CN114927237B - Disease prevention and control disease control facility configuration method with capacity limitation - Google Patents

Abstract

The application discloses a disease prevention and control facility configuration method with capacity limitation, and belongs to the field of urban planning. A disease prevention control facility configuration method, comprising: the interval time of users reaching the disease control facilities successively is taken as poisson distribution, and the facilities providing user services for the disease control facilities are taken as service desks and queuing rules are established in a first-come first-get way; the attraction element of the disease control facility, the shortest travel time of the user to the disease control facility, the waiting time of the user at the disease control facility and the probability of the user refusing by the disease control facility are taken as influencing factors; compared with the prior art, the application aims at providing fair and reachable public health service, and provides a planning method of a disease prevention and control facility with capacity limitation under the constraint of limited budget. The method considers the capacity limitation of the disease control facilities and adopts a primary and secondary target method to realize fairness, thereby providing scientific basis for site selection and scale decision of the disease control facilities.

Description

Disease prevention and control disease control facility configuration method with capacity limitation

Technical Field

The invention relates to the field of urban planning, in particular to a disease prevention and control disease control facility configuration method with capacity limitation.

Background

The existing medical system with disease treatment as the center has defects, and disease prevention and control services, in particular disease screening, isolation sickbed, vaccination and the like, are necessary for the timely treatment and control of diseases. Thus, governments around the world are beginning to appreciate the importance of disease prevention control. Therefore, how to optimize the medical resources with limited layout and provide fair and accessible epidemic prevention and control services for people is a problem to be solved.

Reachability generally refers to the ease of reaching a destination or activity distributed in space. There are generally a number of ways in which the accessibility of a controlled facility may be measured. The meaning of reachability in the present invention is more direct and defined as a need that can be met. In fact, there are two sources of demand unmet: firstly, the demand loss caused by insufficient coverage, and secondly, the demand loss caused by the congestion of disease control facilities. In the first source, demand is flexible with respect to cost, and users are typically assigned to the nearest disease control facilities to maximize the overall system demand. In the second source, due to the limited capacity of the facility, when users reach the facility they may be denied access to the service facility (i.e., blocked). This second source has been studied by few scholars in the past because capacity constrained disease control facilities are more complex than non-capacity constrained disease control facilities, and travel costs are typically defined in terms of travel time and queuing delay, but rejection costs are ignored. This results in a contradictory situation where the user would prefer those controlled facilities in the model setting that have a high likelihood of rejection, because it would minimize the total time spent in the system, ignoring the demand for non-service. However, although system reachability is maximized, the probability of a user being denied may be different between different disease control facilities. This may lead to serious service fairness issues. Accordingly, the present invention seeks to provide a disease prevention and control facility configuration method that reduces service unfairness from a second source.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a disease prevention and control disease control facility configuration method with capacity limitation.

The aim of the invention can be achieved by the following technical scheme:

A disease prevention control facility configuration method, comprising:

the interval time of users reaching the disease control facilities successively is taken as poisson distribution, and the facilities providing user services for the disease control facilities are taken as service desks and queuing rules are established in a first-come first-get way;

Establishing a utility function of the user reaching the disease control facility by taking the attraction element of the disease control facility, the shortest travel time of the user reaching the disease control facility, the waiting time of the user at the disease control facility and the probability of the user refused by the disease control facility as influence factors;

The method comprises the steps of taking the probability that a user is refused by a disease control facility as a main target, taking the minimum of the longest waiting time of the user disease control facility as a secondary target, and taking budget of the disease control facility as a constraint condition to construct an upper model; constructing a lower model by taking the number of users of the facility in a balance state as a target;

And combining the upper model and the lower model to construct a double-layer decision structure, and determining the user allocation in a balanced state and the configuration scheme of the disease control facility.

Further, the queuing system isWherein the first twoIndicating that the user is approaching or departing from a markov (or poisson) distribution, or equivalently, indicating that the user is approaching or servicing a time distribution following a negative exponential interval,Indicating disease control facilitiesThe number of service desks in the network,As space physical constraint, represent disease control facilitiesThe number of users can be accommodated; Is an optional location set of the disease control facility;

budgeting at a disease control facility Under the constraint of (a), three sets of decision variables are set:

=disease control facility Is provided with a number of service desks,,

=Slave nodeTo the positionIs a function of the number of users of the system,,

For a selected set of locationsIt is possible to obtain:

user arrives at disease control facility Is the arrival rate of (a),It is possible to obtain:

disease control facility Is the arrival rate of (a)And the number of service desks isThen there is in the queueThe probability of individual users is:

Wherein the method comprises the steps of Is the queuing strength of the queuing process, and the probability of no user in the queue is,

Each disease control facilityProbability of (2)Is thatAndIs a function of (a) and (b),Is due to the probability of being rejected due to limited capacity, which allows the arrival rate of the controlled facility to actually exceed the service rate without the queue growing infinitely, so that the effective arrival rate is usedThe representation is:

。

further, the utility function of the user reaching the disease control facility is as follows:

Wherein therein is For the average length of the queue expressed by the number of users,Refers to the effective arrival rate of the incoming call,Refers toIndividual user in disease control facilityProbability of (a); mean latency; for coming from the demand node Is at the location of the user of (a)Observed effects when receiving services

Using; And Coefficients respectively representing the travel time and the waiting time; Indicating the cost of not having access to the service.

Further, the upper layer model is:

The main object is:

secondary objective:

The constraint conditions are as follows:

Wherein the method comprises the steps of Is a disease control facilityIs used to minimize the maximum rejection probability; is a disease control facility Position variable of (2); is a disease control facility Is the number of service stations; is a disease control facility A limited scale of the number of service desks; from the demand node for the user To the disease control facilityIs a balanced stream of positions; To reach the disease control facility Is a user arrival rate of (1); is a disease control facility () Fixed construction costs of (2); to add a per-unit operating cost of a service desk.

Further, the method comprises the steps of,In position variableNumber of related servicesAfter the determination, the lower model is used for determining that:

The constraint conditions are as follows:

。

Further, the lower model is solved by adopting a successive averaging method.

Further, the upper model is solved by adopting a genetic algorithm based on elite strategy.

The invention has the beneficial effects that:

the invention aims to provide a fair and reachable public health service, and provides a planning method of a disease prevention and control disease control facility with capacity limitation under the constraint of a limited budget. The method considers the capacity limitation of the disease control facilities and adopts the primary and secondary target method to realize fairness, can provide scientific basis for site selection and service capability decision of the disease control facilities, and has important application value.

Drawings

The invention is further described below with reference to the accompanying drawings.

FIG. 1 is a diagram of a model framework;

FIG. 2 is a diagram of Sioux Falls test networks;

FIG. 3 is a flowchart of the evolution process of a genetic algorithm;

FIG. 4 is a graph of sensitivity analysis under a variable budget;

Fig. 5 is a graph of sensitivity analysis under variable demand.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

The invention considers key characteristics of congestion of disease control facilities in a user selection environment, and aims to provide fair planning software of disease prevention and control disease control facilities with capacity constraint. The problem is expressed as a double-layer decision structure with leader-follower features, and a double-layer double-objective nonlinear integer programming model is constructed according to the double-layer decision structure. The upper layer is a two-objective planning model with budget constraints, where the primary objective is to minimize the probability that the user is blocked (i.e., the user is denied service) and the secondary objective is to minimize the longest waiting time. The lower layer is a user competition balance model generated by the selection of the service disease control facilities by the user, and the user competition balance model determines the distribution mode of the user demands in the specific disease control facilities. The invention adopts Genetic Algorithm (GA) with elite strategy to solve the upper layer problem, and adopts successive average Method (MSA) to solve the lower layer problem. The technical scheme of the invention comprises the following steps:

1. Mathematical modeling

Assume thatIs a node with a group of nodesAnd a set of connectionsWherein the nodes represent demand nodes, disease control facility locations or road intersections and the road segments are the main traffic trunks between the nodes. We assume that demand nodesThe need for preventive medical services is the average rateIs a poisson process of (c). The optional location set of the disease control facility isWhileIs the set of locations selected. Slave nodeTo the positionFor the shortest path travel time of (a)And (3) representing. The budget available to governments for constructing disease control facilities and service desks is. We assume that the service desks are homogenous, the service times are exponentially distributed, and the service is averaged per unit timeAnd the individual users. We also assume that the users are homogenous, the number of people arriving at each disease facility follows a poisson distribution, and the queuing rules are First Come First Served (FCFS). These assumptions are reasonable for a disease control facility that does not require a subscription, which applies to most conventional health check services. Thus, the user is at the disease control facilityIs assumed to beQueuing system, wherein the first twoIndicating that the user is approaching or departing from a markov (or poisson) distribution, or equivalently, indicating that the user is approaching or servicing a time distribution following a negative exponential interval,Indicating disease control facilitiesThe number of service desks in the network,As space physical constraint, represent disease control facilitiesThe number of users can be accommodated. Every time a disease control facilityIs provided with thereinWhen a user is located, any arriving user will be denied service and will leave the system as a lost user.The value of (2) is predetermined and depends on the particular disease control facility conditions.

The problem is that of budgetingUnder the constraint of (1), the decision of selecting address and the number of relevant service stations is made by taking the fair rejection probability as a target. To this end, we define three sets of decision variables:

=disease control facility Is provided with a number of service desks,,

=Slave nodeTo the positionIs a function of the number of users of the system,,。

Thus, for a selected set of locationsIt is possible to obtain:

(1)

defining user arrival at disease control facility Is the arrival rate of (a),It is possible to obtain:

(2)

which defines the demand of each disease control facility as the sum of the demands originating from the demand nodes. If the disease control facility Is the arrival rate of (a)And the number of service desks isThen there is in the queueThe probability of individual users is:

(3)

Wherein the method comprises the steps of Is the queuing strength of the queuing process, and the probability of no user in the queue is,

(4)

Note that each disease control facilityProbability of (2)Is thatAndIs a function of (a) and (b),Is the probability of being rejected due to limited capacity. It allows the arrival rate of the controlled facility to actually exceed the service rate without the queue growing indefinitely. For effective arrival rate (i.e. the number of users having access to a service)The representation is:

(5)

1.1 User utility function

It is assumed that the principle of the user selecting a disease control facility is to maximize their personal utility, i.e. minimize their negative utility. Therefore, it is important to know how the user makes the selection. The user selection model is essentially a utility function defined based on the attractiveness of the disease control facility known to the user. Setting upFor coming from the demand nodeIs at the location of the user of (a)Utility observed when served. For a disease control facility with capacity constraints, it mainly comprises four parts: (1)Position ofMay include intrinsic factors such as parking convenience, hardware conditions, practitioner reputation, etc.; (2)From the departure nodeTo the position of the target disease control facilityIs the shortest travel time of (a); (3)At the position ofIs the arrival rate, including queuing time and service timeAnd number of service desksIs a function of (2); (4)This increase in part is more realistic due to the probability of capacity constraints not meeting the service (i.e., being rejected), because in reality the disease control facilities all have capacity constraints, and the cost of this part is not considered by the prior art patent technology, which is a major innovation of this patent.

Due to the position of the disease control facilityIs oneQueuing system, for any ofThe average latency can be expressed according to classical queuing theory by the following system of equations：

(6)

(7)

Wherein the method comprises the steps ofFor the average length of the queue expressed by the number of users,Is the effective arrival rate according to equation (5),Is according to formula (3)Individual user in disease control facilityIs used as a basis for the probability of a failure,For the service strength defined above.

We assume thatIs a conventional linear additive functional form containing the four variables described above. Meanwhile, assume thatBenefit (benefit)Positively correlated with cost,AndAnd (5) negative correlation. Under these circumstances of the assumption that the user is,Expressed as:

(8)

Wherein the method comprises the steps of AndCoefficients representing the travel time and the waiting time respectively,Indicating the cost of not having access to the service. In practice, parameters、AndThe estimation may be based on survey data. The present invention allows for different weights for travel time and latency, both of which, while time, are often not equivalent. In addition to these specific costs, utility functions may also be extended to include other observable attributes, such as parking costs and service prices, depending on the available data.

Notably, the arrival ratePredicted wait timeAnd the likelihood of being rejectedInterdependencies exist. According to the model of the model,Is thatIs used in the method of the present invention,And also depend onThat is dependent onAndWhich in turn depends onThat is, the first and second substrates are,The value of (2) depends indirectly on itself. Since we consider a competitive medical facility network, this means we need to solve the user balancing problem to determine the allocation of user needs for a given facility location and number of relevant service desks.

1.2 User equalization model

Assuming that the users always select the disease control facility with the highest observable utility, the competition among the users will reach the equilibrium state of the users according to the basic principle of the game theory. By usingRepresenting demand nodesThe highest utility of the upper user, i.e

(9)

Assume that a known disease control facility planning schemeNumber of service desksIn the user equilibrium state, no user wants to change his own selection, i.e. no user can promote personal utility through unilateral behavioral decision. Thus, the equalization conditions can be expressed as complementary systems

(10)

Wherein the method comprises the steps ofAndRepresenting from demand nodes respectivelyIs used by the user of the disease control facilityUtility and user equilibrium state demand nodeIs the user's maximum utility. In addition, note that:

,

Wherein the method comprises the steps of Disease control facility for representing user balanceIs used to determine the user arrival rate of (a),Representing slave demand nodes when users are balancedTo the position of the disease control facilityIs a number of users.

The equalization condition (10) indicates that if there is a slave demand nodeTo the disease control facilityThen, nodeTo the disease control facilityUser utility of (a)Must be equal to the highest utility; Otherwise, it is not higher than the maximum value. This condition means that each user will use the service control facility with the greatest observable appeal. Thus, in an equilibrium state, users emanating from one common node will experience the same utility, thereby achieving a user equilibrium state.

Since the utility function has a symmetric jacobian matrix, we can solve the equivalent nonlinear mathematical programming to get a given positionLower part (C)And：

(11)

The constraint conditions are that,

(12)

(13)

Wherein,(14)

Theorem 1. Given positionMathematical plans (11) - (14) are equivalent to equalization condition (10).

To demonstrate that mathematical programming is equivalent to equation (10), we reformulate it as a lagrangian function with only non-negative constraints, i.e.,

(15)

Wherein in the objective functionIs the Lagrangian multiplier of constraint (12).

According to Karush-Kuhn-Tucker (KKT) conditions, the optimal conditions for the lagrangian function are,

(16)

(17)

(18)

(19)

Obviously, equation (18) is equivalent to equation (12). Formulas (16) and (17) can be expressed as,

(20)

Note that the number of the components to be processed,(21)

Thus, equation (20) can be further rewritten as equation (21):

(22)

it can also be restated in complementary form as follows:

(23)

(24)

(25)

Equation (22) shows that if there is a demand flow, i.e Then utility isEqual toIf there is no demand flow, i.eThen utility isNot greater than. Thus, the Lagrangian multiplierCan be interpreted as the user is at the demand nodeThe highest utility producedI.e., equation (22) is equivalent to equation (10). Therefore, the solutions of the mathematical plans (11) - (14) satisfy the equalization condition (10). We can get an equalized user flow by solving this mathematical programming problem.

1.3 Double-layer double-target planning model

The whole problem considered by the invention belongs to a double-layer decision structure, wherein the upper layer problem is to determine the positions of the disease control facilities and the number of related service stations, and the lower layer problem is to determine the balanced flow from the demand nodes to the positions of the disease control facilities by the user under the condition of giving the upper layer decision. Note that the streams are equalizedArrival rateNot decision variables. They are determined endogenously by the underlying model. Decision variables are position variables in the upper layer modelNumber of related services. Once these variables are set, all remaining auxiliary variables and parameters can be calculated.

In practice, there is typically only a limited budget to support the establishment and operation of disease prevention control and disease control facilities. The budget constraints may be used to take into account the cost differences in setting up and operating the disease control facilities at different locations in the urban area. Assuming budget is set to，Is a disease control facility() Is used for fixing the construction cost of the vehicle,To add a service desk, the unit operation cost is the same for each disease control facility location. Furthermore, for cost-effectiveness reasons we assume that only when the number of users exceeds the minimum workload requirementAnd the disease control facilities can only operate. In addition, under the constraint condition of the space of the field, the disease control facilityThe number of service desks in a network cannot exceed a limited sizeThe number of users that can be accommodated cannot exceed。AndThe values of (2) are typically given by the system planner on a case-by-case basis and may vary from location to location.

In order to solve the problem of disease prevention and control disease control facility planning based on fairness, an upper model adopts double-objective optimization. Its main objective is to minimize the maximum rejection probability,. Since the user demand may be unsaturated flows and the primary goal may be all zero, a secondary goal is introduced, namely minimizing the longest latency of the disease control facility to achieve fair queuing. The primary target and the secondary target are introduced, so that the method is very stable for different demand intensities, and can be suitable for different demand scenes. Therefore, the upper model of the problem of the disease control facility network design is that,

The main object is:(26)

secondary objective: (27)

The constraint conditions are as follows:

(28)

(29)

(30)

(31)

(32)

(33)

(34)

(35)

Wherein the method comprises the steps of In position variableNumber of related servicesAfter the determination, the determination is made by the lower model:

(36)

The constraint conditions are that,

(37)

.(38)

The primary objective function (26) is to minimize the maximum rejection probability and the secondary objective function (27) is to minimize the maximum latency. They are Min-Max optimization problems to achieve service fairness, which is robust to any scale of requirements. Constraint (28) ensures that at least one service desk is allocated to each planned disease control facility, while ensuring decision variablesIs not negative of (a). Constraints (29) limit the number of kiosks. Constraint (30) defines arrival rate. Constraints (31) ensure that the user only gets service from the proposed disease control facility. Constraints (32) define the effective arrival rate. Constraints (33) specify that the arrival rate of the plant to be controlled must meet minimum workload requirements. Constraint (34) is a budget constraint, constraint (35) represents a decision variableAndIs a feasible region of (2).

2. Solving method

Since the dual-objective dual-layer planning model is highly nonlinear and contains integer decision variables, it is difficult to solve accurately. Therefore, we use efficient heuristic algorithms and our solution algorithms closely follow the double-layer framework. For the upper layer problem, a meta heuristic general algorithm based on elite strategy is provided to find the optimal position and scale. For the underlying problem, we use a successive averaging Method (MSA) to solve the user equalization model. The demand distribution algorithm can obtain the balanced flow of the user to the disease control facility after the upper layer decision setting. Therefore, the demand assignment algorithm can be used as an embedded module of the disease control facility site selection algorithm, and we describe the lower layer algorithm first and then the upper layer algorithm.

2.1 Demand distribution algorithm of lower model

Decision making for a given upper layer disease control facilityAnd,The underlying problem of the user selection model is to calculate the equalization stream. The algorithm we employ is the successive averaging Method (MSA). Is provided withIn order to be an iteration counter,Is the maximum number of iterations. Is provided withIs a predetermined fault tolerance parameter, is set,Is the firstStep size parameter at the time of iteration. The specific calculation steps are as follows:

Step 0 (initialization): setting up AndIs a suitable value of (a); setting up; An initial allocation is set up and the initial allocation,

.

Step 1 (computational utility): setting up; Calculated from formula (2),; Calculation of shortest travel time using Dijkstra algorithm,,; Calculating the maximum rejection probability from equation (3)Calculating the effective arrival rate from equation (5)Equation (6) calculates the latency; Calculated from equation (8),,; Calculated from equation (9),。

Step 2 (all with all without allocation): calculating flow according to all-in-all distribution rulesI.e., all the demands of the user are distributed to the disease control facilities of greatest interest to the user,

Step 3 (generating search direction): definition of the definition,,As a search direction.

Step 4 (flow update): updating user flows,,Step size parameterIt is defined that the first and second components,

.

Step 5 (stop iteration): if continuousAndTo a relative error, orSetting upAnd stop; otherwise, step 1 is performed. The relative error is defined as the relative error of the two,

.

Step 6 (return result): the equalization traffic, reject probability and latency are returned to the upper layer model.

In each iteration, the algorithm finds in step 3Is then updated in step 4 in steps. The whole process is repeated until any one of the stop conditions in step 5 is satisfied. Step size for each iterationIs preset. Setting upThere are a number of ways in which, in general, this should be followedIncrease and decrease of (2)And between 0 and 1 to ensure convergence. The invention is setFor the number of iterationsIs the inverse of (c). Note that in step 4The updated results make it possible for the arrival rate of the controlled facility to be greater than the maximum value. In such a case, too many users will be denied acceptance of medical services, and the needs of these users are not satisfied.

2.2 Disease control facility site selection algorithm of upper model

We have established a genetic algorithm based on elite strategy to solve the upper-layer problem, since it is one of the most successful meta-heuristic algorithms to solve the combinatorial optimization problem, with the ability to explore other areas of the feasible space and avoid local optimizations. In genetic algorithms, each chromosome represents one solution to the problem, the quality of which is represented by fitness. When the two targets are the same, the secondary targets are adopted. In the present invention, integer codes are used to represent chromosomes, each chromosome being a series of genetic components. Each gene corresponds toThe value of which represents the number of service desks assigned to that location. If there is no service desk available, the disease control facility will not be addressed at that location. We implement the genetic algorithm as follows:

Step 0 (initialization): setting parameters, population size Maximum algebraCrossover probabilityProbability of variationSubstituted labelsPart of elite。

Step 1 (generation of initial population): randomly generating feasible solutions as an initial population of chromosomesSo that it is dispersed throughout the range of possible solutions. If it is judged to be not viable based on the constraint, another is generated until it is viable.

Step 2 (fitness calculation): for each chromosome in the population, fitness values, i.e., objective function values, are generated. Which is used to evaluate the performance of each chromosome in the population. Note that there are two objective functions in the upper model: one is the primary target and the other is the secondary target. Therefore, there are two fitness values in sequence in the solving process.

Step 3 (generation of new population):

Step 3.1 (selection): will perform best according to the fitness value evaluated in step 2 Part is marked as elite and the worst performing is discardedPart(s). Using a hierarchical ordering method, primary target values are ordered first, and secondary target values are ordered afterwards.

Step 3.2 (crossover): the remainderChromosomes are used for crossover operations. These chromosomes are randomly paired with a crossover probability of. If two chromosomes are selected for crossover, then one gene location crossover is randomly determined to generate two offspring as new chromosomes. If the new chromosome is judged to be infeasible based on constraints in the upper model, another gene location is tried until it is feasible.

Step 3.3 (mutation): probability of useMutation of one chromosome is determined. Randomly selecting two genes, at least one of which is positive, and exchanging their values. If the new chromosome is not viable, two additional gene positions are tried until it is a viable offspring.

Step 3.4 (elite): a new population is generated. Genetic manipulation still existsAnd a viable chromosome. With the addition of marksElite to ensure population size. This allows the best chromosomes in the current generation to continue unchanged to the next generation, ensuring that the quality of the solution does not drop from one generation to the next. Let the label of the generation be。

Step 4 (stop iteration): if the maximum algebra is reachedI.e.Terminating the iterative process and outputting the result. Otherwise, go to step 2.

Examples

The present invention devised a computational experiment to evaluate the effectiveness of the proposed model and algorithm. The experiments employed Sioux Falls networks which were widely used in network design. As shown in fig. 2, the network is a medium-scale network consisting of 24 nodes and 76 segments. For the calculation experiments, 8 demand nodes and 8 candidate locations are assumed. Thus, there are 64 pairs of origin-destination points. The values of the travel time and length of the road segments are shown in table 1. Assuming that the travel speeds on the road segments are all 30 miles per hour (mile/h), the road segment length may be converted to road segment travel time. Disease control demand data calculated as number of users per hour (users/hour) is shown in table 2.

Table 1 Sioux Falls network characteristics

Table 2 Sioux Falls disease control demand data for network

Based on the proposed model and solution algorithm, the following parameter values were used in experimental study:

Problem parameters:

Service speed of single service desk User/hour;

fixed disease control facility attraction ；

Sensitivity coefficient to travel timeAnd sensitivity coefficient to latency；

Cost of service failure；

Maximum number of service desks；

Fixed cost of construction of disease control facilities；

Cost per unit service desk；

Budget for a vehicle；

Minimum workloadUser/hour;

continuous average parameters:

Maximum number of iterations ；

Error margin；

Genetic algorithm parameters:

Population number ；

Maximum algebra；

Crossover probability；

Probability of mutation；

Probability of elite。

The algorithm is programmed using the free open source language R3.6.3. All runs were performed on a personal computer equipped with 3.6ghz intel i7-4790 CPU and 16g memory. In this experiment, the genetic algorithm was stopped after 1.42 hours of operation. As shown in fig. 3, after 19 generations, the evolution process began to stabilize. Thus, it can be concluded that the end result is an approximate globally optimal solution. The locations selected to establish disease prevention and control facilities are nodes 3, 9, 16, 19 and 23, respectively, with corresponding numbers of service stations 6,9, 8, 7 and 10, respectively. The quality of service for each disease control facility is shown in table 3. The maximum reject probability for node 3 is 0.132 and the maximum latency for node 23 is 1.22 hours. It can be concluded that the quality of service between all the disease control facilities is almost equal in terms of reject probability and waiting time, achieving reachability-based service fairness, i.e. a predetermined policy objective.

Table 3 network design scale and service level

The demand distribution in the equilibrium state is shown in table 4. It shows that users from the same demand node will typically visit the same disease control facility, e.g. nodes 1,2, 4, 5, 13 and 14, even though they may be free to travel to different disease control facilities. If the user's utility is approximately equal, however, the user may be assigned to multiple disease control facilities, such as nodes 19 and 23.

Table 4 demand assignment in equilibrium

Sensitivity analysis is always beneficial and can provide valuable administrative advice. The present invention performs sensitivity analysis, i.e., cost-effectiveness analysis, of different budgets. In the sensitivity analysis, it is assumed that the budget is increased from 30 to 60 in steps 5, and the result is shown in FIG. 4, where the horizontal axis is the budget and the vertical axis is the maximum rejection probability for all disease control facility locations. Initially, with budget 30, the maximum reject probability is 37.4%, which is an unacceptably low level of service. Undoubtedly, the probability of rejection decreases with increasing budget. When the budget is 45, the maximum reject probability is reduced to 2.2%. The maximum waiting time at this time was 1.67 hours. Whether the budget is good enough depends on the policy maker. As the budget increases, the rejection probability will continue to decrease until zero. After a budget of more than 50, the user will not be denied access. At this point the disease control facility network is less crowded and there are sufficient free space for the user to use. Since then, the secondary objective of minimizing the maximum latency will play an important role, as the primary objective will not be optimized and remain zero. Thus, the proposed method is robust to capacity constrained disease control facility site selection problems.

The present invention also performs sensitivity analysis of demand at a given investment budget. The demand is fixed for a short period of time but may vary over time in the long term. To investigate the return on the investment budget, it was assumed that the demand expansion coefficient was varied from 0.7 to 1.3 in steps of 0.1. The result is shown in fig. 5, where the horizontal axis is the changing demand and the vertical axis is the maximum rejection probability, with budget set to 40. Initially, the rejection probability is 0, and the disease prevention and control disease control facility cannot reject the user from obtaining medical services due to insufficient requirements. When the required expansion coefficient is 0.7, the maximum waiting time is 0.546 hours. If the demand becomes less, the likelihood of equipment idling increases, which means a waste of investment. The maximum probability of rejection will, of course, increase with increasing demand. When the required expansion coefficient is 1.3, the maximum probability of rejection will increase to 35.3%. If this probability is not acceptable, more investment needs to be added to increase the service level.

The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims.

Claims (5)

1. A disease prevention and control disease control facility configuration method with capacity limitation, comprising:

the interval time of users reaching the disease control facilities successively is taken as poisson distribution, and the facilities providing user services for the disease control facilities are taken as service desks and queuing rules are established in a first-come first-get way;

Establishing a utility function of the user reaching the disease control facility by taking the attraction element of the disease control facility, the shortest travel time of the user reaching the disease control facility, the waiting time of the user at the disease control facility and the probability of the user refused by the disease control facility as influence factors;

The method comprises the steps of taking the probability that a user is refused by a disease control facility as a main target, taking the minimum of the longest waiting time of the user disease control facility as a secondary target, and taking budget of the disease control facility as a constraint condition to construct an upper model; constructing a lower model by taking the number of users of the facility in a balance state as a target;

Combining the upper model and the lower model to construct a double-layer decision structure, and determining the user allocation in a balanced state and the configuration scheme of disease control facilities;

the queuing system is Wherein the first twoIndicating that the user is approaching or departing from a markov distribution, or equivalently, indicating that the user is approaching or departing from a negative exponential interval,Indicating disease control facilitiesThe number of service desks in the network,As space physical constraint, represent disease control facilitiesAccommodating the number of users; Is an optional location set of the disease control facility;

budgeting at a disease control facility Under the constraint of (a), three sets of decision variables are set:

=disease control facility Is provided with a number of service desks,,

=Slave nodeTo the positionIs a function of the number of users of the system,,

For a selected set of locationsThe method comprises the following steps of:

user arrives at disease control facility Is the arrival rate of (a), The method comprises the following steps of:

disease control facility Is the arrival rate of (a)And the number of service desks isThen there is in the queueThe probability of individual users is:

Wherein the method comprises the steps of Is the queuing strength of the queuing process, and the probability of no user in the queue is,

Each disease control facilityProbability of (2)Is thatAndIs a function of (a) and (b),Is due to the probability of being rejected due to limited capacity, which allows the arrival rate of the controlled facility to actually exceed the service rate without the queue growing infinitely, so that the effective arrival rate is usedThe representation is:

；

The utility function of the user reaching the disease control facility is as follows:

Wherein therein is For the average length of the queue expressed by the number of users,Refers to the effective arrival rate of the incoming call,Refers toIndividual user in disease control facilityProbability of (a); mean latency; for coming from the demand node Is at the location of the user of (a)Utility observed when served; And Coefficients respectively representing the travel time and the waiting time; Indicating the cost of not having access to the service.

2. The method for configuring a disease prevention and control facility with capacity restriction according to claim 1, wherein the upper layer model comprises,

The main object is:

secondary objective:

The constraint conditions are as follows:

Wherein the method comprises the steps of Is a disease control facilityIs used to minimize the maximum rejection probability; is a disease control facility Position variable of (2); is a disease control facility Is the number of service stations; is a disease control facility A limited scale of the number of service desks; from the demand node for the user To the disease control facilityIs a balanced stream of positions; To reach the disease control facility Is a user arrival rate of (1); is a disease control facility Fixed construction costs of (2); to add a per-unit operating cost of a service desk.

3. The method for configuring a disease prevention and control facility with capacity restriction according to claim 2,In position variableNumber of related servicesAfter the determination, the lower model is used for determining that:

The constraint conditions are as follows:

。

4. The method for configuring a disease prevention and control facility with capacity limitation according to claim 1, wherein the lower model is solved by a successive averaging method.

5. The capacity-limited disease prevention and control facility configuration method according to claim 1, wherein the upper model is solved by employing genetic algorithm based on elite strategy.