Ambulance parking site selection and capacity determination method considering fairness

Abstract

The application discloses an ambulance site selection and capacity determination method considering fairness, which can optimize the selection of an ambulance stop station and the number of ambulance stops at each stop station based on the site selection of the ambulance stop station. Three models are involved, which are divided into an emergency demand coverage maximization model, a two-step mobile search method-based ambulance accessibility fairness maximization model and a multi-objective optimization model of an ambulance travel cost minimization model. A weight coefficient method is used to integrate multiple objective functions into a single objective function, a mixed integer nonlinear programming model is established, a Gurobi solver is used for solving, the definition of the model is input, including variables, constraint conditions and an objective function, and the solution of the model, i.e. the value of the variable and the optimal value of the objective function, is output, so that the simultaneous decision of the site selection and capacity determination of the ambulance stop station is realized. The method reduces the time and error of manual judgment, and improves the scheduling efficiency and response speed of the ambulance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of medical first aid, and particularly relates to an ambulance parking site selection and capacity determination method considering fairness. BACKGROUND

[0002] In modern society, an efficient medical emergency rescue system plays a crucial 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 patient treatment and prognosis. However, with the acceleration of urbanization, population growth and distribution changes, and the increasing complexity of traffic conditions, traditional ambulance site selection and capacity determination methods have exposed many limitations.

[0003] Previous studies have focused on minimizing the average response time or maximizing the coverage range. However, this approach may result in a severe lack of emergency services in remote areas or areas inhabited by vulnerable groups, leading to a "Matthew effect" in service resource allocation, i.e., the strong become stronger and the weak become weaker, which violates the principle of social fairness.

[0004] The population in different areas not only differs in quantity, but also differs in age structure, disease spectrum, and socioeconomic status. For example, communities with high aging levels may have more frequent and urgent emergency needs for cardiovascular diseases and other emergencies. Traditional site selection and capacity determination methods do not fully consider these population structure factors, and cannot ensure that different characteristic patients can enjoy fair ambulance emergency services.

[0005] Traffic flow shows significant dynamic changes in time and space. In traffic congestion periods and sections, the actual running speed of ambulances will be greatly reduced, resulting in an extended response time. Traditional methods have considered traffic factors, but have deficiencies in addressing the impact of traffic congestion on fairness in different areas. For example, in the central business district of a city, although the daily traffic flow is large, the response time of ambulances during peak hours may still be better than in remote suburbs due to the relatively abundant medical resources and traffic management measures, exacerbating the imbalance in service fairness between regions. Therefore, an ambulance parking site selection and capacity determination method considering fairness is proposed to address the existing deficiencies. SUMMARY

[0006] The technical problem to be solved by the present application is to overcome the defects of the above-mentioned technology, and to provide an ambulance parking site selection and capacity determination method considering fairness:

[0007] The method can optimize the selection of ambulance parking stations, and optimize the number of ambulance parking stations based on the selection of ambulance parking stations. Three models are involved, which are divided into an emergency demand coverage maximization model, an ambulance accessibility fairness maximization model based on a two-step mobile search method, and a multi-objective optimization model of an ambulance travel cost minimization model. By using the weight coefficient method, multiple objective functions are integrated into a single objective function, a mixed integer nonlinear programming model is established, and a Gurobi solver is used for solving. The definition of the model is input, including variables, constraints and objective functions, and the solution of the model is output, that is, the value of the variable and the optimal value of the objective function, so as to realize the simultaneous decision of the selection and capacity of the ambulance parking station.

[0008] Compared with the prior art, the advantages of the present application are that:

[0009] 1. The existing parking site selection and capacity method mostly optimizes the demand coverage rate maximization, profit maximization, and cost minimization, and lacks research on the accessibility fairness optimization of the ambulance site selection and capacity. The present application introduces the accessibility fairness gap minimization, that is, the fairness maximization as the optimization target. In addition, the present application introduces the service probability threshold of the relatively weak medical resource area and the relatively strong medical resource area based on the traditional emergency maximum coverage model, realizes the individualized emergency service, introduces the gravity model based on the comprehensive evaluation value based on the traditional P-median model, realizes the organic combination of the evaluation method and the parking site selection and capacity model.

[0010] 2. The present application realizes the optimal allocation of medical resources, avoids the waste of ambulance resources, ensures the most effective use of resources in emergency situations, and has wide application prospect and social value.

[0011] 3. The implementation of the method reduces the error of manual scheduling decision, improves the scheduling efficiency and response speed of the ambulance, and thus improves the success rate of emergency treatment. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 It is a flowchart of an ambulance parking site selection and capacity method considering fairness.

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

[0014] In order to make the purpose, technical scheme and advantages of the embodiments of the application clearer, the technical scheme in the embodiments of the application will be described clearly and completely with reference to the drawings in the embodiments of the application.

[0015] A method for ambulance parking site selection and capacity determination considering fairness in combination with the drawings:

[0016] Step 1: Extract basic data

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

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

[0019] (3) The number of ambulance parking at the candidate site of the ambulance parking station is limited, and the maximum number of ambulance parking at each candidate point is determined according to the parking capacity of the actual candidate point.

[0020] Step 2: Establish a target function of the method for ambulance parking site selection and capacity determination considering fairness In actual planning, managers should be user-oriented, 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 invention selects three objectives of emergency user demand, ambulance accessibility and ambulance travel cost for multi-objective optimization.

[0021] (1) Maximum emergency demand coverage model

[0022] The maximum coverage model of emergency is to meet the demand of more emergency users by optimizing the location of each ambulance parking candidate point under the condition of limited fixed cost and operating cost of ambulance. The model formula is as follows:

[0023]

[0024] Where m is the total number of patients, D i1 represents the demand for rescue and monitoring type ambulance at the patient site, D i2 represents the demand for ordinary type ambulance at the patient site, Y i is the decision variable, if the probability of the patient site i in the area with relatively weak medical resources being served by the candidate ambulance parking station j is greater than or equal to α i , then it is 1, otherwise it is 0; if the probability of the patient site i in the area with relatively strong medical resources being served by the candidate ambulance parking station j is greater than or equal to β i , then it is 1, otherwise it is 0.

[0025] (2) Maximum ambulance accessibility model

[0026] Two-step moving search method, the core idea is: respectively with the supply side and the demand side as the reference, according to the set distance threshold to search each other once, therefore it is called two-step moving search method, its general form is expressed as:

[0027] First step: for ambulance station j, search the patient set within its threshold range d0 (derived from historical data according to the geographical layout of the city, traffic conditions, response speed of ambulances, severity of patient conditions, etc.) and calculate its supply-demand ratio R j , as a measure of its service accessibility, for each ambulance station, its ambulance resources S j are shared by users around it, but accessibility decreases with distance. When d ij ≤d0:

[0028]

[0029] Where S j represents the service capacity of candidate ambulance station j (i.e. the maximum number of stops), D i represents the demand for ambulances at patient i within the search range d ij ≤d0, d ij is the distance between patient i and ambulance station j, f is the distance decay function, and m is the total number of patients.

[0030] Second step: for patient i, search the set of ambulance stations within its threshold range d0, and sum the supply-demand ratios of the ambulance stations that fall within the distance threshold range. When d ij ≤d0:

[0031]

[0032] Where A i is the spatial accessibility of patient i, d ij is the distance between patient i and ambulance station j, f is the distance decay function, and n is the total number of ambulance stations.

[0033] Based on the extended form of 2SFCA with the introduction of distance decay function, the present application introduces Gaussian distance decay function to extend the two-step moving search method, and the distance decay function is expressed as:

[0034] When d ij ≤d0,

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

[0036] The fairness maximization model based on accessibility is that every emergency user can get ambulance service, and the equilibrium degree can be reflected by the accessibility gap of different traffic zones. The smaller the accessibility gap is, the more balanced the configuration of ambulance stations is, that is, the greater the fairness is. Every emergency user can get ambulance service, including ordinary ambulance service and rescue 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 i, D i represents the demand of patient i when d ij ≤d0, S represents the total supply capacity, D represents the total number of ambulances required by patient sites, 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 by patient sites.

[0039] For easy solution, z2 is converted into the form of quadratic type:

[0040]

[0041] Among them:

[0042] S=[S1 S2 … S n ] T

[0043]

[0044] A=[a a … a] T ,|A|=m

[0045]

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

[0047] Among them: S represents the service capacity of ambulance stations, which is a column vector containing the ambulance resources of each ambulance station; D represents the number of ambulances required by patient sites, which is an m×m matrix containing the number of ambulances required by each patient site; A represents the spatial accessibility of patient sites, which is a column vector containing the spatial accessibility of patient sites, |A| is the modulus of vector A, which is equal to the total number of patient sites m; q represents the distance attenuation coefficient, which is an m×n matrix containing the distance attenuation coefficient between patient i and ambulance station j; q ijD represents the distance decay function value between patient i and ambulance station j; G represents the relative difficulty coefficient of resource allocation of ambulance station, which is a matrix, G j F represents the relative difficulty coefficient of resource allocation of ambulance station j, and F is the comprehensive evaluation of the actual availability or service ability of resources from ambulance station to patient.

[0048] The objective function is converted into the standard form of quadratic programming, which is shown as follows:

[0049]

[0050] Wherein, x represents the service ability of ambulance station, which is a vector obtained by S; H represents the degree of resource allocation pressure, which is a matrix obtained by multiplying F, D and the transpose of F; f represents the comprehensive rescue difficulty, which is a vector obtained by A, D and the transpose of F.

[0051] x = S

[0052] H = F T DF

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

[0054] The above-mentioned each call user can obtain ambulance service, which includes ordinary ambulance service and rescue monitoring ambulance service, that is, the fairness of the two types of services is maximized, and the specific formula is:

[0055] When d ij ≤ d0, S j1 = W j1 θ1

[0056] When d ij ≤ d0, S j2 = W j2 θ2

[0057] Wherein, R j1 is the supply-demand ratio of rescue monitoring ambulance, R j2 is the supply-demand ratio of ordinary ambulance, which is a measure of its service availability; for each ambulance station j, its rescue monitoring ambulance resource S j1 and ordinary ambulance resource S j2 are shared by the emergency users around it, but the accessibility will decrease with the increase of distance. A i1 is the spatial accessibility of rescue monitoring ambulance at patient i, A i2is the spatial accessibility of the basic ambulance service at patient i, D i is the demand at patient i within the search range d ij ≤d0, D represents the total number of ambulances needed at patient i, m is the total number of patient i, and n is the total number of ambulance stations. W j1 is the number of rescue ambulance stations j that rescue the candidate ambulance station, θ1 represents the rescue ambulance dispatch frequency, and W j2 is the number of basic ambulance stations j at the candidate ambulance station, and θ2 represents the basic ambulance dispatch frequency.

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

[0059]

[0060] For hospital k, search for the set of patient i within its threshold range d1, and sum the supply-demand ratio of patient i falling within the distance threshold. When d ik ≤d1:

[0061]

[0062] where A k is the spatial accessibility of hospital k, S i represents the service capacity of patient i, D k represents the demand at patient i within the search range d ik ≤d1, d ik is the distance between patient i and hospital k, f is the distance decay function, m is the total number of patient i, and l is the total number of hospitals.

[0063]

[0064] where a1 and a2 are the weighted average of the spatial accessibility of rescue ambulance and basic ambulance, respectively.

[0065] The objective function aims to minimize the gap in emergency ambulance accessibility between different regions, with each region being treated equally. Introduce D i1 and D i2 to minimize inequality among emergency users, i.e. areas with more potential patients have greater weight than other areas, Di1 D i2 D

[0066] (3) Ambulance travel cost minimization model

[0067] To maximize service efficiency by minimizing the ambulance travel cost of patients, the ambulance travel cost is represented by the weighted distance sum of emergency users. The smaller the ambulance travel cost, the faster and more convenient the emergency users can obtain the required service. The specific formula is as follows:

[0068]

[0069] Where: P ij is the probability of patient i being served by candidate ambulance stop j (probability prediction is generated by analyzing historical data using quantile regression forest machine learning method), d ij is the distance between patient i and ambulance stop j, D i represents the demand of patient i within the search range d ij ≤d0, X j is the decision variable, which is 1 if the candidate ambulance stop dispatches an ambulance, otherwise it is 0.

[0070] Step 3: Establish a constraint condition for the ambulance stop site selection and sizing method considering fairness

[0071] The constraint conditions of the ambulance stop site selection and sizing model mainly include site selection quantity constraint, service threshold constraint, supply and demand constraint, and ambulance quantity constraint, which are as follows:

[0072] (1) Site selection quantity constraint

[0073]

[0074] Where T represents the site selection quantity limit, and the pre-hospital care site is set up in the urban area with a service radius of 3-5 kilometers, at least one is set up for every 10-15 million people; the pre-hospital care site in rural areas is set up according to every 1-2 administrative townships or according to a service radius of 5-8 kilometers.

[0075] (2) Service threshold constraint

[0076]

[0077] Where, α i is the probability threshold of patient i in the weak medical resource area being served by the candidate ambulance stop, and its value is 0.6, β iY is the probability threshold of a patient's location in an area with abundant medical resources being served by a candidate ambulance stop, with a value of 0.8. M1 is the set of patient locations in areas with limited medical resources, and M2 is the set of patient locations in areas with abundant medical resources. i It is a decision variable; if the probability that patient i in an area with weak medical resources will be served by candidate ambulance stop j is greater than or equal to α... i If the probability of a patient at location i being served by candidate ambulance station j is greater than or equal to β, then the value is 1; otherwise, it is 0. i If the result is positive, the value is 1; otherwise, it is 0.

[0078] Since the selection of a particular ambulance stop for dispatch is an uncertain situation with probabilistic randomness, the service probability index is introduced. The probability that patient i will be served by candidate ambulance stop j is expressed as:

[0079] When d ij When ≤d0,

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

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

[0082] Probability of missing services at the patient's site It must be less than a specific missing service threshold level 1-α i (1-β i That is, for each patient, if Y i If α = 1, then the probability of it being satisfied must be greater than a threshold. For patients in areas with limited medical resources, the threshold is α. i The threshold for patients in areas with abundant medical resources is β. i .

[0083] Nonlinear constraints are transformed into equivalent linear constraints through logarithmic transformation.

[0084]

[0085] (3) Supply and demand constraints

[0086]

[0087] This means that the total supply of each selected candidate ambulance stop must not exceed its service capacity (i.e., the maximum number of stops), where W j1is the number of rescue and monitoring ambulances at candidate ambulance stop j, θ1 is the rescue and monitoring ambulance dispatch frequency, W j2 is the number of general ambulances at candidate ambulance stop j, θ2 is the general ambulance dispatch frequency.

[0088] (4) Ambulance quantity constraint

[0089]

[0090] denotes the sum of the number of rescue and monitoring ambulances and the number of general ambulances at candidate ambulance stop j as the total number of ambulances. W j denotes the total number of ambulances at candidate ambulance stop j.

[0091]

[0092] denotes that if candidate ambulance stop j is selected to dispatch ambulances, the number of rescue and monitoring ambulances and the number of general ambulances are both greater than or equal to 1.

[0093] Step 4: Conversion of multi-objective function 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] In the formula, ω1, ω2 and ω3 are non-negative weight coefficients, and the weights ω1, ω2 and ω3 are respectively set to 1 / 3.

[0097] The above detailed the specific embodiments of the present application. It should be understood that those skilled in the art can make many modifications and changes without creative labor according to the concept of the present application. Therefore, any technical solution that can be obtained by logical analysis, reasoning or limited experiment by those skilled in the art on the basis of the prior art according to the concept of the present application shall be within the protection scope determined by the claims.

Claims

1. An ambulance stop site selection and sizing method considering fairness, characterized in that, The method comprises the following steps: Step 1: Extracting basic data (1) Dividing the emergency area into several traffic zones; (2) Taking the centric coordinate point of the traffic zone where the patient is located as the common coordinate of all patients in the traffic zone; (3) Determining the maximum number of ambulances parked at each candidate site according to the parking capacity of the actual candidate site; Step 2: Establishing a target function of an ambulance parking site selection and capacity determination method considering fairness Three objectives, i.e., emergency user demand, ambulance accessibility fairness and ambulance travel cost, are selected for multi-objective optimization; for the convenience of formula expression, the model symbols and definitions are explained as follows: (1) Emergency demand coverage maximization model The emergency maximum coverage model is to optimize the location of each ambulance parking candidate site to meet more emergency user demands under the condition of limited fixed cost and operating cost of the ambulance; the model formula is as follows: (2) Ambulance accessibility fairness maximization model The two-step moving search method is extended by introducing a Gaussian distance attenuation function, which is expressed as: When d ij ≤ d0, when d ij when d0, where d ij is the distance between the patient i and the ambulance stop j, do is the distance threshold, and f is the distance decay function. The fairness maximization model based on accessibility is embodied in that each emergency user can be served by an ambulance, and the specific formula is: When d ij ≤ d0, S j1 = W j1 θ1 When d ij ≤ d0, S j2 = W j2 θ2 where R j1 is the supply-to-demand ratio of rescue-ambulance, R j2 is the supply-to-demand ratio of ordinary ambulance, as a measure of its service availability; for each ambulance stop j, its rescue-ambulance resource S j1 and ordinary ambulance resource S j2 are shared by its surrounding emergency users, but the accessibility decreases as the distance increases; A i1 is the rescue-ambulance spatial accessibility at patient i, A i2 is the ordinary ambulance spatial accessibility at patient i, D i denotes the demand at patient i within search range d ij ≤ d0, D denotes the total number of ambulances needed at patients, m is the total number of patients, and n is the total number of ambulance stops; For each patient i, search for the set of hospitals k within the threshold range di derived from historical data for i, and compute its supply-demand ratio R k ; when d ik ≤ di: For each hospital k, search the set of patient locations within its threshold range di, and sum the supply-to-demand ratios of patient locations that fall within this distance threshold range; when di ik ≤ d1: where A k is the spatial accessibility of hospital k, S i denotes the service capacity at patient site i, D k denotes the search range, d ik is the ambulance arrival volume at hospital k when 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; Wherein, a1 and a2 are the weighted average of the spatial accessibility of rescue monitoring ambulances and the spatial accessibility of ordinary ambulances, respectively; The objective function aims to minimize the disparity in emergency accessibility between different regions, each of which is treated equally; introducing D i1 and D i2 to minimize the inequality among emergency users, i.e., the region with more potential patients is given a larger weight than other regions, D i1 is the demand for rescue ambulance for patient at i, D i2 is the demand for general ambulance for patient at i; (3) Ambulance travel cost minimization model The ambulance travel cost is represented by the weighted distance sum of emergency users to maximize service efficiency; the smaller the ambulance travel cost, the faster and more convenient the emergency users can obtain the required service; the specific formula is: where: P ij is the probability that a patient at i is served by candidate ambulance stop j, d ij is the distance between a patient at i and ambulance stop j, D i denotes the search range within d ij is the demand at patient i when d < do, X j is the decision variable, 1 if the candidate ambulance stop dispatches an ambulance, otherwise 0; Step 3: Establishing constraint conditions of an ambulance parking site selection and capacity determination method considering fairness The constraint conditions of the ambulance parking site selection and capacity determination model mainly include site number constraint, service threshold constraint, supply and demand constraint, and ambulance number constraint, which are as follows: (1) Site number constraint Wherein, T represents the site number limit; (2) Service threshold constraint wherein, α i is the probability threshold of the patient in the medical resource weak area being served by the candidate ambulance stop station, and its value is 0.6, β i is the probability threshold of the patient in the medical resource strong area being served by the candidate ambulance stop station, and its value is 0.8, M1 is the set of the patients in the medical resource weak area, M2 is the set of the patients in the medical resource strong area; Y i is a decision variable, if the probability of the patient in the medical resource weak area i being served by the candidate ambulance stop station j is greater than or equal to α i , then it is 1, otherwise it is 0; if the probability of the patient in the medical resource strong area i being served by the candidate ambulance stop station j is greater than or equal to β i , then it is 1, otherwise it is 0; Since it is uncertain to select a certain ambulance parking station to dispatch an ambulance, it has probabilistic randomness, therefore, a service probability index is introduced, and the probability that the patient at i is served by the candidate ambulance parking station j is expressed as: When d ij ≤ d0, When d ij = 0, P ij = 0 wherein E j is the comprehensive evaluation value of the ambulance stop station, which represents the attractiveness of the ambulance stop station; d ij is the distance between the patient i and the ambulance stop station j, the distance decay function adopts a power function form, and β is the distance decay parameter; Probability of a patient being underserved Must be less than a specific underserved threshold level 1 - a i (1 - b i ), that is, for each patient site, if Y i = 1, the probability that it is satisfied must be greater than a threshold, a i for patients in a medically underserved area and b i for patients in a medically well-served area; The nonlinear constraint is converted into an equivalent linear constraint by logarithmic transformation; (3) Supply and demand constraint W represents the total supply of each selected candidate ambulance stop station, which shall not exceed its service capacity, i.e. the maximum number of stops, wherein W = ∑θ1j j1 is the number of rescue and monitoring ambulances at candidate ambulance stop station j, θ1is the rescue and monitoring ambulance dispatch frequency, W j2 is the number of ordinary ambulances at candidate ambulance stop station j, θ2is the ordinary ambulance dispatch frequency; (4) Ambulance number constraint The sum of the number of rescue monitoring ambulances and the number of ordinary ambulances at the candidate ambulance parking station j is equal to the total number of ambulances; If the candidate ambulance parking station j is selected to dispatch an ambulance, the number of rescue monitoring ambulances and the number of ordinary ambulances are both greater than or equal to 1; Step 4: Multi-objective function conversion based on weight coefficient method The weights of the three objective functions z1, z2 and z3 are ω1, ω2 and ω3, and the integrated single objective function is expressed as: F(x) = ω1z1 + ω2z2 + ω3z3 In the formula, ω1, ω2 and ω3 are non-negative weight coefficients, and the weights ω1, ω2 and ω3 are set to 1 / 3.

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