A medical emergency resource scheduling method based on robust optimization

Abstract

The application belongs to the technical field of intelligent health, and particularly relates to a medical emergency resource scheduling method based on robust optimization, which comprises the following steps: obtaining current rescue information, constructing a ground cost matrix according to the rescue information; judging whether rescue resources are needed according to the current rescue information, if rescue resources are needed, establishing an optimal transport model of a resource allocation problem according to the ground cost matrix and optimal transport theory; if it is uncertain whether rescue resources are needed, constructing an uncertainty set based on robust optimization theory, and establishing a robust optimization model of a transport problem based on the uncertainty set; solving the optimal transport model of the resource allocation problem and the robust optimization model of the transport problem respectively to obtain a resource allocation matrix and an optimal decision; and scheduling rescue resources according to the resource allocation matrix and the optimal decision; the application can ensure that emergency demands can be responded quickly and economically under emergency conditions by accurately calculating and optimizing resource allocation, and the success rate of treatment is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of intelligent health technology, and particularly relates to a medical emergency resource scheduling method based on robust optimization. BACKGROUND

[0002] The intelligent management and control of regional linkage of medical emergency resources for batch emergency needs has become a hot topic in the field of intelligent health technology. Here, the batch medical emergency event refers to an event in which more than three people need medical emergency treatment due to a major accident, such as a large-scale traffic accident or a gas explosion causing mass casualties. This type of medical emergency event is different from the individual-oriented routine medical emergency task, the difference including the scale of more than three people; it is different from the medical emergency task for large-scale activities or events, the difference being that the time and place of the accident are unpredictable as a whole and occur in activities that have not been planned in advance; it is also different from the medical emergency task for large-scale disasters (such as earthquakes), the difference being the range of the dispatchable resources for the medical emergency task, which may be directly dispatched by the state level, while the batch medical emergency event referred to herein is usually handled by regional medical centers in a routine manner, and it occurs more frequently than the medical emergency task for large-scale disasters but in a smaller range. However, the existing urban medical emergency centers lack methods and systems for intelligent management and control of batch medical emergency events, although these medical emergency centers have accumulated cases and stored certain data cases in the medical emergency center database. However, these cases have not been fully utilized and their potential knowledge has not been mined to support the regional linkage intelligent management and control for batch medical emergency. Therefore, a systematic solution for the regional linkage intelligent management and control for batch medical emergency is urgently needed. SUMMARY

[0003] To solve the problems in the prior art, the application provides a medical emergency resource scheduling method based on robust optimization, which comprises the following steps: obtaining current rescue information, constructing a ground cost matrix according to the rescue information; determining whether rescue resources are needed according to the current rescue information, if the rescue resources are needed, establishing an optimal transport model of a resource allocation problem according to the ground cost matrix and optimal transport theory; if it is uncertain whether the rescue resources are needed, constructing an uncertainty set based on robust optimization theory, and establishing a robust optimization model of a transport problem based on the uncertainty set; solving the optimal transport model of the resource allocation problem and the robust optimization model of the transport problem respectively to obtain a resource allocation matrix and an optimal decision; and scheduling the rescue resources according to the resource allocation matrix and the optimal decision.

[0004] The application has the following beneficial effects:

[0005] This invention, through precise calculation and optimized resource allocation, ensures a rapid and economical response to emergency needs in critical situations, while simultaneously improving the success rate of treatment. It provides medical decision-makers with scientific data support, enhances the system's adaptability and flexibility, and enables more efficient coordination of medical resources across the entire region. Attached Figure Description

[0006] Figure 1 This is a flowchart illustrating the overall technical framework of the present invention;

[0007] Figure 2 This is a tree structure diagram of the model of the present invention;

[0008] Figure 3 This is a flowchart of the optimal route-based ambulance resource scheduling method of the present invention;

[0009] Figure 4 This is a flowchart of the decision optimization process of the present invention. Detailed Implementation

[0010] 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.

[0011] Example 1

[0012] A robust optimization-based method for scheduling medical emergency resources, such as Figure 3 As shown, the method includes: acquiring current ambulance information and constructing a ground cost matrix based on the ambulance information; determining whether ambulance resources are needed based on the current ambulance information; if ambulance resources are needed, establishing an optimal transmission model for the resource allocation problem based on the ground cost matrix and optimal transmission theory; if it is uncertain whether ambulance resources are needed, constructing an uncertainty set based on robust optimization theory and establishing a robust optimization model for the transportation problem based on the uncertainty set; solving the optimal transmission model for the resource allocation problem and the robust optimization model for the transportation problem respectively to obtain the resource allocation matrix and the optimal decision; and scheduling ambulance resources based on the resource allocation matrix and the optimal decision.

[0013] In this embodiment, after obtaining the rescue information, the data needs to be preprocessed, which specifically includes cleaning and standardizing the collected data to ensure the quality and consistency of the data, and providing an accurate basis for subsequent resource allocation. The rescue information includes the actual distance between medical resource points and emergency demand points, traffic conditions, and resource capacity. According to the actual distance between medical resource points and emergency demand points, traffic conditions, resource capacity and other factors, a ground cost matrix (C) is constructed. This matrix records in detail the allocation cost from each resource point to each demand point, providing a quantitative basis for resource optimization allocation.

[0014] The optimal transport theory, especially the Wasserstein distance and Sinkhorn algorithm, is used to solve the resource allocation problem. After obtaining the transport matrix solved by the OT model, the model will determine which demand points each resource point should allocate resources to and the specific amount of allocation. The model is verified in a simulated environment by comparing the response time and cost under different scheduling strategies to evaluate the performance and accuracy of the model. The OT resource scheduling model is integrated into the regional linkage intelligent management and control system to realize real-time resource allocation. In actual medical emergency events, the system will automatically generate a resource allocation plan according to the model to guide medical personnel to respond quickly.

[0015] Specifically, the Kantorovich optimal transport problem is the most typical OT problem. It seeks an optimal coupling γ that minimizes the displacement cost of discrete measure a to discrete measure b with respect to the ground cost To be a transport plan, γ must be part of the set When the ground cost is a metric, the optimal value of the OT problem is also a metric, called the Wasserstein distance. In this discrete case, the OT problem is defined as:

[0016] W C (a,b)=min γ∈Π(a,b) <γ,C>,

[0017] where 1 n1 is an n2-dimensional vector with all components equal to 1, is the transpose of the optimal coupling matrix, is an n1-dimensional vector with all components equal to 1, and W C is the Wasserstein loss based on the ground cost C.

[0018] The above optimization problem usually includes a regularization term for the transport plan γ, such as entropy regularization or squared L2. For the entropy regularized OT problem, the Sinkhorn-Knopp algorithm (or variants) or stochastic optimization algorithms can be used.

[0019] A set of probability measures {a1, a2,..., aN} is given as follows: N

[0020]

[0021] where a * is such that a value of a, N is the transmission dimension.

[0022] When using entropy regularization, an efficient Bregman projection algorithm is provided in POT, while on the other hand, an LP solver is used to solve the unregularized problem. The computation process includes:

[0023] The Kantorovich optimal transport problem is:

[0024]

[0025] where U is the set of all possible transport plans (also called couplings), C is the cost matrix, γ is the transport plan matrix, C i,j is the cost of transporting a unit mass of material from source i to target j, γ i,j is the quantity of material transported from source i to target j.

[0026] The p-Wasserstein distance is:

[0027]

[0028] The primal and dual problems are:

[0029]

[0030] where c T is the transpose of the cost vector, γ is the vector representation of the transport plan matrix P, A is the constraint matrix that ensures that the rows and columns of the transport plan γ are equal to the source probability measures a and the target probability measures b, respectively, h is the dual variable of the primal optimization problem.

[0031] The entropy regularization is:

[0032]

[0033] where the non-negative matrix γ is the transport plan, its elements γ i,j is the quantity of material transported from source i to target j, U(a,b) denotes the set of transport plans, is the optimal transport distance from a to b, ε is the regularization parameter, H(γ) is the entropy function

[0034] ​The iteration process of Sinkhorn algorithm is as follows:

[0035] Step 1: Initialization: Select a non-negative matrix γ (0) , which can be initialized as an identity matrix.

[0036] Step 2: Iterative update: Alternately update the rows and columns of matrix γ

[0037]

[0038] where e is a vector with all elements being 1, and the superscript T represents the transpose of the matrix.

[0039] Step 3: Iterate until convergence: Repeat step 2 until the rows and columns of γ

[0040] In this embodiment, in the context of vehicle pre-allocation, the sample robust model can be written as a two-stage problem as follows:

[0041]

[0042] where is a vector of intermediate variables representing the worst-case recovery cost under each scenario, and is an ε-neighborhood uncertainty set defined by a general norm ||·|| around each demand sample .

[0043] Note that the multi-policy approximation of the waiting decision y allows each demand sample to have a different affine mapping, resulting in a two-dimensional decision rule (y(d)) s∈[S],j∈[J] .

[0044] Embodiment 2

[0045] The present application is based on an optimal transport distance resource scheduling model, aiming to solve the resource allocation problem in batch medical emergency events. This model calculates the "ground cost" (i.e. the cost of resource allocation) between different medical resource points (such as hospitals, emergency centers, ambulances, etc.) and emergency demand points, to optimize the allocation strategy of resources, and ensure that emergency demand is met in the shortest time and at the lowest cost. As shown in Figure 1 , the specific steps include:

[0046] Step S11: Rescue resources include search and rescue teams, medical emergency vehicles, emergency medical equipment, etc. It is necessary to determine how these resources are optimally allocated to the accident site and how to quickly and effectively transport the injured to the hospital. For this, the POT (Python Optimal Transport) library of Python can be used to calculate the optimal transport distance. By loading the dataset, the coordinates of the locations of various rescue resources and accidents are obtained.

[0047] Step 12: According to the actual distance between medical resource points and emergency demand points, traffic conditions, resource capacity, etc., a ground cost matrix (C) is constructed, where the element C_ij represents the deployment cost from resource point i to demand point j. The ot.dist function is used to calculate the cost matrix, i.e., the transportation cost matrix.

[0048] Step 13: To solve the optimal transport problem, the Earth Mover's Distance (EMD) or Sinkhorn algorithm can be chosen. The goal is to find a transport matrix gamma such that:

[0049]

[0050] s.t.γ1=a

[0051] γ T 1=b

[0052] γ≥0

[0053] where C is the cost matrix, a and b are the source and target distributions, respectively.

[0054] Step S14: When the algorithm takes a long time to calculate, it is regularized to obtain a simpler or faster solution to the problem. The Sinkhorn algorithm achieves this by adding an entropy regularization term, thus solving the following problem.

[0055]

[0056] s.t.γ1=a

[0057] γ T 1=b

[0058] γ≥0

[0059] where reg is a hyperparameter, and Ω is the entropy regularization term, defined as follows:

[0060]

[0061] Step S15: In the actual resource scheduling operation, the Sinkhorn algorithm is first used to calculate the optimal transport matrix. This can be achieved by calling the ot.sinkhorn function in the POT library. The resource source distribution (such as the available resources of a hospital) and the target distribution (such as the emergency demand at the scene of an accident) and the cost matrix (C) are input parameters. The choice of the regularization parameter (reg) will affect the calculation speed of the algorithm and the sparsity of the results. In an emergency, a smaller regularization parameter is chosen to quickly obtain a solution.

[0062] Step S16: After obtaining the optimal transport matrix (gamma), it is used for actual resource scheduling. Each element gamma i,j gamma_ij represents the optimal transport quantity from resource point i to demand point j. Rescue teams can allocate ambulances, medical equipment, and personnel according to this matrix. For example, if the value of gamma_ij is large, resource point i should prioritize allocating resources to demand point j. In actual operations, rescue teams will develop detailed rescue plans based on this matrix and adjust them during execution according to actual conditions.

[0063] Example 3

[0064] The present application is based on a robust vehicle pre-allocation method, aiming to solve the problem of regional joint intelligent control in batch medical emergency. As shown in the figure, this method predicts and optimizes the allocation of vehicles between different emergency demand points to ensure that in emergency situations, it can respond quickly and effectively, while reducing resource waste. The specific steps include: Figure 4

[0065] Step S21: Before the accident occurs, by analyzing historical data and real-time information, a network model containing supply nodes (such as hospitals, emergency centers) and demand nodes (accident scenes) is established. The goal is to achieve optimal pre-allocation of vehicles under uncertain emergency demand, so a reasonable model assumption is extremely important. Assume that there are I supply nodes and J demand nodes in a city area. In the random demand Before implementation, the unit cost c ij x ij vehicles are allocated from supply nodes i∈[I] (where there are a large number of idle vehicles) to demand nodes j∈[J], achieving uncertain demand, and the revenue is calculated as:

[0066]

[0067] ​The parameters of the network model are as follows: the number of supply nodes I = 1; the number of demand nodes J = 10; the income coefficient τ = (4.50, 4.41, 3.61, 4.49, 4.38, 4.58, 4.53, 4.64, 4.58, 4.32); the cost coefficient c j = 3, where j = 1, 2, …, J; the maximum supply of vehicles q i = 400, where i = 1, 2, …, I.

[0068] Step S22: Use a robust optimization method, such as the RSOME framework, to handle the uncertainty of demand. Specifically, the vehicle pre-allocation will be solved by using the robust and sample-robust optimization methods of the RSOMEro framework.

[0069]

[0070] where y represents the expected decision-making of the revenue, which is approximated by a linear decision rule , which means that each affine y j depends on the realization of demand d. Here is a box uncertainty set, where the upper and lower bounds are determined based on historical data.

[0071] Step S23: In the RSOME framework, the expected revenue of the decision-making is approximated by a linear decision rule (ldr), ensuring that each decision depends on the realization of demand. This allows for effective resource allocation under uncertainty.

[0072] Step S24: Construct a robust model that includes a worst-case objective function and robust constraints. This requires that the vehicle allocation decision can meet all demands in the worst case while not exceeding the maximum supply of vehicles.

[0073] Step S25: Solve the robust model using the Gurobi solver to obtain the optimal vehicle pre-allocation decision. In this case, the optimal vehicle pre-allocation decision x = (0, 0, 0, 0, 0, 39.6138, 0, 0, 0, 0) is conservative, and the optimal objective value is -62.59. This method can help rescue teams make more efficient and adaptive decisions in uncertain situations to address the challenges of urban traffic management.

[0074] In addition, the sample-robust model method described in the specification can be used to further optimize the vehicle pre-allocation decision. In this method, historical demand samples are integrated into the decision-making process to better adapt to uncertainty. By defining an ε-neighborhood uncertainty set, the upper and lower bounds of demand can be adjusted to obtain a new vehicle allocation decision.

[0075] In the sample robust model, each demand sample has a corresponding worst-case backtracking cost to ensure efficient vehicle allocation in various scenarios. Assuming a conservative parameter ε = 0.25, the optimal vehicle pre-allocation decision is x = (0.341, 0.358, 0, 4.289, 0, 69.456, 2.452, 4.578, 5.229, 2.486), and the optimal objective value is -103.656. Note that in the special case of ε = 0, the sample robust model is equivalent to the sample mean approximation method. By this method, the rescue team can better utilize historical data and real-time information to make vehicle allocation decisions in a more flexible and efficient manner, thereby improving the efficiency of urban traffic management and response capabilities.

[0076] Step S26: After implementing the rescue plan, adjust the upper and lower bounds of demand based on actual conditions, i.e., the status of demand nodes (J) and supply nodes (I), vehicle maximum supply (q), cost coefficient (c), and income coefficient (r) to define box-type uncertainty sets to obtain new vehicle allocation decisions. In this way, the rescue team can make more efficient and adaptive decisions under uncertain conditions.

[0077] Embodiment 3

[0078] The present application is based on a distributionally robust vehicle pre-allocation method aimed at solving the problem of regional joint intelligent management and control in batch medical emergency events. This method predicts emergency demand and pre-allocates medical vehicles to ensure rapid response and effective management of resources in emergency situations. Specifically, it includes:

[0079] Step S31: Establish the following distributionally robust optimization model:

[0080]

[0081] where, is the vector of all random variables, including random demand quantity and possible auxiliary random variables, whose distribution characteristics are an event uncertainty set The RSOME dro module provides modeling tools specifically for handling such event uncertainty sets and related event assistance adaptability

[0082] Step S32: Use the robust model of the dro framework to convert the vehicle pre-allocation problem into a distributionally robust optimization problem. The uncertainty set is written as:

[0083]

[0084] The random vector is and for each sample s ∈ [S], the weight w s= 1 / S, and the corresponding support (uncertainty set) is defined as An e-neighborhood sample data point around The multiple policy approximation mentioned by Bertsimas et al. shows that each y j The affine depends on the demand realization d, and the affine dependence of each sample record is different, so it can be captured by event adaptation, where and

[0085] Step S33: Create a DRO model through the dro module, define random variables, uncertainty sets, scenario weights, etc. Convert the sample robust model into a distribution robust optimization problem.

[0086] Step S34: Define decision variables in each scenario, which are adapted to random variables through affine to adapt to demand changes in different situations. The model will consider the expected value in the worst case, robust constraints and deterministic constraints during the solving process.

[0087] Step S35: Generate uncertainty sets through decision tree regressors, considering conditional mean and variance to build more accurate scenarios and parameters. The construction of uncertainty sets is to consider the conditional mean μ s and variance φ s , for S scenarios, the expression is:

[0088]

[0089] where, is the uplift support rate of each scenario s, and the vector of all random variables is The vector w represents the scenario weight, which is equivalent to the score of the data point in each scenario.

[0090] Step S36: Use Gurobi solver to solve the distribution robust optimization model to obtain the optimal ambulance scheduling scheme. Gurobi is a high-efficiency solver suitable for handling large-scale optimization problems. Specifically, if λ is within the uncertainty set, input y, the conservatism parameter e, and the historical sample demand information d; according to the sample robust optimization modeling, it includes determining the decision variable, constructing the e-neighborhood uncertainty set, establishing the objective function, and setting the constraint condition; call Gurobi solver, output the optimal deployment decision xij and the minimum resource allocation cost.

[0091] If λ is in the uncertain set and considering the covariates, including: input historical sample demand D and covariate information, call the decision tree regressor to calculate the conditional mean mu and variance phi, scenario weight w, demand upper and lower bounds d ub, d lb; distributed robust optimization modeling, specifically: determine the decision variable, construct the scenario fuzzy set F, establish the objective function, and set the constraint condition; call Gurobi to solve, output the optimal deployment decision x ij and the minimum resource allocation cost.

[0092] Step S37: analyze the solution results and evaluate the effectiveness of the vehicle allocation strategy under different scenarios to ensure that the strategy can achieve the expected effect in actual application. For example Figure 2 The tree structure is shown, taking four leaf nodes as an example, and the minimum sample size of each node is three.

[0093] The specified formula for event affine adaptation is and This means that each appeal decision y j Affine adaptation random variable And in each case, affine adaptation may be different.

[0094] Step S38: adjust the actual operation strategy according to the model output, such as adjusting vehicle allocation, optimizing route selection, etc., to improve response speed and service quality. Adjust the model parameters according to the actual application effect feedback to improve the accuracy and adaptability of the model.

[0095] The above examples further illustrate the purpose, technical solutions and advantages of the present application. It should be understood that the above examples are only preferred embodiments of the present application and do not limit the present application. Any modification, equivalent replacement, improvement, etc. made to the present application within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A robust optimization-based method for scheduling medical emergency resources, characterized in that, include: The current emergency medical information is obtained, and a ground cost matrix is ​​constructed based on the emergency medical information; Based on the current rescue information, determine whether rescue resources are needed. If rescue resources are needed, establish an optimal transport model for the resource allocation problem based on the ground cost matrix and optimal transport theory. If it is uncertain whether rescue resources are needed, construct an uncertainty set based on robust optimization theory, and establish a robust optimization model for the transport problem based on the uncertainty set. Solve the optimal transport model for the resource allocation problem and the robust optimization model for the transport problem respectively to obtain the resource allocation matrix and the optimal decision. Emergency medical resources are allocated based on the resource allocation matrix and optimal decision-making. Based on uncertain sets, robust optimization models for transportation problems are established. Specifically, this includes: achieving optimal vehicle pre-allocation under uncertain emergency needs, and constructing a robust optimization model for box-type uncertain sets; considering the worst case, ensuring that vehicle allocation decisions can meet all needs while not exceeding the maximum supply of vehicles, and constructing a sample robust optimization model for domain uncertain sets; and establishing a distributed robust optimization model and constructing a scenario fuzzy set of covariates. The robust optimization model expression for the box-shaped uncertainty set is: ； Where y represents demand fulfillment, x is the decision variable representation matrix, and d is the demand quantity matrix. Let [I] be the set of box uncertainties, where the upper and lower bounds are determined based on historical data; [I] is the vehicle supply point, [J] is the vehicle demand point, and c ij r is the unit cost of scheduling. j x represents the unit revenue of the demand node. ij y represents the number of vehicles allocated from supply point i to demand point j. j For the fulfillment of requirements that depends on the quantity d, d j For the demand at the j-th demand point, For linear decision rules, q i S represents the maximum number of vehicles available; S represents the number of historical data samples, and [S] represents the set of samples. The expression for the robust optimization model of the domain uncertainty set is: ； in, It is a vector of intermediate variables representing the worst-case recovery cost for each scenario, and It is an ε-neighborhood uncertainty set, consisting of each demand sample The general norm of the surrounding area ||·|| is defined; y sj To await a decision, the two-dimensional decision rule (y(d)) is followed. s∈[S],j∈[J] ; The expression for the distributed robust optimization model is: ； in, for Uncertain set of expected values ​​under a given distribution It is a random scenario variable. It is a vector of all random variables, including the number of random demands. and possible auxiliary random variables Its distribution is characterized by an uncertain set of events. ; For y j The affine adaptation rule, i.e., y j According to the scenario and events Different linear functions were selected for adjustment, among which... For the scene, For the event; Construct a scene fuzzy set considering covariates, its expression is: ； in, It represents the increased support rate for each scenario s, and the vector of all random variables is... μ s and φ s Let w be the conditional mean and variance of scene s. For scene s, vector w s This represents the scenario weight, which is equivalent to the score of the data point in each scenario. For the set of all uncertain distributions, For a J-dimensional space, It has an uncertain distribution.

2. The medical emergency resource scheduling method based on robust optimization according to claim 1, characterized in that, Emergency information includes the actual distance between medical resource points and emergency demand points, traffic conditions, and resource capacity.

3. The medical emergency resource scheduling method based on robust optimization according to claim 1, characterized in that, Establishing an optimal transmission model for the resource allocation problem includes: determining the required amount of rescue resources based on rescue information; if the supply and demand of rescue resources are balanced, then constructing a distance-based discrete optimal transmission model; if the supply exceeds the demand, then constructing a distance-based entropy regularized optimal transmission model.

4. The medical emergency resource scheduling method based on robust optimization according to claim 3, characterized in that, The expression for the distance-based discrete optimal transmission model is: ； The expression for the distance-based entropy regularized optimal transmission model is: ； Where a represents the supply quantity distribution; b represents the demand quantity distribution; C represents the ground cost matrix; and F represents the Frobenius inner product, which is the sum of the corresponding matrix elements after multiplication. This is the optimal transportation matrix, where T is the transpose. For hyperparameters, Let be the entropy regularization term, i be the row of the OT matrix, and j be the column of the OT matrix.

5. A robust optimization-based medical emergency resource scheduling method according to claim 4, characterized in that, Solving the optimal transmission model for the resource allocation problem includes: calculating the optimal solution of the distance-based discrete optimal transmission model and the optimal solution of the distance-based entropy regularized optimal transmission model; Calculating the optimal solution for a distance-based discrete optimal transmission model includes: Step 11: Use the minimum cost method or the potential method to obtain an initial feasible solution; mark each supply point and demand point, set the potential of the supply point to 0, calculate the potential of the demand point according to the minimum cost method, and determine the initial basic variables; Step 12: Calculate the test number for each non-basic variable; the specific process includes calculating the test number for each non-basic variable. Its test number is ,in It is the unit transportation cost from supply point i to demand point j. and These are the potentials of supply point i and demand point j, respectively; Step 13: Select the non-basic variable with the smallest negative test number as the basic variable to be transferred in; starting from the basic variable to be transferred in, perform a closed loop along the transportation network to obtain the basic variables in the loop; calculate the ratio of the transportation volume of each basic variable in the loop to the negative test number of the basic variable to be transferred in, and select the basic variable corresponding to the smallest ratio as the basic variable to be transferred out. Step 14: Adjust the transport volume of the basic variables that were transferred out and those that were transferred in, and update the transport routes and transport volumes in the network; recalculate the geopotential of the supply points and demand points according to the new transport plan; Step 15: Repeat steps 12 to 14 until the optimal solution is found; Step 16: Output the OT matrix based on the optimal solution; Calculating the optimal solution for the distance-based entropy-regularized optimal transmission model includes: Step 21: Parameter input. The input parameters include the cost matrix C, the supply quantity distribution a, the demand quantity distribution b, the regularization hyperparameter reg, and the convergence parameter itermax. Step 22: Initialize the parameters, respectively , ; Step 23: Set the number of iterations, and let i be the current iteration number; Step 24: Update parameters ; ; Step 25: Repeat steps 23 and 24 until the convergence parameter itermax is reached, then stop iterating; Step 26: Output the OT matrix .

6. The medical emergency resource scheduling method based on robust optimization according to claim 1, characterized in that, Uncertain sets include box-type uncertain sets, domain uncertain sets, and scenario uncertain sets.

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