A method for equipment operation scheduling decision considering resource constraints

Abstract

This invention discloses a method for equipment operation scheduling decision-making considering resource constraints, belonging to the field of equipment scheduling management technology. This invention embeds equipment operation scheduling conflicts into the continuous time domain by constructing a temporally coupled conflict analysis graph model and establishing an event-driven state transition mechanism, achieving unified modeling of discrete decision-making and continuous-time system dynamics. By transforming the decision objective into a utility density function and integrating it along the state trajectory, the cumulative utility value of path dependence is obtained, generating a preference ranking of each decision-maker for the state trajectory. The stability of each state trajectory is tested through a temporally coupled stability definition, and state trajectories that satisfy the temporally coupled stability definition are determined as balanced scheduling schemes. This invention achieves deep integration of resource constraints, multi-objective trade-offs, and multi-agent strategy interactions in the continuous time domain, and is applicable to multi-agent resource-constrained scheduling scenarios such as equipment rotation and industrial equipment cluster maintenance.

Description

Technical Field

[0001] This invention relates to the field of equipment scheduling and management technology, and specifically to a method for making equipment operation scheduling decisions that takes into account resource constraints. Background Technology

[0002] In critical sectors such as industrial manufacturing, aerospace, energy and power, and heavy equipment operation and maintenance, the continuous and reliable operation of equipment clusters is a core prerequisite for ensuring production continuity and system safety. However, constrained by resources such as maintenance bays, transport vehicles, and spare parts inventory, equipment clusters inevitably face a "run-maintenance-redeployment" rotation scheduling problem during long-term operation. The core of this rotation scheduling problem is to coordinate multiple functional entities with independent decision-making power and interests under limited resource constraints to formulate a reasonable equipment operation and maintenance scheduling plan to optimize the overall system efficiency. In actual scheduling, equipment cluster scheduling exhibits significant temporal coupling characteristics. On the one hand, equipment health shows a continuous degradation trend over operating time, and its failure risk has a time-cumulative effect. Scheduling decisions must consider the impact of this continuous degradation process on future equipment availability. On the other hand, the occupation of maintenance and transportation resources is asynchronous and competitive, and the operational instructions of different decision-makers to the equipment are intertwined and mutually constrained on the timeline. This dynamic characteristic makes it impossible to simply divide the system state evolution into several isolated decision moments.

[0003] For the equipment scheduling problem, existing technologies mainly include centralized optimization methods, classical game theory methods, and conflict analysis graph model methods.

[0004] Centralized optimization methods formulate the scheduling problem as a global optimization problem with a single optimization objective or weighted multi-objectives, and solve it using mathematical programming or heuristic algorithms. While these methods can yield effective solutions in specific scenarios, they are based on a centralized decision-making framework, assuming a single global decision-maker that coordinates all resources and tasks. In practice, however, equipment users, maintenance providers, and scheduling coordinators often have their own independent objectives and decision-making authority. This approach neglects the strategic interactions and conflicts of interest among these functional entities, fails to characterize and predict the game-theoretic behavior of independent decision-makers during the scheduling process, and lacks the ability to explain the mechanisms underlying the stability of scheduling schemes.

[0005] Classical game theory methods, including non-cooperative games and stochastic games, have been introduced into scheduling problems to describe the conflict relationships between agents. However, the modeling forms of standard or extended games are insufficient to concisely represent the vast combinatorial strategy space and asynchronous temporal logic in equipment scheduling. Furthermore, most game theory frameworks lack systematic methods for analyzing the stability of equilibrium solutions, failing to guarantee that the obtained scheduling strategies can resist the unilateral deviation motivations of each party during dynamic execution.

[0006] Conflict analysis graphical models employ an option-based modeling paradigm, allowing each decision-maker to control multiple strategy options. This approach can handle problems involving multiple decision-makers, multiple options, and multiple states, and predicts the equilibrium outcome of conflicts through stability analysis. However, classic conflict analysis graphical models are built on a static discrete state space, and their state transitions lack temporal attributes. Within the model, state transitions are instantaneous logical jumps, failing to depict the physical process of continuous degradation of equipment health over time, the fixed time required for support activities such as transportation and maintenance, or the cumulative effect of decision utility along the state trajectory. While subsequent research has attempted to extend the model by introducing time labels, these improvements still fall within the scope of discrete-time modeling, treating time as an additional attribute of states rather than an endogenous variable of system evolution, failing to establish an event-driven continuous-time state evolution mechanism. Furthermore, the model's preference acquisition relies on decision-makers qualitatively ranking states, which is difficult to quantify accurately in multi-attribute decision-making environments. Existing quantitative improvements, while introducing cost functions, neglect the cumulative utility of path dependence and fail to reflect the temporal coupling characteristics of decision consequences in the continuous-time domain.

[0007] Therefore, how to enable conflict analysis graph models to characterize continuous time evolution and path-dependent utility, so as to be applicable to equipment scheduling scenarios under resource constraints, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a device operation scheduling decision-making method that considers resource constraints. By constructing a temporally coupled conflict analysis graph model, device operation scheduling conflicts are embedded in the continuous time domain, and an event-driven state transition mechanism is established to jointly characterize continuous time dynamics, multi-type resource constraints, and multi-agent strategy interactions within a unified framework, and to solve for balanced scheduling schemes.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] This invention proposes a device operation scheduling decision-making method considering resource constraints, comprising the following steps:

[0011] S1. Determine the set of decision-makers and the set of strategy options for each decision-maker in the equipment operation scheduling decision, and construct a time-coupled state vector. The time-coupled state vector is used to characterize the equipment's operating mode, health, spatial location and mode dwell time in the continuous time domain.

[0012] The initial state space is constructed based on the set of decision-makers, the set of policy options, and the time-series coupled state vector.

[0013] The initial state space is reduced by resource constraints to generate a temporally feasible state space.

[0014] S2. Define option-triggered events and clock-triggered events in the continuous time domain. The option-triggered events and clock-triggered events constitute an event set. When any event in the event set occurs, update the device state in the temporally feasible state space through a state transition function to generate several state trajectories.

[0015] S3. Transform each decision-maker's decision objective into a utility density function. For each utility density function, perform time integration along each state trajectory to obtain the cumulative utility value of each decision-maker on each state trajectory. Sort all state trajectories according to the cumulative utility value to generate a preference ranking of each decision-maker for all state trajectories.

[0016] S4. Extend the stability definition in the classic conflict analysis graph model to a temporal coupling stability definition based on state trajectories. Perform stability checks on each state trajectory according to the preference ranking. Determine the state trajectory that satisfies the temporal coupling stability definition as a balanced scheduling scheme and output the balanced scheduling scheme.

[0017] Furthermore, in S1, the time-coupled state vector includes the device mode, health status, location tag, and mode dwell clock of each device at each moment; the device mode includes operating mode, standby mode, transportation mode, and maintenance mode; the location tag includes the work site, central maintenance warehouse, route from the work site to the central maintenance warehouse, and route from the central maintenance warehouse to the work site.

[0018] Furthermore, in S1, the resource constraints include at least one of the following: continuous operation rules, resource quantity limit rules, mode switching rules, logical consistency rules, clock synchronization rules, and uninterruptible rules;

[0019] The continuous operation rule ensures that at least one device is in operating mode at any given time; the resource quantity limit rule ensures that the number of currently occupied transport vehicles and maintenance bays does not exceed their respective maximum quantities; the mode switching rule ensures that device mode switching occurs sequentially in the order of operating mode, transport mode, and maintenance mode; the logical consistency rule ensures that the matching between device mode and location tag conforms to physical logic; the clock synchronization rule ensures that the evolution of device health is synchronized with the evolution of clock timers; and the uninterruptible rule is used to constrain the device to maintain operating mode until the end of its current operating cycle.

[0020] Furthermore, in S2, the option triggering events include a replacement request event, a maintenance allocation event, a backup activation event, and a transportation scheduling event; the clock triggering events include a transportation completion event and a maintenance completion event.

[0021] Furthermore, in S2, the state trajectory is a set of states in the temporally feasible state space within a continuous time interval; when any event in the event set occurs, the device state in the temporally feasible state space is updated instantaneously through the state transition function. During the time interval when no event occurs, the device state in the temporally feasible state space evolves continuously over time, the health level continuously decays according to a preset degradation rate, and the mode dwell clock continuously accumulates.

[0022] Furthermore, in S3, the utility density function is a weighted sum of multiple penalty functions; the multiple penalty functions include at least two of the following: a health deviation from the optimal value penalty function, a maintenance waiting time penalty function, an equipment standby idle loss penalty function, a transportation cost penalty function, a vehicle idle penalty function, and a transportation delay penalty function.

[0023] Furthermore, in S4, the definition of temporal coupling stability includes temporal coupling Nash stability, temporal coupling general metaphysical stability, temporal coupling symmetric metaphysical stability, temporal coupling sequential stability, and temporal coupling symmetric sequential stability.

[0024] If there is no unilateral boost transition for any decision-maker starting from the current state trajectory, then the current state trajectory is determined to satisfy temporally coupled Nash stability.

[0025] The unilateral boost transfer is defined as follows: the decision-maker changes the state trajectory by unilaterally triggering an event, and the cumulative utility value of the changed state trajectory to the decision-maker is higher than that of the current state trajectory.

[0026] Furthermore, in S4, if a state trajectory satisfies at least one of the temporal coupling stability definitions for each decision-maker, then the state trajectory is determined to be a balanced scheduling scheme; if a state trajectory satisfies all five temporal coupling stability definitions for each decision-maker, then the state trajectory is determined to be a strong balanced scheduling scheme, and the strong balanced scheduling scheme is output.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0028] (1) This invention introduces a temporally coupled state vector, incorporating the device's operating mode, health status, spatial location, and mode dwell time into a unified state description framework, so that the device state itself carries all the information of continuous time evolution. On this basis, this invention further distinguishes two types of state transition driving mechanisms: option-triggered events and clock-triggered events. Option-triggered events reflect the active intervention of the decision-maker, while clock-triggered events reflect the autonomous passage of physical time. Through the co-definition of event sets and state transition functions, a formal relationship is established between discrete decision-making behavior and continuous-time system dynamics. The device state evolution is no longer cut into several isolated decision moments, but forms a continuous state trajectory carrying complete time information, so that the cumulative degradation effect of device health and the temporal competition relationship of guarantee resources can be accurately expressed within a unified modeling framework.

[0029] (2) This invention transforms the multi-attribute decision objectives of each decision-maker into a utility density function defined along the state trajectory. This function is a weighted sum of multiple normalized penalty functions. By integrating the utility density function along the entire state trajectory over time, the path-dependent cumulative utility value is obtained. Since the integration process includes the utility density at every moment within the time interval, the decision consequences with temporal order, such as the health degradation of the equipment in the early operation stage, the time cost of maintenance waiting in the middle stage, and the economic loss of transportation delays in the later stage, can all be quantitatively compared using a unified cumulative utility scale. This makes the decision-maker's preference no longer a static ranking of isolated states, but a comprehensive evaluation of the overall satisfaction of the entire state trajectory within the complete time interval, providing a quantitative criterion for subsequent stability analysis.

[0030] (3) This invention unifies and adapts five classical stability definitions—Nash stability, general metarational stability, symmetric metarational stability, sequential stability, and symmetric sequential stability—to the state trajectory framework. One-sided transitions are redefined as decision-makers using a one-sided trigger event to shift equipment from one state trajectory to another. Preference comparison is redefined as a comparison of the cumulative utility values ​​between the target trajectory and the current trajectory. Based on this, the stability test can determine whether any decision-maker has the motivation to transfer to a state trajectory with a higher cumulative utility value through a one-sided trigger event, and whether this deviation motivation will be eliminated by subsequent sanctions from other decision-makers. Since the stability determination comprehensively considers the preference ranking of all decision-makers and all possible one-sided deviation paths, the solved equilibrium scheduling scheme possesses the ability to resist the unilateral deviation motivations of all parties. The strong equilibrium scheduling scheme satisfies all five stability definitions simultaneously for each decision-maker. Even considering subsequent counterattacks and complex sanction paths from other decision-makers, no decision-maker can obtain higher cumulative utility by unilaterally changing their strategy. Therefore, this scheme has the strongest anti-deviation capability, can be consciously complied with by all parties without external coercion, and effectively breaks the decision-making deadlock caused by multi-objective conflicts. Attached Figure Description

[0031] Figure 1 This is a flowchart of a device operation scheduling decision-making method considering resource constraints in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram illustrating the transition relationships between various state trajectories in an embodiment of the present invention; Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Example

[0035] This embodiment uses a cluster of 6 homogeneous devices as an example to further illustrate the method proposed in this invention. The cluster is equipped with 2 transport vehicles and 2 maintenance bays, and the simulation time is set to [0, 400]. The optimal health of the devices is 100, and the initial health is uniformly distributed within the range of [80, 100]. The operational degradation coefficient is set to 0.025, and the transport degradation coefficient is set to 0.0025. The high threshold for device health is 50, and the low threshold is 30. The transport time is fixed at 2 time units, and the loading / unloading time is fixed at 0.5 time units. The maintenance rate is set to 8, meaning the health recovery amount per unit time is 8. Initially, 2 devices are located at the work site and are in operating mode, 1 device is located at the work site and is in standby mode, and 3 devices are located in the central maintenance warehouse and are in standby mode. (Reference) Figure 1 This embodiment provides a device operation scheduling decision method that considers resource constraints, which is executed according to the following steps:

[0036] S1. Determine the set of decision-makers in equipment operation and scheduling decisions. And the set of strategic options for each decision-maker.

[0037] In this embodiment, the decision-maker set .

[0038] Maintaining the decision-maker's set of strategic options for:

[0039]

[0040] in, To change the request strategy, it indicates that the decision-maker is maintaining the status quo. For the Taiwan equipment initiated a replacement request. ; To maintain the allocation strategy, it means maintaining the decision-making party at time... The first The equipment was allocated to the first One repair bay. ; As a backup activation strategy, it indicates that the maintenance decision-maker is always on standby. The first The device is switched to operating mode.

[0041] Set of strategic options for transportation decision-makers for:

[0042]

[0043] in, The transportation allocation strategy represents the transportation decision-maker's position at time [time]. The first The equipment was assigned to the first A number of transport vehicles were used for transportation. ; The transportation priority ranking strategy indicates the transportation decision-maker's priorities at time [time]. A priority sorting function for all queues of equipment awaiting transport.

[0044] To characterize the complete state of the device in the continuous time domain, this embodiment introduces a time-coupled state vector. The equipment is at all times Temporal coupling state vector for:

[0045]

[0046] in, For the first The equipment is at all times The modes include operating mode, standby mode, transportation mode, and maintenance mode;

[0047] For the first The equipment is at all times The health level ranges from [0, 100], with 100 being the optimal health level.

[0048] For the first The equipment is at all times Location tags include the work site, central maintenance warehouse, route from the work site to the central maintenance warehouse, and route from the central maintenance warehouse to the work site;

[0049] For the first The equipment is at all times The mode dwell time clock is used to capture the time the device remains in the current mode.

[0050] The calculation formula is:

[0051]

[0052] in This indicates the equipment degradation factor when the equipment is in operating mode. =0.025; when the equipment is in transport mode, =0.0025; When the equipment is in standby or maintenance mode, =0.

[0053] The calculation formula is:

[0054]

[0055] When the device mode changes, the mode dwell clock is reset to zero.

[0056] For time The temporally coupled state vectors of all devices constitute the device state set at that moment. The initial state space is constructed by completely combining the decision-maker set, the policy option set, and the device state set.

[0057] By reducing the initial state space through resource constraints, states that do not meet the constraints are eliminated, resulting in a temporally feasible state space. Resource constraints include:

[0058] Continuous operation rule: At any given time, at least one device must be in operating mode to ensure continuous system operation. This rule is formally expressed as:

[0059]

[0060] In the formula, This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise.

[0061] Resource quantity limit rule: The number of currently occupied transport vehicles and maintenance bays shall not exceed their respective maximum limits. This rule is formally expressed as:

[0062]

[0063]

[0064] In the formula, For at any time The number of transport vehicles that are occupied. This refers to the total number of transport vehicles; This represents the number of maintenance workstations that are currently occupied. In this embodiment, the total number of maintenance workstations is [number]. , .

[0065] Mode switching rules: The equipment mode switching shall be carried out in the order of operation mode, transportation mode and maintenance mode. That is, the equipment cannot be directly switched from operation mode to maintenance mode. It must be connected through transportation mode.

[0066] Logical consistency rule: The matching between the device's mode and its spatial location conforms to physical logic. When the device is in operating mode, its location label must be the work site; when the device is in maintenance mode, its location label must be the central maintenance warehouse; when the device is in transportation mode, its location label must be the route from the work site to the central maintenance warehouse or the route from the central maintenance warehouse to the work site.

[0067] Clock synchronization rules: The evolution of equipment health and the evolution of the mode dwell clock occur simultaneously on the timeline. The equipment health recovery rate in maintenance mode is the maintenance rate multiplied by the time increment; the equipment health decay rate in operation mode is the operation degradation coefficient multiplied by the time increment; the equipment health decay rate in transportation mode is the transportation degradation coefficient multiplied by the time increment; the equipment health remains unchanged in standby mode.

[0068] Uninterruptible rule: The device remains in operating mode until the end of the current operating cycle, meaning that the device cannot be interrupted once it enters operating mode.

[0069] For each state in the initial state space, if it does not satisfy any of the rules in the resource constraints, then that state is removed.

[0070] S2. In the continuous time domain, state transitions are not only triggered by changes in the decision-maker's strategy options, but also by the autonomous evolution of time itself. Therefore, this embodiment defines option-triggered events and clock-triggered events in the continuous time domain. Option-triggered events represent events actively triggered by changes in the decision-maker's strategy options, while clock-triggered events represent events triggered by the completion of physical processes due to the passage of time.

[0071] Option-triggered events include:

[0072] Replacement request event: Maintaining decision-makers at all times For the A device initiates a replacement request, triggered by the maintenance decision-maker's replacement request policy. This event is triggered when the device is in operating mode and its health level is below a preset threshold.

[0073] Maintaining the allocation of events: Maintaining the decision-making party at any given time. The first The equipment was allocated to the first Each maintenance workstation is triggered by the maintenance allocation strategy of the maintenance decision-maker.

[0074] Backup activation event: Maintain decision-makers at all times The first The device switches to operating mode, triggered by the backup activation strategy of the maintenance decision-maker.

[0075] Transportation scheduling events: Transportation decision-makers at specific times Priority sorting is performed on all queues of equipment to be transported, triggered by the transport decision-maker's transport priority sorting strategy.

[0076] Clock-triggered events include:

[0077] Transportation completion event: The transportation task of the equipment is completed, triggered by the mode dwell clock reaching the transportation time.

[0078] Maintenance Complete Event: The maintenance task of the equipment is completed and is triggered when the maintenance duration is reached by the mode dwell clock.

[0079] The event set consists of all option-triggered events and all clock-triggered events.

[0080] In event-driven continuous-time scheduling, the operational behavior of the device cluster is governed by the interaction between continuous-time evolution and discrete trigger points. A state trajectory is defined as a set of states in the temporally feasible state space within a continuous time interval. For each strategy option combination, when any event in the event set occurs, the device states in the temporally feasible state space are instantaneously updated through a state transition function. During time intervals without events, the device states in the temporally feasible state space evolve continuously over time, device health decays continuously according to a preset degradation rate, and the mode dwell time continuously accumulates. As the simulation progresses, a state trajectory is generated. In this embodiment, there are 16 strategy option combinations, each generating a state trajectory under event-driven conditions, for a total of 16 state trajectories.

[0081] State transition functions are used to describe the instantaneous changes in the device state when an event occurs. Suppose the state is updated using a state transition function:

[0082]

[0083] In the formula, For a moment Device states in the temporally feasible state space. For at any time Events that occur in the event set To The updated device status This is the state transition function.

[0084] In this embodiment, each strategy option combination undergoes an event-driven simulation in the temporally feasible state space, experiencing an average of 3972 state transitions and triggering 7428 events, generating a corresponding state trajectory. Figure 2 This diagram illustrates the transition relationships between 16 state trajectories, where each node represents a state trajectory, and directed edges represent the transitions between state trajectories achieved by the decision-maker through unilaterally triggered events.

[0085] S3. Transform each decision-maker's decision objective into a utility density function. For each utility density function, perform time integration along each state trajectory to obtain the cumulative utility value of each decision-maker on each state trajectory. Sort all state trajectories according to the cumulative utility value to generate a preference ranking of each decision-maker for all state trajectories.

[0086] Traditional preference-inducing methods in game theory are limited to discrete policy spaces and static preference sequences, failing to capture dynamic preferences that evolve over time. This embodiment, based on multi-attribute utility theory, transforms each decision-maker's objective into a utility density function. The utility density function is a weighted sum of multiple penalty functions, generating a path-dependent utility metric that quantifies the strength of the decision-maker's preference for each state trajectory.

[0087] The decision-making objectives of the maintenance decision-maker include: maintaining equipment health near its optimal value, minimizing maintenance waiting time, minimizing equipment idle time losses, and reducing risk costs. The utility density function of the maintenance decision-maker is:

[0088]

[0089]

[0090]

[0091]

[0092] in, To maintain the decision-making body at all times The utility density function value;

[0093] A penalty function for equipment health deviating from the optimal value; Indicates the operating mode. Indicates standby mode; To achieve optimal device health, in this embodiment, =100.

[0094] A penalty function for maintenance waiting time; This indicates the central maintenance warehouse. In this embodiment, for the sake of repair speed, .

[0095] A penalty function for equipment idle time; For a moment Number of devices in the maintenance queue This represents the total number of maintenance workstations.

[0096] Let $\frac{ ... When only one piece of equipment is in operating mode and no equipment is in standby mode at the work site, ,otherwise =0.

[0097] , , , They are respectively , , and The penalty weight satisfies In this embodiment, =0.4、 =0.3、 =0.2、 =0.1.

[0098] The decision-making objectives of transportation decision-makers include: low transportation costs, minimal vehicle idle time, and minimal transportation delays. The utility density function of the transportation decision-makers is:

[0099]

[0100]

[0101]

[0102]

[0103] in, For transportation decision-makers at time The utility density function value;

[0104] For transportation cost penalty function, Indicates the mode of transport. In this embodiment, for the duration of transportation, ;

[0105] For the vehicle idle penalty function, In this embodiment, the total number of transport vehicles is [number]. ;

[0106] For the transportation delay penalty function, For a moment A set of indexes of delayed devices. For the first The planned completion time for each transportation task;

[0107] , , They are respectively , , The penalty weight, In this embodiment =0.4、 =0.35、 =0.25.

[0108] For each state trajectory, the utility density function is integrated over time along that trajectory to obtain:

[0109]

[0110]

[0111] in, To safeguard the decision-making body's rights and interests in the first place The cumulative utility value on the state trajectory, For a moment Maintaining the decision-making body in the The utility density function value on the state trajectory, For transportation decision-makers in the first The cumulative utility value on the state trajectory, For a moment The transportation decision-maker in the first The utility density function value on the state trajectory, This represents the total simulation time. The cumulative utility value reflects the decision-maker's overall satisfaction along the entire state trajectory. A higher cumulative utility value indicates a stronger preference for that state trajectory.

[0112] Based on the calculated cumulative utility values, the state trajectories are arranged in descending order of cumulative utility values ​​to obtain each decision-maker's preference ranking for each state trajectory. If the decision-maker's preference ranking for each state trajectory is... State Trajectory The cumulative utility value on is higher than that on State Trajectory The cumulative utility value of the above, then the decision-maker in Strict preference .

[0113] S4. Extend the definitions of Nash stability, general metarational stability, symmetric metarational stability, sequential stability, and symmetric sequential stability in the classic conflict analysis graph model to the definitions of time-coupled Nash stability, time-coupled general metarational stability, time-coupled symmetric metarational stability, time-coupled sequential stability, and time-coupled symmetric sequential stability based on state trajectories. Based on the preference ranking of each decision-maker for each state trajectory obtained in S3, perform stability tests on each state trajectory and identify the equilibrium scheduling scheme.

[0114] In the classic conflict analysis graph model, stability is defined on a static discrete state space. The decision-maker's preferences are obtained by qualitatively ranking the states, and state transitions are represented by the decision-maker's logical jump from one state to another. This embodiment adapts the stability definition from the classic conflict analysis graph model to a state trajectory framework: the decision-maker's preferences are ranked based on the cumulative utility value along the entire state trajectory, and state transitions are represented by the decision-maker using a unilateral trigger event to switch the device from one state trajectory to another.

[0115] A unilateral transition is a transition between state trajectories initiated by a decision-maker through a unilaterally triggered event. For each decision-maker, from the state trajectory... Starting from this point, a unilateral triggering event controlled by the decision-maker alters the state trajectory, leading to another state trajectory. Then this transition is called a unilateral transition by the decision-maker. If the decision-maker moves from the state trajectory... Unilateral transition to state trajectory ,and The cumulative utility value for the decision-maker is higher than If so, the transfer is called a unilateral promotion transfer by the decision-maker.

[0116] Based on the definition of unilateral lift transition, the five temporal coupling stability definitions based on state trajectories are as follows:

[0117] Temporally Coupled Nash Stability: If there is no unilateral upward transition for any decision-maker starting from the current state trajectory, then the current state trajectory is considered to satisfy temporally coupled Nash stability. That is, no decision-maker can transition to a state trajectory that increases its cumulative utility value through a unilaterally triggered event.

[0118] Temporally Coupled General Metarational Stability: For any decision-maker's unilateral upward transition from the current state trajectory, if there exists at least one sanction path initiated by another decision-maker that reduces or does not improve the decision-maker's cumulative utility, then the current state trajectory is deemed to satisfy temporally coupled general metarational stability. This definition considers the possibility that other decision-makers may subsequently sanction the deviation. Sanction refers to a unilateral transition by another decision-maker that reduces or does not improve the cumulative utility of the decision-maker who initiated the deviation.

[0119] Temporally Coupled Symmetric Meta-Rational Stability: If, in addition to satisfying the general temporally coupled meta-rational stability, the decision-maker, after encountering sanctions, does not experience any unilateral upward transition, then the current state trajectory is deemed to satisfy temporally coupled symmetric meta-rational stability. This definition considers the scenario where the decision-maker anticipates a counterattack and attempts to mitigate losses but is unsuccessful.

[0120] Temporally coupled sequential stability: If for any decision-maker any unilateral boost transition starting from the current state trajectory, there exists at least one unilateral transition initiated by another decision-maker that constitutes a sanction against that decision-maker and can increase the cumulative utility value of the sanctioning decision-maker, then the current state trajectory is determined to satisfy temporally coupled sequential stability.

[0121] Temporally coupled symmetric sequential stability: If, on the basis of satisfying temporally coupled sequential stability, each intermediate state trajectory in the sanction process satisfies the definition of temporally coupled sequential stability, then the current state trajectory is determined to satisfy temporally coupled symmetric sequential stability.

[0122] For each state trajectory, based on the preferences of each decision-maker, stability is tested according to the five temporal coupling stability definitions mentioned above. If a state trajectory satisfies at least one of the five temporal coupling stability definitions for every decision-maker, then the state trajectory is determined to be a balanced scheduling scheme, and a balanced scheduling scheme is output. Furthermore, if a state trajectory satisfies all five temporal coupling stability definitions for every decision-maker, then the state trajectory is determined to be a strong equilibrium scheduling scheme, and a strong equilibrium scheduling scheme is output. The strong equilibrium scheduling scheme has the strongest resistance to deviation; no decision-maker has any incentive to unilaterally deviate, and even considering subsequent sanctions from other decision-makers cannot change this conclusion.

[0123] In this embodiment, four equilibrium state trajectories were identified. One of these trajectories represents a strong equilibrium scheduling scheme, constituting the optimal operation scheduling scheme for all decision-makers. The management department can optimize the overall system performance by executing equipment operation scheduling according to the strong equilibrium scheduling scheme. Meanwhile, the other three equilibrium state trajectories serve as alternative schemes, allowing the management department to flexibly choose in special circumstances.

[0124] The specific embodiments of the present invention are provided to enable those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.

[0125] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for equipment operation scheduling decision-making considering resource constraints, characterized in that, Includes the following steps: S1. Determine the set of decision-makers and the set of strategy options for each decision-maker in the equipment operation scheduling decision, and construct a time-coupled state vector. The time-coupled state vector is used to characterize the equipment's operating mode, health, spatial location and mode dwell time in the continuous time domain. The initial state space is constructed based on the set of decision-makers, the set of policy options, and the time-series coupled state vector. The initial state space is reduced by resource constraints to generate a temporally feasible state space. S2. Define option-triggered events and clock-triggered events in the continuous time domain. The option-triggered events and clock-triggered events constitute an event set. When any event in the event set occurs, update the device state in the temporally feasible state space through a state transition function to generate several state trajectories. S3. Transform each decision-maker's decision objective into a utility density function. For each utility density function, perform time integration along each state trajectory to obtain the cumulative utility value of each decision-maker on each state trajectory. Sort all state trajectories according to the cumulative utility value to generate a preference ranking of each decision-maker for all state trajectories. S4. Extend the stability definition in the classic conflict analysis graph model to a temporal coupling stability definition based on state trajectories. Perform stability checks on each state trajectory according to the preference ranking. Determine the state trajectory that satisfies the temporal coupling stability definition as a balanced scheduling scheme and output the balanced scheduling scheme.

2. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S1, the time-coupled state vector includes the device mode, health status, location tag, and mode dwell clock of each device at each moment; the device mode includes operating mode, standby mode, transportation mode, and maintenance mode; the location tag includes the work site, central maintenance warehouse, route from the work site to the central maintenance warehouse, and route from the central maintenance warehouse to the work site.

3. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S1, the resource constraints include at least one of the following: continuous operation rules, resource quantity limit rules, mode switching rules, logical consistency rules, clock synchronization rules, and uninterruptible rules. The continuous operation rule ensures that at least one device is in operation mode at any given time; the resource quantity limit rule ensures that the number of currently occupied transport vehicles and maintenance bays does not exceed their respective maximum quantities; the mode switching rule ensures that device mode switching occurs sequentially in the order of operation mode, transport mode, and maintenance mode; the logical consistency rule ensures that the matching between device mode and location tag conforms to physical logic; and the clock synchronization rule ensures that the evolution of device health is synchronized with the evolution of clock timers. The uninterruptible rule is used to constrain the device to maintain its operating mode until the end of its current operating cycle.

4. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S2, the option triggering events include the replacement request event, maintenance allocation event, standby activation event, and transportation scheduling event; the clock triggering events include the transportation completion event and the maintenance completion event.

5. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S2, the state trajectory is a set of states in the temporally feasible state space within a continuous time interval; when any event in the event set occurs, the device state in the temporally feasible state space is updated instantaneously through the state transition function. In the time interval when no event occurs, the device state in the temporally feasible state space evolves continuously over time, the health level continuously decays according to a preset degradation rate, and the mode dwell clock continuously accumulates.

6. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S3, the utility density function is a weighted sum of multiple penalty functions; the multiple penalty functions include at least two of the following: a health deviation from the optimal value penalty function, a maintenance waiting time penalty function, an equipment standby idle loss penalty function, a transportation cost penalty function, a vehicle idle penalty function, and a transportation delay penalty function.

7. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S4, the definition of temporal coupling stability includes temporal coupling Nash stability, temporal coupling general metaphysical stability, temporal coupling symmetric metaphysical stability, temporal coupling sequential stability, and temporal coupling symmetric sequential stability. If there is no unilateral boost transition for any decision-maker starting from the current state trajectory, then the current state trajectory is determined to satisfy temporally coupled Nash stability. The unilateral boost transfer is defined as follows: the decision-maker changes the state trajectory by unilaterally triggering an event, and the cumulative utility value of the changed state trajectory to the decision-maker is higher than that of the current state trajectory.

8. The equipment operation scheduling decision method considering resource constraints according to claim 1, characterized in that, In S4, if a state trajectory satisfies at least one of the temporal coupling stability definitions for each decision-maker, then the state trajectory is determined to be a balanced scheduling scheme; if a state trajectory satisfies all five temporal coupling stability definitions for each decision-maker, then the state trajectory is determined to be a strong balanced scheduling scheme, and the strong balanced scheduling scheme is output.

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