Model construction method for urban rail emergency facility site selection-distribution problem

Abstract

The invention relates to a model construction method for an urban rail emergency facility site selection-distribution problem, and belongs to the field of emergency facility site selection and planning. The method comprises the following steps: S1, evaluating vulnerability parameters of a site; s2, urban rail emergency facility site selection and material distribution strategy making; s3, symbolized definition of parameters and decision variables; s4, constructing a two-stage site selection-distribution model under the uncertain transportation time; and S5, carrying out dynamic site selection and material distribution on the facility. The method is used for solving the technical problems that when current urban rail transit deals with rainstorm and flood disasters, emergency facilities are lack of reasonable layout, the material distribution efficiency and fairness are low, and the flexibility of dealing with disaster changes is insufficient.

Description

Technical Field

[0001] The invention belongs to the field of emergency facility site selection and planning, and in particular relates to a model building method for urban rail emergency facility site selection-allocation problems. Background Art

[0002] Overview of site selection for urban rail emergency facilities:

[0003] Urban rail transit is developing rapidly, but its ability to respond to emergencies is insufficient. Especially when hit by rainstorm disasters, effective and reasonable emergency rescue facilities need to be established. Limited emergency resources should be effectively distributed to demand points to reduce the losses caused by emergencies. If the facility site is not set up in a suitable location, it will greatly increase capital investment and inventory costs and affect service quality. What is more serious is that improper site selection of emergency facilities will also lead to untimely emergency rescue, resulting in an increase in accident casualties. Therefore, a method for site selection of emergency facilities suitable for urban rail transit (hereinafter referred to as urban rail) is developed to provide key technical guarantees for the rapidly developing urban rail transit to respond to sudden natural disasters.

[0004] Model approach to traditional facility site selection:

[0005] Traditional emergency facility site selection methods rely on expert experience and simple qualitative analysis and lack theoretical basis; or use classic site selection models including P-median model, P-center model and coverage model, among which the coverage model includes set coverage and maximum coverage. P-median and P-center models both determine the location of facilities by minimizing the sum of demand-distance products and minimizing the maximum distance respectively when the number of facilities is specified. Set coverage and maximum coverage models determine the location of facilities by minimizing the number of facilities when the demand points remain unchanged and maximizing the number of demand points when the number of facilities remains unchanged. It is a universal site selection model method.

[0006] Characteristics of site selection for urban rail emergency facilities:

[0007] According to the requirements of the "Safety Assessment Specifications during Urban Rail Transit Operation", urban rail emergency facilities are usually a two-level emergency facility structure of "region-base", and the material capacity, site selection location, material distribution function and rescue scope of each level of emergency facilities are different, so it is necessary to consider adopting a logistics network distribution model that suits the above characteristics. The functional positioning differences of the base and regional levels of urban rail emergency facilities in emergency rescue are as follows: Functional difference, that is, the function of regional facilities is to provide basic emergency rescue; base-level facilities are supplementary rescue for regional emergency facilities, and provide supplementary rescue when the capacity of regional facilities is insufficient or large equipment is required. Material warehouses are set up in base-level facilities, and distribution centers are set up in regional-level facilities, forming a two-level logistics structure of material warehouse-distribution center-demand site. Inventory difference, the candidate points for the establishment of material warehouses are limited to vehicle depots and parking lots, and the material inventory is far more than that of distribution centers. Distribution centers consider capacity-limited facilities. Location difference, material warehouses occupy a large area and can only be built in vehicle depots or parking lots; distribution centers can be built at any site, but cannot be located at the same site as material warehouses.

[0008] Characteristics of urban rail accident rescue under sudden rainstorm disasters:

[0009] Ordinary urban rail accidents usually occur at a single station or line, presenting a single demand. However, in urban rail accidents caused by sudden rainstorm disasters, the accident sites are widely distributed and numerous in the whole area. The demand is large and the delivery timeliness requirements are high.

[0010] The shortcomings of the traditional facility location model method in dealing with the location selection of urban rail emergency facilities:

[0011] The site selection of urban rail emergency facilities should not only consider the timeliness of emergency material distribution, but also consider the limited capacity of facilities. In the early stage of a disaster, the reserved emergency materials may not be enough to meet the actual needs. Therefore, when considering the site selection of urban rail emergency facilities, the material distribution problem should also be considered to ensure the fairness of material distribution. It is necessary to coordinate the site selection of emergency facilities and the distribution of materials. Under heavy rain disasters, urban roads are limited and the material distribution time is uncertain. In addition, the urgency of material demand and the quantity of material demand at the demand site will change with the disaster. Therefore, it is also necessary to consider the dynamic site selection and resource allocation of emergency facilities under uncertainty. However, the existing general site selection methods lack consideration of the characteristics of facility hierarchy and characteristics, capacity constraints, facility resource allocation, uncertain environment, and multiple model objectives. Therefore, they can only be applied to some simple single facility site selection problems. It cannot effectively deal with the problem of site selection of urban rail emergency facilities with large-scale facilities, complex network structures, and large demands in the same period. Summary of the invention

[0012] The purpose of the present invention is to solve the shortcomings of the existing technology and to provide a model construction method for the site selection and allocation problem of urban rail emergency facilities for the current technical problems of the lack of reasonable layout of emergency facilities, low efficiency and fairness of material distribution, and insufficient flexibility in responding to disaster changes when urban rail transit responds to rainstorm and flood disasters.

[0013] To achieve the above object, the technical solution of the present invention is: a model construction method for the site selection and allocation problem of urban rail emergency facilities, comprising:

[0014] Step S1, evaluation of site vulnerability parameters;

[0015] Step S2: formulation of urban rail emergency facility site selection and material distribution strategy;

[0016] Step S3, symbolic definition of parameters and decision variables;

[0017] Step S4: constructing a two-stage location selection-allocation model under uncertain transportation time;

[0018] Step S5: Dynamic site selection and material allocation of facilities.

[0019] In one embodiment of the present invention, in step S1, based on the index system for analyzing and evaluating the vulnerability of rail transit rainstorm waterlogging disasters, the vulnerability degree of each station is evaluated, and the vulnerability degree of each station is divided into three emergency levels: level I, level II, and level III. The material demand quantity and the minimum material satisfaction rate of each level are different, and the material demand quantity of each station is determined according to the vulnerability degree; wherein the vulnerability degree refers to the degree of adverse impact suffered by the subway station when it suffers from rainstorm and flood disasters; the vulnerability degree of the station is affected by the sensitivity of the station and the disaster response capacity of the station, and the mathematical expression formula of the vulnerability degree of the station is as follows:

[0020]

[0021] In the formula, μ is the vulnerability degree of the site; is the site sensitivity; δ is the disaster response capacity of the area where the site is located.

[0022] In one embodiment of the present invention, step S2 is specifically implemented as follows:

[0023] Urban rail emergency facilities adopt a multi-level facility network structure of material warehouse-distribution center-demand site. The depot is an alternative point for material warehouse with no capacity limit, and the station is an alternative point for distribution center with capacity limit. The distribution center is a temporary facility that can change dynamically.

[0024] Considering the continuous demand for materials, a two-stage material satisfaction strategy is adopted. When responding to disasters, the material demand of the demand site is met in two stages; the distribution center is responsible for the emergency material distribution stage, and the material warehouse is responsible for the supplementary material distribution stage; in the first stage, a single demand site is distributed by a single or multiple distribution centers, and the total amount of distributed materials should be greater than the minimum emergency demand of the corresponding demand site, which is called the emergency distribution stage, pursuing timeliness; in the second stage, a single material warehouse distributes and supplements the materials missing from the demand site, which is called the supplementary distribution stage, requiring full coverage of the demand site; the site selection of the material warehouse is a fixed facility site selection, which does not change with the changes in the disaster situation; the site selection of the distribution center is a temporary facility site selection, and the site selection plan and material allocation plan can be adjusted with the changes in the disaster situation, and dynamic site selection and material allocation optimization are carried out; the site selection of the distribution center and the material warehouse do not affect each other, and the site selection plan of the material warehouse will be used as a fixed parameter of the site selection-allocation problem of the distribution center. Then the model of the urban rail emergency facility site selection and material allocation problem includes two sub-models, as follows:

[0025] In the first stage, whether to build a material warehouse on the depot is taken as the decision variable, the facility construction cost is taken as the target, and the number limit of material warehouses, the location selection of material warehouses, and the full coverage of demand sites are taken as constraints. A single-objective full coverage site selection model from the material warehouse to the demand site in the first stage is constructed, which is referred to as the material warehouse site selection model.

[0026] In the second stage, based on the solution of the site selection model in the first stage, i.e., the location of the material warehouse, whether to build a distribution center at the alternative site and the amount of materials allocated between the distribution center and the demand site are used as decision variables, and the logistics system cost, total system distribution time, material distribution fairness and distribution center work efficiency are used as goals. With restrictions on the number of distribution centers, facility location selection restrictions and capacity restrictions, and the minimum quantity of initial material allocation as constraints, a multi-objective site selection-allocation model from the distribution center to the demand site in the second stage is constructed, which is referred to as the distribution center site selection-allocation model.

[0027] In one embodiment of the present invention, step S3 is specifically implemented as follows:

[0028] The h stations in the subway network constitute the station set H. The station set H{j|j=1,2,…,h} can all be selected as distribution centers. Then the distribution center candidate station set P=H, P{i|i=1,2,…,m}, m is the total number of distribution center candidate stations, m=h; according to practical experience, the maximum number of distribution centers is 1 / 10 of the number of stations, that is, the number of distribution centers p≤h / 10; stations are candidate points for distribution centers, and stations that are not selected as distribution centers are demand stations. After p distribution centers are selected, the number of demand stations is n=h-p; the b depots in the subway network constitute the material warehouse candidate point set A{a|a=1,2,…,b}, and p selected sA material warehouse.

[0029] In one embodiment of the present invention, step S4 is specifically implemented as follows:

[0030] Step S4.1, processing of uncertain transportation time;

[0031] Step S4.2, constructing the objective function and problem constraints of the first-stage material warehouse location model;

[0032] Step S4.3: Construction of the objective function and problem constraints of the second-stage distribution center location-allocation model.

[0033] In one embodiment of the present invention, step S4.1 is specifically implemented as follows:

[0034] (1) Characterization of transportation time: The transportation time is converted into time satisfaction in a soft time window, and the fuzzy membership function is constructed using the soft time window to characterize the time satisfaction. The fuzzy membership function f(T ij )for:

[0035]

[0036] in, is the actual material transportation time between distribution center i and site j, is the ideal material transportation time between distribution center i and site j, is the shortest distance from distribution center i to site j, v is the vehicle speed, is the delay time in the transportation of materials from distribution center i to site j caused by environmental factors, is the time allowed for the emergency distribution materials to arrive at the demand site j with a vulnerability of μ, is the expected arrival time of emergency distribution materials for demand site j with vulnerability μ; f(T ij ) is 1, which means that the demand station is satisfied with the transportation time. ij ) is between 0 and 1, which means that the demand site is generally satisfied with the transportation time. ij ) When the value is 0, it means that the demand site is not satisfied with the transportation time;

[0037] (2) Dealing with the uncertainty of transportation time. Affected by the disaster situation, the uncertainty of transportation time directly affects the time satisfaction of the disaster-stricken area with the distribution of emergency materials. The constraint of transportation time is processed into a chance constraint condition using the chance constraint planning method, so that the probability that the time for the materials to arrive at the disaster-stricken area meets the time window is not less than the confidence level θ. The specific expression is as follows:

[0038]

[0039] In one embodiment of the present invention, step S4.2 is specifically implemented as follows:

[0040] The objective function of the material warehouse location selection model in the first stage is the material warehouse construction cost, that is:

[0041]

[0042] Among them, z a is a binary decision variable. If a material warehouse is built at the material warehouse alternative site a, then z a =1, otherwise it is equal to 0, c 1 The cost of building a warehouse for materials;

[0043] The problem constraint of the first-stage material warehouse location model is to limit the requirement that all sites are covered by at least one material warehouse, that is:

[0044]

[0045] Among them, τ aj If site j is within the coverage range R of material warehouse a, then τ aj =1, otherwise 0.

[0046] In one embodiment of the present invention, step S4.3 is specifically implemented as follows:

[0047] The objective function of the second-stage distribution center location-allocation model is as follows:

[0048] (1) The total distribution time target of the site selection-allocation model, that is, the total satisfaction function of the demand site during the emergency material distribution stage, is mathematically expressed as:

[0049]

[0050] Among them, x ij Assign decision variables to binary sites. If the demand site j is in the emergency material distribution stage and is distributed by distribution center i, then x ij =1, otherwise equal to 0;

[0051] (2) The distribution efficiency target of the distribution center in the location selection-allocation model is the optimization function of the minimum maximum average distribution time among all distribution centers in the emergency material distribution system. The mathematical expression is:

[0052] minf 2 =min(T)

[0053] Among them, T is the material processing time limit of a single distribution center;

[0054] (3) The fairness objective of material distribution in the site selection-allocation model is the material shortage rate and function of the emergency material distribution system. The mathematical expression is:

[0055]

[0056] Among them, μ j is the vulnerability level of site j; is the material allocation decision variable, the material transportation volume from distribution center i to site j; is the demand for materials at site j with vulnerability μ under disaster risk level r (r∈R);

[0057] (4) The cost objective of the site selection-allocation model, that is, the comprehensive cost function of the emergency material distribution system, is mathematically expressed as:

[0058]

[0059] Among them, y i is a binary decision variable. If a distribution center is established at the distribution center alternative site i, then y i =1, otherwise equal to 0; c 2 is the storage cost of unit materials in the distribution center; c 3 is the transportation cost per kilometer of unit materials; is the distance from site j to the nearest material warehouse during the supplementary distribution phase; Q is the material capacity of the distribution center;

[0060] The problem constraints of the second-stage distribution center location-allocation model are as follows:

[0061] (1) Site allocation constraint, which means that when a site is selected as a facility, it will not participate in emergency material distribution as a demand site. The mathematical expression is:

[0062]

[0063] Among them, ρ j If a distribution center is established at the distribution center alternative site i, when j = i, then site j is not used as a demand site, ρ j =0, otherwise ρ j =1;

[0064] (2) The demand site allocation constraint means that site i can participate in emergency material distribution only when it is selected as a distribution center. The mathematical expression is:

[0065]

[0066] (3) The number constraints of distribution centers and material warehouses are expressed as follows:

[0067]

[0068] (4) The capacity constraint of the distribution center means that the quantity of materials transported by the distribution center during emergency distribution should not exceed its own material capacity. The mathematical expression is:

[0069]

[0070] (5) The requirement of full coverage of demand sites means that at least one distribution center is assigned to the demand site. The mathematical expression is:

[0071] And y j =1

[0072] (6) The quantity limit of materials received by the demand site during the emergency distribution phase is expressed as:

[0073] And y j =1

[0074] in, is the material allocation decision variable, the material transportation volume from distribution center i to site j;

[0075] (7) The total material quantity limit of the distribution center means that the total material quantity of all distribution centers shall not be less than 80% of the total material demand quantity of all demand sites. The mathematical expression is:

[0076]

[0077] (8) The material handling time limit of the distribution center means that the average delivery time of any distribution center does not exceed time T. The mathematical expression is:

[0078]

[0079] (9) The amount of materials received from the nearest material warehouse during the replenishment distribution phase of the demand site is expressed mathematically as:

[0080] And y j =1

[0081] in, is the quantity of materials received by station j from the nearest material warehouse during the replenishment and distribution phase;

[0082] (10) Transportation time T in the emergency distribution stage ij The chance constraint condition indicates that the probability that the materials arrive at the disaster site at the time that meets the time window is not less than the confidence level θ. The mathematical expression is:

[0083]

[0084] The present invention also provides a model building system for the urban rail emergency facility site selection-allocation problem, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0085] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0086] Compared with the prior art, the present invention has the following beneficial effects:

[0087] Compared with the existing general facility site selection technology, the two-stage site selection-allocation model proposed by the method of the present invention for coping with the uncertain transportation time under the rainstorm disaster takes the time, coverage, cost, and fairness of material distribution as the optimization objectives. On the demand side, the characteristics of large material demand and wide spatial distribution under the rainstorm disaster are taken into account; on the facility side, the structural characteristics of the "region-base" two-level emergency capacity-limited facilities of the urban rail facilities are taken into account. At the same time, the opportunity constraint planning method and dynamic distribution center site selection are used to deal with the uncertainty and variability of sudden disasters respectively, so that the location of emergency facilities and the material distribution plan can well meet the emergency rescue work of the urban rail in response to the rainstorm disaster. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 Flowchart of the model approach for the urban rail emergency facility location-allocation problem;

[0089] Figure 2 Schematic diagram of the urban rail emergency facilities-allocation problem model;

[0090] Figure 3 Schematic diagram of material distribution strategy;

[0091] Figure 4 Schematic diagram of the fuzzy membership function of time satisfaction. DETAILED DESCRIPTION

[0092] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0093] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0094] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0095] like Figure 1 As shown, this embodiment provides a model building method for the emergency facility location-allocation problem, comprising the following steps:

[0096] Step S1, evaluation of site vulnerability parameters;

[0097] Step S2: formulation of urban rail emergency facility site selection and material distribution strategy;

[0098] Step S3, symbolic definition of parameters and decision variables;

[0099] Step S4: Construction of a two-stage location-allocation model under uncertain transportation time

[0100] Step S5: Dynamic site selection and material allocation of facilities.

[0101] In this embodiment, step S1 is specifically as follows:

[0102] Based on the index system for analyzing and evaluating the vulnerability of rail transit torrential rain and flooding disasters, the vulnerability level of each station is evaluated. The vulnerability level of each station is divided into three emergency levels: Level I, Level II, and Level III. The quantity of material requirements and the minimum material satisfaction rate of each level are different. The quantity of material requirements of each station is determined according to the degree of vulnerability. The degree of vulnerability refers to the degree of adverse impact on subway stations when they suffer from torrential rain and flood disasters. The vulnerability level of the station is mainly affected by the sensitivity of the station and the disaster response capacity of the station. The mathematical expression formula of the vulnerability level of the station is as follows:

[0103]

[0104] In the formula, μ is the vulnerability degree of the site; is the site sensitivity; δ is the disaster response capacity of the area where the site is located.

[0105] In this embodiment, step S2 is specifically as follows:

[0106] Urban rail emergency facilities adopt a multi-level facility network structure of material warehouse-distribution center-demand site, such as Figure 2 As shown in the figure, the depot has no capacity limit as a material warehouse alternative, while the station has capacity limit as a distribution center alternative. The distribution center is a temporary facility that can be changed dynamically.

[0107] Considering the need for material continuity, a two-stage material satisfaction strategy is adopted, such as Figure 3 As shown. When responding to disasters, the material needs of demand sites are met in two stages. The distribution center is responsible for the emergency material distribution stage, and the material warehouse is responsible for the supplementary material distribution stage. In the first stage, a single demand site is distributed by a single or multiple distribution centers, and the total amount of distributed materials should be greater than the minimum emergency demand of the demand site, which is called the emergency distribution stage, pursuing timeliness; the second stage is distributed by a single material warehouse to supplement the materials lacking in the demand site, which is called the supplementary distribution stage, requiring full coverage of the demand site. The site selection of the material warehouse is a fixed facility site selection, which does not change with the changes in the disaster situation; the site selection of the distribution center is a temporary facility site selection, and the site selection plan and material allocation plan can be adjusted with the changes in the disaster situation, and dynamic site selection and material allocation optimization are carried out. The site selection of the distribution center and the material warehouse does not affect each other. The site selection plan of the material warehouse will be used as a fixed parameter of the site selection-allocation problem of the distribution center. Then the model of the urban rail emergency facility site selection and material allocation problem mainly includes two sub-models, as follows:

[0108] In the first stage, whether to build a material warehouse on the vehicle depot is taken as the decision variable, the facility construction cost is taken as the target, and the number limit of material warehouses, location selection of material warehouses and full coverage of demand sites are taken as constraints. A single-objective full coverage site selection model from the first stage material warehouse to the demand site is constructed, which is referred to as the material warehouse site selection model.

[0109] In the second stage, based on the solution of the site selection model in the first stage, i.e., the location of the material warehouse, the decision variables are whether to build a distribution center at the alternative site and the amount of materials allocated between the distribution center and the demand site. The goals are the logistics system cost, the total system distribution time, the fairness of material distribution and the work efficiency of the distribution center. The constraints are the number of distribution centers, the facility location selection and capacity restrictions, the minimum quantity of initial material allocation, etc., to construct a multi-objective site selection and allocation model from the distribution center to the demand site in the second stage, referred to as the distribution center site selection and allocation model.

[0110] In this embodiment, step S3 is specifically as follows:

[0111] The h stations in the subway network constitute the site set H. The site set H{j|j=1,2,…,h} can all be selected as distribution centers, so the distribution center candidate site set P=H. According to practical experience, the maximum number of distribution centers is 1 / 10 of the number of sites, that is, the number of distribution centers p≤h / 10. The site is the candidate point of the distribution center, and the site that is not selected as the distribution center is the required site. After p distribution centers are selected, the number of required sites is n=h-p. The b depots in the subway network constitute the material warehouse candidate point set A{a|a=1,2…,b}. The model parameters and decision variables are shown in Table 1.

[0112] Table 1 Model parameters and decision variables

[0113]

[0114]

[0115] In this embodiment, step S4 is specifically as follows:

[0116] Step S4.1, processing of uncertain transportation time;

[0117] Step S4.2, constructing the objective function and problem constraints of the first-stage material warehouse location model;

[0118] Step S4.3: Construction of the objective function and problem constraints of the second-stage distribution center location-allocation model.

[0119] Furthermore, the step S4.1 includes the following contents:

[0120] (1) Characterization of transportation time: converting transportation time into soft time windows (e.g. Figure 4 The fuzzy membership function is constructed using the soft time window to characterize the time satisfaction. ij )for:

[0121]

[0122] f(T ij ) is 1, which means that the demand station is satisfied with the transportation time. ij ) is between 0 and 1, which means that the demand site is generally satisfied with the transportation time. ij ) value is 0, which means that the demand site is not satisfied with the transportation time.

[0123] (2) Dealing with the uncertainty of transportation time. Affected by the disaster situation, the uncertainty of transportation time directly affects the time satisfaction of the disaster-stricken area with the distribution of emergency materials. The opportunity constraint programming method is used to treat the transportation time constraint as an opportunity constraint condition, so that the probability that the time for the materials to arrive at the disaster-stricken area meets the time window is not less than the confidence level θ. The specific expression is as follows:

[0124]

[0125] Furthermore, the step S4.2 includes the following contents:

[0126] In step S4.2, the objective function is the material warehouse construction cost, that is:

[0127]

[0128] In step S4.2, the problem constraint is to limit the requirement that all sites are covered by at least one material warehouse, that is:

[0129]

[0130] Furthermore, the step S4.3 includes the following contents:

[0131] In step S4.3, the objective function is as follows:

[0132] (1) The total distribution time target of the site selection-allocation model, that is, the total satisfaction function of the demand site during the emergency material distribution stage, is mathematically expressed as:

[0133]

[0134] (2) The distribution efficiency target of the distribution center in the location selection-allocation model is the optimization function of the minimum maximum average distribution time among all distribution centers in the emergency material distribution system. The mathematical expression is:

[0135] minf 2 =min(T)

[0136] (3) The fairness objective of material distribution in the site selection-allocation model is the material shortage rate and function of the emergency material distribution system. The mathematical expression is:

[0137]

[0138] (4) The cost objective of the site selection-allocation model, that is, the comprehensive cost function of the emergency material distribution system, is mathematically expressed as:

[0139]

[0140] In step S4.3, the problem constraints are as follows:

[0141] (1) Site allocation constraint, which means that when a site is selected as a facility, it will not participate in emergency material distribution as a demand site. The mathematical expression is:

[0142]

[0143] (2) The demand site allocation constraint means that site i can participate in emergency material distribution only when it is selected as a distribution center. The mathematical expression is:

[0144]

[0145] (3) The number constraints of distribution centers and material warehouses are expressed as follows:

[0146]

[0147] (4) The capacity constraint of the distribution center means that the quantity of materials transported by the distribution center during emergency distribution should not exceed its own material capacity. The mathematical expression is:

[0148]

[0149] (5) The requirement of full coverage of demand sites means that at least one distribution center is assigned to the demand site. The mathematical expression is:

[0150] And y j =1

[0151] (6) The quantity limit of materials received by the demand site during the emergency distribution phase is expressed as:

[0152] And y j =1

[0153] (7) The total material quantity limit of the distribution center means that the total material quantity of all distribution centers shall not be less than 80% of the total material demand quantity of all demand sites. The mathematical expression is:

[0154]

[0155] (8) The material handling time limit of the distribution center means that the average delivery time of any distribution center does not exceed time T. The mathematical expression is:

[0156]

[0157] (9) The amount of materials received from the nearest material warehouse during the replenishment distribution phase of the demand site is expressed mathematically as:

[0158] And y j =1

[0159] (10) Transportation time T in the emergency distribution stage ij The chance constraint condition indicates that the probability that the materials arrive at the disaster site at the time that meets the time window is not less than the confidence level θ. The mathematical expression is:

[0160]

[0161] In this embodiment, step S5 is specifically as follows:

[0162] Dynamic site selection and material allocation of facilities, considering the material demand of each site under the intensity changes of rainstorm and flood disasters in different time periods in the urban area As changes occur, the location of the distribution center and the material allocation plan need to be dynamically adjusted.

[0163] The present invention also provides a model building system for the urban rail emergency facility site selection-allocation problem, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0164] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0165] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0166] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0167] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0168] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0169] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A model construction method for the location-allocation problem of urban rail emergency facilities, characterized in that: include: Step S1, evaluation of site vulnerability parameters; Step S2: formulation of urban rail emergency facility site selection and material distribution strategy; Step S3, symbolic definition of parameters and decision variables; Step S4: constructing a two-stage location selection-allocation model under uncertain transportation time; Step S5: Dynamic site selection and material allocation of facilities.

2. A model building method for the urban rail emergency facility location-allocation problem according to claim 1, characterized in that: In step S1, based on the index system for analyzing and evaluating the vulnerability of rail transit rainstorm waterlogging disasters, the vulnerability degree of each station is evaluated, and the vulnerability degree of each station is divided into three emergency levels: level I, level II, and level III. The material demand quantity and the minimum material satisfaction rate of each level are different. The material demand quantity of each station is determined according to the vulnerability degree; the vulnerability degree refers to the degree of adverse impact suffered by the subway station when it suffers from rainstorm and flood disasters; the vulnerability degree of the station is affected by the sensitivity of the station and the disaster response capacity of the station. The mathematical expression formula of the vulnerability degree of the station is as follows: In the formula, μ is the vulnerability degree of the site; is the site sensitivity; δ is the disaster response capacity of the area where the site is located.

3. A model building method for the urban rail emergency facility location-allocation problem according to claim 2, characterized in that: Step S2 is specifically implemented as follows: Urban rail emergency facilities adopt a multi-level facility network structure of material warehouse-distribution center-demand site. The depot is an alternative point for material warehouse with no capacity limit, and the station is an alternative point for distribution center with capacity limit. The distribution center is a temporary facility that can change dynamically. Considering the continuous demand for materials, a two-stage material satisfaction strategy is adopted. When responding to disasters, the material demand of the demand site is met in two stages; the distribution center is responsible for the emergency material distribution stage, and the material warehouse is responsible for the supplementary material distribution stage; in the first stage, a single demand site is distributed by a single or multiple distribution centers, and the total amount of distributed materials should be greater than the minimum emergency demand of the corresponding demand site, which is called the emergency distribution stage, pursuing timeliness; in the second stage, a single material warehouse distributes and supplements the materials missing from the demand site, which is called the supplementary distribution stage, requiring full coverage of the demand site; the site selection of the material warehouse is a fixed facility site selection, which does not change with the changes in the disaster situation; the site selection of the distribution center is a temporary facility site selection, and the site selection plan and material allocation plan can be adjusted with the changes in the disaster situation, and dynamic site selection and material allocation optimization are carried out; the site selection of the distribution center and the material warehouse do not affect each other, and the site selection plan of the material warehouse will be used as a fixed parameter of the site selection-allocation problem of the distribution center. Then the model of the urban rail emergency facility site selection and material allocation problem includes two sub-models, as follows: In the first stage, whether to build a material warehouse on the depot is taken as the decision variable, the facility construction cost is taken as the target, and the number limit of material warehouses, the location selection of material warehouses, and the full coverage of demand sites are taken as constraints. A single-objective full coverage site selection model from the material warehouse to the demand site in the first stage is constructed, which is referred to as the material warehouse site selection model. In the second stage, based on the solution of the site selection model in the first stage, i.e., the location of the material warehouse, whether to build a distribution center at the alternative site and the amount of materials allocated between the distribution center and the demand site are used as decision variables, and the logistics system cost, total system distribution time, material distribution fairness and distribution center work efficiency are used as goals. With restrictions on the number of distribution centers, facility location selection restrictions and capacity restrictions, and the minimum quantity of initial material allocation as constraints, a multi-objective site selection-allocation model from the distribution center to the demand site in the second stage is constructed, which is referred to as the distribution center site selection-allocation model.

4. A model building method for the urban rail emergency facility location-allocation problem according to claim 3, characterized in that: Step S3 is specifically implemented as follows: The h stations in the subway network constitute the station set H. The station set H{j|j=1,2,…,h} can all be selected as distribution centers. Then the distribution center candidate station set P=H, P{i|i=1,2,…,m}, m is the total number of distribution center candidate stations, m=h; according to practical experience, the maximum number of distribution centers is 1 / 10 of the number of stations, that is, the number of distribution centers p≤h / 10; stations are candidate points for distribution centers, and stations that are not selected as distribution centers are demand stations. After p distribution centers are selected, the number of demand stations is n=h-p; the b depots in the subway network constitute the material warehouse candidate point set A{a|a=1,2,…,b}, and p selected s A material warehouse.

5. A model building method for the urban rail emergency facility location-allocation problem according to claim 4, characterized in that: Step S4 is specifically implemented as follows: Step S4.1, processing of uncertain transportation time; Step S4.2, constructing the objective function and problem constraints of the first-stage material warehouse location model; Step S4.3: Construction of the objective function and problem constraints of the second-stage distribution center location-allocation model.

6. A model building method for the urban rail emergency facility location-allocation problem according to claim 5, characterized in that: Step S4.1 is specifically implemented as follows: (1) Characterization of transportation time: The transportation time is converted into time satisfaction in a soft time window, and the fuzzy membership function is constructed using the soft time window to characterize the time satisfaction. The fuzzy membership function f(T ij )for: in, is the actual material transportation time between distribution center i and site j, is the ideal material transportation time between distribution center i and site j, is the shortest distance from distribution center i to site j, v is the vehicle speed, is the delay time in the transportation of materials from distribution center i to site j caused by environmental factors, is the time allowed for the emergency distribution materials to arrive at the demand site j with a vulnerability of μ, is the expected arrival time of emergency distribution materials for demand site j with vulnerability μ; f(T ij ) is 1, which means that the demand station is satisfied with the transportation time. ij ) is between 0 and 1, which means that the demand site is generally satisfied with the transportation time. ij ) When the value is 0, it means that the demand site is not satisfied with the transportation time; (2) Dealing with the uncertainty of transportation time. Affected by the disaster situation, the uncertainty of transportation time directly affects the time satisfaction of the disaster-stricken area with the distribution of emergency materials. The constraint of transportation time is processed into a chance constraint condition using the chance constraint planning method, so that the probability that the time for the materials to arrive at the disaster-stricken area meets the time window is not less than the confidence level θ. The specific expression is as follows:

7. A model building method for the urban rail emergency facility location-allocation problem according to claim 6, characterized in that: Step S4.2 is specifically implemented as follows: The objective function of the material warehouse location selection model in the first stage is the material warehouse construction cost, that is: Among them, z a is a binary decision variable. If a material warehouse is built at the material warehouse alternative site a, then z a =1, otherwise it is equal to 0, c1 is the construction cost of the material warehouse; The problem constraint of the first-stage material warehouse location model is to limit the requirement that all sites are covered by at least one material warehouse, that is: Among them, τ aj If site j is within the coverage range R of material warehouse a, then τ aj =1, otherwise 0.

8. A model building method for the urban rail emergency facility location-allocation problem according to claim 7, characterized in that: Step S4.3 is specifically implemented as follows: The objective function of the second-stage distribution center location-allocation model is as follows: (1) The total distribution time target of the site selection-allocation model, that is, the total satisfaction function of the demand site during the emergency material distribution stage, is mathematically expressed as: Among them, x ij Assign decision variables to binary sites. If the demand site j is in the emergency material distribution stage and is distributed by distribution center i, then x ij =1, otherwise equal to 0; (2) The distribution efficiency target of the distribution center in the location selection-allocation model is the optimization function of the minimum maximum average distribution time among all distribution centers in the emergency material distribution system. The mathematical expression is: minf2=min(T) Among them, T is the material processing time limit of a single distribution center; (3) The fairness objective of material distribution in the site selection-allocation model is the material shortage rate and function of the emergency material distribution system. The mathematical expression is: Among them, μ j is the vulnerability level of site j; is the material allocation decision variable, the material transportation volume from distribution center i to site j; is the demand for materials at site j with vulnerability μ under disaster risk level r (r∈R); (4) The cost objective of the site selection-allocation model, that is, the comprehensive cost function of the emergency material distribution system, is mathematically expressed as: Among them, y i is a binary decision variable. If a distribution center is established at the distribution center alternative site i, then y i =1, otherwise it is equal to 0; c2 is the storage cost of unit materials in the distribution center; c3 is the transportation cost per kilometer of unit materials; is the distance from site j to the nearest material warehouse during the supplementary distribution phase; Q is the material capacity of the distribution center; The problem constraints of the second-stage distribution center location-allocation model are as follows: (1) Site allocation constraint, which means that when a site is selected as a facility, it will not participate in emergency material distribution as a demand site. The mathematical expression is: x ij ≤ρ j , Among them, ρ j If a distribution center is established at the distribution center alternative site i, when j = i, then site j is not used as a demand site, ρ j =0, otherwise ρ j =1; (2) The demand site allocation constraint means that site i can participate in emergency material distribution only when it is selected as a distribution center. The mathematical expression is: x ij ≤y i , (3) The number constraints of distribution centers and material warehouses are expressed as follows: (4) The capacity constraint of the distribution center means that the quantity of materials transported by the distribution center during emergency distribution should not exceed its own material capacity. The mathematical expression is: (5) The full coverage constraint of the demand site means that at least one distribution center is assigned to the demand site. The mathematical expression is: (6) The quantity limit of materials received by the demand site during the emergency distribution phase is expressed as: in, is the material allocation decision variable, the material transportation volume from distribution center i to site j; (7) The total material quantity limit of the distribution center means that the total material quantity of all distribution centers shall not be less than 80% of the total material demand quantity of all demand sites. The mathematical expression is: (8) The material handling time limit of the distribution center means that the average delivery time of any distribution center does not exceed time T. The mathematical expression is: (9) The amount of materials received from the nearest material warehouse during the replenishment distribution phase of the demand site is expressed mathematically as: in, is the quantity of materials received by station j from the nearest material warehouse during the replenishment and distribution phase; (10) Transportation time T in the emergency distribution stage ij The chance constraint condition indicates that the probability that the materials arrive at the disaster site at the time that meets the time window is not less than the confidence level θ. The mathematical expression is:

9. A model building system for the location and allocation problem of urban rail emergency facilities, characterized in that: The method comprises a memory, a processor and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps as claimed in any one of claims 1 to 8 can be implemented.

10. A computer-readable storage medium having stored thereon computer program instructions that can be executed by a processor, and when the processor executes the computer program instructions, the method steps according to any one of claims 1 to 8 can be implemented.

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