Emergency logistics transportation network time reliability assessment method and system

Abstract

The invention relates to an emergency logistics transportation network time reliability assessment method and system, and belongs to the technical field of emergency logistics. The invention provides an efficient evaluation scheme based on state space decomposition and a Dijkstra shortest path algorithm in order to solve the technical problems that a traditional network communication reliability index cannot meet the timeliness requirement of emergency logistics and an existing algorithm is too high in calculation complexity. The technical scheme comprises the steps of determining network basic data; calculating and determining a state edge set; searching a feasible path in the determined working edge set; if not, searching in a larger edge set to judge the property of the state set; decomposing the uncertain state set based on the feasible path edge set and identifying feasible subsets; and recursively processing each subset. According to the method, the service level of the emergency logistics network under the rescue time constraint can be accurately evaluated, the calculation efficiency of a large-scale network is remarkably improved through algorithm optimization, and a scientific basis is provided for optimization management of the emergency logistics network.

Description

Technical Field

[0001] This invention belongs to the field of emergency logistics technology and relates to a method and system for assessing the time reliability of emergency logistics transportation networks. Background Technology

[0002] Emergency logistics transportation networks, serving as a crucial link between the supply and demand sides of emergency supplies, have become an indispensable infrastructure in modern emergency management systems. Unlike conventional logistics, emergency logistics is characterized by its suddenness, extremely high timeliness requirements, and complex transportation environments. However, the presence of numerous uncertainties during emergencies poses severe challenges to emergency logistics transportation networks. Factors such as road damage, traffic congestion, severe weather, and infrastructure failures can all lead to various states, including complete disruption of transportation routes or significant reduction in capacity, thereby affecting the operational efficiency and reliability of the entire network. Based on this stochastic characteristic, many studies model logistics transportation networks as two-state stochastic networks, where each transportation edge has an independent working or failed state, and the state probabilities of each edge are typically determined based on historical data and real-time monitoring information.

[0003] Traditional network reliability refers to the probability that at least one connected path exists within a network. This metric primarily focuses on network connectivity and can effectively assess a network's basic service capability under random failure conditions. However, emergency response has extremely high time requirements, and simply ensuring network connectivity is far from sufficient. Time constraints indicate that emergency logistics transportation not only needs to guarantee connectivity but also needs to complete tasks under strict time constraints.

[0004] Therefore, traditional network connectivity reliability indicators are no longer sufficient to comprehensively and accurately assess the actual service capacity of emergency logistics transportation networks. Successfully completing material transportation within the stipulated time is as important as, or even more critical than, basic network connectivity. Based on this, this invention proposes a new indicator that integrates connectivity reliability and time constraints, termed the "emergency logistics transportation network time reliability." This time reliability indicator refers to the probability that at least one path in the network meets the transportation time constraint. Compared to traditional reliability indicators, travel time reliability not only considers network connectivity but also comprehensively assesses the travel time of the path, thus providing a more comprehensive reflection of the service level of the emergency logistics network under time constraints. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method and system for evaluating the time reliability of emergency logistics transportation networks, so as to solve the technical problems that traditional connectivity reliability indicators cannot meet the timeliness requirements of emergency logistics, and that the computational complexity of existing exhaustive algorithms and disjoint sum algorithms is too high.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for assessing the time reliability of an emergency logistics transportation network, comprising the following steps:

[0008] 1) Determine the basic data of the emergency logistics transportation network: Let G(M,E) represent the emergency logistics transportation network, where M={s,1,2,…,n,t} represents the set of all nodes in the network, node s represents the supply location of emergency supplies, node t represents the demand location of emergency supplies; nodes 1,2,…,n represent transit stations or transfer stations, and E={e i |1≤i≤m} represents all transport edges e i The set of transport edges, where m is the total number of transport edges; in the network, each transport edge e i Each transport edge has two states: active and inactive. When an edge is in the active state, it indicates that it is passable; when an edge is in the inactive state, it indicates that it is inactive. Each transport edge e i The probability of being in a working state is When transport side e i When in working condition, its travel time is t. i The initial state vector set X = {x = (x1, x2, ..., x...} m )|x i = 0 or 1, where 1 ≤ i ≤ m}, where x = (x1, x2, ..., xm) m ) represents the state vector, x i (1≤i≤m) represents the transport edge e i The state; given the transportation time constraint T0, the time reliability of the emergency logistics transportation network. The definition is: the probability that there exists at least one path in the network that satisfies the transport time constraint T0, such that the initial time reliability is...

[0009] 2) Calculate edge sets E1(X) and E2(X): Define E1(X) = {e i |For any x∈X, x i =1}, E2(X)={e i |For any x∈X, x i =0}, and let E(X) = E1(X)∪E2(X);

[0010] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X): with transport edge e i The travel time t for (1≤i≤m) i As weights, Dijkstra's shortest path algorithm is used in E1(X) to search for the shortest path P from the starting point s to the ending point t. The travel time T(P) of path P is defined as the sum of the travel times of all edges in P, i.e. If T(P) ≤ T0, then P is a feasible path, and X is a set of feasible state vectors. Let Where Pr(X) is the probability of the feasible state vector set X, then proceed to step 6);

[0011] 4) Search for a feasible path P in E-E2(X) using Dijkstra's shortest path algorithm: Search for the shortest path P from the starting point s to the ending point t in E-E2(X). If the shortest path does not satisfy T(P)≤T0, then there is no feasible path in E-E2(X), and X is an infeasible state vector set, proceeding to step 6); conversely, if the shortest path satisfies T(P)≤T0, then P is a feasible path, and X is an uncertain state vector set. Here, E-E2(X) is the subtraction operation between set E and set E2(X), representing the set of edges that belong to set E but not to set E2(X), i.e.

[0012] 5) Decompose the uncertain state vector set X: Based on the feasible path P found in step 4), let Based on EM, the state vector set X is decomposed into k+1 subsets X 1 ,X 2 ,…,X k and X 0 , where X 1 ={x=(x1,x2,…,x m )|x i =1 when e i ∈E1(X),x i =0 when e i ∈(E2(X)∪{e q1}),x i =0 or 1 when e i ∈(EE(X)-{e q1})},

[0013] X 2 ={x=(x1,x2,…,x m )|x i =1 when e i ∈(E1(X)∪{e q1}),x i =0 when e i ∈(E2(X)∪{e q2}),x i =0 or 1 when e i ∈(EE(X)-{e q1 ,e q2})},

[0014]

[0015] X k ={x=(x1,x2,…,x m )|x i =1 when e i ∈(E1(X)∪{e q1 ,e q2 ,...,e qk-1}),x i =0 when e i ∈(E2(X)∪{e qk}),x i =0 or 1 when e i ∈(EE(X)-EM)},

[0016] X 0 ={x=(x1,x2,…,x m )|x i =1 when e i ∈(E1(X)∪EM),x i =0 when e i ∈E2(X),x i =0 or 1 when e i ∈(EE(X)-EM)}.

[0017] in, make Where Pr(X) 0 X is the set of feasible state vectors. 0 The probability of;

[0018] 6) Continue the calculation for each subset: calculate each subset X 1 ,X 2 ,…,X k Each subset is treated as a new set of state vectors X, and the calculation continues in step 2) until all subsets have been calculated; finally, the time reliability value is output.

[0019] Furthermore, in step 5), X is decomposed into subsets Xi. 1 ,X 2 ,...,X k and X 0 , where X 0 For a subset of feasible state vectors, the probability Pr(X) 0 The calculation formula is: in

[0020] An emergency logistics transportation network time reliability assessment system, the system comprising:

[0021] The data determination module is used to determine the basic data for the emergency logistics transportation network;

[0022] The edge set calculation module is used to calculate the edge sets E1(X) and E2(X) corresponding to the state vector set X;

[0023] The path search module is used to search for feasible paths in a specified edge set using Dijkstra's shortest path algorithm.

[0024] The state determination module is used to determine the properties of the state vector set based on the path search results.

[0025] The spatial decomposition module is used to decompose an uncertain state vector set;

[0026] The recursive calculation module is used to recursively perform the evaluation process on the decomposed subsets;

[0027] The results output module is used to output the final time reliability value.

[0028] Furthermore, the path search module is configured to first search for the shortest path in E1(X), and if no feasible path is found, then search for the shortest path in E-E2(X).

[0029] Furthermore, the spatial decomposition module decomposes the uncertain state vector set X into multiple disjoint subsets based on the edge set EM of the feasible path P, and identifies the feasible state vector subset X among them. 0 .

[0030] Furthermore, the recursive calculation module is configured to treat each decomposed subset as a new set of state vectors, and then re-call the edge set calculation module, path search module, state determination module, and space decomposition module for processing until all subsets are evaluated.

[0031] The beneficial effects of this invention are as follows:

[0032] (1) This invention creatively proposes a time reliability index for emergency logistics transportation networks that integrates time constraints. Compared to traditional reliability indices that only focus on network connectivity, this invention uses timeliness requirements as the core evaluation dimension, enabling accurate assessment of the actual service level of emergency logistics networks under rescue time constraints. This innovative index makes the evaluation results more in line with the practical needs of emergency rescue, providing a more scientific and reliable basis for emergency decision-making.

[0033] (2) This invention employs advanced state space decomposition technology, effectively avoiding the traditional exhaustive method of enumerating each state vector in the state vector space one by one. By systematically decomposing the uncertain state space and prioritizing the identification of feasible paths, this algorithm significantly reduces computational complexity, making it possible to conduct efficient and rapid time reliability assessments of large-scale emergency logistics transportation networks, thus solving a key bottleneck problem in practical applications.

[0034] (3) This invention not only considers network connectivity, but also comprehensively evaluates the travel time of the path, realizing an upgrade in the evaluation dimension from "whether it can be connected" to "whether it can be connected in a timely manner". This comprehensive evaluation perspective can more realistically reflect the service capabilities of the emergency logistics network in a complex and uncertain environment, and provide deeper decision support for network optimization, resource allocation and emergency plan formulation.

[0035] (4) This invention is an extension of the mature Dijkstra's shortest path algorithm. The method has a clear structure and standardized process, and is highly practical and operable. This method can be easily integrated into existing emergency management information systems and can be put into use without complex technical modifications, which is conducive to its rapid promotion and application in actual emergency command systems.

[0036] (5) This invention is based on a solid theoretical foundation, including random network theory and state-space analysis, and its method has rigorous logic and reliability. This technical framework is not only applicable to the field of emergency logistics, but its core ideas can also be extended to multiple fields that require reliability assessment of network timeliness, such as communication networks and traffic planning, showing broad application prospects.

[0037] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0038] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0039] Figure 1 This is a flowchart illustrating the framework of the present invention;

[0040] Figure 2 This is a network diagram for a specific embodiment. Detailed Implementation

[0041] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0042] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0043] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0044] This invention provides a method for assessing the time reliability of emergency logistics transportation networks, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0045] 1) Determine the basic data for the emergency logistics transportation network.

[0046] Let G(M,E) denote an emergency logistics transportation network, where M = {s,1,2,…,n,t} represents the set of all nodes in the network, node s represents the supply location of emergency supplies, node t represents the demand location of emergency supplies; nodes 1,2,…,n represent transit stations or transfer stations, and E = {e i |1≤i≤m} represents all transport edges e i The set of e, where e i (1≤i≤m) represents the transport edges connecting a pair of nodes, where m is the total number of transport edges; the complete set of network state vectors Θ={x=(x1,x2,…,x…} m )|x i= 0 or 1, where 1 ≤ i ≤ m} is the set of all state vectors x, containing all possible combinations of transport edge states. The initial state vector set X = {x = (x1, x2, ..., xm} m )|x i = 0 or 1, where 1 ≤ i ≤ m} is a subset of the universal set Θ, where the state vector x = (x1, x2, ..., xm) m This indicates that each transport edge e i The current state indicates whether the network is currently connected; in the network, each transport edge e i Both have two states: working state and failed state, denoted by x. i (1≤i≤m) can be used to represent: x i =1 means e i In working condition, x i =0 means e i In a failed state; when a transport edge is in a working state, it indicates that it can pass normally; when a transport edge is in a failed state, it indicates that it cannot pass normally; each transport edge e i The probability of being in a working state is (1≤i≤m), when transport edge e i When in working condition, its travel time is t. i Accordingly, each transport edge e i The probability of being in a failed state is When transport side e i When in a failed state, the transport edge cannot pass normally, and its passage time is infinite; given the transport time constraint T0, the time reliability of the emergency logistics transport network... The definition is: the probability that there exists at least one path in the network that satisfies the transport time constraint T0, such that the initial time reliability is...

[0047] 2) Calculate edge sets E1(X) and E2(X).

[0048] Define E1(X) = {e i |For any x∈X, x i =1}, E2(X)={e i |For any x∈X, x i =0}, and let E(X) = E1(X)∪E2(X), and calculate the edge set E(X).

[0049] 3) Use Dijkstra's algorithm to search for a feasible path P in E1(X).

[0050] With each transport edge e i Travel time t iAs weights, Dijkstra's shortest path algorithm is used in E1(X) to search for the shortest path P from the starting point s to the ending point t. The travel time T(P) of path P is defined as the sum of the travel times of all edges in P, i.e. If T(P) ≤ T0, then P is a feasible path, and X is a set of feasible state vectors. Let Where Pr(X) is the probability of the feasible state vector set X, then proceed to step 6);

[0051] Here, a feasible path P is a path p from the starting point s to the ending point t, satisfying all transport edges e. i All are in a working state, and the sum of their travel times T(p) ≤ T0; a feasible state vector set X refers to a set in which each state vector has at least one feasible path from s to t in the network; the probability of the feasible state vector set X is Pr(X) = Pr(E(X)) = Pr(E1(X))Pr(E2(X)), and...

[0052] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0053] If no feasible path is found in step 3), Dijkstra's shortest path algorithm is used to search for the shortest path P from the starting point s to the ending point t in E-E2(X). If the shortest path does not satisfy T(P)≤T0, then there is no feasible path in E-E2(X), and X becomes an infeasible state vector set, proceeding to step 6). Conversely, if the shortest path satisfies T(P)≤T0, then X becomes an uncertain state vector set. Here, E-E2(X) is the subtraction operation between set E and set E2(X), representing the set of edges that belong to set E but not to set E2(X), i.e.

[0054] Here, the infeasible state vector set X refers to a set in which there is no feasible path from s to t for each state vector in the network; if X is neither a feasible state vector set nor an infeasible state vector set, then X is an uncertain state vector set.

[0055] 5) Decompose the uncertain state vector set X.

[0056] Based on the feasible path P found in step 4), let Based on EM, the state vector set X is decomposed into k+1 subsets X 1 ,X 2 ,…,X k and X 0 ,in

[0057] X 1={x=(x1,x2,…,x m )|x i =1 when e i ∈E1(X),x i =0 when e i ∈(E2(X)∪{e q1}),x i =0 or 1 when e i ∈(EE(X)-{e q1})},

[0058] X 2 ={x=(x1,x2,…,x m )|x i =1 when e i ∈(E1(X)∪{e q1}),x i =0 when e i ∈(E2(X)∪{e q2}),x i =0 or 1 when e i ∈(EE(X)-{e q1 ,e q2})},

[0059]

[0060] X k ={x=(x1,x2,…,x m )|x i =1 when e i ∈(E1(X)∪{e q1 ,e q2 ,...,e qk-1}),x i =0 when e i ∈(E2(X)∪{e qk}),x i =0 or 1 when e i ∈(EE(X)-EM)},

[0061] X 0 ={x=(x1,x2,…,x m )|x i =1 when e i ∈(E1(X)∪EM),x i =0 when e i ∈E2(X),x i =0 or 1 when e i ∈(EE(X)-EM)}.

[0062] in, Uncertain state vector set X and subset X 1 X 2 ,…,X k X 0 The following relationship must be satisfied: X = X 1 ∪X 2 ∪…∪X k ∪X 0 Furthermore, subset X is disjoint; in addition, subset X... 0 There is a property that subset X 0 Let be the set of feasible state vectors, let Where Pr(X) 0 X is the set of feasible state vectors. 0 The probability of;

[0063] 6) Continue the calculation for each subset: calculate each subset X 1 ,X 2 ,…,X k Each subset is treated as a new set of state vectors X, and the calculation continues in step 2) until all subsets have been calculated; finally, the time reliability value is output.

[0064] Table 1. Probability of working status and passage time at the transport side

[0065]

[0066] The present invention will be described in detail below with reference to specific embodiments:

[0067] A specific implementation example Figure 2 As shown, Figure 2 This is an undirected network graph corresponding to an emergency logistics transportation network. The network has four nodes, namely M = {s, 1, 2, t}, and five transportation edges, namely E = {e1, e2, e3, e4, e5}. Node s represents the supply location of emergency supplies in the network, node t represents the demand location of emergency supplies in the network, and nodes 1 and 2 represent transit stations or transfer stations. Table 1 shows the transportation edge e in the network. i The probability of working status and the passage time.

[0068] The method of this invention is used below to measure the probability that the logistics transportation network can transport a certain amount of relief supplies from the starting point s to the destination t with the total network travel time being less than or equal to the time constraint T0 = 35, i.e., the time reliability of the emergency logistics transportation network.

[0069] The solution process according to the method steps of this invention is as follows:

[0070] 1) Determine the basic data for the emergency logistics transportation network.

[0071] Based on the known conditions, the initial values ​​are set as follows: T0 = 35. X=Θ={x=(x1,x2,…,x5)|x i = 0 or 1, where 1 ≤ i ≤ 5}.

[0072] 2) Calculate E1(X) and E2(X).

[0073] but Next step.

[0074] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0075] No feasible path exists. Next step.

[0076] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0077] The shortest path P = {e1, e4} has been found, and T(P) = 13 ≤ T0. A feasible path exists. Proceed to the next step.

[0078] 5) Decompose the uncertain state vector set X.

[0079] EM is calculated based on the feasible paths found in step 4), where EM = {e1, e4}. X is then decomposed into the following subsets: X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i = 0 or 1, where 2 ≤ i ≤ 5, X 2 ={x=(x1,x2,x3,x4,x5)|x1=1,x4=0,x i = 0 or 1, where i ∈ {2, 3, 5}, and X 0 ={x=(x1,x2,x3,x4,x5)|x1=x4=1,x i = 0 or 1, where i∈{2,3,5}}, X 0 Let be the set of feasible state vectors, let

[0080] 6) Continue the calculation for each subset.

[0081] Subset X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i = 0 or 1, where 2 ≤ i ≤ 5 and X 2 ={x=(x1,x2,x3,x4,x5)|x1=1,x4=0,x i= 0 or 1, where i∈{2,3,5}} is not solved. Let's discuss X first. 2 , put X 2 Let X = X 2 Proceed to step 2) and continue the calculation.

[0082] 2) Calculate E1(X) and E2(X).

[0083] If E1(X) = {e1} and E2(X) = {e4}, then E(X) = {e1,e4}. Next step.

[0084] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0085] Since E1(X) = {e1}, no feasible path can be formed. Next step.

[0086] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0087] The shortest path P = {e2, e5} has been found, and T(P) = 21 ≤ T0. A feasible path exists. Proceed to the next step.

[0088] 5) Decompose the uncertain state vector set X.

[0089] EM is calculated based on the feasible paths found in step 4), where EM = {e2, e5}. X is then decomposed into the following subsets: X 2-1 ={x=(x1,x2,x3,x4,x5)|x1=1,x2=x4=0,x i = 0 or 1, where i ∈ {3, 5}, X 2-2 ={x=(x1,x2,x3,x4,x5)|x1=x2=1,x4=x5=0,x3=0 or 1}, X 2-0 ={x=(x1,x2,x3,x4,x5)|x1=x2=x5=1,x4=0,x3=0 or 1} (because these subsets are from X) 2 To avoid confusion, these subsets are represented by X. 2-1 X 2-2 X 2-0 (to represent), X 0 Let be the set of feasible state vectors, let

[0090] 6) Continue the calculation for each subset.

[0091] Subset X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i= 0 or 1, where 2 ≤ i ≤ 5, X 2-1 ={x=(x1,x2,x3,x4,x5)|x1=1,x2=x4=0,x i = 0 or 1, where i ∈ {3, 5} and X 2-2 The expression {x = (x1, x2, x3, x4, x5) | x1 = x2 = 1, x4 = x5 = 0, x3 = 0 or 1} has not been solved. Let's discuss X first. 2-2 , put X 2-2 Let X = X 2-2 Proceed to step 2) and continue the calculation.

[0092] 2) Calculate E1(X) and E2(X).

[0093] If E1(X) = {e1, e2} and E2(X) = {e4, e5}, then E(X) = {e1, e2, e4, e5}. Next step.

[0094] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0095] Since E1(X) = {e1, e2}, no feasible path can be formed. Next step.

[0096] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0097] If there is no feasible path for E-E2(X), then X is an infeasible state vector set, and proceed to step 6).

[0098] 6) Continue the calculation for each subset.

[0099] Subset X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i = 0 or 1, where 2 ≤ i ≤ 5 and X 2-1 ={x=(x1,x2,x3,x4,x5)|x1=1,x2=x4=0,x i = 0 or 1, where i∈{3,5}} is not solved. Let's discuss X first. 2-1 , put X 2-1 Let X = X 2-1 Proceed to step 2) and continue the calculation.

[0100] 2) Calculate E1(X) and E2(X).

[0101] If E1(X) = {e1} and E2(X) = {e2,e4}, then E(X) = {e1,e2,e4}. Next step.

[0102] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0103] Since E1(X) = {e1}, no feasible path can be formed. Next step.

[0104] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0105] The shortest path P = {e1, e3, e5} has been found, and T(P) = 31 ≤ T0. Therefore, a feasible path exists. Proceed to the next step.

[0106] 5) Decompose the uncertain state vector set X.

[0107] EM is calculated based on the feasible paths found in step 4), where EM = {e3, e5}. X is then decomposed into the following subsets: X 2-1-1 ={x=(x1,x2,x3,x4,x5)|x1=1,x2=x3=x4=0,x5=0 or 1}, X 2-1-2 ={x=(x1,x2,x3,x4,x5)|x1=x3=1,x2=x4=x5=0} and X 2-1-0 ={x=(x1,x2,x3,x4,x5)|x1=x3=x5=1,x2=x4=0} (Similarly, because these subsets are from X) 2-1 To avoid confusion, these subsets are represented by X. 2-1-1 X 2-1-2 X 2-1-0 (to represent), X 2 -1-0 Let be the set of feasible state vectors, let

[0108] 6) Continue the calculation for each subset.

[0109] Subset X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i = 0 or 1, where 2 ≤ i ≤ 5, X 2-1-1 ={x=(x1,x2,x3,x4,x5)|x1=1,x2=x3=x4=0,x5=0 or 1} and X 2-1-2 The expression {x = (x1, x2, x3, x4, x5) | x1 = x3 = 1, x2 = x4 = x5 = 0} has not been solved. Let's discuss X first. 2-1-2 , put X 2-1-2 Let X = X 2-1-2 Proceed to step 2) and continue the calculation.

[0110] 2) Calculate E1(X) and E2(X).

[0111] If E1(X) = {e1, e3} and E2(X) = {e2, e4, e5}, then E(X) = {e1, e2, e3, e4, e5}. Next step.

[0112] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0113] Since E1(X) = {e1, e3}, no feasible path can be formed. Next step.

[0114] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0115] If there is no feasible path for E-E2(X), then X is an infeasible state vector set, and proceed to step 6).

[0116] 6) Continue the calculation for each subset.

[0117] Subset X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i = 0 or 1, where 2 ≤ i ≤ 5 and X 2-1-1 The expression {x = (x1, x2, x3, x4, x5) | x1 = 1, x2 = x3 = x4 = 0, x5 = 0 or 1} has not been solved. Let's discuss X first. 2-1-1 , put X 2-1-1 Let X = X 2-1-1 Proceed to step 2) and continue the calculation.

[0118] 2) Calculate E1(X) and E2(X).

[0119] If E1(X) = {e1} and E2(X) = {e2,e3,e4}, then E(X) = {e1,e2,e3,e4}. Next step.

[0120] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0121] Since E1(X) = {e1}, no feasible path can be formed. Next step.

[0122] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0123] If there is no feasible path for E-E2(X), then X is an infeasible state vector set, and proceed to step 6).

[0124] 6) Continue the calculation for each subset.

[0125] Subset X 1 ={x=(x1,x2,x3,x4,x5)|x1=0,x i =0 or 1, where 2≤i≤5} is not solved. Discuss X 1 , put X 1 Let X = X 1 Proceed to step 2) and continue the calculation.

[0126] 2) Calculate E1(X) and E2(X).

[0127] E1(X) = {e1}, Then E(X) = {e1}, next step.

[0128] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0129] Since E1(X) = {e1}, no feasible path can be formed. Next step.

[0130] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0131] The shortest path P = {e2, e5} has been found, and T(P) = 21 ≤ T0. A feasible path exists. Proceed to the next step.

[0132] 5) Decompose the uncertain state vector set X.

[0133] EM is calculated based on the feasible paths found in step 4), where EM = {e2, e5}. X is then decomposed into the following subsets: X 1-1 ={x=(x1,x2,x3,x4,x5)|x1=x2=0,x i = 0 or 1, where i∈{3,4,5}}, X 1-2 ={x=(x1,x2,x3,x4,x5)|x2=1,x1=x5=0,x i = 0 or 1, where i ∈ {3, 4} and X 1-0 ={x=(x1,x2,x3,x4,x5)|x2=x5=1,x1=0,x i = 0 or 1, where i ∈ {3, 4}, X 1-0 Let be the set of feasible state vectors, let

[0134] 6) Continue the calculation for each subset.

[0135] Subset X 1-1={x=(x1,x2,x3,x4,x5)|x1=x2=0,x i = 0 or 1, where i∈{3,4,5}}, X 1-2 ={x=(x1,x2,x3,x4,x5)|x2=1,x1=x5=0,x i = 0 or 1, where i∈{3,4}} is not solved. Let's discuss X first. 1-2 , put X 1-2 Let X = X 1-2 Proceed to step 2) and continue the calculation.

[0136] 2) Calculate E1(X) and E2(X).

[0137] If E1(X) = {e2} and E2(X) = {e1,e5}, then E(X) = {e1,e2,e5}. Next step.

[0138] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0139] Since E1(X) = {e2}, no feasible path can be formed. Next step.

[0140] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0141] The shortest path P = {e2, e3, e4} has been found, and T(P) = 33 ≤ T0. Therefore, a feasible path exists. Proceed to the next step.

[0142] 5) Decompose the uncertain state vector set X.

[0143] EM is calculated based on the feasible paths found in step 4), where EM = {e3, e4}. X is then decomposed into the following subsets: X 1-2-1 ={x=(x1,x2,x3,x4,x5)|x2=1,x1=x3=x5=0,x4=0 or 1},X 1-2-2 ={x=(x1,x2,x3,x4,x5)|x2=x3=1,x1=x4=x5=0} and X 1-2-0 ={x=(x1,x2,x3,x4,x5)|x2=x3=x4=1,x1=x5=0},X 1-2-0 Let be the set of feasible state vectors, let

[0144] 6) Continue the calculation for each subset.

[0145] Subset X 1-1 ={x=(x1,x2,x3,x4,x5)|x1=x2=0,xi = 0 or 1, where i∈{3,4,5}}, X 1-2-1 ={x=(x1,x2,x3,x4,x5)|x2=1,x1=x3=x5=0,x4=0 or 1} and X 1-2-2 The expression {x = (x1, x2, x3, x4, x5) | x2 = x3 = 1, x1 = x4 = x5 = 0} has not been solved. Let's discuss X first. 1-2-2 , put X 1-2-2 Let X = X 1-2-2 Proceed to step 2) and continue the calculation.

[0146] 2) Calculate E1(X) and E2(X).

[0147] If E1(X) = {e2,e3} and E2(X) = {e1,e4,e5}, then E(X) = {e1,e2,e3,e4,e5}. Next step.

[0148] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0149] Since E1(X) = {e2, e3}, no feasible path can be formed. Next step.

[0150] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0151] If there is no feasible path for E-E2(X), then X is an infeasible state vector set, and proceed to step 6).

[0152] 6) Continue the calculation for each subset.

[0153] Subset X 1-1 ={x=(x1,x2,x3,x4,x5)|x1=x2=0,x i = 0 or 1, where i ∈ {3, 4, 5} and X 1-2-1 The expression {x = (x1, x2, x3, x4, x5) | x2 = 1, x1 = x3 = x5 = 0, x4 = 0 or 1} has not been solved. Let's discuss X first. 1-2-1 , put X 1-2-1 Let X = X 1-2-1 Proceed to step 2) and continue the calculation.

[0154] 2) Calculate E1(X) and E2(X).

[0155] If E1(X) = {e2} and E2(X) = {e1,e3,e5}, then E(X) = {e1,e2,e3,e5}. Next step.

[0156] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0157] Since E1(X) = {e2}, no feasible path can be formed. Next step.

[0158] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0159] If there is no feasible path for E-E2(X), then X is an infeasible state vector set, and proceed to step 6).

[0160] 6) Continue the calculation for each subset.

[0161] Subset X 1-1 ={x=(x1,x2,x3,x4,x5)|x1=x2=0,x i = 0 or 1, where i∈{3,4,5}} is not solved. Discuss X 1-1 , put X 1-1 Let X = X 1-1 Proceed to step 2) and continue the calculation.

[0162] 2) Calculate E1(X) and E2(X).

[0163] If E2(X) = {e1, e2}, then E(X) = {e1, e2}. Next step.

[0164] 3) Use Dijkstra's shortest path algorithm to search for a feasible path P in E1(X).

[0165] No feasible path can be established. Next step.

[0166] 4) Use Dijkstra's shortest path algorithm to search for a feasible path P in E-E2(X).

[0167] If there is no feasible path for E-E2(X), then X is an infeasible state vector set, and proceed to step 6).

[0168] 6) Continue the calculation for each subset.

[0169] There is no subset of state vectors that have not been computed; therefore, the reliability value of the output travel time is determined.

[0170] In other words, the probability that the logistics transportation network can transport relief supplies from the starting point s to the destination t with a total travel time less than or equal to the time constraint T0 = 35 is 0.990483.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for evaluating time reliability of an emergency logistics transportation network, characterized in that: The method comprises the following steps: Step 1): determining the basic data of the emergency logistics transportation network, the basic data comprising network structure, working state probability and passing time of transportation edges; Step 2): calculating edge sets E1(X) and E2(X), wherein E1(X) represents a set of transportation edges whose state vectors in the state vector set X are all in working states, and E2(X) represents a set of transportation edges whose state vectors in the state vector set X are all in failure states; Step 3): search the feasible path P from the start point s to the end point t in the edge set E1(X) by using Dijkstra shortest path algorithm, if the travel time T(P) of the path P satisfies T(P)≤T0, then determine that X is the feasible state vector set, and accumulate its probability to the time reliability value Step 4): if no feasible path is searched in step 3), searching for a feasible path P in the edge set E-E2(X) by using the Dijkstra shortest path algorithm, if no path satisfying T(P)≤T0 exists, determining that the state vector set X is an infeasible state vector set, and if a path exists, determining that the state vector set X is an uncertain state vector set; Step 5): Decompose the set of uncertain state vectors X into a number of mutually disjoint subsets and identify the subset of feasible state vectors X 0 , accumulate their probabilities to Step 6): recursively performing steps 2) to 5) on each subset after decomposition, until all subsets are processed, outputting the final time reliability value 2. The method for evaluating time reliability of emergency logistics transportation network according to claim 1, characterized in that: The emergency logistics transportation network in step 1) is represented as an undirected graph G(M, E), wherein M is a node set, and E is a transportation edge set; the node set M includes an emergency material supply site s, a demand site t, and a transfer station node; each transportation edge e i with working state probability and passing time t i .

3. The method for evaluating time reliability of emergency logistics transportation network according to claim 2, characterized in that: Time reliability in step 1) is defined as the probability that there exists at least one path from s to t in the network with a travel time not exceeding the time constraint To.

4. The method for evaluating time reliability of emergency logistics transportation network according to claim 1, characterized in that: The path P in step 3) has a travel time T(P) calculated by the formula: where t i is the travel time of the transport edge e i .

5. The method for evaluating time reliability of emergency logistics transportation network according to claim 1, characterized in that: The decomposition of the uncertain state vector set X in step 5) is based on the edge set EM searched by the feasible path P, wherein EM=E(P)-E1(X), and E(P) is a set of transportation edges contained in the path P.

6. The method for evaluating time reliability of emergency logistics transportation network according to claim 5, characterized in that: In step 5), X is decomposed into subsets X 1 2 k 0 where X 0 is a feasible state vector subset, and the probability Pr(X0) is calculated as: where ​​​ 7. An emergency logistics transportation network time reliability evaluation system, characterized in that: The system comprises: a data determining module configured to determine the basic data of the emergency logistics transportation network; an edge set calculating module configured to calculate edge sets E1(X) and E2(X) corresponding to the state vector set X; a path searching module configured to search for a feasible path in a specified edge set by using the Dijkstra shortest path algorithm; a state determining module configured to determine the properties of the state vector set according to the path searching result; a space decomposition module configured to decompose the uncertain state vector set; a recursive calculation module configured to perform the evaluation process on the decomposed subsets recursively; A result output module is configured to output the final time reliability value 8. The emergency logistics transportation network time reliability evaluation system of claim 7, wherein: The path searching module is configured to search for the shortest path in E1(X) firstly, and search for the shortest path in E-E2(X) if no feasible path is found.

9. The emergency logistics transportation network time reliability evaluation system of claim 7, wherein: The space decomposition module decomposes the set of uncertain state vectors X into a plurality of mutually disjoint subsets based on the edge set EM of the feasible path P and identifies a subset of feasible state vectors X 0 .

10. The emergency logistics transportation network time reliability evaluation system of claim 7, wherein: The recursive calculation module is configured to take each decomposed subset as a new state vector set, and call the edge set calculating module, the path searching module, the state determining module and the space decomposition module for processing again until all the subsets are evaluated.

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