Ambulance parking site selection and constant volume method considering fairness

Abstract

The invention discloses an ambulance locating and sizing method considering fairness. According to the method, ambulance stops can be optimally selected, and the number of ambulances parked at each stop is optimized on the basis of ambulance stop site selection. The method relates to three models, namely a multi-target optimization model of an emergency demand coverage maximization model, an ambulance reachable fairness maximization model based on a two-step mobile search method and an ambulance travel cost minimization model. Integrating a plurality of objective functions into a single objective function by utilizing a weight coefficient method, establishing a mixed integer nonlinear programming model, solving by utilizing a Gurobi solver, inputting the definition of the model, including variables, constraint conditions and the objective functions, and outputting the solution of the model, namely the value of the variables and the optimal value of the objective functions. And simultaneous decision-making of ambulance stop site selection and constant volume is realized. According to the method, the time and errors of manual judgment are reduced, and the scheduling efficiency and response speed of the ambulance are improved.

Description

Technical Field

[0001] The present invention relates to the field of medical emergency technology, and in particular to a method for ambulance stop site selection and capacity determination taking fairness into consideration. Background Art

[0002] In modern society, an efficient medical emergency rescue system plays a vital role in protecting people's lives and health. As a key carrier of medical emergency services, the rapid response and reasonable layout of ambulances can significantly affect the success rate of treatment and prognosis of patients. However, with the acceleration of urbanization, the growth and distribution of population, and the increasingly complex traffic conditions, the traditional ambulance site selection and capacity determination methods have exposed many limitations.

[0003] Previous studies have focused on minimizing average response time or maximizing coverage. However, this approach may lead to a serious lack of emergency services in remote areas or areas where vulnerable groups live, resulting in a "Matthew effect" in the allocation of service resources, where the strong get stronger and the weak get weaker, which violates the principle of social fairness.

[0004] The populations of different regions differ not only in numbers, but also in age structure, disease spectrum, socioeconomic status, etc. For example, communities with a high degree of aging may have more frequent and urgent needs for emergency care such as cardiovascular disease. Traditional site selection and capacity determination methods fail to fully consider these demographic factors and cannot ensure that patients with different characteristics can enjoy fair ambulance emergency services.

[0005] Traffic flow presents significant dynamic changes in time and space. During traffic congestion periods and sections, the actual operating speed of ambulances will be greatly reduced, resulting in longer response times. Although traditional methods take traffic factors into consideration, they are insufficient in dealing with the impact of traffic congestion on fairness in different regions. For example, in the central business district of a city, despite the large daily traffic volume, due to the relatively abundant medical resources and many traffic management measures, the response time of ambulances during peak hours may still be better than that of remote suburbs, exacerbating the imbalance of service fairness among regions. Therefore, a method for site selection and capacity determination of ambulance stops considering fairness is proposed to address the current shortcomings. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the defects of the above-mentioned technologies and provide a method for ambulance parking site selection and capacity determination that takes fairness into consideration:

[0007] This method can optimize the selection of ambulance stops and optimize the number of ambulance stops at each stop based on the location of the ambulance stops. A total of three models are involved, which are divided into a multi-objective optimization model of emergency demand coverage maximization model, an ambulance accessibility fairness maximization model based on a two-step mobile search method, and an ambulance travel cost minimization model. Using the weight coefficient method, multiple objective functions are integrated into a single objective function, and a mixed integer nonlinear programming model is established. The Gurobi solver is used to solve the problem. The definition of the model, including variables, constraints, and objective functions, is input, and the solution of the model, i.e., the values ​​of the variables and the optimal value of the objective function, is output, so as to achieve simultaneous decision-making on the location and capacity of ambulance stops.

[0008] The advantages of the present invention compared with the prior art are:

[0009] 1. Most of the existing methods for docking site selection and capacity determination are optimized with the goals of maximizing demand coverage, maximizing profits, minimizing various costs, etc., and there is a lack of research on site selection and capacity determination based on the optimization of ambulance accessibility fairness. The present invention introduces the optimization of minimizing the gap in ambulance accessibility fairness, that is, maximizing fairness; in addition, the present invention introduces the service probability threshold indicator for areas with relatively weak medical resources and areas with relatively strong medical resources on the basis of the traditional emergency maximum coverage model to achieve personalized and targeted emergency services; on the basis of the traditional P-median model, a gravity model based on the comprehensive evaluation value is introduced to construct a gravity P-median model to achieve an organic combination of the evaluation method with the docking site selection and capacity determination model.

[0010] 2. Optimize the allocation of medical resources, avoid wasting ambulance resources, and ensure the most effective use of resources in emergency situations. This invention is not only suitable for daily emergency services, but can also play an important role in large-scale events or emergencies, and has broad application prospects and social value.

[0011] 3. The implementation of this method reduces the errors in manual dispatch decisions, improves the dispatch efficiency and response speed of ambulances, buys more treatment time for patients, and thus improves the success rate of emergency treatment. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 The present invention is a flowchart of an ambulance stop location selection and capacity determination method considering fairness.

[0013] Figure 2 It is a schematic diagram of the two-step mobile search method. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solution and advantages of the embodiments of the invention more clear, the technical solution in the embodiments of the invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the invention.

[0015] Combined with the attached figure, a method for ambulance parking site selection and capacity determination considering fairness:

[0016] Step 1: Extract basic data

[0017] (1) Divide the emergency area into several traffic zones.

[0018] (2) The centroid coordinate point of the patient’s traffic zone is regarded as the common coordinate point of all patients in the traffic zone.

[0019] (3) The number of ambulances that can stop at the candidate ambulance stops is limited. The maximum number of ambulances that can stop at each candidate stop is determined based on the actual stop capacity of the candidate stops.

[0020] Step 2: Establish an objective function for the ambulance stop site selection and capacity determination method that takes fairness into account. In actual planning, managers should be guided by emergency users, which means that in the planning and implementation process, the needs of emergency users should be placed in the first place, and the interests and needs of emergency users should be fully considered. The present invention selects three objectives: emergency user needs, ambulance accessibility fairness, and ambulance travel costs for multi-objective optimization.

[0021] (1) Model for maximizing coverage of emergency demand

[0022] The maximum emergency coverage model is to meet the needs of more emergency users by optimizing the locations of candidate ambulance stops under the condition that the fixed cost and operating cost of ambulances are limited. The model formula is as follows:

[0023]

[0024] Where m is the total number of patients, D i1 Denotes the demand for emergency care ambulances at the patient's location, D i2 represents the demand for ordinary ambulances at the patient's location, Y i is a decision variable. If the probability that a patient i in an area with relatively weak medical resources is served by a candidate ambulance stop j is greater than or equal to α i , then it is 1, otherwise it is 0; if the probability that the patient i in the area with relatively abundant medical resources is served by the candidate ambulance stop j is greater than or equal to β i , then it is 1, otherwise it is 0.

[0025] (2) Ambulance accessibility fairness maximization model

[0026] The core idea of ​​the two-step mobile search method is to use the supply side and the demand side as references to each other and conduct a mutual search based on the set distance threshold. Therefore, it is called the two-step mobile search method. Its general form is expressed as:

[0027] Step 1: For ambulance stop j, search for the patient set within the threshold range d0 (derived from historical data based on the city's geographical layout, traffic conditions, ambulance response speed, patient severity, etc.) and calculate its supply-demand ratio R j , as a measure of its service accessibility, for each ambulance stop, its ambulance resource S j It is shared by the users around it, but its accessibility decreases as the distance increases. ij When ≤d0:

[0028]

[0029] Among them, S j represents the service capacity of candidate ambulance stop j (i.e., the maximum number of stops), D i Indicates the search range d ij The demand for ambulances at patient location i when ≤d0, d ij is the distance between patient site i and ambulance stop j, f is the distance decay function, and m is the total number of patient sites.

[0030] Step 2: For patient location i, search for the set of ambulance stops within the threshold range d0, and sum the supply-demand ratios of the ambulance stops that fall within the distance threshold range. ij When ≤d0:

[0031]

[0032] Among them, A i is the spatial accessibility of patient location i, d ij is the distance between patient location i and ambulance stop j, f is the distance decay function, and n is the total number of ambulance stops.

[0033] Based on the 2SFCA extended form of the distance decay function, the present invention introduces the Gaussian distance decay function to expand the two-step moving search method. The distance decay function is expressed as:

[0034] When ij When ≤d0,

[0035] When ij >d0, f(d ij )=0

[0036] The fairness maximization model based on accessibility is reflected in that every emergency user can get ambulance service, and its balance can be reflected by the accessibility gap between different traffic communities. The smaller the accessibility gap, the more balanced the configuration of ambulance stops, that is, the greater the fairness. Every emergency user can get ambulance service, including both ordinary ambulance service and emergency care ambulance service, that is, the fairness of the two types of services is maximized. The specific formula is:

[0037]

[0038] In the formula, A i is the spatial accessibility of patient location i, D i Indicates the search range d ij ≤d0, S represents the total supply capacity, D represents the total number of ambulances required at the patient locations, and a is the weighted average of accessibility, which is equal to the ratio of the total supply capacity to the total number of ambulances required at the patient locations.

[0039] To facilitate the solution, z2 is converted into a quadratic form:

[0040]

[0041] in:

[0042] S=[S1 S2 … S n ] T

[0043]

[0044] A=[aa … a] T ,|A|=m

[0045]

[0046] q ij =f(d ij ), F=qG

[0047] Where: S represents the service capacity of the ambulance stop, which is a column vector containing the ambulance resources of each ambulance stop; D represents the number of ambulances required at the patient, which is an m×m matrix containing the number of ambulances required at each patient; A represents the spatial accessibility of the patient, which is a column vector containing the spatial accessibility of the patient, |A| is the modulus of vector A, and its size is equal to the total number of patients m; q represents the distance attenuation coefficient, which is an m×n matrix containing the distance attenuation coefficient between patient i and ambulance stop j; q ijrepresents the distance attenuation function value between patient location i and ambulance stop j; G represents the relative difficulty coefficient of resource allocation at the ambulance stop, which is a matrix, G j represents the relative difficulty coefficient of resource allocation at ambulance stop j, and F is a comprehensive assessment of the actual availability or service capacity of resources from the ambulance stop to the patient.

[0048] The objective function is transformed into the standard form of quadratic programming and is expressed as follows:

[0049]

[0050] Among them: x represents the service capacity of the ambulance stop, which is a vector obtained by S; H represents the degree of resource allocation pressure, which is a matrix obtained by multiplying the transpose of F, D and F; f represents the comprehensive rescue difficulty, which is a vector obtained by transposing A, D and F.

[0051] x=S

[0052] H=F T DF

[0053] f=(-A T DF) T =-F T DA

[0054] As mentioned above, every calling user can get ambulance service, including both ordinary ambulance service and emergency care ambulance service, that is, to achieve the maximum fairness of the two types of services. The specific formula is:

[0055] When ij When ≤d0, S j1 =W j1 θ1

[0056] When ij When ≤d0, S j2 =W j2 θ2

[0057] Among them, R j1 is the supply-demand ratio of emergency care ambulances, R j2 is the supply-demand ratio of ordinary ambulances, which is used as a measure of their service availability; for each ambulance stop j, its emergency care ambulance resources S j1 and ordinary ambulance resources S j2 It is shared by the emergency users around it, but accessibility decreases with distance. i1 is the spatial accessibility of the emergency care ambulance at patient location i, A i2is the spatial accessibility of a normal ambulance to patient location i, D i Indicates the search range d ij ≤d0, D represents the total number of ambulances required for the patient locations, m is the total number of patient locations, and n is the total number of ambulance stops. j1 represents the number of emergency and intensive care ambulances at candidate ambulance stop j, θ1 represents the dispatch frequency of emergency and intensive care ambulances, and W j2 represents the number of ordinary ambulances at candidate ambulance stop j, and θ2 represents the dispatch frequency of ordinary ambulances.

[0058] For patient i, search for the set of hospitals k within the threshold range d1 derived from historical data (based on factors such as the city's geographical layout, traffic conditions, ambulance response speed, and the severity of the patient's condition), and calculate its supply-demand ratio R k , as a measure of its service availability, for each hospital, its resource S k It is shared by the users around it, but its accessibility decreases as the distance increases. ik When ≤d1:

[0059]

[0060] For hospital k, search for the set of patients within the threshold range d1, and sum the supply-demand ratios of the patients within the distance threshold range. ik When ≤d1:

[0061]

[0062] Among them, A k is the spatial accessibility of hospital k, S i represents the service capacity of patient i, D k Indicates the search range d ik The number of ambulance arrivals at hospital k when ≤d1, d ik is the distance between patient site i and hospital k, f is the distance decay function, m is the total number of patient sites, and l is the total number of hospitals.

[0063]

[0064] Among them, a1 and a2 are the weighted averages of the spatial accessibility of emergency care ambulances and ordinary ambulances, respectively.

[0065] The objective function aims to minimize the gap in emergency accessibility between different regions, and each region is treated equally. i1 and D i2 To minimize inequality among emergency users, regions with more potential patients are given more weight than other regions.i1 The demand for emergency care ambulances for patients at i, D i2 The demand for ordinary ambulances for patient i (determined by analyzing historical data, conducting demand forecasts, considering special events, etc.).

[0066] (3) Ambulance travel cost minimization model

[0067] The service efficiency is maximized by minimizing the ambulance travel cost at the patient's location. The ambulance travel cost is represented by the weighted distance sum of the emergency users. The smaller the ambulance travel cost, the faster and more conveniently the emergency users can get the required services. The specific formula is:

[0068]

[0069] Where: P ij The probability that patient i will be served by candidate ambulance stop j (by analyzing historical data and using the machine learning method of quantile regression forest to generate probability predictions), d ij is the distance between patient location i and ambulance stop j, D i Indicates the search range d ij ≤d0, the demand of patient i, X j is a decision variable, which is 1 if the candidate ambulance stop dispatches an ambulance and 0 otherwise.

[0070] Step 3: Establish a constraint condition for the location and capacity determination method of ambulance stops considering fairness

[0071] The constraints of the ambulance stop site selection and capacity model mainly include site selection quantity constraints, service threshold constraints, supply and demand constraints, and ambulance quantity constraints, as follows:

[0072] (1) Site quantity constraints

[0073]

[0074] Where T represents the number limit of site selection. The service radius of pre-hospital emergency stations set up in urban areas is 3 to 5 kilometers, and at least one is set up for every 100,000 to 150,000 people. In rural areas, one pre-hospital emergency station is set up for every 1 to 2 townships or with a service radius of 5 to 8 kilometers.

[0075] (2) Service Threshold Constraints

[0076]

[0077] Among them, α i is the probability threshold of patients in areas with weak medical resources being served by candidate ambulance stops, and its value is 0.6, β iY is the probability threshold of patients in areas with abundant medical resources being served by candidate ambulance stops, and its value is 0.8. M1 is the set of patients in areas with weak medical resources, and M2 is the set of patients in areas with abundant medical resources. i is a decision variable. If the probability that a patient i in an area with weak medical resources is served by a candidate ambulance stop j is greater than or equal to α i , then it is 1, otherwise it is 0; if the probability that the patient i in the area with abundant medical resources is served by the candidate ambulance stop j is greater than or equal to β i , then it is 1, otherwise it is 0.

[0078] Since selecting a certain ambulance stop to dispatch an ambulance is an uncertain scenario with probabilistic randomness, the service probability indicator is introduced. The probability of patient i being served by candidate ambulance stop j is expressed as:

[0079] When ij When ≤d0,

[0080] When ij >d0, P ij =0

[0081] Among them, E j is the comprehensive evaluation value of the ambulance stop, which is used to characterize the attractiveness of the ambulance stop; d ij is the distance between patient location i and ambulance stop j, the distance decay function takes the form of a power function, and β is the distance decay parameter.

[0082] Probability of missing services for patients Must be less than a certain loss of service threshold level 1-α i (1-β i ), that is, for each patient, if Y i =1, then the probability of being satisfied must be greater than a threshold, and the threshold for patients in areas with weak medical resources is α i , the threshold for patients in areas with abundant medical resources is β i .

[0083] Nonlinear constraints are converted to equivalent linear constraints by logarithmic transformation.

[0084]

[0085] (3) Supply and demand constraints

[0086]

[0087] It means that the total supply of each selected candidate ambulance stop shall not exceed its service capacity (i.e. the maximum number of stops), where W j1is the number of emergency and intensive care ambulances at candidate ambulance stop j, θ1 is the dispatch frequency of emergency and intensive care ambulances, and W j2 is the number of ordinary ambulances at candidate ambulance stop j, and θ2 is the dispatch frequency of ordinary ambulances.

[0088] (4) Restrictions on the number of ambulances

[0089]

[0090] The sum of the number of emergency and intensive care ambulances and the number of ordinary ambulances at candidate ambulance stop j is the total number of ambulances. j represents the total number of ambulances at candidate ambulance stop j.

[0091]

[0092] It means that if candidate ambulance stop j is selected to dispatch an ambulance, the number of emergency care ambulances and the number of ordinary ambulances are both greater than or equal to 1.

[0093] Step 4: Transformation of multi-objective functions based on weight coefficient method

[0094] The three objective functions z1, z2 and z3 correspond to weights ω1, ω2 and ω3, and the integrated single objective function can be expressed as:

[0095] F(x)=ω1z1-ω2z2-ω3z3

[0096] Wherein, ω1, ω2 and ω3 are non-negative weight coefficients, and the weights ω1, ω2 and ω3 are set to 1 / 3 respectively.

[0097] The specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for selecting a location and determining the capacity of ambulance stops taking into account fairness, characterized in that: This method can optimize the selection of ambulance stops and optimize the number of ambulance stops at each stop based on the location of the ambulance stops. A total of three models are involved, which are divided into a multi-objective optimization model of emergency demand coverage maximization model, an ambulance accessibility fairness maximization model based on a two-step mobile search method, and an ambulance travel cost minimization model. Using the weight coefficient method, multiple objective functions are integrated into a single objective function, and a mixed integer nonlinear programming model is established. The Gurobi solver is used to solve the problem. The definition of the model, including variables, constraints, and objective functions, is input, and the solution of the model, i.e., the values ​​of the variables and the optimal value of the objective function, is output, so as to achieve simultaneous decision-making on the location and capacity of ambulance stops.

2. The method for ambulance parking site selection and capacity determination considering fairness according to claim 1, characterized in that: Step 1: Extract basic data (1) Divide the emergency area into several traffic zones. (2) The centroid coordinate point of the patient’s traffic zone is regarded as the common coordinate point of all patients in the traffic zone. (2) The number of ambulances that can stop at the candidate ambulance stops is limited. The maximum number of ambulances that can stop at each candidate stop is determined based on the actual stop capacity of the candidate stops.

3. The method for ambulance parking site selection and capacity determination considering fairness according to claim 1, characterized in that: Step 2: Establish an objective function for ambulance stop location and capacity determination considering fairness In actual planning, managers should be oriented to emergency users, which means that in the process of planning and implementation, the needs of emergency users should be placed in the first place, and the interests and needs of emergency users should be fully considered. The present invention selects three objectives, namely, the needs of emergency users, the fairness of ambulance accessibility, and the cost of ambulance travel, for multi-objective optimization. For the convenience of formula expression, the model symbols and definitions are explained here, as shown in Table 1. Table 1 Model symbols and definitions 4. The method for ambulance parking site selection and capacity determination considering fairness according to claim 1, characterized in that: (1) Model for maximizing coverage of emergency demand The maximum emergency coverage model is to meet the needs of more emergency users by optimizing the locations of candidate ambulance stops under the condition that the fixed cost and operating cost of ambulances are limited. The model formula is as follows:

5. The method for ambulance parking site selection and capacity determination considering fairness according to claim 1, characterized in that: (2) Ambulance accessibility fairness maximization model The present invention introduces a Gaussian distance decay function to expand the two-step moving search method. The distance decay function is expressed as: When ij When ≤d0, When ij >d0, Among them, d ij is the distance between patient location i and ambulance stop j, d0 is the distance threshold derived from historical data (based on factors such as the city’s geographical layout, traffic conditions, ambulance response speed, and the severity of the patient’s condition), and f is the distance decay function. The fairness maximization model based on accessibility is reflected in that every emergency user can get ambulance service. The degree of balance can be reflected by the accessibility gap between the ambulance stop and the patient and the accessibility gap between the patient and the hospital. The smaller the accessibility gap, the more balanced the configuration of the ambulance stop, that is, the greater the fairness. Every emergency user can get ambulance service, including both ordinary ambulance service and emergency care ambulance service, that is, the fairness of the two types of services is maximized. The specific formula is: When ij When ≤d0, S j1 =W j1 θ1 When ij When ≤d0, S j2 =W j2 θ2 Among them, R j1 is the supply-demand ratio of emergency care ambulances, R j2 is the supply-demand ratio of ordinary ambulances, which is used as a measure of their service availability; for each ambulance stop j, its emergency care ambulance resources S j1 and ordinary ambulance resources S j2 It is shared by the emergency users around it, but accessibility decreases with distance. i1 is the spatial accessibility of the emergency care ambulance at patient location i, A i2 is the spatial accessibility of a normal ambulance to patient location i, D i Indicates the search range d ij ≤d0, the demand for patient location i, D represents the total number of ambulances required for patient locations, m is the total number of patient locations, and n is the total number of ambulance stops. For patient i, search for the set of hospitals k within the threshold range d1 derived from historical data (based on factors such as the city's geographical layout, traffic conditions, ambulance response speed, and the severity of the patient's condition), and calculate its supply-demand ratio R k , as a measure of its service availability, for each hospital, its resource S k It is shared by the users around it, but its accessibility decreases as the distance increases. ik When ≤d1: For hospital k, search for the set of patients within the threshold range d1, and sum the supply-demand ratios of the patients within the distance threshold range. ik When ≤d1: Among them, A k is the spatial accessibility of hospital k, S i represents the service capacity of patient i, D k Indicates the search range d ik The number of ambulance arrivals at hospital k when ≤d1, d ik is the distance between patient site i and hospital k, f is the distance decay function, m is the total number of patient sites, and l is the total number of hospitals. Among them, a1 and a2 are the weighted averages of the spatial accessibility of emergency care ambulances and ordinary ambulances, respectively. The objective function aims to minimize the gap in emergency accessibility between different regions, and each region is treated equally. i1 and D i2 To minimize inequality among emergency users, regions with more potential patients are given more weight than other regions. i1 The demand for emergency care ambulances for patients at i, D i2 The demand for ordinary ambulances to treat patients.

6. The method for ambulance parking location selection and capacity determination considering fairness according to claim 1, characterized in that: (3) Ambulance travel cost minimization model The service efficiency is maximized by minimizing the ambulance travel cost at the patient's location. The ambulance travel cost is represented by the weighted distance sum of the emergency users. The smaller the ambulance travel cost, the faster and more conveniently the emergency users can get the required services. The specific formula is: Where: P ij For patients i Candidate for an ambulance stop j The probability of service, d ij is the distance between patient location i and ambulance stop j, D i Indicates the search range d ij ≤d0, the demand of patient i, X j is a decision variable, which is 1 if the candidate ambulance stop dispatches an ambulance and 0 otherwise.

7. The method for ambulance parking site selection and capacity determination considering fairness according to claim 1, characterized in that: Step 3: Establish a constraint condition for ambulance stop location and capacity determination method considering fairness The constraints of the ambulance stop site selection and capacity model mainly include site quantity constraints, service threshold constraints, supply and demand constraints, and ambulance quantity constraints, as follows: (1) Site quantity constraints Where T represents the number of site selection restrictions.

8. The method for ambulance parking site selection and capacity determination considering fairness according to claim 1, characterized in that: (2) Service Threshold Constraints Among them, α i is the probability threshold of patients in areas with weak medical resources being served by candidate ambulance stops, and its value is 0.6, β i Y is the probability threshold of patients in areas with abundant medical resources being served by candidate ambulance stops, and its value is 0.

8. M1 is the set of patients in areas with weak medical resources, and M2 is the set of patients in areas with abundant medical resources. i is a decision variable. If the probability that a patient i in an area with weak medical resources is served by a candidate ambulance stop j is greater than or equal to α i , then it is 1, otherwise it is 0; if the probability that the patient i in the area with abundant medical resources is served by the candidate ambulance stop j is greater than or equal to β i , then it is 1, otherwise it is 0; Since selecting a certain ambulance stop to dispatch an ambulance is an uncertain scenario with probabilistic randomness, the service probability indicator is introduced. The probability of patient i being served by candidate ambulance stop j is expressed as: When ij When ≤d0, When ij >d0, P ij =0 Among them, E j is the comprehensive evaluation value of the ambulance stop, which is used to characterize the attractiveness of the ambulance stop; d ij is the distance between patient location i and ambulance stop j, the distance decay function adopts a power function, and β is the distance decay parameter. Probability of missing services for patients Must be less than a certain loss of service threshold level 1-α i (1-β i ), that is, for each patient, if Y i =1, then the probability of being satisfied must be greater than a threshold, and the threshold for patients in areas with weak medical resources is α i , the threshold for patients in areas with abundant medical resources is β i . Nonlinear constraints are converted to equivalent linear constraints by logarithmic transformation.

9. The method for ambulance parking location selection and capacity determination considering fairness according to claim 1, characterized in that: (3) Supply and demand constraints It means that the total supply of each selected candidate ambulance stop shall not exceed its service capacity (i.e. the maximum number of stops), where W j1 is the number of emergency and intensive care ambulances at candidate ambulance stop j, θ1 is the dispatch frequency of emergency and intensive care ambulances, and W j2 is the number of ordinary ambulances at candidate ambulance stop j, and θ2 is the dispatch frequency of ordinary ambulances.

10. The method for ambulance parking location selection and capacity determination considering fairness according to claim 1, characterized in that: (4) Restrictions on the number of ambulances The sum of the number of emergency care ambulances and the number of ordinary ambulances at candidate ambulance stop j is the total number of ambulances. It means that if candidate ambulance stop j is selected to dispatch an ambulance, the number of emergency care ambulances and the number of ordinary ambulances are both greater than or equal to 1.

11. The method for ambulance parking location selection and capacity determination considering fairness according to claim 1, characterized in that: Step 4: Transformation of multi-objective functions based on weight coefficient method The three objective functions z1, z2 and z3 correspond to weights ω1, ω2 and ω3, and the integrated single objective function can be expressed as: F(x)=ω1z1+ω2z2+ω3z3 Wherein, ω1, ω2 and ω3 are non-negative weight coefficients, and the weights ω1, ω2 and ω3 are set to 1 / 3 respectively.

Images