A data-driven modeling and analysis method for heterogeneous elderly care service demand

Abstract

This invention discloses a data-driven modeling and analysis method for heterogeneous elderly care service demand, including: collecting and extracting individual big data such as the elderly's living abilities, health status, and sociodemographic characteristics; modeling individualized prediction models for different levels of elderly care service usage, and quantitatively analyzing the utilization rate of elderly care services; establishing an elderly care service demand identification system based on identification variables such as the elderly's living abilities and rehabilitation care levels, and quantitatively analyzing individual differences in daily elderly care service demand; based on the fine-grained demand prediction model, combining computer simulation technology to achieve high-fidelity service demand uncertainty analysis and modeling; and constructing a stochastic optimization model based on the elderly care service demand analysis to achieve optimal bed allocation and optimal work scheduling decision optimization, ensuring the quality of elderly care services and reducing costs. This invention improves prediction accuracy and decision credibility, enhances the effectiveness of elderly care service resource allocation strategies, and has high flexibility and strong scalability.

Description

Technical Field

[0001] This invention patent relates to the field of health and elderly care and the direction of data modeling and analysis, specifically to a data-driven method for modeling and analyzing heterogeneous elderly care service needs. Background Technology

[0002] In recent years, China's elderly population has increased rapidly, exacerbating the burden on the healthcare system. With population aging, the probability of disability, incapacitation, and chronic diseases among the elderly has significantly increased, leading to a sharp rise in demand for elderly care. Different levels of elderly care services, including institutional, community-based, and home-based services, can provide seniors with varying levels of professional, 24 / 7 personal medical care, rehabilitation services, and daily living assistance. Developing a low-cost, high-efficiency solution to address the allocation of elderly care service resources is of great significance, as it can meet the diverse medical and nursing needs of the elderly, ensure the quality of elderly care, and improve economic efficiency.

[0003] The diverse and complex needs for elderly medical services and care exhibit significant heterogeneity, posing a substantial challenge to the rational and efficient allocation of elderly care service resources. These diverse and heterogeneous needs manifest in three main ways: First, different elderly individuals possess different individual characteristics, including varying sociodemographic features, clinical diagnoses and chronic diseases, and different levels of disability. Second, these individual characteristics lead to differences in the utilization rate of elderly care services; for example, different elderly individuals show variations in the duration of use for different levels of elderly care services, such as institutional, community, and home-based care. Third, the varying health conditions of individual elderly individuals also prompt different levels of elderly care service providers, including physicians, professional nurses, and caregivers, to tailor their work hours and service categories to each individual.

[0004] Current methods for allocating elderly care service resources and implementing strategies primarily rely on expert experience and subjective decision-making. They fail to truly utilize and leverage the individual characteristics and health big data of the elderly, resulting in a lack of rational and efficient resource allocation strategies and consequently, low-quality elderly care services and high costs. Furthermore, some data-driven decision-making methods for elderly care services use the number of people as the basis for demand, ignoring individual differences and failing to accurately analyze the heterogeneous and complex needs for elderly care services, leading to inefficient supply strategies. Most existing methods primarily analyze the level or category of elderly care service needs, failing to achieve fine-grained, individualized demand quantification analysis, lacking effective decision-making basis, and thus unable to achieve efficient individualized elderly care service allocation.

[0005] To address the challenges and problems of existing methods, we propose a data-driven method for modeling and analyzing the demand for heterogeneous elderly care services. This method enables fine-grained and accurate prediction of the complex and heterogeneous demand for elderly care services and efficient allocation of elderly care service resources based on demand analysis. Summary of the Invention

[0006] This invention proposes a data-driven method for modeling and analyzing the heterogeneous service demands of the elderly, aiming to accurately analyze their diverse and complex service needs, thereby determining the appropriate amount of resources and allocating them rationally. This method framework combines advanced statistical modeling and predictive analysis, computer simulation, and demand analysis-based stochastic optimization methods.

[0007] The allocation of elderly care service resources is crucial for ensuring sufficient service supply resources (such as beds and labor), guaranteeing the quality of elderly care services, and reducing costs. However, due to the complex and heterogeneous characteristics of the elderly's individual needs for elderly care services, achieving optimal allocation of elderly care service resources faces significant challenges. This invention provides a data-driven method for modeling and analyzing heterogeneous elderly care service needs to address the problem of optimal allocation of elderly care service resources under complex, changing, and uncertain demand conditions. The method includes: collecting and extracting individual big data on the elderly's living abilities, health status, and sociodemographic characteristics; building individualized prediction models for different levels of elderly care service usage based on the elderly's individual characteristics, and quantitatively analyzing the utilization rate of elderly care services; establishing an elderly care service demand identification system based on identification variables such as the elderly's living abilities and rehabilitation care levels, and quantitatively analyzing individual differences in daily elderly care service needs; achieving high-fidelity service demand uncertainty analysis and modeling based on the fine-grained demand prediction model and computer simulation technology; and constructing a stochastic optimization model based on the elderly care service demand analysis to achieve optimal bed allocation and optimal work scheduling decision optimization, ensuring the quality of elderly care services and reducing costs. This invention enables fine-grained modeling and analysis of elderly care service demand and automated optimization of service resource allocation decisions, improving prediction accuracy and decision credibility, enhancing the effectiveness of elderly care service resource allocation strategies, and possessing high flexibility and strong scalability.

[0008] A data-driven modeling and analysis method for heterogeneous elderly care service demand includes the following steps:

[0009] 1) Obtain personal characteristic data of the elderly;

[0010] In step 1), the elderly person's personal characteristics data include:

[0011] Sociodemographic characteristics, including age, sex, and economic status;

[0012] Medical conditions, including acute and chronic conditions;

[0013] Assessment of Activities of Daily Living Score (ADS), including physical function and cognition;

[0014] Personal physiological data, including body surface temperature, heart rate, blood pressure, and sleep quality data.

[0015] 2) Input the personal characteristic data of the elderly in step 1), establish a prediction model for the number of days of elderly care services used, and obtain the influence of the factors on the number of days of elderly care services used after model parameter estimation and training, and obtain the prediction model for the number of days of elderly care services used after estimation and training.

[0016] Step 2) involves establishing a predictive model for the number of days the elderly will use elderly care services, specifically including:

[0017] Step 2.1): Design a model formula, including N elderly people and M types of discontinuation of elderly care services, using... Representing the elderly and arrangements for discontinuing elderly care services Service usage days i = 1...N, = 1...M, Given any given variable, the proposed prediction model formula is as follows:

[0018]

[0019] in ; Refers to the elderly Under specific deactivation arrangements The risk of ceasing the use of elderly care services It is a suspension arrangement The baseline risk of the elderly population ceasing to use elderly care services. =1...M; and These represent arrangements for discontinuing elderly care services. Relevant covariate coefficients and individual characteristics of the elderly; This indicates the lower limit of the number of days that elderly care services can be used under all suspension arrangements. Indicates time interval, Represents conditional probability. , It is an exponential function, and the superscript T indicates the transpose operator.

[0020] In step 2), the influence of the number of days of elderly care service use is obtained through model parameter estimation and training, specifically including:

[0021] Step 2.2): Introducing augmenting variables , i = 1...N, = 1...M to indicate the arrangements after the elderly stop using elderly care services, if the elderly The arrangements after the service is suspended are as follows ,but ,otherwise Provide augmented data ,in Representing the elderly Number of days of use of elderly care services For the above augmented variables, For the elderly Personal characteristics, and a set of unknown parameters , among which ∪ m Indicates a specific deactivation arrangement The union operation of all corresponding unknown parameters, They are mutually exclusive, and ,in It is a suspension arrangement The baseline risk of the elderly population ceasing to use elderly care services. Indicates suspension of elderly care service arrangements The relevant covariate coefficients, further decoupled from the likelihood function, are shown in formula (2):

[0022] in This represents a series of multiplication operations. Indicates discontinuation arrangements The baseline risk of the elderly population ceasing to use elderly care services. It is an exponential function. For summation, Indicates the integral symbol, For integration variables, This is a service suspension arrangement. The corresponding likelihood function, All decommissioning arrangements are as follows A collection of elderly people's ID numbers.

[0023] Step 2.3): Employ a semi-parametric estimation method: First, use partial likelihood maximization to estimate... , ,in This represents the state that maximizes the objective function. Take the value, and then use the Efron Morris estimator to estimate. ,pass Quantitative analysis revealed the magnitude of the influence factor on the number of days of elderly care service use.

[0024] Step 3): Service supply time clustering analysis and generation of service demand identification tree;

[0025] Step 3.1), service supply time cluster analysis, specifically includes:

[0026] The average direct and indirect service delivery times were quantified, and a hierarchical clustering method was used for cluster analysis. Jensen-Shannon divergence was used as a similarity measure. The number of clusters for the target service delivery time was determined by the minimum cluster size, which ensured that the maximum Jensen-Shannon divergence within each cluster did not exceed the tolerance. conditions;

[0027] Step 3.2): Generate a service requirement identification tree:

[0028] Using personal characteristics from elderly individuals' personal characteristic data as identification variables, we mine and learn the association rules between the identification variables and service supply time clusters to construct a service demand identification tree.

[0029] Step 4): Based on the individual characteristics of the admitted elderly, prediction and random sampling are performed. Using the elderly's elderly care service usage days prediction model trained in Step 2), the number of days of elderly care services used is predicted. At the same time, using the service demand identification tree obtained in Step 3), the supply time clusters corresponding to the elderly's service demand are predicted based on the identification variables related to the elderly's characteristics. Based on this, computer simulation methods are used to quantitatively analyze the uncertainty of elderly care service demand in the real world and obtain the supply time (minutes) corresponding to the demand for elderly care services. ,in For the elderly Indicator variables for the service provision time cluster to which they belong. Indicates a sub-exponential distribution. Here is the rate parameter, where and These represent direct and indirect services, respectively. Cluster The corresponding average time for direct / indirect service supply can be used to obtain the total daily demand for elderly care services. ,in t represents the total number of elderly people using elderly care services each day. The elderly care service demand simulator will randomly sample the daily elderly care service demand for each elderly person using elderly care services until they stop using the services.

[0030] Step 5: Allocation of elderly care service resources based on demand analysis;

[0031] In step 5.1), the bed capacity allocation adopts a stochastic optimization model with chance constraints, expressed as:

[0032]

[0033] in This represents the variable value that minimizes the objective function. Represents the probability value. Indicates bed capacity. This is the minimum number of beds required. Represents the set of positive integers. Given bed capacity And the average service quality level over the allocated time period T, It is a standard for the quality of elderly care services. It is a threshold. Combined with computer simulation, the optimal capacity is iteratively searched to check whether the quality requirements of elderly care services are met, until a suitable bed capacity that meets the conditions is found.

[0034] In step 5.2), the work scheduling of service providers is solved using a two-stage stochastic optimization model, and the loss function can be defined as:

[0035] (4)

[0036] in =[ [This indicates the demand for elderly care services during the allocation period.] Denotes the job scheduling decision variables, where Scheduling mode The number of staff to be recruited. This indicates the cost of hiring personnel. Labor costs under , Indicates that it is given at will. This represents the total number of all work scheduling modes. and These represent the penalties for shortages and surpluses of elderly care service providers, respectively. (Operator) and They can be represented as and ,in Refers to the quantity value to be determined. and These represent finding the minimum and maximum values, respectively. This indicates that the first sample obtained using the high-fidelity random sampling method described in step 4) is... The demand for elderly care services , Assign a cycle to the work scheduling. Indicates the first The workload of providing services per day can be further expressed as ,in This refers to the daily service workload of each staff member. The work scheduling pattern matrix is ​​generated based on work constraints and personal preferences, constructing a feasible solution region if the work scheduling pattern... Including working days ,but ;otherwise The goal of achieving optimal job scheduling is to use an optimization solution method, that is, to minimize the total cost represented by the above loss function.

[0037] The method includes the following steps:

[0038] Step 1: Develop an individual characteristic data acquisition system for the elderly to easily and quickly acquire individual big data such as the elderly's sociodemographic characteristics, living abilities, physical condition and disease information.

[0039] Step 2: Establish a predictive model for the length of time the elderly use institutional, community, and home-based elderly care services. This involves modeling the length of stay for the elderly in different levels of elderly care facilities and quantitatively analyzing the utilization rate of heterogeneous elderly care services.

[0040] Step 3: Establish a system for identifying the demand for elderly care services, predict and analyze the supply working hours corresponding to the daily demand for elderly care services, and quantitatively analyze the individual differences in daily demand for elderly care services.

[0041] Step 4: Combine computer simulation technology to develop a demand simulator for elderly care services, quantitatively analyze the uncertainty of demand for elderly care services in the real world, and thus achieve high-fidelity service demand analysis and modeling;

[0042] Step 5: Develop a resource allocation method for elderly care services based on demand analysis, establish a stochastic optimization model, and optimize the decision on optimal capacity and optimal labor force to achieve an efficient and optimized supply strategy for elderly care services.

[0043] Specifically, the elderly individual characteristic data acquisition system mentioned in step 1 refers to: acquiring information such as occupancy status, nursing resource usage, and treatment records for elderly people in institutional and community-based elderly care facilities; and acquiring, storing, and managing individual characteristic data such as individual sociodemographic characteristics, daily living and cognitive abilities and physical functions, health status, and disease diagnosis and treatment records for elderly people in elderly care service facilities of different levels.

[0044] Furthermore, the duration of use of different levels of elderly care services described in step 2 is an important indicator for measuring the utilization of elderly care services. There is significant individual variation in the duration (number of days) of stay at various elderly care service locations. In addition, elderly people may be placed in different and competing elderly care and medical service providers due to differences in their physical conditions. For example, elderly people in nursing homes may return to home or community-based elderly care facilities for rehabilitation, or be transferred to more specialized acute care facilities such as hospitals due to accidents such as falls or infections. To fully consider multiple competing elderly care and medical service arrangements and improve the accuracy of service usage duration prediction, we established a semi-parametric competition risk prediction model and developed a parameter estimation method. This model can effectively utilize the individual characteristic data of the elderly collected based on the system described in step 1 to more accurately analyze, mine, and predict individualized elderly care service usage. Furthermore, the developed model achieves high model interpretability by identifying the influencing factors of specific elderly care service arrangements and quantifying their impact on elderly care service usage.

[0045] Furthermore, the service demand identification system described in step 3 can perform fine-grained analysis of elderly care service demands. Through the individual diversity of elderly care service usage time analyzed in step 2, we further explore the individual diversity of daily service demands during the elderly's stay. In the integrated medical and elderly care model, elderly care and medical services include various types such as professional nursing services, caregiving, and basic living services. The daily service demands of the elderly can be quantified as the service provision time (minutes / day) corresponding to various types of elderly care services tailored to their individual needs. Due to various acute and chronic diseases, physical and cognitive limitations, different types of rehabilitation and recovery, various treatments received, and daily living conditions of the elderly, the service provision time corresponding to their needs exhibits high individual variation. Combining domain knowledge, we utilize the elderly's daily living and activity ability assessment scores and care intensity (such as rehabilitation and convalescence levels) as identification variables to establish a daily elderly care service demand identification system, including the following steps:

[0046] ① Service supply time clustering: In order to uncover potential similar patterns in the working hours of service supply personnel, we combine domain knowledge to quantify service supply time and then conduct cluster analysis to identify the supply workload clusters corresponding to the demand for elderly care services.

[0047] ② Service demand identification: In order to establish an automated analysis mechanism for the diversity of service needs among different elderly people, we used the Apriori method to mine the association rules between identification variables and service supply time clusters, and generated an identification tree, so as to predict the daily elderly care service needs based on the individual identification variables of the elderly.

[0048] Furthermore, the elderly care service demand simulator mentioned in step 4 specifically refers to: combining the prediction model and system described in steps 2 and 3, using computer simulation methods to randomly sample the supply time corresponding to the daily service demand of the elderly during the use of different levels of elderly care services, and quantitatively analyze the uncertainty of elderly care service demand.

[0049] Furthermore, the demand-based elderly care service resource allocation method described in step 5 specifically refers to: to meet the heterogeneous and complex elderly care service needs of seniors while ensuring service quality and reducing costs, we further established a stochastic optimization model to determine the optimal resource allocation decision at different time scales, including the capacity of institutional and community-based elderly care beds, the number of professional nursing staff, caregivers, and nannies to be hired, as well as daily work scheduling and daily staffing levels. The specific steps for allocating elderly care service resources include:

[0050] ① Bed capacity allocation: The goal of capacity allocation decisions is to determine an appropriate number of beds to ensure service quality. We established a chance-constrained stochastic optimization model, combined with computer simulation methods and a heuristic search method, to determine the minimum bed capacity levels for institutional and community-based elderly care service providers.

[0051] ② Work Scheduling of Service Providers: Given a fixed bed capacity, we establish a two-stage stochastic optimization model with simple compensation. By assigning appropriate work schedules to elderly care service providers, we minimize the sum of fixed costs and daily penalties for service shortages or surpluses. We simultaneously consider work scheduling constraints in accordance with labor regulations and the personal preferences of elderly care service providers, constructing a feasible solution region. Based on this, we sample using the elderly care service demand simulator described in step 4 and solve the problem using a sample average approximation method.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] 1) High prediction accuracy and fine granularity: This invention refines the analytical granularity of elderly care service demand, improves the prediction accuracy of heterogeneous elderly care service demand, and achieves high-fidelity analysis and modeling of the elderly care service needs of different elderly people.

[0054] 2) High credibility and efficiency of decision-making: This invention provides effective support for decision optimization, can reasonably optimize the allocation strategy of elderly care service resources, improve the credibility of decision-making, enhance the efficiency of decision-making, ensure the quality of elderly care services, reduce costs, and alleviate the burden on the elderly care and medical service systems.

[0055] 3) High degree of automation and flexibility: The present invention has high automation efficiency and can automatically perform analysis and decision optimization based on elderly data with different characteristics. It has high flexibility and can adaptively adjust the allocation strategy of elderly care service resources as the characteristics of elderly data change and the composition of the elderly population changes.

[0056] 4) Strong versatility and scalability: The data-driven service requirement modeling method and data analysis-based decision optimization method proposed in this invention have good versatility and scalability. They can be directly applied or customized accordingly, and can realize requirement analysis and decision optimization on other different service systems. Attached Figure Description

[0057] Figure 1 This invention presents a framework diagram for the heterogeneous elderly care service demand modeling and analysis method.

[0058] Figure 2 This diagram illustrates the elderly care service demand identification system in step 3 of the present invention.

[0059] Figure 3 This diagram shows the flowchart of the elderly care service demand simulation method in step 4 of the present invention.

[0060] Figure 4 The diagram shows the results verification of the heterogeneous elderly care service demand modeling and analysis method proposed in this invention.

[0061] Figure 5 This diagram illustrates the optimal bed capacity allocation method in step 5 of the present invention.

[0062] Figure 6 This diagram illustrates the work scheduling mode generation method in step 5 of the present invention.

[0063] Figure 7 This diagram illustrates the optimal labor allocation method for service providers in step 5 of the present invention. Detailed Implementation

[0064] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and implementation examples.

[0065] This invention proposes a data-driven method for modeling and analyzing heterogeneous elderly care service demands, such as... Figure 1 As shown, individual characteristic data of the elderly in different levels of elderly care services are obtained, and fine-grained service demand modeling and analysis are carried out to predict and simulate the demand for elderly care services. Based on data analysis, a decision optimization model is established to achieve the optimal allocation of elderly care service resources.

[0066] This implementation example uses the allocation of institutional elderly care service resources as an example, and includes the following steps:

[0067] Step 1: Obtain personal characteristic data of the elderly in the nursing home. Staff will conduct medical examinations on the elderly during their stay according to the data acquisition schedule, and record their basic personal information and health data. The obtained personal characteristic data includes detailed admission and discharge records, as well as rich health assessment information, including sociodemographic characteristics, clinical diagnosis, acute and chronic diseases (such as cancer, hypertension, anemia, diabetes, etc.), assessment of daily living functions (such as physical function and cognition), required level of rehabilitation care and treatment, and personal physiological data (such as body surface temperature, heart rate, blood pressure, sleep quality data, etc.).

[0068] Step 2: Establish a predictive model for the number of days elderly people use elderly care services in nursing homes. Its implementation includes the following sub-steps:

[0069] Step 2.1: Design the model formula. Considering the diverse population in elderly care institutions, including N elderly people and M discharge arrangements, we use... Representing the elderly and discharge arrangements Service usage days i = 1...N, = 1...M, Given any given variable, the proposed prediction model formula is as follows:

[0070]

[0071] in ; Refers to the elderly Under specific deactivation arrangements The risk of ceasing the use of elderly care services It is a suspension arrangement The baseline risk of the elderly population ceasing to use elderly care services. =1...M; and These represent arrangements for discontinuing elderly care services. Relevant covariate coefficients and individual characteristics of the elderly (such as demographics, clinical diagnosis, daily living abilities, etc.); This indicates the lower limit of the number of days that elderly care services can be used under all suspension arrangements. Indicates time interval, Represents conditional probability. This represents the limit value as the time interval approaches 0. It is an exponential function, and the superscript T indicates the transpose. Based on the above formula (1), we can further estimate the model parameters and quantify the impact of individual influencing factors on the use of elderly care services.

[0072] Step 2.2: Model Estimation. Due to the multiple discharge arrangements, the original likelihood function has a complex structure, making model parameter estimation challenging. To address this estimation problem, we introduce augmented variables. , i = 1...N, =1...M to represent the discharge arrangement type and further decouple the likelihood function. If the elderly... Discharge arrangements are ,but ,otherwise Provide augmented data. ,in Representing the elderly Number of days spent in a nursing home For the above augmented variables, For the elderly Personal characteristics, and a set of unknown parameters , among which ∪ m Indicates a specific deactivation arrangement The union operation of all corresponding unknown parameters, They are mutually exclusive, and ,in It is a suspension arrangement The baseline risk of the elderly population ceasing to use elderly care services. Indicates discharge arrangements The relevant covariate coefficients. The original likelihood function can be decomposed into several specific likelihood functions, as shown below:

[0073] in This represents a series of multiplication operations. Indicates discharge arrangements Baseline risk for elderly patients discharged from hospitals It is an exponential function. For summation, Indicates the integral symbol, For integration variables, Discharge arrangements The corresponding likelihood function, All discharge arrangements are as follows The set of elderly individuals' ID numbers. Furthermore, to address the parameter estimation problem, we employ a semi-parametric estimation method. We first use partial likelihood maximization to estimate... ,For example, ,in This represents the state that maximizes the objective function. Take the value, and then use the Efron Morris estimator to estimate. .

[0074] Step 3: Establish a system for identifying the needs of elderly care services, such as... Figure 2 As shown, by combining domain knowledge mining to identify similar patterns in the supply time corresponding to the demand for elderly care services, and utilizing identification variables composed of individual characteristics of the elderly and the level of care, the daily elderly care service demand can be identified. Its specific implementation includes the following sub-steps:

[0075] Step 3.1: Service Supply Time Clustering. To uncover potential similarity patterns in the service supply time corresponding to the demand for elderly care services, we conduct cluster analysis based on domain knowledge. Specifically, we consider the direct service supply time in elderly care institutions, i.e., the time corresponding to the daily services (such as feeding, helping with dressing, and administering medication) directly provided to the elderly by professional caregivers, caregivers, and nannies, as well as the indirect service supply time, including the time corresponding to activities such as storing medications, implementing management, attending training courses, resting, and eating. We quantify the average direct and indirect service supply time using domain knowledge, conduct cluster analysis using a hierarchical clustering method, and use Jensen-Shannon divergence as a similarity measure. The number of target service supply time clusters is obtained by the minimum number of clusters, which satisfies the condition that the maximum Jensen-Shannon divergence within a cluster does not exceed the tolerance. The conditions are as follows. A defined cluster of working hours can effectively reflect similar patterns in service supply time, and different clusters exhibit significant differences in the distribution of service supply time.

[0076] Step 3.2: Service Needs Identification. To establish an automated analysis mechanism for the diversity of service needs among different elderly individuals, we explored the correspondence between individual characteristics and service supply time clusters to generate a service needs identification tree. Specifically, we used the elderly's activities of daily living (ADL) scores and care levels as identification variables, employed the Apriori method to learn the association rules between the identification variables and service supply time clusters, and constructed a service needs identification tree based on this. When an elderly person's ADL score is higher, indicating a more severe disability and a greater need for daily living assistance and care, the service supply time clusters identified by the identification tree reflect a greater demand for caregiver services for daily living needs. Overall, the created service needs identification tree can automatically predict daily elderly care service needs based on individual elderly identification variables and ensure the accuracy of modeling diverse service needs.

[0077] Step 4: Develop a demand simulator for elderly care services, using computer simulation methods to quantitatively analyze the uncertainty of real-world demand for elderly care services. The simulation method for elderly care service demand is as follows: Figure 3As shown, we simulate the arrival and admission of elderly people to elderly care institutions. For each newly admitted elderly person, we use an elderly care service usage days prediction model to predict and randomly sample based on the individual characteristics of the admitted elderly person to determine the service usage duration (days). At the same time, we use an elderly care service demand identification system to predict the supply time cluster corresponding to the elderly person's service demand based on the identification variables related to the characteristics of the admitted elderly person. We use indicator variables to represent the elderly. The cluster of elderly care service needs was identified as ,Right now Based on the service demand clusters, the average daily working hours for direct and indirect services can be obtained, respectively using... and To ensure simplicity and practicality in modeling, we consider a single-parameter exponential distribution to simulate the daily direct and indirect service times of service providers, further assuming they are independent. We use a sub-exponential distribution to simulate the total service provisioning time, with a rate parameter of... ,in and These represent direct service and indirect service, respectively. Indicating clusters of demand for elderly care services The corresponding average time for direct / indirect service provision. Each day during the simulation sampling process, we determine the elderly... Whether they remain in the elderly care facility or not, if they have reached the end of their service period, they will be discharged; otherwise, we will randomly sample the elderly. Supply time (minutes) corresponding to demand for elderly care services ,Right now ,in Indicates a given condition. This indicates that it follows a probability distribution. This represents a sub-exponential distribution. We use the number of elderly people in the nursing home on each day t as the basis. The daily working hours for elderly care services provided by the entire elderly care institution Calculate the total service requirements, i.e. .

[0078] Based on the developed modeling and analysis method for elderly care service demand, we further evaluated its predictive performance, such as... Figure 4 As shown, by comparing the survival curves between the predicted and actual values ​​of the elderly care service usage duration model, we found that the survival curves of the predicted and observed service usage durations are very close. The results indicate that the accuracy of the elderly care service usage duration prediction model meets the requirements. Furthermore, we combined simulation methods to further verify the performance of the method. We compared the number of people in randomly sampled elderly care institutions with the actual number of people; the simulation results and the actual data have a similar distribution, as shown in the figure. Figure 4 As shown in the figure, we used the Kolmogorov-Smirnov test to compare the statistical differences between the simulation and the real data, and obtained a p-value of 0.52, indicating that there is no significant statistical difference between the two. The results verify the effectiveness of the elderly care service demand modeling and analysis method proposed in this invention.

[0079] Step 5: Develop a method for allocating elderly care service resources based on demand analysis. Its implementation includes the following sub-steps:

[0080] Step 5.1: Bed Capacity Allocation. We use the daily elderly occupancy rate (e.g., 85% or higher) as a measure of service quality. The optimal bed capacity allocation problem can be represented by a stochastic optimization model with chance constraints, modeled as follows:

[0081]

[0082] in This represents the variable value that minimizes the objective function. Represents the probability value. Indicates bed capacity. This is the minimum number of beds required. Represents the set of positive integers. Given bed capacity And the average service quality level over the allocated time period T, It is a standard for the quality of elderly care services. This is a threshold. To account for the uncertainty of elderly residents moving between elderly care facilities, we combine simulation methods with a heuristic search method. The optimal bed allocation method is as follows: Figure 5 As shown. In each iteration, we combine computer simulation to obtain the average service quality level for each sampled scenario. We check whether the existing decision meets the performance requirements, i.e., the probability of meeting the service quality standard in a given number of beds exceeds a certain quantile threshold. If the stopping condition is not met, we update the existing solution and perform the check again using stochastic simulation. The iterative search process continues until we determine a suitable bed capacity that can meet the service standard.

[0083] Step 5.2: Work Scheduling of Service Providers. Given the optimal bed capacity, we establish a two-stage stochastic optimization model with simple compensation to allocate and schedule the work of service providers. We construct a feasible solution region by combining work scheduling constraints imposed by labor regulations with the personal preferences of elderly care service providers, such as... Figure 6 As shown. The generated scheduling pattern is presented in matrix form. Let P be the number of work scheduling modes and T be the work scheduling allocation period. If the scheduling mode... Including working days ,but ;otherwise The total cost of labor allocation and work scheduling for elderly care service providers includes fixed employment costs, penalty costs for scheduling temporary caregivers to compensate for insufficient elderly care service supply, and penalty costs for service oversupply. We use and These represent penalties for shortages and surpluses of elderly care service personnel, respectively. We use... Denotes the job scheduling decision variables, where Scheduling mode Need to recruit quantity, This indicates the cost of hiring personnel. Labor costs under The loss function can be defined as:

[0084] (4)

[0085] in =[ [] Represents the demand for elderly care services within the allocation period. Operators and They can be represented as and ,in Refers to the quantity value to be determined. and These represent finding the minimum and maximum values, respectively. Represented as the first The demand for elderly care services in the day Random sampling is performed using the elderly care service demand simulator described in step 4. Indicates the first The daily service supply workload (in minutes) can be expressed as: ,in This refers to the daily service delivery workload (in minutes) for each staff member. The goal of elderly care service delivery work scheduling is to allocate appropriate work plans to elderly care service delivery personnel, minimizing the sum of fixed costs and penalties for daily service shortages or surpluses, such as... Figure 7 As shown. Due to the uncertainty of service demand, we use a sample averaging approximation method for solution.

Claims

1. A data-driven modeling analysis method for heterogeneous long-term care service demand, characterized in that, The method comprises the following steps: Step 1): obtaining the personal characteristic data of the old people; Step 2): inputting the personal characteristic data of the old people in step 1), establishing a service use day prediction model of the old people, and obtaining the influence factors of the service use day through model parameter estimation training, thereby obtaining the service use day prediction model of the old people after estimation and training; The service use day prediction model of the old people comprises the following steps: Step 2.1): Designing the model formula, containing N number of elderly and M number of deactivation of elderly service arrangements, to express the service usage days of the elderly and the deactivation of elderly service arrangements i = 1...N, = 1...M, The proposed prediction model formula is expressed as follows for any given one​​ ; in ; Refers to the elderly Under specific deactivation arrangements The risk of ceasing the use of elderly care services It is a suspension arrangement The baseline risk of the elderly population ceasing to use elderly care services. = 1...M; and These represent arrangements for discontinuing elderly care services. Relevant covariate coefficients and individual characteristics of the elderly; This indicates the lower limit of the number of days that elderly care services can be used under all suspension arrangements. Indicates time interval, Represents conditional probability. This represents the limit value as the time interval approaches 0. It is an exponential function, and the superscript T indicates the transpose operator; Step 3): service supply time clustering analysis and generation of service demand identification tree; Step 4) Predicting and randomly sampling according to the individual characteristics of the old people admitted, predicting the number of days of use of the old-age service of the old people by using the trained old-age service use day prediction model estimated in Step 2), and predicting the supply time cluster corresponding to the service demand of the old people according to the identification variables related to the characteristics of the old people by using the service demand identification tree obtained in Step 3) ; Computer simulation methods are used to quantitatively analyze the uncertainty of elderly care service demand in the real world, and to obtain information about the elderly. Supply time corresponding to demand for elderly care services , can be represented as ,in For the elderly Indicator variables for the service provision time cluster to which they belong. Indicates a sub-exponential distribution. Here is the rate parameter, where and These represent direct and indirect services, respectively. Cluster The corresponding average time for direct / indirect service supply can be used to obtain the total daily demand for elderly care services. ,in It is every day The total number of elderly people using elderly care services will be determined by the elderly care service demand simulator, which will randomly sample the daily elderly care service demand for each elderly person using elderly care services until they stop using elderly care services. Step 5: allocation of service resources based on demand analysis, comprising: Step 5.1): allocation of bed capacity by using a stochastic optimization model with chance constraints; Step 5.2): solving the work allocation of service supply personnel by using a two-stage stochastic optimization model; In step 5.1), the allocation of bed capacity uses a stochastic optimization model with chance constraints, which is expressed as: ; wherein, denotes a variable value that minimizes the objective function, denotes a probability value, denotes a bed capacity, is the minimum number of beds required, denotes a set of positive integers, is a given bed capacity and the average of the quality of service levels for the allocation time period T, is a quality of service standard for elderly care, is a threshold value, in combination with computer simulation, iteratively searching for an optimal capacity, checking whether the quality of service requirement for elderly care is met, until a suitable bed capacity is found that meets the condition; In step 5.2), the service provider work allocation scheduling is solved by a two-stage stochastic optimization model, and the loss function is defined as: (4); wherein, [ ] denotes the demand of elderly care services within the allocation period, denotes the work scheduling decision variable, wherein denotes the scheduling mode denotes the number of staff to be recruited, denotes the cost of hiring staff, denotes the labor cost under the scheduling mode , denotes the total amount of all work scheduling modes, and denote the penalty of shortage and surplus of elderly care service staff, respectively, and the operator and can be represented as and , respectively, wherein denotes the undetermined number value, and denote the minimum and maximum values, respectively, denotes the demand of elderly care services on the th day obtained using the high-fidelity random sampling method, , denotes the work scheduling allocation period, denotes the service supply workload on the th day, which can be further represented as , wherein is the daily service supply workload of each staff, and the matrix denotes the work scheduling mode matrix, which is generated based on work restrictions and personal preferences, and a feasible solution region is constructed, and if the work scheduling mode contains the workday , ; otherwise , an optimization solution method is adopted to achieve the goal of optimal work scheduling, i.e., to minimize the total cost overhead represented by the above loss function.

2. The data-driven based modeling analysis method of heterogeneous long-term care service demand according to claim 1, wherein, In step 1), the personal characteristic data of the old people comprises: Sociological characteristics, including age, gender and economic status; Disease conditions, including acute and chronic disease conditions; Daily life function assessment; Personal physiological data, including body temperature, heart rate, blood pressure and sleep quality data. 3.The data-driven modeling analysis method for heterogeneous long-term care service demand according to claim 1, wherein, In step 2), the influence factors of the service use day are obtained through model parameter estimation training, which comprises the following steps: Step 2.2): Introducing Augmented Variables , i = 1...N, = 1...M to indicate the arrangement after the elderly stop using the service, if the elderly stop using the service , , otherwise ; give the augmented data , where denotes the number of days of service use by the elderly , is the augmented variable described above, is the personal characteristics of the elderly , and a set of unknown parameters , where m denotes the union operation of all unknown parameters corresponding to a specific stop arrangement , are mutually exclusive, and , where is the risk baseline of the elderly group stopping the service under the stop arrangement , denotes the covariate coefficient related to the stop service arrangement , further decoupling the likelihood function as shown in equation (2): ; wherein represents a multiplication operation, represents a deactivation schedule a risk baseline for the lower age group to stop using the pension service, is an exponential function, is a summation symbol, represents an integration symbol, is an integration variable, is a deactivation service schedule a corresponding likelihood function, is all deactivation schedules for a set of old people numbers; Step 2.3): Employ a semi-parametric estimation method: First, use partial likelihood maximization to estimate... , ,in This represents the state that maximizes the objective function. Take the value, and then use the Efron Morris estimator to estimate. and through Quantitative analysis revealed the magnitude of the influence factor on the number of days of elderly care service use.

4. The data-driven based modeling analysis method of heterogeneous long-term care service demand according to claim 1, wherein, In step 3), the service supply time clustering analysis comprises the following steps: Quantify the average direct service and average indirect service supply time, use hierarchical clustering method for clustering analysis, and use Jensen-Shannon divergence as similarity measure, the number of target service supply time clusters is obtained by the minimum cluster number which can meet the condition that the maximum Jensen-Shannon divergence in the cluster does not exceed the tolerance ​ 5. The data-driven based modeling analysis method of heterogeneous long-term care service demand according to claim 1, wherein, In step 3), the service demand identification tree is generated, which comprises the following steps: Using the personal characteristics in the personal characteristic data of the old people as identification variables, the association rules between the identification variables and the service supply time clusters are mined and learned, and a service demand identification tree is constructed.

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