A rehabilitation resource collaborative scheduling method and system considering multi-dimensional space-time constraints

Abstract

The application discloses a kind of rehabilitation resource collaborative scheduling method and system considering multidimensional space-time constraints, it is related to medical information management technical field.The method includes: response scheduling request and obtain basic data;Standardized pretreatment is carried out to data and the degree of matching of doctor and patient is calculated;Mixed integer linear programming mathematical model is constructed, including oxygenated block therapy time sequence continuity constraint, resource group sharing capacity constraint and personnel skill matching constraint, and multiple objective optimization function including treatment amount, matching degree and load balancing is set;Branch and bound algorithm is called to solve model, and global optimal scheduling scheme and exception analysis report are generated.The application effectively solves the long-term project continuity guarantee difficulty, shared resource conflict and low individual matching degree in rehabilitation scheduling by mathematical programming technology, and significantly improves the resource utilization and operation efficiency of rehabilitation center.

Description

Technical Field

[0001] This invention relates to the field of resource collaborative scheduling technology, and in particular to a method and system for collaborative scheduling of rehabilitation resources that considers multidimensional spatiotemporal constraints. Background Technology

[0002] With the rapid development of rehabilitation medicine and the increasing diversification of patients' rehabilitation needs, rehabilitation centers are experiencing explosive growth in the number of patients and the variety of treatment programs offered. Against this backdrop, rehabilitation scheduling, as a core link connecting patient needs and medical resources, is becoming increasingly complex and challenging. Rehabilitation scheduling is essentially a typical multi-constraint, multi-objective, and strongly coupled resource allocation optimization problem. Its core difficulty lies in the cross-coupling of three dimensions: the heterogeneity of treatment needs, the diversity of resource constraints, and the necessity of personalized matching.

[0003] In existing technologies, traditional rehabilitation scheduling mainly relies on manual experience or simple greedy algorithms based on a "first-come, first-served" rule. Manual scheduling is inefficient, struggles to handle large-scale concurrent demands, and is highly susceptible to resource conflicts or scheduling violations due to human error. While simple greedy algorithms offer some speed improvements, they lack a global perspective, struggle to handle the continuity requirements of long-duration, interconnected projects like oxygen therapy, and are unable to effectively address the complex constraints of resource-sharing groups such as musculoskeletal rehabilitation. Furthermore, they fail to balance multiple objectives such as treatment volume, patient-doctor matching, and load balancing, often resulting in a situation where "high-value equipment is idle" and "critical resources are congested," severely restricting the service efficiency and treatment quality of rehabilitation centers. Therefore, there is an urgent need for a rehabilitation scheduling method that can comprehensively consider time continuity, resource sharing, and personalized matching needs, achieving 24 / 7, multi-resource, and multi-objective global optimization. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a collaborative scheduling method and system for rehabilitation resources that considers multidimensional spatiotemporal constraints. By deeply integrating various medical data from rehabilitation centers, a MILP mathematical model is constructed, incorporating constraints on the continuity of oxygenation block treatment sequences, resource group shared capacity, and personnel skill matching. A multi-objective optimization function is established, including treatment volume, matching degree, and load balancing. A branch-and-bound algorithm is used to achieve the global optimal solution, thereby significantly improving the utilization efficiency of rehabilitation resources, ensuring the medical compliance of scheduling, and optimizing the patient's medical experience.

[0005] In a first aspect, the present invention provides a collaborative scheduling method for rehabilitation resources that considers multidimensional spatiotemporal constraints, employing the following technical solution:

[0006] A collaborative scheduling method for rehabilitation resources that considers multidimensional spatiotemporal constraints includes:

[0007] Obtain rehabilitation scheduling request data, and based on the request data, obtain related clinical diagnosis and treatment data and resource allocation data;

[0008] Data cleaning and preprocessing are performed based on the acquired data;

[0009] A scheduling optimization mechanism is constructed based on preprocessed data, and a scheduling decision objective function is constructed based on the scheduling optimization mechanism.

[0010] The improved branch and bound method is used to generate the scheduling variable solution of the scheduling decision objective function;

[0011] A rehabilitation schedule plan is generated based on the scheduling variables.

[0012] Furthermore, the data cleaning and preprocessing based on the acquired data includes constructing a mathematical model input set containing patient needs, treatment item attributes, resource capability matrices, and doctor-patient matching relationships based on the acquired data, and loading the data association input table into a scheduling optimization mechanism configured on the server side; wherein, a patient set is generated through the first data construction unit. and treatment program collection , Represents any one patient in the patient set. For any one of the treatment options in the set of treatment options, For patients A subset of recommended medical orders; a set of time slices is generated through the second data construction unit. , For any standard time period in the time slice set, the duration of each time slice is set to a fixed value; a resource set is generated through the third data construction unit. Gather with physical therapists , For general equipment resources, For any physical therapist; generate a set of oxygenation time blocks using the fourth data construction unit. , For any pre-defined fixed time block of oxygen therapy, each time block Contains a set of consecutive time periods The fifth data construction unit is used to calculate the doctor-patient skills matching matrix. A score is generated based on the matching results between patient diagnostic keywords and the physical therapist's skill priority list.

[0013] Furthermore, the preprocessed data-based scheduling optimization mechanism includes generating a set of allocation variables for scheduling variable control based on the preprocessed mathematical model input set through an allocation variable mechanism, wherein the time period occupancy variable is generated through the first allocation unit. ,in Used to determine the patient Is it within a time period? Conducting projects Treatment; generating block selection variables through the second allocation unit. ,in Used to determine the patient Do you want to choose the first one? Treatment is administered in oxygenation time blocks; personnel assignment variables are generated through the third allocation unit. ,in Used to determine the patient In time period Treatment Program Whether or not it is done by a therapist Provide services; generate load deviation variables through the fourth allocation unit. ,in Used to represent time periods The resource load deviates from the average level.

[0014] Furthermore, the preprocessed data-based scheduling optimization mechanism also includes, based on the allocation variable set, using a constraint control mechanism to construct a set of conditional constraints, including constraints on the continuity of oxygen-assisted block treatment time, to constrain the scheduling variables. This includes constraining the continuity of oxygen-assisted block treatment time through a first constraint unit, specifically: constructing a block selection uniqueness constraint. Limit each patient to selecting a maximum of one oxygenation time block per day; construct time-block linkage constraints: This constraint is used to ensure that if a time block is selected, all consecutive time periods covered by that block must be synchronously occupied without interruption; it also establishes cabin capacity constraints. This is used to constrain the number of patients treated simultaneously in each time block to not exceed the maximum capacity of the treatment ward. The second constraint unit is used to constrain the shared capacity of resource groups, which is used to constrain the set of non-interruptible items that need to share the total capacity. The formula for the total concurrency within the same time period is:

[0015] ,in This defines the maximum number of concurrent users allowed for this resource group within a single time period; it also uses a third constraint unit to implement personnel-project binding constraints, including task-person consistency constraints. Used to determine projects that require manual intervention if the scheduling decides to proceed. Therefore, only one therapist can be assigned; and there are also skill and qualification constraints. Used to determine the assigned therapist Project Skills and qualifications; patient single-time period mutual exclusion constraints are implemented through the fourth constraint unit to determine the same patient within the same time frame. A maximum of one treatment can be performed within a given timeframe, and the formula is as follows: The fifth constraint unit is used to enforce compliance with medical orders, and is used to determine which patient medical order recommendation lists will be used only. The items in the list, and each non-oxygenated item can be performed a maximum of once a day.

[0016] Furthermore, the construction of the scheduling decision objective function based on the scheduling optimization mechanism includes constructing sub-objective functions including total treatment output, matching quality, and load smoothing based on the scheduling optimization mechanism, which are then weighted and combined to form the scheduling decision objective function. Maximize ;in, The total number of treatments completed throughout the day, used to maximize treatment output, is calculated using the following formula: ; The sum of the TCM-patient skills matching scores for all scheduled physical therapy sessions is used to maximize the quality of personalized treatment. The formula is: ; Resource load and average load for each time period The sum of absolute deviations is used to minimize load fluctuations to achieve balanced scheduling, and the formula is: ; These are the corresponding weighting coefficients.

[0017] Furthermore, the step of generating scheduling variable solutions for the scheduling decision objective function using the improved branch and bound algorithm includes solving for the scheduling variable solutions of the scheduling decision objective function using the improved branch and bound algorithm. First, solver parameters are configured, including maximum solution time and relative error tolerance. Then, the MILP scheduling optimization model is iteratively searched based on the improved branch and bound algorithm, and the upper and lower bounds of the solution are determined using relaxed linear programming. If there is no feasible solution under the preset constraints, a conflict resolution mechanism is triggered. According to the preset priority strategy, non-critical constraints are relaxed in turn or the scheduling needs of low-priority patients are temporarily removed, and the set of conflict constraints that lead to no solution is recorded.

[0018] Furthermore, the iterative search of the MILP scheduling optimization model based on the improved branch and bound algorithm utilizes relaxed linear programming to determine the upper and lower bounds of the solution. This includes addressing the problem that traditional branch and bound algorithms are prone to the curse of dimensionality when dealing with large-scale binary variables. An improved branch and bound algorithm, which integrates heuristic preprocessing and domain-specific pruning strategies, is employed to solve the problem. Specifically, to accelerate search convergence, an initial feasible solution is first generated using a multi-level priority rule greedy algorithm. As the initial lower bound of the branch-bound tree, it is defined as: based on the doctor-patient matching degree The system prioritizes filling oxygenation block requests into pre-defined time blocks (Block A and Block B) in descending order. Projects requiring specific scarce equipment or qualified therapists are given priority in assignment to ensure critical resources are not redundantly consumed by ordinary projects. Then, ordinary projects are greedily filled using... Filling in the remaining idle time slots is represented as: if the greedy algorithm finds a feasible solution... Then set a global lower bound. ;otherwise Then, based on heuristic variable selection and branching strategies using business weights, nodes to be expanded are selected in the search tree. In this case, instead of conventional random selection, a branching strategy based on business sensitivity is adopted, along with a variable selection operator based on pseudo-cost. A scoring function is constructed when selecting branching decision variables. Quantitative evaluation of candidate variables:

[0019] ,

[0020] in, and Variables The average unity gain generated when branching downwards and upwards at the current node; This is the balance coefficient; As a business relevance weight, the algorithm prioritizes the selection of... The maximized variable is split to force the model to collapse toward the solution space with the highest medical value gain.

[0021] Furthermore, the iterative search of the MILP scheduling optimization model based on the improved branch and bound algorithm, and the determination of the upper and lower bounds of the solution using relaxed linear programming, also includes linear relaxation and upper bound estimation for nodes. Perform linear relaxation and use the simplex method to calculate the local upper bound of the node. Then, pruning criteria are applied; if... If the optimal potential of the current node is less than that of a known feasible solution, then the node and all its child nodes are directly pruned. Furthermore, a logical pruning mechanism is introduced for rehabilitation scenarios to remove invalid branches before solving the problem. During the solution process, a logical conflict detection operator is defined. For the oxygenation block constraint, a logical pruning decision formula is constructed:

[0022] ,

[0023] in, For indicator functions, Represents a node The current domain of the variable, if If the current local solution space conflicts with the consistency semantics of the oxygenated connected component, then according to the principle of logical implication, none of the sub-topological spaces of this node contain feasible solutions, and forced pruning is immediately performed; at any decision node in the branch-bound search tree... The department, through evaluation of the shared resource group The lower bound of resource consumption is used to predict the feasibility of the current search subspace and construct a resource conflict detection operator. The mathematical form of is defined as follows:

[0024] ,

[0025] in, For indicator functions, Representing decision variables At the node The lower bound of the value at that point.

[0026] Furthermore, if no feasible solution is found under the preset constraints, a conflict resolution mechanism is triggered, which includes transforming the original MILP model into a Lagrange relaxation form when the search space is closed and there is no solution, searching for a suboptimal feasible solution, and introducing an elastic variable. Rewrite the objective function:

[0027] ,

[0028] in, This refers to the set of core conflict constraints identified by the irreducible inconsistency subsystem IIS detection algorithm. To determine the penalty order for the corresponding constraints, the system performs a minimum violation calculation on the soft constraints to achieve smooth load shedding and self-healing scheduling schemes under resource limit conflict scenarios. The system iterates repeatedly until the search tree is empty or a preset time limit is reached. During the iteration process, if the scheduling decision objective function value of a new candidate scheduling solution is better than that of the current optimal solution, then the new candidate scheduling solution is updated as the current optimal scheduling variable solution. Otherwise, relaxed linear programming is used to determine the upper and lower bounds of the solution, and inferior branches are pruned to avoid invalid searches.

[0029] Furthermore, the step of generating a rehabilitation schedule plan based on the scheduling variable solution includes extracting the corresponding rehabilitation treatment scheduling information based on the scheduling variable solution to generate the optimized rehabilitation schedule plan, including: parsing the optimal scheduling decision solution. and The data is then mapped back to the original business data: a structured patient schedule is generated, including patient ID, treatment items, treatment time, designated therapist, and equipment used; a resource load view is generated, including the time period occupancy rate of each resource component; and an anomaly analysis report is generated, including a list of items not included in the schedule and their specific reason codes.

[0030] Secondly, a collaborative scheduling system for rehabilitation resources that considers multidimensional spatiotemporal constraints includes:

[0031] The data acquisition module is configured to acquire rehabilitation scheduling request data and, based on the request data, acquire related clinical diagnosis and treatment data and resource configuration data.

[0032] The preprocessing module is configured to perform data cleaning and preprocessing based on the acquired data;

[0033] The decision module is configured to construct a scheduling optimization mechanism based on preprocessed data, and to construct a scheduling decision objective function based on the scheduling optimization mechanism.

[0034] The computation module is configured to generate scheduling variable solutions to the scheduling decision objective function using improved branch and bound.

[0035] The generation module is configured to generate a rehabilitation schedule plan based on scheduling variables.

[0036] Thirdly, the present invention provides a computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the aforementioned method for collaborative scheduling of rehabilitation resources considering multidimensional spatiotemporal constraints.

[0037] Fourthly, the present invention provides a terminal device, including a processor and a computer-readable storage medium, wherein the processor is used to implement various instructions; the computer-readable storage medium is used to store multiple instructions, the instructions being adapted to be loaded and executed by the processor to provide a collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints.

[0038] In summary, the present invention has the following beneficial technical effects:

[0039] This invention integrates multi-dimensional data from rehabilitation centers and applies mixed-integer linear programming techniques to handle complex constraints such as oxygenation block scheduling, resource sharing, and personnel matching, thereby achieving automation and intelligence in rehabilitation scheduling. By constructing a sophisticated mathematical optimization model, this invention not only completely solves the problem of interruptions in long-term treatment programs but also achieves precise matching of medical and patient skills and global balancing of resource load.

[0040] Achieving accurate modeling of complex block therapy: By introducing a two-way binding constraint between "block variables" and "time period variables", the continuity of clinical implementation of uninterrupted projects such as oxygenation is ensured, and the fragmentation problem caused by traditional algorithms is solved.

[0041] Supports a flexible resource sharing mechanism: By constructing resource group sharing capacity constraints, it effectively solves the congestion problem in scenarios such as multiple projects sharing a physical therapy area, and improves space utilization.

[0042] Improving the quality of personalized treatment: By introducing four-dimensional personnel assignment variables and a skill matching objective function, the precise matching of therapists' expertise with patients' diseases was achieved, thus optimizing rehabilitation efficacy.

[0043] Enhanced operational decision support: Through conflict resolution mechanisms and anomaly analysis reports, the system provides hospital administrators with quantifiable data on resource bottlenecks, helping to achieve refined operational management. Attached Figure Description

[0044] Figure 1 This is a flowchart of the steps of a collaborative scheduling method and system for rehabilitation resources that considers multidimensional spatiotemporal constraints according to the present invention.

[0045] Figure 2 This is a scheduling visualization diagram of the scheduling optimization method in this embodiment of the invention;

[0046] Figure 3 This is a bar chart comparing the core compliance indicators of the four scheduling methods in this invention regarding overall demand fulfillment rate (SR) and oxygen therapy compliance rate (HBO-SR).

[0047] Figure 4 This is a comparison chart of service quality based on the four scheduling methods in this embodiment of the invention, in terms of patient skill matching score and therapist load balancing variance (LB-Var).

[0048] Figure 5 This is a comparison chart of the algorithm solution time and computational efficiency of four scheduling methods in the embodiments of the present invention;

[0049] Figure 6 This is a radar chart comparing the comprehensive performance of four scheduling methods under multi-dimensional evaluation indicators in the embodiments of the present invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings.

[0051] Example 1

[0052] Reference Figure 1 This embodiment of a collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints includes:

[0053] like Figure 1 As shown, this invention provides a collaborative scheduling method and system for rehabilitation resources that considers multi-dimensional spatiotemporal constraints. By integrating multi-dimensional constraints such as time, resources, priority, and personnel skills of rehabilitation centers, it achieves intelligent and efficient rehabilitation scheduling. The steps include:

[0054] Step S1: Construct a multi-source heterogeneous rehabilitation data acquisition interface to respond to scheduling requests and acquire all pending scheduling data in real time; specifically including:

[0055] Multi-source data access: Establish data communication channels with systems such as Hospital Information System (HIS), Electronic Medical Record System (EMR), and Rehabilitation Management System (RMS) through standard medical data exchange protocols;

[0056] Data fusion objectification: After cleaning the above-mentioned scattered heterogeneous data using ETL tools, it is mapped and converted into a unified format JSON scheduling request object, which serves as the standard input for subsequent mathematical models.

[0057] Step S2: Based on the rehabilitation scheduling request, obtain the basic data of the rehabilitation schedule to be optimized in the system and perform data cleaning and preprocessing. Construct a mathematical model input set that includes patients, treatment items, rehabilitation resources and doctor-patient matching relationships, and load the data association input table into the scheduling optimization mechanism configured on the server.

[0058] This process involves acquiring basic data for the rehabilitation schedule to be optimized, performing data cleaning and preprocessing, and loading all data resources related to the rehabilitation schedule, including basic data on patient management, treatment program configuration, therapist skills, and oxygen chamber operation times. Specifically, this includes:

[0059] Acquire basic rehabilitation scheduling data, and simultaneously clean, transform, and organize this data. The basic rehabilitation scheduling data includes a patient medical order information table, a treatment item attribute table, a rehabilitation resource allocation table, a therapist skill matrix, and an oxygen therapy schedule. The patient medical order information table includes patient ID, diagnosis information (e.g., stroke, spinal cord injury), a list of medical order items (e.g., PT, OT, oxygen therapy), length of hospital stay, and priority weight. The treatment item attribute table includes item ID, standard duration (usually 40 minutes / unit), and other relevant information. Required resource type, whether continuous time periods are required (e.g., oxygenation requires 3 consecutive time periods); Rehabilitation resource configuration table: includes equipment resource ID, equipment type, location, maximum concurrent capacity per time period (e.g., musculoskeletal rehabilitation area is limited to 4 people) and operating time window; Therapist skill matrix: includes therapist ID, list of diseases they are good at and matching score (between 0 and 1) for each disease, used to guide personalized matching; Oxygenation operation schedule: includes the preset fixed time block definition of the oxygenation chamber (e.g., Block A: 08:00-10:00) and the capacity of each block.

[0060] Secondly, the basic data for the rehabilitation schedule was cleaned, transformed, and organized, including:

[0061] Data cleaning: Remove invalid records with missing medical order items or conflicting contraindications, such as records of people with metal implants applying for magnetic stimulation therapy;

[0062] Data transformation: Standardize the mapping of unstructured medical order texts, uniformly mapping "transcranial magnetic resonance imaging" and "rTMS" to standard item codes; map patient diagnostic keywords to standard disease classification labels;

[0063] Data processing: Calculate the skill fit score between each patient and each physical therapist. Construct a doctor-patient matching matrix.

[0064] In step S2, the mathematical model input set is constructed and a data input set for scheduling optimization is generated through the association construction module, including:

[0065] Preprocessed surgical scheduling data is obtained from the information system, including department code tables, treatment group information tables, operating room configuration tables, surgical day plans, and surgical request forms. Based on the foreign key relationships and / or semantic field mappings between the tables in the surgical scheduling data, a data association table is constructed through the association construction module, and a data input set for scheduling optimization is generated. The data input set is used as the basic data for variable allocation by the variable allocation submodule, and as the surgical scheduling information for constructing scheduling constraints by the constraint control submodule.

[0066] The association building module constructs a data association table and generates a data input set for scheduling optimization, including:

[0067] A patient set is generated using the first data construction unit. and treatment program collection The For any patient in the patient set, the For any one of the treatment items in the set of treatment items, the For patients A subset of recommended medical orders;

[0068] A time slice set is generated using the second data construction unit. The For any standard time period in the set of time slices, set the duration of each time slice to a fixed value (e.g., 40 minutes).

[0069] Resource sets are generated through the third data construction unit. Gather with physical therapists The For general equipment resources, the For any physical therapist;

[0070] A set of oxygenation time blocks is generated using the fourth data construction unit. The For any pre-defined fixed time block of oxygen therapy, each time block Contains a set of consecutive time periods (like correspond A set of shared resource groups is generated through the fifth data construction unit. Identify uninterrupted project combinations that require sharing of total capacity (such as musculoskeletal rehabilitation groups).

[0071] Step S3: The scheduling optimization mechanism is based on the mathematical model input set. The allocation variable submodule generates an allocation variable set for scheduling variable control, and the constraint control submodule constructs a set of condition constraints, including the continuity constraint of oxygenation block treatment time, to constrain the scheduling variables. The objective optimization submodule constructs at least three sub-objective functions, which are then weighted and combined to form the scheduling decision objective function.

[0072] In step S3, the scheduling optimization mechanism, based on the mathematical model input set, generates a set of allocation variables for scheduling variable control through the allocation variable submodule, including:

[0073] Step S31: Receive the mathematical model input set as the basis for variable assignment;

[0074] Step S32: The allocation variable submodule constructs multiple scheduling variables based on the mathematical model input set and allocates them. The allocation variable submodule includes a first allocation unit, a second allocation unit, a third allocation unit, and a fourth allocation unit.

[0075] Time period occupancy variables are generated through the first allocation unit. ,in Used to determine the patient Is it within a time period? Conducting projects Treatment;

[0076] Block selection variables are generated through the second allocation unit. ,in Used to determine the patient Do you want to choose the first one? Treatment is administered in oxygenation time blocks; this variable is specifically designed to address long-term block scheduling issues.

[0077] Personnel assignment variables are generated through the third allocation unit. ,in Used to determine the patient In time period Treatment Program Whether or not it is done by a therapist Provide services;

[0078] The load deviation variable is generated through the fourth allocation unit. ,in Used to represent time periods The resource load deviates from the average level.

[0079] In step S3, the constraint control submodule constructs a set of conditional constraints, including constraints on the continuity of oxygenation block treatment timing, to constrain the scheduling variables, including:

[0080] It receives the set of assigned variables and the set of mathematical model inputs; it applies condition constraints through the constraint control submodule, which includes a first constraint unit, a second constraint unit, a third constraint unit, a fourth constraint unit, and a fifth constraint unit.

[0081] The first constraint unit constrains the timing continuity of oxygenation therapy, ensuring the continuity of oxygenation therapy and compliance with cabin regulations. The formula includes:

[0082] Block selection uniqueness constraint: Each patient is limited to choosing only one oxygenation time block per day;

[0083] Time-block linkage constraints: It mandates that if a time block is selected, all consecutive time periods covered by that block must be synchronously occupied and cannot be interrupted.

[0084] Cabin capacity constraints: Ensure that the number of patients treated simultaneously in each time block does not exceed the maximum capacity of the treatment ward. ;

[0085] The second constraint unit is used to constrain the shared capacity of resource groups, thereby constraining the set of uninterrupted items that need to share the total capacity. The formula for the total concurrency in the same time period is: ,in This represents the maximum number of concurrent users allowed for this resource group within a single time period.

[0086] The third constraint unit is used to implement personnel-project binding constraints to achieve personalized skill matching. The formula includes: Task-Personnel Consistency Constraint: If the scheduling determines that a project requires manual intervention, then... Therefore, only one therapist must be assigned; skill and qualification constraints: Determine the assigned therapist Project Skills and qualifications;

[0087] The fourth constraint unit is used to implement mutual exclusion constraints for patients within a single time period, which is used to determine the same patient in the same time slice. A maximum of one treatment can be performed within a given timeframe, and the formula is as follows: ;

[0088] The fifth constraint unit is used to enforce compliance with medical orders, and is used to determine whether to only schedule the recommended list of patient medical orders. The items in the formula are as follows: each non-oxygenated item can be performed a maximum of once a day. .

[0089] In step S3, at least three sub-objective functions are constructed through the objective optimization sub-module, and then weighted and combined to form the scheduling decision objective function, including:

[0090] The objective optimization submodule constructs sub-objective functions including total treatment output, match quality, and load smoothing. These sub-objective functions are then weighted and combined to form the scheduling decision objective function. for:

[0091] ,

[0092] in, The total number of treatments completed throughout the day (including oxygen blocks) is used to maximize treatment output, and the formula is: ; The sum of the TCM-patient skills matching scores for all scheduled physical therapy sessions is used to maximize the quality of personalized treatment. The formula is: ; Resource load and average load for each time period The sum of absolute deviations is used to minimize load fluctuations to achieve balanced scheduling, and the formula is: ; These are the corresponding weighting coefficients.

[0093] Step S4: Based on the constructed MILP model, an improved branch and bound algorithm that integrates heuristic preprocessing and domain-specific pruning strategies is used to solve the problem. Traditional branch and bound algorithms struggle with handling large-scale binary variables (such as...). When faced with the curse of dimensionality, this invention improves upon it through the following specific calculation process:

[0094] S41: Heuristic initial solution generation (warm-start strategy). To accelerate search convergence, an initial feasible solution is first generated using a multi-level priority rule greedy algorithm. This serves as the initial lower bound of the branch-bound tree. Rule definition:

[0095] 1. Prioritize patients receiving oxygen therapy: based on doctor-patient matching rate. Arrange in descending order, prioritizing the filling of oxygenation block requirements into preset time blocks such as Block A and Block B.

[0096] 2. Secondary scheduling of projects with time continuity constraints: Prioritize projects that require specific scarce equipment or designated qualified therapists to ensure that critical resources are not redundantly occupied by ordinary projects.

[0097] 3. Greedy fill for ordinary items: utilizing... Fill the remaining idle time slots. Mathematical expression: If the greedy algorithm finds a feasible solution... Then set a global lower bound. ;otherwise .

[0098] S42: Heuristic variable selection and branching strategy based on business weights to select nodes to be expanded in the search tree. In this invention, the conventional random selection is abandoned in favor of a branching strategy based on business sensitivity.

[0099] A variable selection operator based on pseudo-cost is used to construct a score function when selecting branch decision variables. Quantitative evaluation of candidate variables:

[0100] ,

[0101] in, and Variables The average unity gain generated when branching downwards and upwards at the current node; This is the balance coefficient (usually taken as 0.15). For business relevance weights. The algorithm prioritizes those that... The maximized variable is split to force the model to collapse toward the solution space with the highest “medical value gain”.

[0102] S43: Linear relaxation and upper bound estimation, for nodes Perform linear relaxation (to Relaxed to The local upper bound of the node is calculated using the simplex method. .

[0103] Pruning criteria: If If the optimal potential of the current node is less than that of the known feasible solution, then the node and all its child nodes are directly pruned.

[0104] S44: A domain-specific logical decision pruning mechanism embedding industry prior knowledge. In addition to conventional mathematical pruning, this invention introduces logical decision pruning for rehabilitation scenarios, eliminating invalid branches in advance before solving the problem.

[0105] During the solution process, a logical conflict detection operator is defined. For the oxygenated connected block constraint, the following logical pruning decision formula is constructed:

[0106] ,

[0107] in, For indicator functions, Represents a node The current domain of the variable. If If the current local solution space conflicts with the consistency semantics of the oxygenated block, according to the principle of logical implication, none of the sub-topological spaces of this node contain feasible solutions, and forced pruning is immediately performed.

[0108] At any decision node in the branch and bound search tree At this point, the algorithm evaluates shared resource groups. This invention constructs a resource conflict detection operator by using a lower bound on resource consumption in areas such as musculoskeletal rehabilitation zones and comprehensive physical therapy zones to predict the feasibility of the current search subspace. Its mathematical form is defined as follows:

[0109] ,

[0110] in, For indicator functions, Representing decision variables At the node The lower bound of the value at that point. Its core decision-making logic is: before entering a deeper search, the algorithm first statistically analyzes all relevant decision variables that have been fixed at 1 in the current branch path. If in any discrete time interval... Within this context, the total resource demand will inevitably exceed the rated physical capacity limit of this resource group. Then the indicator function The value is 1. Based on the monotonicity principle of the search space, any subsequent expansion of child nodes will only increase resource consumption and cannot eliminate existing conflicts. Therefore, it is determined that there is no feasible solution that satisfies the hard constraints in the local solution space. The system immediately performs a forward-looking logic pruning operation to avoid invalid branch traversal and significantly reduce the time complexity of the algorithm.

[0111] S45: Conflict resolution based on Lagrange relaxation: When the search space is closed and there is no solution, the system transforms the original MILP model into a Lagrange relaxation form to find a suboptimal feasible solution. Elasticity variables are introduced. Rewrite the objective function:

[0112] ,

[0113] in, This refers to the set of core conflicting constraints identified by the Irrevocable Inconsistency Subsystem (IIS) detection algorithm. This represents the penalty order for the corresponding constraint. By performing a minimum violation calculation on the soft constraints, a smooth load reduction and self-healing scheduling scheme are achieved under resource limit conflict scenarios.

[0114] Repeat steps S42 to S45 until the search tree is empty or the preset time limit is reached. During the iteration process, if the scheduling decision objective function value of a new candidate scheduling solution is better than that of the current optimal solution, then the new candidate scheduling solution is updated as the current optimal scheduling variable solution; otherwise, relaxed linear programming is used to determine the upper and lower bounds of the solution, and inferior branches are pruned to avoid invalid searches.

[0115] If a feasible solution cannot be obtained under all hard constraints, the system enters a flexible solution mode. Some soft constraints (such as load balancing requirements) or suboptimal priority hard constraints in the original model are transformed into objective function factors with penalty terms.

[0116] Step S5: Analyze the optimal solution of the model to generate a visual scheduling plan, and execute anomaly feedback and dynamic closed-loop management; specifically including:

[0117] Solution visualization: Based on the solution results, a treatment instruction sheet (time, location, project, therapist) from the patient's perspective and a Gantt chart from the resource perspective are generated to intuitively show the busy and idle distribution of each treatment area and personnel;

[0118] Anomaly source analysis: For pending tasks that the model cannot schedule, the system automatically backtracks and outputs conflict cause codes (e.g., insufficient capacity in the oxygen chamber Block A or conflicting therapist schedules) to assist human decision-making.

[0119] A visualization view is generated based on the final scheduling variable solution, such as Figure 2 As shown, this step also includes generating a resource Gantt chart using visualization tools, with the horizontal axis representing time and the vertical axis representing therapists or equipment. Color blocks distinguish patients with different diseases, visually displaying the occupancy of oxygenation blocks and the workload distribution of therapists, supporting manual fine-tuning, and calculating resource utilization.

[0120] Experimental verification

[0121] To systematically verify the performance advantages of the method of this invention in complex, multi-constraint rehabilitation scheduling scenarios, we used a large-scale simulation dataset constructed based on anonymized data from a real tertiary hospital rehabilitation center. This dataset records the patient treatment demand flow over 30 consecutive working days, covering three typical scenarios: neurological rehabilitation, orthopedic rehabilitation, and geriatric rehabilitation.

[0122] The data is rich in dimensions, mainly including: Patient dimension: daily medical orders (including treatment items, duration, and frequency), disease diagnoses, and physical function ratings for 100 patients; Resource dimension: skill matrix (areas of expertise and levels) for 10 physical therapists, oxygen chamber operation schedule (4 fixed time blocks), and shared capacity limits for the musculoskeletal rehabilitation area; Rule dimension: temporal mutual exclusion and dependency relationships between items. The dataset contains approximately 860 treatment item requests, which we have divided into different load levels to ensure coverage of two typical operational states: "stable daily operation" and "resource limit pressure".

[0123] To comprehensively evaluate the performance of the method of this invention, the following three categories of mainstream comparative methods, which are representative of the fields of operations research and medical management, are set up:

[0124] (1) Manual scheduling: Simulates the experience of senior schedulers to schedule, adopts the traditional approach of "starting with the difficult and then moving to the easy", prioritizes major items such as oxygenation, and fills in the blanks of other items manually, which represents the benchmark of traditional manual management.

[0125] (2) FCFS-Greedy (First Come First Served Greedy Algorithm): A basic automated scheduling logic that strictly follows the order in which patients submit their medical orders, traversing the timeline to find the earliest available time slot for insertion. It represents the basic scheduling function that most hospital information systems (HIS) currently come with.

[0126] (2) GA (Genetic Algorithm): It adopts the classic metaheuristic evolutionary algorithm, encodes the scheduling scheme into chromosomes, and iteratively searches for a better solution through selection, crossover and mutation operations, representing the global optimization idea of ​​non-exact solution.

[0127] All methods were evaluated under the same hardware environment and dataset conditions. Evaluation metrics included: demand fulfillment rate (SR, %), oxygenation scheduling success rate (HBO-SR, %), therapist skill matching degree (Match-Score, 0-1), resource load balancing variance (LB-Var), and solution time (Time, s).

[0128] Table 1 Comparison of data from different methods under five major indicators

[0129] Method Name SR(%) HBO-SR (%) Match-Score LB-Var Time(s) Manual scheduling 88.5 92.0 0.65 0.35 3600+ FCFS-Greedy 75.2 61.5 0.52 0.42 0.5 GA 92.4 88.6 0.81 0.15 300 Method of the present invention 99.2 100.0 0.94 0.04 60

[0130] The experimental results are shown in Table 1 and Figure 3 , Figure 4 , Figure 5 , Figure 6 As shown. To achieve a fair and intuitive comparison of overall performance, this invention has standardized the indicators (inverse indicators such as time and variance have been normalized and inverted) so that the advantages and disadvantages can be clearly displayed in the radar chart.

[0131] In core compliance indicators ( Figure 3 In the comparison of SR and HBO-SR, the traditional FCFS-Greedy algorithm performed the worst. Its blind sequential insertion resulted in many oxygenation needs being unscheduled due to fragmented time periods, with an HBO-SR of only 61.5%, severely impacting treatment continuity. While manual scheduling can guarantee a high success rate based on experience, its ability to handle complex conflicts reaches its limit as the number of patients reaches hundreds, leading to a significant drop in the overall demand fulfillment rate (SR). The GA algorithm, as a heuristic algorithm, can find good solutions, but its random search nature makes it difficult to guarantee the absolute satisfaction of hard constraints (such as blocks), resulting in fluctuations in HBO-SR. In contrast, the method of this invention constructs rigorous "block-time period" linkage mathematical constraints, forcibly ensuring the continuity of oxygenation, achieving a 100% oxygenation scheduling success rate, and increasing the overall demand fulfillment rate to 99.2%, reaching the optimal level of medical compliance.

[0132] In terms of service quality and experience Figure 3 In comparing Match-Score and Load Balancing (LB-Var), traditional methods (manual and greedy) often only aim to "get assigned" without considering "who is assigned," resulting in a low Match-Score and uneven workload among therapists, which can easily lead to dissatisfaction among medical staff. Although the GA algorithm introduces an optimization objective, its convergence process is unstable and prone to getting trapped in local optima. The method of this invention uses skill matching degree as the core weight term of the objective function and introduces a four-dimensional variable for precise assignment, resulting in a Match-Score as high as 0.94, truly achieving "specialized treatment for specific diseases"; at the same time, the load balancing variance is as low as 0.04, which effectively smooths out peaks and valleys, preventing some therapists from becoming overworked.

[0133] In solving for efficiency ( Figure 4 While FCFS-Greedy offers extremely fast response times, it sacrifices solution quality and cannot be used as a final solution. Manual scheduling takes several hours and is completely unsuitable for dynamic adjustments. The GA algorithm requires extensive population iterations and mutations, resulting in long processing times and randomness, with potentially different results each time. Although the method of this invention has a higher computational complexity than the greedy algorithm, it benefits from the efficient pruning strategy of the branch and bound algorithm, enabling global optimization for a scale of hundreds of people to be completed within one minute. This demonstrates that while pursuing the global optimum, the computation time of this invention remains completely within a clinically acceptable range, and the results are deterministic and reproducible.

[0134] In terms of overall performance ( Figure 5On the radar chart, the overall performance of all methods is clearly displayed. The area enclosed by the outline of the method of this invention is significantly larger than that of all the comparison methods, presenting a full pentagonal structure. Compared with traditional methods, this invention solves the problems of "fragmentation" and "blindness"; compared with heuristic GA algorithms, this invention solves the problems of "instability" and "hard constraint violation".

[0135] In summary, this invention, through the coordinated processing of multiple complex constraints such as block constraints, resource sharing constraints, and skill matching constraints in oxygen therapy projects, significantly improves the efficiency of scheduling scheme generation and resource utilization while ensuring clinical compliance, and has practical engineering value.

[0136] Example 2

[0137] This embodiment provides a collaborative scheduling system for rehabilitation resources that considers multidimensional spatiotemporal constraints, including:

[0138] The data acquisition module is configured to acquire rehabilitation scheduling request data and, based on the request data, acquire related clinical diagnosis and treatment data and resource configuration data.

[0139] The preprocessing module is configured to perform data cleaning and preprocessing based on the acquired data;

[0140] The decision module is configured to construct a scheduling optimization mechanism based on preprocessed data, and to construct a scheduling decision objective function based on the scheduling optimization mechanism.

[0141] The computation module is configured to generate scheduling variable solutions to the scheduling decision objective function using improved branch and bound.

[0142] The generation module is configured to generate a rehabilitation schedule plan based on scheduling variables.

[0143] A computer-readable storage medium storing a plurality of instructions adapted for loading and execution by a processor of a terminal device of the aforementioned method for collaborative scheduling of rehabilitation resources considering multidimensional spatiotemporal constraints.

[0144] A terminal device includes a processor and a computer-readable storage medium, the processor being configured to implement various instructions; the computer-readable storage medium being configured to store multiple instructions adapted for loading and execution by the processor of the aforementioned collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints.

[0145] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints, characterized in that, include: Obtain rehabilitation scheduling request data, and based on the request data, obtain related clinical diagnosis and treatment data and resource allocation data; Data cleaning and preprocessing are performed based on the acquired data; A scheduling optimization mechanism is constructed based on preprocessed data, and a scheduling decision objective function is constructed based on the scheduling optimization mechanism. The improved branch and bound method is used to generate the scheduling variable solution of the scheduling decision objective function; Generate a rehabilitation schedule plan based on the scheduling variables; The data cleaning and preprocessing based on the acquired data includes constructing a mathematical model input set containing patient needs, treatment item attributes, resource capability matrices, and doctor-patient matching relationships based on the acquired data, and loading the data association input table into a scheduling optimization mechanism configured on the server side; wherein, a patient set is generated through the first data construction unit. and treatment program collection , Represents any one patient in the patient set. For any one of the treatment options in the set of treatment options, For patients A subset of recommended medical orders; a set of time slices is generated through the second data construction unit. , For any standard time period in the time slice set, the duration of each time slice is set to a fixed value; a resource set is generated through the third data construction unit. Gather with physical therapists , For general equipment resources For any physical therapist; generate a set of oxygenation time blocks using the fourth data construction unit. , For any pre-defined fixed time block of oxygen therapy, each time block Contains a set of consecutive time periods The fifth data construction unit is used to calculate the doctor-patient skills matching matrix. A score is generated based on the matching results between patient diagnostic keywords and the physical therapist's skill priority list; The preprocessed data-based scheduling optimization mechanism includes generating a set of allocation variables for scheduling variable control based on the preprocessed mathematical model input set through an allocation variable mechanism. Specifically, a time period occupancy variable is generated through a first allocation unit. ,in Used to determine the patient Is it within a time period? Conducting projects Treatment; generating block selection variables through the second allocation unit. ,in Used to determine the patient Do you want to choose the first one? Treatment is administered in oxygenation time blocks; personnel assignment variables are generated through the third allocation unit. ,in Used to determine the patient In time period Treatment Program Whether or not it is done by a therapist Provide services; generate load deviation variables through the fourth allocation unit. ,in Used to represent time periods The resource load deviates from the average level. The preprocessed data-based scheduling optimization mechanism further includes, based on the allocation variable set, using a constraint control mechanism to construct a set of conditional constraints, including constraints on the continuity of oxygen-assisted block treatment time, to constrain the scheduling variables. This includes constraining the continuity of oxygen-assisted block treatment time through a first constraint unit, specifically: constructing a uniqueness constraint for block selection. Limit each patient to selecting a maximum of one oxygenation time block per day; construct time-block linkage constraints: This constraint is used to ensure that if a time block is selected, all consecutive time periods covered by that block must be synchronously occupied without interruption; it also establishes cabin capacity constraints. This is used to constrain the number of patients treated simultaneously in each time block to not exceed the maximum capacity of the treatment ward. The second constraint unit is used to constrain the shared capacity of resource groups, which is used to constrain the set of non-interruptible items that need to share the total capacity. The formula for the total concurrency within the same time period is: ,in This defines the maximum number of concurrent users allowed for this resource group within a single time period; it also uses a third constraint unit to implement personnel-project binding constraints, including task-person consistency constraints. Used to determine projects that require manual intervention if the scheduling decides to proceed. Therefore, only one therapist can be assigned; and there are also skill and qualification constraints. Used to determine the assigned therapist Project Skills and qualifications; patient single-time period mutual exclusion constraints are implemented through the fourth constraint unit to determine the same patient within the same time frame. A maximum of one treatment can be performed within a given timeframe, and the formula is as follows: The fifth constraint unit is used to enforce compliance with medical orders, and is used to determine which patient medical order recommendation lists will be used. The items in the list, and each non-oxygenated item can be performed a maximum of once a day.

2. The collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints according to claim 1, characterized in that, The scheduling decision objective function constructed based on the scheduling optimization mechanism includes constructing sub-objective functions including total treatment output, matching quality, and load smoothing based on the scheduling optimization mechanism, which are then weighted and combined to form the scheduling decision objective function. For: Maximize ;in, The total number of treatments completed throughout the day, used to maximize treatment output, is calculated using the following formula: ; The sum of the TCM-patient skills matching scores for all scheduled physical therapy sessions is used to maximize the quality of personalized treatment. The formula is: ; Resource load and average load for each time period The sum of absolute deviations is used to minimize load fluctuations to achieve balanced scheduling, and the formula is: ; These are the corresponding weighting coefficients.

3. The collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints according to claim 2, characterized in that, The process of generating scheduling variable solutions for the scheduling decision objective function using the improved branch and bound algorithm includes solving the scheduling variable solutions for the scheduling decision objective function using the improved branch and bound algorithm. First, the solver parameters are configured, including the maximum solution time and relative error tolerance. Then, the MILP scheduling optimization model is iteratively searched based on the improved branch and bound algorithm, and the upper and lower bounds of the solution are determined using relaxed linear programming. If no feasible solution is found under the preset constraints, the conflict resolution mechanism is triggered. Based on the preset priority strategy, non-critical constraints are relaxed in turn or the scheduling needs of low-priority patients are temporarily removed, and the set of conflict constraints that led to the unsolvable problem is recorded.

4. The collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints according to claim 3, characterized in that, The improved branch-and-bound algorithm iteratively searches the MILP scheduling optimization model, using relaxed linear programming to determine the upper and lower bounds of the solution. This includes addressing the problem of traditional branch-and-bound algorithms easily falling into the curse of dimensionality when dealing with large-scale binary variables. An improved branch-and-bound algorithm, integrating heuristic preprocessing and domain-specific pruning strategies, is employed to solve the problem. To accelerate search convergence, an initial feasible solution is first generated using a multi-level priority rule greedy algorithm. As the initial lower bound of the branch-bound tree, it is defined as: based on the doctor-patient matching degree The system prioritizes filling oxygenation block requests into multiple pre-defined candidate consecutive time blocks, sorting them in descending order. Projects requiring specific scarce equipment or qualified therapists are given priority in assignment to ensure critical resources are not redundantly consumed by ordinary projects. Then, ordinary projects are greedily filled using... Filling in the remaining idle time slots is represented as: if the greedy algorithm finds a feasible solution... Then set a global lower bound. ;otherwise Then, based on heuristic variable selection and branching strategies using business weights, nodes to be expanded are selected in the search tree. In this case, instead of conventional random selection, a branching strategy based on business sensitivity is adopted, along with a variable selection operator based on pseudo-cost. A scoring function is constructed when selecting branching decision variables. Quantitative evaluation of candidate variables: ， in, and Variables The average unity gain generated when branching downwards and upwards at the current node; This is the balance coefficient; As a business relevance weight, the algorithm prioritizes the selection of... The maximized variable is split to force the model to collapse toward the solution space with the highest medical value gain.

5. The collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints according to claim 4, characterized in that, The iterative search of the MILP scheduling optimization model based on the improved branch and bound algorithm, using relaxed linear programming to determine the upper and lower bounds of the solution, also includes linear relaxation and upper bound estimation for nodes. Perform linear relaxation and use the simplex method to calculate the local upper bound of the node. Then, pruning criteria are applied; if... If the optimal potential of the current node is less than that of a known feasible solution, then the node and all its child nodes are directly pruned. Furthermore, a logical pruning mechanism is introduced for rehabilitation scenarios to remove invalid branches before solving the problem. During the solution process, a logical conflict detection operator is defined. For the oxygenation block constraint, a logical pruning decision formula is constructed: ， in, For indicator functions, Represents a node The current domain of the variable, if If the current local solution space conflicts with the consistency semantics of the oxygenated connected component, then according to the principle of logical implication, none of the sub-topological spaces of this node contain feasible solutions, and forced pruning is immediately performed; at any decision node in the branch-bound search tree... The department, through evaluation of the shared resource group The lower bound of resource consumption is used to predict the feasibility of the current search subspace and construct a resource conflict detection operator. The mathematical form of is defined as follows: ， in, For indicator functions, Representing decision variables At the node The lower bound of the value at that point.

6. The collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints according to claim 5, characterized in that, If no feasible solution is found under the preset constraints, a conflict resolution mechanism is triggered. This includes transforming the original MILP model into a Lagrange relaxation form when the search space is closed and no solution is found, searching for a suboptimal feasible solution, and introducing elastic variables. Rewrite the objective function: ， in, This refers to the set of core conflict constraints identified by the irreducible inconsistency subsystem IIS detection algorithm. To determine the penalty order for the corresponding constraints, the system performs a minimum violation calculation on the soft constraints to achieve smooth load shedding and self-healing scheduling schemes under resource limit conflict scenarios. The system iterates repeatedly until the search tree is empty or a preset time limit is reached. During the iteration process, if the scheduling decision objective function value of a new candidate scheduling solution is better than that of the current optimal solution, then the new candidate scheduling solution is updated as the current optimal scheduling variable solution. Otherwise, relaxed linear programming is used to determine the upper and lower bounds of the solution, and inferior branches are pruned to avoid invalid searches.

7. A collaborative scheduling system for rehabilitation resources considering multidimensional spatiotemporal constraints, executing the collaborative scheduling method for rehabilitation resources considering multidimensional spatiotemporal constraints as described in claim 1, characterized in that, include: The data acquisition module is configured to acquire rehabilitation scheduling request data and, based on the request data, acquire related clinical diagnosis and treatment data and resource configuration data. The preprocessing module is configured to perform data cleaning and preprocessing based on the acquired data; The decision module is configured to construct a scheduling optimization mechanism based on preprocessed data, and to construct a scheduling decision objective function based on the scheduling optimization mechanism. The computation module is configured to generate scheduling variable solutions to the scheduling decision objective function using improved branch and bound. The generation module is configured to generate a rehabilitation schedule plan based on scheduling variables.

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