring basic maintenance plans, while most maintenance studies assume an unlimited number of spare parts.

[0006] Elwany and Gebraeel, in their high-profile international paper "Sensor-driven prognostic models for equipment replacement and spare parts inventory" (IIE Transactions, Vol. 40, 2008, pp. 629-939), Wang, Chu, and Mao, in their high-profile international paper "A condition-based order-replacement policy for a single-unit system" (Applied Mathematical Modelling, Vol. 32, 2008, pp. 2274-2289), and Zhao and Xu, in their high-profile international paper "A joint policy for condition-based maintenance and spare provisioning using simulation" (Proceedings of the IEEE conference on prognostics and system healthmanagement, 2012, pp. 1-7), provide other examples of sequential or joint optimization of CBM and spare parts inventory for single-unit systems. In practice, systems typically contain multiple components. Applying a single-unit strategy to such multi-unit systems is often far from optimal for several reasons. First, different types of dependencies can exist in multi-component systems, which can be economic, structural, or fault-dependent. In this case, optimal maintenance and inventory decisions depend on the overall system state, not on individual components.

[0007] Some papers consider (s, S) inventory strategies, which means that once inventory falls below s, an order is placed to refill the inventory position with S units. It is well known that, under fairly common conditions in inventory systems, the order-level, order-to-level (s, S) strategy is optimal. Many authors have also considered this policy for controlling spare parts inventory (e.g., Cohen, Kleindorfer, Lee, and Pyke, 1992, in the high-impact international paper “Multi-item service constrained(s,S)policies for spare parts logistics systems” (Naval Research Logistics, 1992, Vol. 39, pp. 561-577); Kennedy, in the high-impact international paper “An overview of recent literature on spare parts inventories” (International Journal of Production Economics, 2002, Vol. 76, pp. 201-215); Krannburg and van Houtum, in the high-impact international paper “A new partial pooling structure for spare parts networks” (European Journal of Operational Research, 2009, Vol. 199, pp. 908-921)). In practice, this strategy is often referred to as the min-max strategy, where orders will reach their maximum if inventory levels fall to (or below) the minimum. However, intuitively, parts only need to be replaced, so spare parts are needed when approaching failure. Therefore, the conditional information used to schedule maintenance can also be used to determine when to order spare parts. Despite the significant potential for cost savings, this type of (just-in-time) condition-based ordering for multi-component systems has not yet been studied. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this invention is to provide a joint decision-making method and system for multi-device maintenance and spare parts ordering based on probability thresholds.

[0009] A joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds, provided by the present invention, includes:

[0010] Model building steps: Integrate the defined parameters to establish a complete Markov decision process model; the parameters include the state space, action space, state transition probability matrix, and cost function;

[0011] Solution steps: Apply optimization algorithms to solve the Markov decision process model to obtain the joint strategy for equipment maintenance and spare parts ordering.

[0012] Preferably, the model building steps include:

[0013] Step S1.0: Define the state space of the system and form a state vector s; the state space includes component states and inventory states; the state vector s includes the states of N components and the number of spare parts arriving after time unit t;

[0014] Step S1.1: Based on the state vector s, determine the action space that can be acted upon, and form an action vector a that satisfies the constraints of inventory management; the action space includes component replacement decisions and ordering decisions;

[0015] Step S1.2: Construct a state transition probability matrix, including the probability of transitioning from the current state vector s to the next state vector s′ after taking action vector a; the probability includes the component state transition probability and the inventory state transition probability; the action vector a includes whether to replace the Nth component and the number of spare parts ordered.

[0016] Step S1.3: Define a cost function to evaluate the total cost C(s,a) of the system when action vector a is taken; the cost function includes replacement cost, failure penalty cost, ordering cost, and holding cost.

[0017] Preferably, the solution decision steps include:

[0018] Step S2.1: Establish a Markov decision process model, integrating the state space, action space, state transition probability matrix, and cost function to form a complete mathematical model;

[0019] Step S2.2: Solve the mathematical model using an optimization algorithm to obtain a joint strategy for equipment maintenance and spare parts ordering.

[0020] Preferably, step S2.1 further includes calculating the component state transition probability and the inventory state transition probability based on the needs of equipment maintenance and spare parts ordering, the project life cycle, and the randomness of procurement decisions, and using a stochastic programming Markov process to generate a dynamic procurement decision scenario.

[0021] Preferably, step S2.2 further includes randomly generating an initial state, performing simulation, updating the state a preset number of times according to a maintenance and ordering joint strategy based on a probability threshold, and calculating the average cost.

[0022] Preferably, the optimization algorithm includes dynamic programming, simulated annealing, and genetic algorithm.

[0023] A joint decision-making system for multi-device maintenance and spare parts ordering based on probability thresholds, provided by the present invention, includes:

[0024] Model building module: Integrates the defined parameters to establish a complete Markov decision process model; the parameters include state space, action space, state transition probability matrix and cost function;

[0025] Decision Solving Module: Apply optimization algorithms to solve the Markov decision process model to obtain a joint strategy for equipment maintenance and spare parts ordering.

[0026] Preferably, the model building module includes:

[0027] Module M1.0: Defines the system's state space, forming a state vector s; the state space includes component states and inventory states; the state vector s includes the states of N components, and the number of spare parts arriving after time unit t;

[0028] Module M1.1: Based on the state vector s, determine the action space that can be acted upon, and form an action vector a that satisfies the constraints of inventory management; the action space includes component replacement decisions and ordering decisions;

[0029] Module M1.2: Constructs a state transition probability matrix, including the probability of transitioning from the current state vector s to the next state vector s′ after taking action vector a; the probability includes the component state transition probability and the inventory state transition probability; the action vector a includes whether to replace the Nth component and the number of spare parts ordered;

[0030] Module M1.3: Defines a cost function to evaluate the total cost C(s,a) of the system when action vector a is taken; the cost function includes replacement cost, failure penalty cost, ordering cost, and holding cost.

[0031] Preferably, the solution decision module includes:

[0032] Module M2.1: Establish a Markov decision process model, integrating the state space, action space, state transition probability matrix, and cost function to form a complete mathematical model;

[0033] Module M2.2: Uses optimization algorithms to solve the mathematical model and obtain a joint strategy for equipment maintenance and spare parts ordering.

[0034] Preferably, module M2.1 further includes calculating component state transition probabilities and inventory state transition probabilities based on equipment maintenance and spare parts ordering needs, project lifecycle, and the randomness of procurement decisions, and using stochastic programming Markov processes to generate dynamic procurement decision scenarios.

[0035] Preferably, module M2.2 further includes randomly generating an initial state, performing simulation, updating the state a preset number of times according to a maintenance and ordering joint strategy based on a probability threshold, and calculating the average cost.

[0036] Preferably, the optimization algorithm includes dynamic programming, simulated annealing, and genetic algorithm.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. Compared with single-component strategies, this invention integrates a joint optimization strategy for equipment maintenance and spare parts ordering based on probability thresholds, making the system more intelligent and efficient in multi-project procurement; compared with (s,S) inventory strategies, it comprehensively considers the dynamic changes of projects and equipment, enabling the system to more comprehensively meet actual needs and provide decision-makers with more accurate and comprehensive decision support.

[0039] 2. Compared with traditional methods such as corrective maintenance, periodic maintenance, and age-based maintenance, the overall effect of this invention is to reduce the number of failures (therefore reducing downtime), minimize maintenance costs, and improve operational safety. It is also more in line with actual situations, making procurement decisions more scientific and practical.

[0040] 3. This invention can effectively reduce enterprise maintenance and inventory costs, improve equipment reliability and utilization, adapt to dynamic market changes, improve enterprise economic benefits and customer satisfaction, and has good practicality.

[0041] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0042] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0043] Figure 1 This is a flowchart of the method of the present invention.

[0044] Figure 2 This is a flowchart of the optimization algorithm in an embodiment of the present invention. Detailed Implementation

[0045] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0046] Example 1

[0047] Reference Figure 1 As shown, a joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds includes:

[0048] Step S1: Define the state space of the system, including component states and inventory states, forming a state vector s, and consider the in-stock and in-transit inventory of spare parts; the state vector s includes the states of N components and the number of spare parts arriving after time unit t (t>0).

[0049] Step S2: Based on the current system state s, determine the feasible action space, including component replacement decisions and ordering decisions, form action vector a, and ensure that the actions meet the constraints of inventory management;

[0050] Step S3: Construct a state transition probability matrix, describing the probability that the system will transition from the current state s to the next state s′ after taking action a. This includes the component state transition probability and the inventory state transition probability. The action vector a includes whether to replace the Nth component and the quantity of spare parts ordered. The calculation method of the state transition probability matrix considers the Poisson distribution of component states and the dynamic changes in inventory states.

[0051] Step S4: Define a cost function, including replacement cost, failure penalty cost, ordering cost, and holding cost, to evaluate the total cost C(s,a) of the system when action a is taken; the method of constructing the cost function C(s,a) integrates various cost factors to comprehensively evaluate the economic benefits of spare parts inventory management.

[0052] Step S5: Establish a Markov decision process model by integrating the state space, action space, state transition probabilities, and cost function defined in steps S1 to S4 to form a complete mathematical model.

[0053] Step S6: Apply an optimization algorithm to solve the Markov decision process model to obtain a joint strategy for equipment maintenance and spare parts ordering, minimizing total cost and meeting service level requirements. The optimization algorithm can be dynamic programming, simulated annealing, genetic algorithm, or other suitable efficient algorithms.

[0054] Compared to single-component strategies, this invention integrates a probability threshold-based joint optimization strategy for equipment maintenance and spare parts ordering, making the system more intelligent and efficient in multi-project procurement. Compared to strategies such as (s,S) inventory, it comprehensively considers the dynamic changes of projects and equipment, enabling the system to more fully meet actual needs and provide decision-makers with more accurate and comprehensive decision support.

[0055] Example 2

[0056] The following example, using a company's decision-making process regarding the maintenance and spare parts ordering of optical port equipment, will provide a detailed explanation.

[0057] In this embodiment, the number of devices is 5, the component failure threshold is set to 5, the maximum inventory capacity is 5 units, the order price, downtime cost, replacement cost and inventory cost of each device are 400 yuan, 10,000 yuan, 100 yuan and 10 yuan respectively, the lead time for each order is 3 days, and the Poisson distribution parameter μ = 0.2 is followed by component degradation.

[0058] Reference Figure 1 and Figure 2 As shown, instance decisions specifically include:

[0059] Step 1: Define the system's state space S, including component states x and inventory states, forming a state vector s, considering both in-stock and in-transit inventory of spare parts:

[0060] s=(x1,x2,…,x n ,h0,h1,…,h T-1 );

[0061] Where, x n The x represents the state of component n, where n = 1, 2, ..., N. n The range of variation is 0 ≤ x n ≤L, where L represents the failure threshold. h0 represents the inventory of spare parts, h t Let be the inventory of spare parts in transit, representing the number of spare parts that will arrive after t units of time, where t = 2, 3, ..., T-1 (t > 0).

[0062] Step 2: Based on the current system state s, determine the feasible action space A, including component replacement decisions and ordering decisions, forming action vector a:

[0063] a=(δ1,δ2,…,δ N ,o);

[0064] Where, δ n ∈{0,1} indicates whether component n is replaced. If component n is replaced, then δ n =1; otherwise δ n=0. o represents the quantity of spare parts ordered from the spare parts supplier. Furthermore, the action variable 'a' needs to satisfy the following two constraints:

[0065]

[0066] The above formula means that the number of parts replaced cannot exceed the inventory of spare parts.

[0067]

[0068] in, This indicates the upper limit of the inventory level. The above formula means that the spare parts inventory should be less than the upper limit after replacement and ordering.

[0069] Step 3: Construct the state transition probability matrix P a (s,s′), describing the system's action a=(δ1,δ2,…,δ N After (x1, x2, ..., xo), the state transitions from the current state s to the next state s′=(x1′, x2′, ..., xo). N ′,h0′,h1′,…,h T-1 The probability of ′), including the component state transition probability. And the probability of state transition in inventory. Assuming that component degradation is a Poisson process with parameter μ, then under natural degradation, the increment of component state is a random variable following a Poisson distribution with parameter μ. Therefore, the probability of component state transition p(x) under natural degradation is... n ,x n ′) satisfies the following formula:

[0070]

[0071] When replacement occurs (δ) n When x = 1), the state of component n is immediately updated to 0. In summary, component n changes from state x under action a. n Transition to state x n The probability p' of ′ a (x n ,x n The following formula is shown:

[0072]

[0073] The transfer of inventory status follows the formula below:

[0074]

[0075] The two formulas above represent the relationship between spare parts inventory in stock and spare parts in transit at two adjacent time points, respectively. Therefore, combining the component state transition probability and the inventory state transition formula, the formula for calculating the overall system state transition probability can be derived as follows:

[0076]

[0077] Step 4: Define the cost function, including replacement cost, ordering cost, failure penalty cost, and inventory holding cost. When the system is in state s = (x1, x2, ..., x...) N ,h0,h1,…,h T-1 And take action a = (δ1, δ2, ..., δ) N When ,o), the resulting cost function C(s,a) is as follows:

[0078]

[0079] In the formula, C r This represents the unit replacement cost for each component. This represents the system replacement cost. and It is a 0-1 variable, when x n When = L, The value is 1 if o > 0 otherwise. Similarly, when o > 0, The value is 1 if it is 1, otherwise it is 0. d This represents the unit failure penalty cost for each component. This represents the penalty cost for system failure caused by component failure. (C) f C represents the fixed cost of ordering spare parts. o This represents the unit cost of ordering one spare part. This represents the ordering cost of spare parts from the spare parts supplier. (C) h C represents the unit inventory holding cost of each spare part. h •h0 represents the inventory holding cost incurred from storing spare parts.

[0080] Step 5: Establish a Markov decision process model, and convert the state space defined in steps 1 to 4 into a single model. Action space A, state transition probability P a The functions (s,s′) and cost function C(s,a) are integrated to form a complete mathematical model.

[0081] Step 6: Apply optimization algorithms to solve the Markov decision process model to obtain the optimal spare parts inventory management strategy, with the goal of minimizing costs. The algorithm is programmed using Python.

[0082] Optimization algorithms include simulated annealing and genetic algorithms.

[0083] The genetic algorithm is designed as follows:

[0084] Initialize the population: Set the population size POPULATION_SIZE. For each individual, randomly generate decision variables, including the replacement threshold x_Lp, safety stock level x_S, and probability threshold x_PL.

[0085] Calculate fitness: Use the simulation function to calculate the fitness (cost) of each individual. The lower the fitness value, the better the individual.

[0086] Selection operation: Individuals are selected as parents using a roulette wheel selection method based on their fitness ratio. The selected individuals will be used to produce the next generation.

[0087] Crossover operation: Perform a crossover operation on selected individuals to generate new individuals. A random number is used to determine whether to perform the crossover operation; if so, the crossover occurs at a random position.

[0088] Mutation operation: Mutation operations are performed on newly generated individuals to increase population diversity. A random number is used to determine whether to perform a mutation operation; if so, a gene location is randomly selected for mutation.

[0089] Population update: Replace old individuals with newly generated individuals to form the next generation of the population.

[0090] Iterative process: Through multiple iterations, the fitness of individuals is continuously optimized. Each iteration calculates fitness, performs selection, crossover, and mutation operations, and updates the population.

[0091] Output: After the iteration is complete, the individual with the lowest fitness is selected as the optimal solution based on the fitness of the individuals in the final population.

[0092] Output the optimal solution: Output the decision variables of the optimal solution, including the replacement threshold x_Lp, safety stock level x_S, and probability threshold x_PL. Output the fitness value (cost) of the optimal solution.

[0093] Through these steps, the genetic algorithm continuously evolves the population, causing individuals in the population to gradually approach the global optimum, thereby solving optimization problems under given constraints.

[0094] The simulated annealing algorithm is designed as follows:

[0095] Initialization: Set the initial temperature, minimum temperature, cooling rate, current solution, and optimal solution, and calculate the cost of the current solution and the cost of the optimal solution. Also initialize the number of iterations and the maximum number of iterations.

[0096] Iterative process: In each iteration, a new solution is generated by calling the `generate_new_solution` function. This function generates a new solution based on the current temperature and randomness.

[0097] And ensure that x_Lp is an integer.

[0098] Simulation is used to calculate the cost of the new solution.

[0099] The change in calculation cost is delta_cost, which is the cost of the new solution minus the cost of the current solution.

[0100] If delta_cost is less than 0 or a new solution is accepted based on certain probability conditions, the current solution is updated to the new solution, and the new cost is recorded.

[0101] If the cost of the new solution is lower than the cost of the optimal solution, update the current solution with the optimal solution.

[0102] Temperature Adjustment: Calculate the acceptance rate at regular intervals. Adjust the temperature T based on the acceptance rate. If the acceptance rate is low, decrease the temperature. If the acceptance rate is high, increase the temperature.

[0103] Iteration control: In each iteration, update the iteration count and check if the stopping condition is met (T is less than T_min or the maximum number of iterations is reached).

[0104] Output: After the iteration, the optimal solution, i.e., the solution with the lowest cost, is selected as the final result. The decision variables of the optimal solution are output, including the replacement threshold x_Lp, the safety stock level x_S, the probability threshold x_PL, and the cost of the optimal solution.

[0105] Through these steps, the simulated annealing algorithm continuously tries new solutions, explores the potential solution space based on temperature and cost changes, and eventually converges to an optimal solution to solve the given optimization problem.

[0106] Results Comparison

[0107] This invention proposes a probability threshold-based equipment maintenance and spare parts ordering strategy, and applies two optimization algorithms—genetic algorithm and simulated annealing algorithm—to solve this strategy. To verify the effectiveness of this strategy, it is compared with a traditional threshold control strategy. The traditional threshold control strategy makes equipment maintenance and spare parts ordering decisions by setting replacement thresholds and safety stock levels. The comparison results are shown in the table below. Here, Gap represents the percentage cost reduction achieved by the joint strategy obtained from the genetic algorithm and simulated annealing algorithm compared to the traditional threshold control strategy.

[0108] Table 1

[0109]

[0110] As shown above, the simulation cost obtained by the traditional threshold control strategy is 272.56, while the simulation costs obtained by the genetic algorithm and simulated annealing algorithm are 229.17 and 185.85 respectively, both significantly lower than the cost of the traditional threshold control strategy. Compared with traditional methods, these methods can reduce costs by approximately 15.92% and 31.98%. This indicates that the equipment maintenance and spare parts ordering strategy based on probability thresholds proposed in this invention, after heuristic algorithm optimization, can significantly reduce costs. From the simulation costs obtained by the two optimization algorithms, it can be seen that from the perspective of cost reduction, the simulated annealing algorithm has a better optimization effect, achieving a greater cost reduction, but it requires a longer simulation solution time. Therefore, if high computational time is required, the genetic algorithm can be chosen; if a better optimization effect is desired, the simulated annealing algorithm is more suitable. The flexible selection of the two optimization algorithms can adapt to more diverse decision-making needs.

[0111] Compared to traditional methods such as corrective maintenance, periodic maintenance, and age-based maintenance, the overall effect of this invention is to reduce the number of failures (thus reducing downtime), minimize maintenance costs, and improve operational safety. It is also more in line with real-world scenarios, making procurement decisions more scientific and practical.

[0112] Example 3

[0113] A joint decision-making system for multi-device maintenance and spare parts ordering based on probability thresholds, comprising:

[0114] The system's construction module comprehensively considers real-world procurement scenarios involving multiple devices, multiple states, and various stages of procurement. When making equipment maintenance decisions, it takes into account spare parts inventory; when making spare parts ordering decisions, it considers equipment degradation and maintenance decisions. A joint optimization strategy for equipment maintenance and spare parts ordering based on probability thresholds is proposed. When constructing the objective function, the system considers not only ordering costs and inventory holding costs, but also failure penalty costs and replacement costs.

[0115] Constraint Module: This module integrates constraints related to equipment maintenance and spare parts ordering. Due to changes in the project lifecycle and equipment status, the required quantities and maintenance needs will vary in each phase.

[0116] The rewriting module rewrites the multi-stage mixed-integer stochastic programming model M1 into a stochastic programming Markov decision model M2, which more intelligently considers decisions regarding equipment maintenance and spare parts ordering. The construction of the stochastic programming model not only reflects the project's lifecycle changes but also flexibly considers various possibilities for the dynamic evolution of equipment states, providing richer information for subsequent optimization.

[0117] The transformation module not only processes the model's constraints and transforms them into objective functions, but also considers optimization strategies for equipment maintenance and spare parts ordering. This upgrade helps the system to understand the constraints more comprehensively, providing more accurate guidance for the subsequent solution process.

[0118] Generation Module: In the generation module, the system employs stochastic programming and Markov processes. By considering the needs of equipment maintenance and spare parts ordering, the project lifecycle, and the stochasticity of procurement decisions, the system calculates the state transition probabilities of components and inventory, and uses stochastic programming and Markov processes to generate dynamic procurement decision scenarios. The system provides decision-makers with comprehensive and accurate procurement decision solutions, taking into account multiple practical factors.

[0119] The solution module randomly generates an initial state, performs simulation, and updates the state 2,000 times according to a probability threshold-based joint maintenance and ordering strategy, calculating the average cost. Finally, the system employs an improved optimization algorithm in the solution module. Its global optimization capability not only finds more and better solutions but also generates a series of solution sets. This provides decision-makers with diverse procurement decision options, fully balancing the needs of cost minimization and equipment reliability.

[0120] This invention can effectively reduce enterprise maintenance and inventory costs, improve equipment reliability and utilization, adapt to dynamic market changes, improve enterprise economic benefits and customer satisfaction, and has good practicality.

[0121] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0122] In the description of this application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0123] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds, characterized in that, include: Model building steps: Integrate the defined parameters to establish a complete Markov decision process model; the parameters include the state space, action space, state transition probability matrix, and cost function; Solution steps: Apply optimization algorithms to solve the Markov decision process model to obtain the joint strategy for equipment maintenance and spare parts ordering.

2. The joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 1, characterized in that, The model construction steps include: Step S1.0: Define the state space of the system and form a state vector s; the state space includes component states and inventory states; the state vector s includes the states of N components and the number of spare parts arriving after time unit t; Step S1.1: Based on the state vector s, determine the action space that can be acted upon, and form an action vector a that satisfies the constraints of inventory management; the action space includes component replacement decisions and ordering decisions; Step S1.2: Construct the state transition probability matrix, including the transition from the current state vector s to the next state vector s after taking action vector a. ′ The probability includes the component state transition probability and the inventory state transition probability; the action vector a includes whether to replace the Nth component and the number of spare parts ordered. Step S1.3: Define a cost function to evaluate the total cost C(s,a) of the system when action vector a is taken; the cost function includes replacement cost, failure penalty cost, ordering cost, and holding cost.

3. The joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 2, characterized in that, The solution decision steps include: Step S2.1: Establish a Markov decision process model, integrating the state space, action space, state transition probability matrix, and cost function to form a complete mathematical model; Step S2.2: Solve the mathematical model using an optimization algorithm to obtain a joint strategy for equipment maintenance and spare parts ordering.

4. The joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 3, characterized in that, Step S2.1 further includes calculating the component state transition probability and inventory state transition probability based on the needs of equipment maintenance and spare parts ordering, the project life cycle, and the randomness of procurement decisions, and using a stochastic programming Markov process to generate dynamic procurement decision scenarios.

5. The joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 3, characterized in that, Step S2.2 further includes randomly generating an initial state, performing simulation, updating the state a preset number of times according to a probability threshold-based maintenance and ordering joint strategy, and calculating the average cost.

6. The joint decision-making method for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 1, characterized in that, The optimization algorithms include dynamic programming, simulated annealing, and genetic algorithms.

7. A joint decision-making system for multi-device maintenance and spare parts ordering based on probability thresholds, characterized in that, include: Model building module: Integrates the defined parameters to establish a complete Markov decision process model; the parameters include state space, action space, state transition probability matrix and cost function; Decision Solving Module: Apply optimization algorithms to solve the Markov decision process model to obtain a joint strategy for equipment maintenance and spare parts ordering.

8. The joint decision-making system for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 7, characterized in that, The model building module includes: Module M1.0: Defines the system's state space, forming a state vector s; the state space includes component states and inventory states; the state vector s includes the states of N components, and the number of spare parts arriving after time unit t; Module M1.1: Based on the state vector s, determine the action space that can be acted upon, and form an action vector a that satisfies the constraints of inventory management; the action space includes component replacement decisions and ordering decisions; Module M1.2: Constructs the state transition probability matrix, including the transition from the current state vector s to the next state vector s after taking action vector a. ′ The probability includes the component state transition probability and the inventory state transition probability; the action vector a includes whether to replace the Nth component and the number of spare parts ordered. Module M1.3: Defines a cost function to evaluate the total cost C(s,a) of the system when action vector a is taken; the cost function includes replacement cost, failure penalty cost, ordering cost, and holding cost.

9. A joint decision-making system for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 8, characterized in that, The solution decision module includes: Module M2.1: Establish a Markov decision process model, integrating the state space, action space, state transition probability matrix, and cost function to form a complete mathematical model; Module M2.2: Uses optimization algorithms to solve the mathematical model and obtain a joint strategy for equipment maintenance and spare parts ordering.

10. A joint decision-making system for multi-device maintenance and spare parts ordering based on probability thresholds according to claim 9, characterized in that, The module M2.1 also includes calculating component state transition probabilities and inventory state transition probabilities based on equipment maintenance and spare parts ordering needs, project lifecycle, and the randomness of procurement decisions, and using stochastic programming Markov processes to generate dynamic procurement decision scenarios.

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