A Preventive Medical Facility Planning Approach Considering Crowding Effects

Abstract

This invention proposes a preventive healthcare facility planning method that considers congestion effects to maximize total social utility. Due to the two-level decision-making structure between system managers and facility users, this invention constructs a two-level nonlinear integer programming model. The upper level is a healthcare facility site selection and service capacity planning problem under budget constraints, while the lower level is a user choice balance problem considering congestion effects. To solve this two-level programming model, this invention employs a genetic algorithm (GA) to solve the upper-level problem and a successive mean average (MSA) method to solve the lower-level problem. Experiments show that this method can be used for preventive healthcare facility planning under budget constraints and can also provide a reference for budget preparation.

Description

Technical fields:

[0001] This invention proposes a method for planning preventive medical facilities that takes into account the congestion effect, belonging to the field of facility planning technology. Background technology:

[0002] Preventive healthcare services are crucial for governments because they can reduce the likelihood and severity of potentially life-threatening diseases through early detection. Preventive healthcare encompasses many services, such as influenza prevention, vaccination, cancer screening, hepatitis screening, and smoking cessation programs. It is well known that prevention is always better than cure. It can save governments significant funds and improve the well-being of society as a whole. However, preventive healthcare services in many countries and regions around the world are currently unsatisfactory.

[0003] This invention focuses on the site selection and related service capacity planning of preventive medical and health service facilities. Unlike traditional facility site selection studies, users do not choose the nearest facility but rather select based on the attractiveness of the medical facility. Therefore, understanding how users make choices is crucial. From the perspective of user behavior choices, previous studies can be divided into two types: (1) system optimal models, i.e., system decision-makers guide users to go where; (2) user choice models, i.e., users can freely choose facilities. Traditional facility site selection studies are usually system optimal models with distance as the main determining factor. However, if the demand for a certain facility is too high, the waiting time will be too long, which can easily lead to facility congestion. Vidyarthi and Kuzgunkaya considered the waiting time in the facility and proposed a system optimization model for the planning of preventive medical and health facilities. Davari et al. not only used the waiting time as a constraint, but also used multi-objective optimization to incorporate demand fairness and fuzzy attractiveness. Recently, Risanger et al. proposed a system optimal model to select pharmacies for COVID-19 testing, where demand is an exponential decay function of distance. In summary, in the system optimal model, each user is assigned to a facility by the system decision-maker. However, in the healthcare services industry, where users are usually free to choose facilities, a user choice model is more appropriate.

[0004] User choice models address the problem of how users choose facilities. They can be further divided into two categories: (1) disequilibrium allocation, which does not consider competition among users; and (2) equilibrium allocation, which considers competition among users. More specifically, there are three types of disequilibrium allocation. The most popular type is all-or-nothing allocation, i.e., winner-take-all allocation, where the time (or distance) for users to reach the facility is considered the primary determinant, and users are assumed to seek services from the nearest medical facility. In addition, the congestion effect of facilities is also considered in the nearest all-or-nothing allocation. For example, Zhang et al. attempted to include waiting time in the total time, while Davari et al. and Dogan et al. used waiting time as a constraint. However, it is unrealistic to assume that all users from the same demand node choose the service from the same facility that is closest to them. In reality, users can have greater flexibility in choosing facilities. The second type is Huff-type allocation, which allocates a portion of the demand to facilities based on the attractiveness of the facility and the user's travel time. The well-known gravity model is a special case of Huff-type allocation. For a given set of parameters, Huff-type allocation degenerates into the gravity model. The third type is the multinomial logit allocation, which can include user characteristics and unobserved attributes in the utility function, but does not consider facility waiting time, treating it only as a constraint, which is unrealistic. In summary, disequilibrium allocations still dominate facility selection because they avoid the complexities of equilibrium problems.

[0005] In contrast, recent studies have begun to employ equilibrium allocation to account for the congestion effect of facilities. Empirical studies have found that waiting time is important to users in service and healthcare settings. However, waiting time is not an exogenous variable like travel time, but rather an endogenous one. More specifically, shorter waiting times attract users, but this in turn prolongs the waiting time for facility services. This means that the equilibrium between waiting time and the number of users must be considered. There are two approaches to equilibrium allocation: (1) deterministic user equilibrium allocation, where waiting time at the facility is an integral part of deterministic utility; and (2) stochastic user equilibrium allocation, where a further stochastic component is included to reflect unobserved utility. It is assumed that users visit facilities with the greatest (stochastic) utility. The game between users will reach a Nash equilibrium, also known as user equilibrium. In equilibrium, each user is satisfied with the facility they visit, meaning that people from the same demand node will obtain the same utility even if they go to different facilities. Recent descriptions of user choice behavior have been further improved. Kucukyazici et al. used latent category analysis to incorporate user preferences into the design of cancer screening facility networks. Krohn et al. further incorporated healthcare quality into the utility function of user choice. It is expected that research will continue to move towards more realistic user choice behaviors. Summary of the Invention:

[0006] Technical problem: The technical problem to be solved by this invention is how to determine the site selection and service capacity planning of preventive medical facilities among candidate sites under limited budget constraints, so as to maximize the overall social utility of the system.

[0007] Technical Solution: This invention aims to propose a preventive healthcare facility planning method considering congestion effects. The problem is formulated as a two-level nonlinear integer programming model. The upper level is a healthcare facility site selection and service capacity planning problem with budget constraints. The lower level is a user choice balance problem, which determines the specific facility allocated to each user. This study uses a genetic algorithm (GA) to solve the upper-level problem and a successive mean averaging (MSA) method to solve the lower-level problem. The technical solution of this invention includes the following steps:

[0008] 1. Problem Description and Mathematical Modeling

[0009] Let G = (NL) be a road network consisting of a set of nodes N and a set of road segments L. Nodes represent urban communities or road intersections, and road segments are major traffic arteries. We assume that the number of users requiring preventive medical services at node i (i∈N) per unit time is h. i The candidate site set for the medical facility is M, and the selected facility planning scheme... The shortest travel time from node i to position j is represented by t. ij The government has a budget control B that allows it to establish one or more service counters at selected facility locations. We assume the service counters are homogeneous, service times follow an exponential distribution, and an average of μ users are served per unit time. We also assume the users are homogeneous, arriving at each facility according to a Poisson distribution, and the queuing rule is first-come, first-served (FCFS). These assumptions are reasonable for facilities without appointments and apply to most routine services. Therefore, each facility here is an M / M / s queuing system, where M represents the arrival or departure of users following a Markov (or Poisson) distribution, or equivalently, an exponential interval or service time distribution, and s represents the number of service counters in the medical facility.

[0010] The goal of this problem is to determine the location and service capacity (i.e., the number of service counters) of each healthcare facility under the constraint of budget B, in order to maximize the total utility of the system. To this end, we define three sets of decision variables:

[0011]

[0012] s j = The number of service points at location j,

[0013] x ij = The number of users from population node i to location j

[0014] Suppose we obtain the scheme S = {j: j∈M, y} j =1}, then we have

[0015]

[0016] Using λ j This represents the user's arrival rate at facility j. It can be obtained

[0017]

[0018] 1.1 Utility Evaluation Function

[0019] Users choose facilities based on their attractiveness. Therefore, understanding how users make these choices is crucial. User choice models are essentially based on a utility function defined by facility attractiveness. Using U... ij This represents the observable utility of a user from demand node i when receiving services at location j. It mainly consists of three parts: (1) u j The inherent attractiveness of location j. This may include intrinsic factors such as parking convenience, facility appearance, and the reputation of the staff. (2)t ij The shortest travel time from origin node i to destination facility j. (3) The estimated waiting time at location j, including queuing time and service time, is the arrival rate λ. j Service Counts j The function. Because it is an M / M / s at node j. j A queuing system, for any s j ≥1 can be obtained using classical queuing theory. It can be represented by a set of equations:

[0020]

[0021]

[0022]

[0023]

[0024] Where L j Let p0 be the expected queue length in terms of the number of users, and ρ be the probability of no users. j For service strength. Note that it is assumed that the stability condition of the queue is satisfied.

[0025] To combine these three costs, we assume U ijIt is in the traditional linearly additive function form. Similarly, the assumption U is reasonable. ij and u j Positive correlation with t ij and Negative correlation. Therefore, U ij It can be represented as

[0026]

[0027] Here, β1 and β2 represent the coefficients for travel time and waiting time, respectively, which can be estimated using measured data. Note that, in addition to these specific costs, this utility function can be extended based on available data to incorporate other observed properties.

[0028] Note the arrival rate λ j and expected waiting time There is a dependency relationship between them. According to our model, λ j It is x ij The sum of, and x ij It also depends on U ij Therefore, it depends on It also depends on λ j That is, λ. j It is indirectly dependent on itself. Since we are considering a competing infrastructure network, this means we need to solve a user equilibrium problem to determine the demand allocation x. ij .

[0029] 1.2 User Equilibrium Model

[0030] Assume the user adopts a utility-maximizing decision rule, meaning the user chooses the facility with the highest observable utility. This represents the most efficient use generated by the user at demand node i, i.e.:

[0031]

[0032] Assume the selected facility planning scheme S and service capacity s are known. j , At user equilibrium, no user wants to change their choice. Therefore, the equilibrium condition can be expressed as:

[0033]

[0034] in and Let $\mathbf$ represent the utility of user $i$ accessing medical facility $j$ and the maximum utility of user $i$ during user equilibrium, respectively. Furthermore, it should be noted that...

[0035]

[0036] in For the user reach rate of facility j during user equilibrium, The number of users from demand node i to facility location j when balancing user needs.

[0037] Equilibrium condition (9) states that if there is a user flow from node i to facility j, then the user utility of node i to facility j is... Must equal maximum efficiency Otherwise, it will not exceed the highest value. This model implies that each user selects the service facility based on the observed highest level of attractiveness.

[0038] To find the value in formula (9) We can solve the following equivalent nonlinear mathematical programming problem:

[0039]

[0040] The constraints are as follows:

[0041]

[0042]

[0043] in,

[0044]

[0045] Theorem 1: For a given facility planning scheme S and s j , Mathematical programming (10)-(13) is equivalent to (9).

[0046] Proof: To prove that the mathematical programming problem is equivalent to (9), we transform it into a Lagrangian function with only nonnegativity constraints, i.e.,

[0047]

[0048] In the objective function w i It is the Lagrange multiplier of constraint (11).

[0049] According to the Karush-Kuhn-Tucker (KKT) conditions, the optimal condition for this Lagrangian function is:

[0050]

[0051]

[0052]

[0053]

[0054] Clearly, (17) is equivalent to (11). Equations (15) and (16) mean that...

[0055]

[0056] Notice,

[0057]

[0058] Therefore, formula (19) can be further rewritten using formula (20) as follows:

[0059]

[0060] It can also be restated in a complementary form as follows:

[0061]

[0062]

[0063]

[0064] Formula (21) indicates that if there is a demand flow x ij >0, utility U ij equals w i If there is no demand flow, i.e., x ij =0, then utility U ij Not greater than w i Therefore, the Lagrange multiplier w i This can be interpreted as the most efficient use of data generated by the user on node i. Therefore, formula (21) is equivalent to formula (9). Thus, we can obtain the equilibrium flow by solving this mathematical programming problem.

[0065] 1.3 Bilevel Programming Model

[0066] The problem considered here is a two-layer decision structure. The upper layer problem is to determine the location of facilities and the associated service capabilities, while the lower layer problem is to determine the balanced flow of users from demand nodes to facility locations, given the decisions of the upper layer.

[0067] In practice, there is usually only a limited budget to support the establishment and operation of preventative healthcare facilities. This budget constraint can be used to account for cost differences in establishing and operating healthcare facilities in different areas of a city. Let c be the fixed construction cost of facility j (j∈M). v The unit cost of adding a service desk to the facility. Furthermore, for cost-effectiveness reasons, only when user demand exceeds the minimum workload requirement R... minFacilities can only be built under certain conditions. Furthermore, due to site constraints, the number of service counters in facility j cannot exceed a finite size.

[0068] Our objective is to maximize the total social utility of the system, i.e., the overall observable utility for users. The upper-level model for healthcare facility network design can be established as follows:

[0069]

[0070] The constraints are as follows:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] Where, x ij Determined by the subsequent lower-level model:

[0080]

[0081] The constraints are as follows:

[0082]

[0083]

[0084] The objective function (25) is to maximize the utility of the entire system. Constraint (26) ensures that at least one service counter is allocated to each proposed facility, while guaranteeing the decision variable s. j The nonnegativity of . Constraint (27) will affect the number of service counters. The size is limited to a finite value. Constraint (28) defines the arrival rate λ. j Constraint (29) represents the stability condition of the queue. Constraint (30) stipulates that the arrival rate of the proposed facility must meet the minimum workload requirement. In constraint (31), T represents the penalty cost, ensuring that users can only obtain services from the constructed facility. Constraint (32) is budget control. Constraint (33) is the feasible region of the decision variable.

[0085] 2. Solution Method

[0086] Because bilevel programming models are highly nonlinear and involve integer decision variables, they are difficult to solve precisely. Therefore, we focus on efficient heuristic algorithms that have many successful applications in preventative healthcare network design. Our solution algorithm follows a bilevel framework. For the lower-level problem, the successive mean averaging (MSA) method is used to solve the user equilibrium model. This allocation algorithm determines the equilibrium flow from users to facilities. For the upper-level problem, a metaheuristic algorithm, namely a genetic algorithm with an elitist strategy, is proposed to find the optimal location and service capacity.

[0087] 2.1 Lower-level allocation algorithm

[0088] Given upper-level decisions S and s j , The next level problem is solving balanced flow. The algorithm used is an iterative method called successive averaging. Let k be the iteration counter, and K be the maximum number of iterations. Let ε be a pre-determined fault tolerance parameter. θ k , k = 1, ..., K, are the step size parameters for iteration, with values ​​between 0 and 1. The specific calculation steps are given below:

[0089] Step 0 (Initialization): Determine suitable values ​​for ε and K, and set k = 0; set

[0090]

[0091] Step 1 (Calculate Utility): Set k: = k+1; Calculate λ according to formula (2). j , Calculate the shortest path travel time t using Dijkstra's algorithm. ij , i∈N, j∈S. Calculate the waiting time according to formulas (3)-(6). Calculate U according to formula (7) ij , i∈N, j∈S; according to formula (8), we get

[0092] Step 2 (All-or-Nothing Assignment): Calculate the flow x′ according to the all-or-nothing rule. ij This means allocating all of a user's needs to the facilities that interest them most.

[0093]

[0094] Step 3 (Generate Search Direction): Define As a search direction.

[0095] Step 4 (Traffic Update): Update the user flow Step size parameter θk Defined as,

[0096]

[0097] Step 5 (Stopping Condition): If consecutive and To achieve a relative error, or k > K, set... And stop; otherwise, proceed to step 1. The relative error is defined as follows:

[0098]

[0099] In each iteration, the algorithm finds x in step 3. ij A new search direction is determined, and then x is updated in step 4 by step size. ij The entire process is repeated until any of the stopping conditions in step 5 are met. The step size θ for each iteration... k It's preset. Set θ k There are many methods. Generally speaking, θ should decrease as k increases. k To ensure convergence, we set θ. k This is the reciprocal of the iteration number k+1. Note that in step 4... The updated result may result in a facility arrival rate greater than the maximum value, which violates the stability condition (29). There are generally two ways to solve this problem: one is to reduce the step size, and the other is to set a larger penalty time.

[0100] 2.2 Upper-layer addressing algorithm

[0101] We developed a genetic algorithm based on an elite selection strategy to solve the upper-level problem because it is one of the most successful metaheuristic algorithms for solving combinatorial optimization problems, with the ability to explore other regions of the feasible space and avoid local optima.

[0102] In genetic algorithms, each chromosome represents a solution to the problem, and the quality of the solution is represented by its fitness. In this study, chromosomes are represented using integer encoding. Each chromosome consists of several integers, similar to genes. Each gene corresponds to a potential location in M, and its value represents the number of available service stations. If no service stations are available, the medical facility will not be located at that location. We implement the genetic algorithm in the following steps:

[0103] Step 0 (Initialization): Set the parameters to be used, including the population size N. pop Maximum algebra Gen, crossover probability p c mutation probability p m The tag for the generation is gen=1, and the elite part is p. e.

[0104] Step 1 (Generation of the initial population): Randomly generate feasible solutions as the initial population N of the chromosome. pop The solutions are distributed across the entire range of possible solutions. If a solution is deemed infeasible based on the constraints, another solution is generated until it becomes feasible.

[0105] Step 2 (Fitness Calculation): For each chromosome in the population, generate a fitness value, i.e., the objective function value. Use this value to evaluate the performance of each chromosome in the population.

[0106] Step 3 (Generation of a new population)

[0107] Step 3.1 (Selection): Based on the fitness values ​​evaluated in Step 2, select the best-performing p. e Some were classified as elites, while the worst performers were discarded. e part.

[0108] Step 3.2 (Cross): The remaining (1-p) e )N pop Chromosomes are used for the crossover operation. These chromosomes are randomly paired. The probability of crossover is p. c If two chromosomes are chosen for crossover, a gene location is randomly selected for crossover to generate two offspring as new chromosomes. If the creation of new chromosomes is not feasible according to the constraints in the upper-level model, another gene location is tried until a feasible outcome is reached.

[0109] Step 3.3 (Mutation): Using probability p m Identify a mutation on a chromosome. Randomly select two genes, at least one of which has a positive value, and swap their values. If the new chromosome is not feasible, try two other gene locations until it produces a viable offspring.

[0110] Step 3.4 (Elite): Generate a new population. After genetic manipulation, (1-p) still exist. e )N pop One feasible chromosome. Add the p-labeled chromosome from step 3.1. e N pop Elites ensure population size N pop This allows the best chromosomes from the current generation to be passed down to the next generation without modification. It guarantees that the quality of the solution will not decline from one generation to the next. The label for the next generation is gen := gen+1.

[0111] Step 4 (Stop Iteration): If the maximum number of algebras is reached, i.e., gen ≥ Gen, terminate the iteration process and output the result. Otherwise, go back to step 2.

[0112] Beneficial Effects: Preventive healthcare services are crucial for governments because they can reduce the likelihood and severity of potentially life-threatening diseases through early detection. Prevention is always better than cure. It can save governments significant funds and improve the well-being of the entire society. This invention proposes a planning method for preventive healthcare facilities that considers the congestion effect under limited budget constraints, thereby maximizing the total social utility of the system. It can provide a scientific basis and operational method for site selection and service capacity decisions for preventive healthcare facilities, and has significant application value. Attached image description:

[0113] Figure 1 This is a logical framework diagram;

[0114] Figure 2 Test network for Sioux Falls;

[0115] Figure 3 This refers to the evolutionary process of a genetic algorithm.

[0116] Figure 4 Sensitivity analysis under variable budget control. Detailed implementation method:

[0117] We conducted a computational experiment to evaluate the effectiveness of the proposed model and algorithm. The experiment used the Sioux Falls network, a widely adopted network design approach. This is a... Figure 2 The network shown is of medium size. It consists of 24 nodes and 76 road segments. For computational experiments, it is assumed that there are 8 demand nodes and 8 candidate locations. Therefore, there are 64 pairs of origin and destination points. The travel time and length of road segment a (a∈L) are denoted as t. a and l a The values ​​are shown in Table 1. Assuming the travel speed on each road segment is 30 miles per hour, the segment length can be converted into travel time. Preventive healthcare demand data calculated per hour of users (users / hour) are shown in Table 2.

[0118] Table 1. Characteristics of the Sioux Falls network

[0119]

[0120] Table 2. Healthcare demand data from the Sioux Falls network.

[0121]

[0122]

[0123] Based on the proposed model and solution algorithm, the following parameter values ​​were used in the experimental study.

[0124] Problem parameters:

[0125] The service speed of a single service desk is μ = 6 users / hour;

[0126] Fixed facility attractiveness u j =0;

[0127] The sensitivity coefficients for travel time β1 = 1 and waiting time β2 = 1;

[0128] Maximum number of servers

[0129] Fixed facility construction costs

[0130] Unit service desk cost c v =1;

[0131] Budget control B = 50;

[0132] Minimum workload R min =10 users / hour;

[0133] Continuous average parameter:

[0134] Maximum number of iterations K = 100;

[0135] Error tolerance ε = 0.01;

[0136] Genetic algorithm parameters:

[0137] Population size N pop =200;

[0138] Maximum algebra Gen = 20;

[0139] Crossover probability p c =0.5;

[0140] Mutation probability p m =0.2;

[0141] The probability p of being an elite e =0.1.

[0142] These algorithms were programmed using the free and open-source language R 3.6.3. All runs were performed on a PC equipped with a 3.6GHz Intel i7-4790 CPU and 16GB of RAM. In this experiment, the genetic algorithm stopped after running for 1.61 hours. Figure 3As shown, the evolutionary process begins to stabilize after 11 generations. Therefore, it can be concluded that the final result is approximately the optimal solution. Table 3 reports the optimal scheme, selecting four possible locations to establish preventive medical facilities: nodes 3, 7, 21, and 23, with corresponding service station numbers of 20, 5, 13, and 12, respectively. Users from demand nodes can be assigned to more than one facility, such as nodes 13 and 20. However, other demand nodes indicate that users from the same node often patronize the same facilities. Table 4 shows that users choose the facility with the highest utility, and users from the same demand node obtain approximately the same utility even when visiting different facilities.

[0143] Table 3 Optimal Planning Scheme and Equilibrium State of Preventive Medical Facilities

[0144]

[0145]

[0146] Table 4 Utility Matrix Between Demand Nodes and Facility Locations

[0147]

[0148] Sensitivity analysis is always beneficial, as it can provide valuable management insights. This study presents a sensitivity analysis, which is also a cost-benefit analysis, of different budget controls. The budget increases from 45 to 75 in increments of 5. The results are as follows... Figure 4 As shown, the horizontal axis represents budget control, and the vertical axis represents total system utility. Since the utility function is defined using only travel time and waiting time, individual utility is negative, and therefore total system utility is also negative. Clearly, marginal benefits are diminishing. Decision-makers cannot obtain the same return with the same additional investment. There exists an optimal budget control where marginal cost equals marginal revenue.

[0149] like Figure 4 As shown, the relationship between utility (benefit) and budget (cost) can be modeled using multinomial regression. Let f represent the total utility of the system, and B represent budget control. Multinomial regression can be expressed as:

[0150] f(B) = α0 + α1B + α2B 2 (37)

[0151] Where α0 is the intercept, α1 is the coefficient of B, and α2 is the coefficient of B. 2 The coefficients. The values ​​of these coefficients can be estimated using the results of sensitivity analysis. The optimal budget B can be obtained when marginal benefit equals marginal cost. * In other words,

[0152]

[0153] Taking this sensitivity analysis as an example, the parameter estimates for formula (37) are shown in Table 5. Hypothesis testing shows that these parameters are significant at the 0.05 level. Therefore, we can reject the null hypothesis. Adjusted R 2 The value of 0.884 indicates that the multinomial regression fits the data well. From formula (38), the optimal budget is 57.9. Increasing investment before reaching the optimal budget is worthwhile. However, continuing to increase investment after reaching the optimal budget is unwise, as the output will be less than the input.

[0154] Table 5. Estimated parameters of polynomial regression

[0155]

Claims

1. A method for planning preventive medical facilities that takes into account the crowding effect, the method comprising the following technical features: (1) It is represented as a two-level planning model, with the upper level being the system administrator and the lower level being the facility user; (2) The upper-level model is a nonlinear integer programming model constructed with the objective function of maximizing the total social utility of the system, the constraint of limited budget input, and the decision variables of the location and service capacity of preventive medical facilities. The allocation of user demand for each facility is determined by the lower-level model. The upper-level model is expressed as: Where E represents the total social utility of the system, x ij This refers to the number of users from population node i to facility j, μ j t represents the inherent attractiveness of facility j. ij This refers to the shortest travel time from node i to facility j, where β1 and β2 represent the coefficients for travel time and waiting time, respectively. This refers to the user's estimated waiting time at facility j, s j Z is the number of service points of facility j. + Let y be the set of positive integers. j Indicates whether to select a location for facility j. To limit the number of service counters in facility j, λ j Let μ be the rate of arrival of users at facility j, M be the set of candidate locations for medical facilities, N be the set of nodes, B be the budget, and R be the number of users. min T represents the minimum workload requirement, and T represents the penalty cost. The goal is to ensure that users can only obtain services from the constructed facilities. That is, when no facility is constructed at point j, there is a cost t′ from point i to point j. ij , For the fixed construction cost of facility j, c v The unit cost of adding a service counter to the facility; (3) The lower-level model considers the user choice equilibrium problem of the congestion effect. It assumes that users choose the medical facility with the highest utility, but too many users will lead to longer waiting times and higher user costs. Some users will switch to other facilities. The result of the game between users will reach a user equilibrium state. Queueing theory is used to calculate the waiting time. The lower-level model is expressed as follows: Where Z represents the user's total utility when choosing a medical facility, U ij (ω,s j ) represents the observable utility of a user from demand node i when receiving services at facility j, h i Let S be the number of users at node i who require preventative medical services, and S be the selected facility planning scheme. (4) A heuristic algorithm was designed to solve the problem, in which a continuous averaging algorithm was used for the lower-level model and a genetic algorithm with an elite strategy was used for the upper-level model.

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