A method for evaluating reliability of fresh logistics network considering distribution distance constraint

Abstract

The present application relates to a kind of fresh logistics network reliability evaluation method considering distribution distance constraint, belong to logistics technical field.The method effectively overcomes the limitation of traditional evaluation means.First, the method can directly process each edge capacity network model with multiple states, more truly reflect the actual fresh logistics network in the characteristics of the random fluctuation of transport capacity influenced by multiple factors, improve the accuracy and practicality of evaluation model.The present application avoids the calculation combination explosion problem caused by indirect algorithm based on enumeration all minimal path by integrating distance constraint network maximum flow algorithm and decomposition technology, so as to significantly improve the calculation efficiency when evaluating larger scale network.Finally, the reliability index R (d,D) At the same time, the two core constraints of traffic demand and distribution distance are considered, providing direct and quantitative decision-making basis for the planning, optimization and management of fresh logistics network.

Description

Technical Field

[0001] This invention belongs to the field of logistics technology and relates to a method for assessing the reliability of fresh food logistics networks that takes into account delivery distance constraints. Background Technology

[0002] With the rapid development of fresh food e-commerce and offline fresh food supermarkets, fresh food logistics networks have become the core distribution carrier connecting product production areas and end consumers. The reliability of this network directly determines the freshness of fresh products, delivery fulfillment efficiency, product spoilage rate, and the consumer experience of end customers.

[0003] In actual operation, fresh food logistics networks are affected by various uncertainties such as traffic congestion, vehicle malfunctions, equipment abnormalities, and fluctuations in delivery load. The actual delivery capacity of each logistics edge, i.e., the transport capacity, usually exhibits multiple random states. Therefore, fresh food logistics networks can be modeled as a multi-state flow network (MFN), where each edge has an independent, finite, and non-negative real random capacity.

[0004] Compared to ordinary goods, fresh produce is subject to stricter constraints on delivery distance. Excessive delivery distance will cause transportation time to exceed the shelf life, leading to a decline in product quality and even spoilage. This not only results in significant resource waste and increased spoilage costs but also fails to meet the stable supply demands of end customers and fresh produce supermarkets. Therefore, the reliability of a fresh produce logistics network considering delivery distance limitations is defined as the probability that the network can successfully deliver at least d units of fresh produce, provided the total length of the delivery path from the supply location to the demand location does not exceed a preset threshold D. This reliability is denoted as R(d,D).

[0005] Traditional algorithms have significant limitations in calculating this reliability metric. Firstly, most existing methods are only applicable to network models where edge capacity has only two states: normal and failed. This makes them difficult to apply to more realistic fresh food logistics network scenarios where edge capacity has multiple states. Secondly, some existing indirect evaluation methods based on enumerating all minimum paths are computationally inefficient when dealing with large-scale fresh food logistics networks, failing to meet the needs of practical planning and real-time evaluation. Therefore, there is an urgent need for an efficient reliability evaluation method that can simultaneously handle multi-state capacity and delivery distance constraints. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a method for evaluating the reliability of fresh food logistics networks that takes into account delivery distance constraints.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for evaluating the reliability of a fresh food logistics network considering distribution distance constraints, the method comprising the following steps: 1) Set basic parameters, given a demand level d and a distribution distance threshold D, let the reliability index R(d, D) = 0, and set the initial capacity vector set C = [L, U], where L = (l1, l2,..., l m ) is the minimum capacity vector in C, U = (u1, u2,..., u m ) is the maximum capacity vector in C, l i and u i are respectively the minimum and maximum transport capacity values of the i-th edge a i in the network, m is the total number of edges in the network, each edge a i has a corresponding distribution distance Len(a i ), and the length Len(Pj) of any path P j from the source point s to the sink point t is the sum of the distribution distances of all the edges it contains. Only the paths satisfying Len(P j ) ≤ D can be used for distribution.

[0008] 2) Judge the type of the initial capacity vector set C, and use the network maximum flow algorithm with distance constraints to calculate the maximum flows F D The (L) and F D (U) of the network under the minimum capacity vector L and the maximum capacity vector U. If F D (L) ≥ d, then C is an acceptable capacity vector set, let R (d,D) = R (d,D) + Pr(C), and then execute step 6); if F D (U) < d, then C is an unacceptable capacity vector set, and directly execute step 6); if F D (L) < d ≤ F<​​​​​​​​​​​​​​​​​​​​i Flow rate

[0010] 4) Separate the set of acceptable capacity vectors. Based on the flow vector F obtained in step 3), determine the set A d (C) = {a i | a i ∈ A and f i d > l i} = {a k1 , a k2 ,..., a kq}, where A is the set of all edges in the network. Taking each edge a d in A kj , j = 1, 2,..., q as the central axis, decompose the current capacity vector set C into q + 1 non - overlapping subsets C 1 , C 2 ,..., C q , C 0 .

[0011] 5) Update the reliability index R (d,D) , among the subsets obtained by decomposition in step 4), the subset C 0 is the set of acceptable capacity vectors. Let R (d,D) = R (d,D) + Pr(C 0 ), where Pr(C 0 ) is the probability of the subset C 0 .

[0012] 6) Check whether there is a subset of capacity vectors of undetermined type remaining. If so, set one of the undetermined subsets as the new initial capacity vector set C = [L, U], and return to step 2) to continue; if all subsets have been determined, output the value of the final reliability index R (d,D) .

[0013] Furthermore, in step 2), if F[[ID=·59]] D (L)≥ d, then all capacity vectors in the initial capacity vector set C can meet the demand d and the delivery distance constraint D, and the initial capacity vector set C is the set of acceptable capacity vectors

[0014] Furthermore, in step 2), if F D (U)< d, then all capacity vectors in the initial capacity vector set C cannot meet the demand d and the delivery distance constraint D, and the initial capacity vector set C is the set of unacceptable capacity vectors

[0015] Further, in step 2), if FD(L) < d ≤ FD(U), then the initial capacity vector set C contains both capacity vectors that can and cannot satisfy the demand d and the distribution distance constraint D, and the initial capacity vector set C is an uncertain capacity vector set.

[0016] Further, in step 4), using edge a kj as the central axis, the capacity vector set C is decomposed into a subset C j and a remaining set C\C j , where the subset C j is defined as: C j = {X|X ∈ C and x kj = u kj}, and the boundary of C j is: the minimum capacity vector L j = (l1, l2,..., l kj-1 , u kj , l kj+1 ,..., l m ), and the maximum capacity vector U j = (u1, u2,..., u kj- 1, u kj , u kj+1 ,..., u m ).

[0017] Further, the network maximum flow algorithm for the distance constraint is that when calculating the maximum flow from the source point to the sink point, only the paths with a total length not exceeding the distribution distance threshold D are considered.

[0018] Further, the calculation formula for the probability Pr(C0) of the acceptable capacity vector set C0 is: [[ID=~49]]

[0019] where, and are respectively the lower bound and upper bound of the capacity interval of the i-th edge a 0 in the acceptable capacity vector set C i , and is the probability when the capacity state of edge a i is x i .

[0020] Further, the reliability index R (d,D) represents the probability that the fresh food logistics network can successfully deliver at least d units of fresh food products from the source point s to the sink point t when the distribution path length does not exceed the threshold D.

[0021] Further, in step 3), the network obtained after adding the virtual edge is an extended network.

[0022] The beneficial effects of this invention are as follows: First, this method can directly handle real-world fresh food logistics network models with multiple random states of edge capacity, breaking through the limitation of traditional methods that are only applicable to two-state networks. This more realistically reflects network capacity fluctuations and significantly improves the accuracy and practicality of reliability assessment. Second, by integrating a distance-constrained maximum flow algorithm and decomposition technology, it avoids the combinatorial explosion problem caused by indirect algorithms based on enumerating all transmission paths when evaluating large-scale networks, thus greatly improving computational efficiency. Finally, the reliability index defined by this method simultaneously considers the two core constraints of minimum delivery demand and maximum allowable delivery distance, providing a direct and quantitative scientific basis for the planning, optimization, and operation management of fresh food logistics networks. This helps to improve network resilience and the overall delivery guarantee level of fresh food products.

[0023] 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

[0024] 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: Figure 1 This is a schematic diagram of the upward decomposition process of a capacity vector set; Figure 2 This is a flowchart of the method of the present invention; Figure 3 This is a network diagram for a specific embodiment. Detailed Implementation

[0025] 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.

[0026] 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.

[0027] 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.

[0028] A reliability assessment method for fresh food logistics networks considering delivery distance constraints, the method comprising the following steps: 1) Set basic parameters: Given the demand level d, the delivery distance threshold D, let R (d,D) =0, the initial capacity vector set C=[L,U], where L=(l1,l2,…,l m U is a vector with minimum capacity in C, where U = (u1, u2, ..., u2) m ) is the maximum capacity vector in C. Here, l i and u i (1≤i≤m) represent the minimum and maximum capacity values ​​of the i-th edge, respectively, where m is the number of edges in the network. Let Len(a i Let P(i) (1≤i≤m) be the delivery distance of the i-th edge; let P be the path from the source point s to the sink point t. j Length Len(P) j Len(P) is the sum of the delivery distances of all edges contained in the path, where only the path length Len(P) is considered. j Paths with a value of ≤ D can participate in fresh food preservation and delivery.

[0029] 2) Determine the type of capacity vector set: Calculate the maximum flow F of the network under the minimum capacity vector L and the maximum capacity vector U using the distance-constrained maximum flow algorithm. D (L) and F D (U). If F D If (L)≥d, then C is a set of vectors with acceptable capacity, and let R (d,D) =R (d,D)+Pr(C), where Pr(C) is the probability of the capacity vector set C, and then proceed to step 6). If F D (U) < d, then C is an unacceptable capacity vector set, and proceed to step 6). If F D (L) < d ≤ F D (U), then C is classified as an uncertain capacity vector set, and proceed to step 3).

[0030] 3) Determine the feasible flow that satisfies the distance constraint: Add a virtual sink t to the network, and introduce a virtual edge from the original sink t to the virtual sink t . The capacity of the virtual edge is set to d, the distribution distance is set to 0, the capacity of other edges is set to the maximum capacity value corresponding in U, and the distribution distance remains the original value. Use the network maximum flow algorithm with distance constraint to calculate the maximum flow of the extended network, and obtain the flow vector F = (f1 d , f2 d ,..., f m <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​0 The probability of.

[0033] 6) Check if there is an undetermined subset of capacity vectors: If there is an undetermined subset of capacity vectors, set one of the undetermined subsets of capacity vectors as the new initial capacity vector set C=[L,U], and return to step 2) to continue solving; otherwise, output the final R. (d,D) value.

[0034] This embodiment provides a reliability assessment method for fresh food logistics networks considering delivery distance constraints. The flowchart of the method is as follows: Figure 2 As shown, it includes the following steps: 1) Set basic parameters.

[0035] Let G(N,A,C,Len) represent a fresh food logistics network with delivery distance constraints. N={s,1,2,…,n,t} is the set of all nodes in the network. Node s represents the fresh food production area and is the source of fresh food delivery, while node t represents the end customer and is the destination for receiving fresh food. The remaining nodes mainly undertake transit, sorting, and temporary storage functions. A={a1,a2,…,a… m Let} be the set of all edges in the fresh food delivery network, m be the total number of edges, and a be the number of edges. i (1≤i≤m) represents the i-th delivery edge. C=[L,U] is the initial capacity vector set, where L=(l1,l2,...,l m U = (u1, u2, ..., u3) is a vector with minimum capacity in C. m ) is the maximum capacity vector in C. i C and u i C (1≤i≤m) represent the minimum and maximum capacity values ​​of the i-th edge in the initial capacity vector set C, respectively. Len=(Len(a1),Len(a2),…,Len(a... m Len(a) is the delivery distance vector. i (1≤i≤m) is the delivery distance of the i-th edge; any delivery path P j Total length Len(P) j ) is the sum of the delivery distances of all edges of the path, satisfying only Len(P) j )≤D path can participate in fresh food preservation and delivery.

[0036] In a real-world fresh food logistics environment, the state of each delivery edge can be described by a random variable, with values ​​ranging from l. i to u i Integers between (inclusive) i and u i), the state probability distributions of each side are known and independent of each other. Set the fresh food delivery demand d and the delivery distance threshold D, and let R (d,D) = 0.

[0037] 2) Determine the type of the capacity vector set.

[0038] Use the maximum flow algorithm of the distance constraint network to calculate the maximum flow F D (L) and F D (U) of the network that satisfies the delivery distance constraint under the conditions of the minimum capacity vector L and the maximum capacity vector U respectively. Since the maximum flow function under the distance constraint has the property of non-decreasing, that is, the larger the capacity of the capacity vector, the larger the maximum flow that the network can transmit. Therefore, the type of the current capacity vector set C can be uniquely determined by the maximum flow results of the minimum capacity vector and the maximum capacity vector.

[0039] If F D (L) ≥ d, it means that all the capacity vectors in the capacity vector set C can meet the double constraints of the fresh food delivery demand d and the delivery path length not exceeding the threshold D. Therefore, C is an acceptable capacity vector set, and let R (d,D) = R (d,D) + Pr(C), where Pr(C) = = represents any capacity vector in the network, x i represents the capacity state of the i-th edge a MISSING END TAG HERE, SHOULD BE i i of, represents the i-th edge a MISSING END TAG HERE, SHOULD BE i i when the capacity state is x MISSING END TAG HERE, SHOULD BE i i the probability at this time. The capacity states of each edge are independent of each other. Therefore, the total probability of the capacity vector set is calculated by multiplying the cumulative probabilities of each edge in the corresponding capacity interval. After completing the probability accumulation, go to step 6).

[0040] If F D (U) < d, it means that all the capacity vectors in the capacity vector set C cannot meet the fresh food delivery demand d and the delivery path length constraint D. At this time, C is an unacceptable capacity vector set and has no contribution to the reliability result. Directly go to step 6).

[0041] If F D (L) < d ≤ F D (U), it means that there are both capacity vectors that meet the constraints and those that do not meet the constraints in the current capacity vector set C, and the overall effectiveness cannot be directly determined. Therefore, C is classified as an uncertain capacity vector set, and it is necessary to further perform the feasible flow solution and state set decomposition operations, and go to step 3).

[0042] 3) Determine the feasible flow that satisfies the distance constraint.

[0043] There seem to be some missing end tags in the original text which might cause issues in a complete and accurate understanding. Please check and correct if possible.Add a virtual rendezvous point t to the initial fresh food logistics network And add a line pointing from the initial sink t to the virtual sink t. Let the newly added virtual edge have a capacity state of d and a delivery distance of 0, while other edges have a. i The state is equal to u i The delivery distance remains unchanged. Using the improved maximum flow algorithm, specifically the delivery distance-constrained network maximum flow algorithm, the maximum flow from the source node s to the virtual sink node t is calculated. The fresh produce delivery flow through each edge in the network then constitutes the feasible flow vector F = (f1...) for the delivery distance-constrained network. d f2 d ,…,f m d ).

[0044] 4) Separate the acceptable capacity vector set.

[0045] Based on the d-flow vector F obtained in step 3), determine the decomposed edge set: A d (C)={a i ∈A|f i d >l i}={a k1 ,a k2 ,…,a k q} where l i For edge a i The minimum transport capacity state in set C. (Using A) d Using each side of (C) as a central axis, following the upward decomposition approach, the original capacity vector set C is decomposed layer by layer into q+1 disjoint subsets Cq+1. 1 C 2 ..., C q C 0 The decomposition process is as follows Figure 1 As shown.

[0046] With a k1 Using the central axis, decompose C into C1. 1 With C\C 1 ; With a k2 Using C\C as the central axis 1 Decompose into C 2 With C(C) 1 ∪C 2 ); And so on, starting with a. k3 -a kq Decompose the remaining set around the central axis to obtain C. 1 -C q With C 0 .

[0047] All subsets are mutually exclusive, non-overlapping, and non-exclusive, where C 0 It must be a vector set with acceptable capacity, and the remaining subsets C i The type of (1≤i≤q) needs to be further determined.

[0048] 5) Calculate R (d,D) value.

[0049] In all subsets obtained in step 4), C 0 It must be a vector set with acceptable capacity, while the remaining subset C i The type of (1≤i≤q) is not yet determined and needs to be further determined sequentially. Calculate subset C. 0 The corresponding probability Pr(C) 0 ), and let R (d,D) =R (d,D) +Pr(C 0 ), where Pr(C 0 It is obtained by multiplying the probabilities of each side within the corresponding capacity range.

[0050] 6) Check for undetermined capacity vector subsets: Check each of the capacity vector subsets obtained in step 4) to determine if any subsets have undetermined types. If undetermined subsets exist, set one of them as the new initial capacity vector set C=[L,U], and proceed to step 2) to continue type determination and subsequent calculations; if all subsets have been determined, output the final R. (d,D) value.

[0051] The present invention will be described in detail below with reference to specific embodiments: An abstraction of a fresh food logistics network yields Figure 3 The network shown contains 4 nodes and 6 delivery edges. Node s represents the fresh produce production area, intermediate nodes 1 and 2 represent transit and distribution stations, and node t represents the terminal store. Table 1 shows the probability distribution of the transport capacity of each delivery edge and the delivery distance values ​​of each edge.

[0052] Assuming the fresh produce delivery demand d=300 (unit: kg / box), that is, under the condition that the delivery route length does not exceed the distance threshold D=400 (unit: km), the probability that the terminal node t can receive no less than 300 units of fresh produce.

[0053] Table 1

[0054] According to the method steps of this invention, the solution process is as follows: 1) Set basic parameters. Based on the known conditions, the initial values ​​are set as follows: d=300, D=400. R (300,400) =0, C=[L,U], L=(0,0,0,0,0,0), U=(300,200,100,100,100,200). Delivery distance vector Len=(101.5,203.8,96.2,104.7,99.1,195.3). 2) Determine the type of capacity vector set. Calculate the network maximum flow F satisfying the delivery distance constraint under the conditions of minimum capacity vector L and maximum capacity vector U using the distance-constrained network maximum flow algorithm. D (L) and F D (U). Since the maximum flow function under distance constraints has the property of monotonically non-decreasing, the type of the current capacity vector set C can be determined by the maximum flow result of the minimum capacity vector and the maximum capacity vector. The calculated F... D (L)=0, F D (U) = 400, satisfying F D (L) <d≤F D (U), therefore, it is determined that the capacity vector set C belongs to the uncertain capacity vector set, and proceed to step 3).

[0055] 3) Determine feasible flows that satisfy the distance constraints. Construct an extended network by adding a virtual sink t to the original network. And introduce a path from the original sink t to t A virtual edge is defined, with a capacity of 300 and a delivery distance of 0. The capacities of edges a1–a6 are set to their maximum values ​​of 300, 200, 100, 100, 100, and 200, respectively, while the delivery distances of each edge remain unchanged. An improved maximum flow algorithm is used to solve the extended network with delivery distance constraints, yielding a feasible flow vector that satisfies the distance limit: F = (200, 200, 0, 0, 100, 100).

[0056] 4) Separate the acceptable capacity vector set. Based on the feasible flow vector F=(200,200,0,0,100,100) obtained in step 3), the set A can be obtained. d (C) = {a1, a2, a5, a6}. Using each edge as a decomposition axis, the capacity vector set C is divided into the following subsets: C 1 =[(0,0,0,0,0,0),(100,200,100,100,100,200)] C 2 =[(200,0,0,0,0,0),(300,100,100,100,100,200)] C 3=[(200,200,0,0,0,0),(300,200,100,100,0,200)] C 4 =[(200,200,0,0,100,0),(300,200,100,100,100,0)] C 0 =[(200,200,0,0,100,100),(300,200,100,100,100,200)] 5) Calculate R (300,400) value.

[0057] Among the subsets obtained in step 4), C 0 is the acceptable capacity vector set, and its corresponding probability: Pr(C 0 ) = 0.85×0.6×1×1×0.9×0.95 = 0.43605 Then R (300,400) = R (300,400) + Pr(C 0 ) = 0.43605. For the remaining subsets C 1 , C 2 , C 3 , C 4 , their types need to be further judged.

[0058] 6) Check whether there is a subset of capacity vectors whose type has not been determined.

[0059] For the subsets C 1 , C 2 , C 3 , C 4 , their types have not been judged. First, discuss C 1 . Set C 1 as the new initial capacity vector set, that is, let C = [L, U] = C 1 , and turn to step 2) to continue the solution.

[0060] 2) Judge the type of the capacity vector set. Use the maximum flow algorithm of the distance constraint network to calculate the maximum flows F D (L) and F D (U) of the network that satisfy the distribution distance constraint under the conditions of the minimum capacity vector L and the maximum capacity vector U respectively. After calculation, F D (L) = 0, F D (U) = 20, and since F D (U) < d, it is determined that the capacity vector set C belongs to the unacceptable capacity vector set, and turn to step 6).

[0061] 6) Check whether there is a subset of capacity vectors whose type has not been determined.

[0062] Subset C 2 C 3 C 4 The type has not been determined; let's discuss C first. 2 , put C 2 Let C = [L, U] = C be the new initial capacity vector set. 2 Proceed to step 2) to continue solving.

[0063] 2) Determine the type of capacity vector set. Calculate the maximum flow F of the network satisfying the delivery distance constraint under the conditions of minimum capacity vector L and maximum capacity vector U using the distance-constrained network maximum flow algorithm. D (L) and F D (U). Calculated F D (L)=0, F D (U) = 300, satisfying F D (L) <d≤F D (U), therefore, it is determined that the capacity vector set C belongs to the uncertain capacity vector set, and proceed to step 3).

[0064] 3) Determine the feasible flow vector for the distance-constrained network. The capacity states of edges a1–a6 are set to the maximum values ​​of 300, 100, 100, 100, 100, and 200, respectively, while the delivery distances of each edge remain unchanged. The improved maximum flow algorithm is used to solve the extended network with delivery distance constraints, resulting in the feasible flow vector that satisfies the distance constraints: F = (200, 200, 100, 0, 0, 100).

[0065] 4) Decompose the capacity vector set. Based on the feasible flow vector F=(200,200,100,0,0,100) obtained in step 3), the set A can be obtained. d (C) = {a2, a3, a5, a6}. Using each edge as a decomposition axis, the capacity vector set C is divided into the following subsets: C 1 =[(200,0,0,0,0,0),(300,0,100,100,100,200)], C 2 =[(200,100,0,0,0,0),(300,100,0,100,100,200)] C 3 =[(200,100,100,0,0,0)(300,100,100,100,0,200)] C 4 =[(200,100,100,0,100,0),(300,100,100,100,100,100)] C0 =[(200,100,100,0,100,200)(300,100,100,100,100,200)] 5) Calculate R (300,400) Value. In the subset obtained in step 4), C 0 Given an acceptable capacity vector set, its corresponding probability is: Pr(C 0 = 0.85 × 0.3 × 0.9 × 1 × 0.9 × 0.7 = 0.144585 Then R (300,400) =R (300,400) +Pr(C 0 =0.43605 + 0.144585 = 0.580635. The remaining subset C 3 C 4 The type needs further judgment.

[0066] 6) Check if there is a subset of capacity vectors of undetermined type.

[0067] Subset C 3 C 4 The type has not been determined; let's discuss C first. 3 , put C 3 Let C = [L, U] = C be the new initial capacity vector set. 3 Proceed to step 2) to continue solving.

[0068] 2) Determine the type of capacity vector set. Calculate the maximum flow F of the network satisfying the delivery distance constraint under the conditions of minimum capacity vector L and maximum capacity vector U using the distance-constrained network maximum flow algorithm. D (L) and F D (U). Calculated F D (L)=200, F D (U) = 300, satisfying F D (L) <d≤F D (U), therefore, it is determined that the capacity vector set C belongs to the uncertain capacity vector set, and proceed to step 3).

[0069] 3) Determine the feasible flow vector for the distance-constrained network. The capacity states of edges a1–a6 are set to the maximum values ​​of 300, 200, 100, 100, 0, and 200, respectively, while the delivery distances of each edge remain unchanged. The improved maximum flow algorithm is used to solve the extended network with delivery distance constraints, resulting in the feasible flow vector that satisfies the distance constraints: F = (300, 200, 100, 0, 0, 100).

[0070] 4) Decompose the capacity vector set. Based on the feasible flow vector F=(300,200,100,0,0,100) obtained in step 3), the set A can be obtained. d(C) = {a1, a3, a6}. Taking each side as the decomposition axis, the capacity vector set C is partitioned into the following subsets: C 1 = [(200, 200, 0, 0, 0, 0), (200, 200, 100, 100, 0, 200)], C 2 = [(300, 200, 0, 0, 0, 0), (300, 200, 0, 100, 0, 200)] C 3 = [(300, 200, 100, 0, 0, 0), (300, 200, 100, 100, 0, 0)] C 0 = [(300, 200, 100, 0, 0, 100), (300, 200, 100, 100, 0, 200)] 5) Calculate the R (300,400) value. Among the subsets obtained in step 4), C 0 is the acceptable capacity vector set, and its corresponding probability: Pr(C 0 ) = 0.6×0.6×0.9×1×(0.1×0.95) = 0.03078 Then R (300,400) = R (300,400) + Pr(C 0 ) = 0.580635 + 0.03078 = 0.611415. The types of the remaining subsets C 4 need to be further determined.

[0071] 6) Check if there are capacity vector subsets of undetermined types.

[0072] [[ID= forty]]The type of the subset C 4 has not been determined. Set C 4 as the new initial capacity vector set, that is, let C = [L, U] = C 4 , and turn to step 2) to continue the solution.

[0073] 2) Determine the type of the capacity vector set. Use the maximum flow algorithm of the distance constraint network to calculate the maximum flows F D (L) and F D (U) of the network that satisfy the delivery distance constraint under the conditions of the minimum capacity vector L and the maximum capacity vector U. After calculation, F D (L) = 200, F D (U) = 200, and since F D (U) < d, it is determined that the capacity vector set C belongs to the unacceptable capacity vector set. [[ID= sixty]]

[0074] Output R (300,400) = 0.611415 It should be noted that there seems to be an error in the probability calculation in the original text where "(0.1×0.95)" is written as "0.1×0.95" without parentheses in the probability calculation formula. The correct calculation should be with parentheses as shown in the translation. Also, the "d" mentioned in the text but not defined. The above translation is based on the provided text while making the necessary adjustments for correct mathematical expression. Therefore, under the constraint of a total delivery distance not exceeding 400km, the reliable probability of this fresh food logistics network stably delivering ≥300 units of fresh food to terminal supermarkets is 61.14%. This reliability information can be used to guide transportation optimization, transit warehouse layout and delivery service management.

[0075] 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 reliability assessment of fresh food logistics networks considering delivery distance constraints, characterized in that: The method includes the following steps: 1) Set basic parameters: given the demand level d and the delivery distance threshold D, let the reliability index R(d, D) = 0, and set the initial capacity vector set C=[L,U], where L=(l1,l2,...,l m Let U be the minimum capacity vector in C, where U = (u1, u2, ..., u2) m Let ) be the maximum capacity vector in C, l i and u i Let a be the i-th edge in the network. i The minimum and maximum capacity values, where m is the total number of edges in the network, and each edge a i It has a corresponding delivery distance Len(a) i Any path P from source point s to sink point t j The length Len(Pj) is the sum of the delivery distances of all its contained edges, and only when Len(Pj) satisfies the condition that Len(Pj) is the delivery distance of all its contained edges is the delivery distance of all edges that are included. j Paths with a value of 0.5 ≤ D can be used for delivery. 2) Determine the type of the initial capacity vector set C, and use the distance-constrained network maximum flow algorithm to calculate the maximum flow F of the network under the minimum capacity vector L and the maximum capacity vector U D (L) and F D (U). If F D (L) ≥ d, then C is an acceptable capacity vector set, and let R (d,D) = R (d,D) + Pr(C), and then execute step 6); if F D (U) < d, then C is an unacceptable capacity vector set, and directly execute step 6); if F D (L) < d ≤ F D (U), then C is an uncertain capacity vector set, and execute step 3). 3) Determine feasible flows that satisfy distance constraints. Add a virtual sink t to the network and add a virtual edge pointing from the original sink t to the virtual sink t. Set the capacity of this virtual edge to d and the delivery distance to 0. Then, add all other edges a in the network except the virtual edge. i The capacity is set to u i The distance-constrained maximum flow algorithm for networks is used to calculate the distance from the source node s to the virtual sink node t. The maximum flow is obtained by the flow vector F = (f1) d f2 d ,...,f m d ), where f i d This indicates that the i-th edge a is used to pass through the i-th edge. i Traffic. 4) Separate the acceptable capacity vector set, and determine set A based on the flow vector F obtained in step 3). d (C)={a i |a i ∈A and f i d >l i }={a k1 ,a k2 ,...,a kq }, where A is the set of all edges in the network, denoted by A. d Each edge a in (C) kj Using j=1,2,...,q as the central axis, decompose the current capacity vector set C into q+1 disjoint subsets Ci. 1 C 2 ,...,C q C 0 . 5) Update reliability index R (d,D) In the subset obtained from the decomposition in step 4), subset C 0 Let R be a vector set with acceptable capacity. (d,D) =R (d,D) +Pr(C 0 ), where Pr(C 0 ) is a subset C 0 The probability of. 6) Check if there are any undetermined subsets of capacity vectors. If so, set one of these undetermined subsets as the new initial capacity vector set C=[L,U], and return to step 2) to continue execution. If all subsets have been determined, output the final reliability index R. (d,D) The value of .

2. The method for reliability assessment of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: In step 2), if F D If (L)≥d, then all capacity vectors in the initial capacity vector set C can satisfy the demand d and the delivery distance constraint D, and the initial capacity vector set C is an acceptable capacity vector set.

3. The method for assessing the reliability of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: In step 2), if F D (U) < d, then all capacity vectors in the initial capacity vector set C cannot satisfy the demand d and the delivery distance constraint D, and the initial capacity vector set C is an unacceptable capacity vector set.

4. The method for assessing the reliability of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: In step 2), if FD(L) < d ≤ FD(U), then the initial capacity vector set C contains both capacity vectors that can satisfy and cannot satisfy the demand d and the delivery distance constraint D, and the initial capacity vector set C is an uncertain capacity vector set.

5. The method for reliability assessment of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: In step 4), the side a kj Decompose the capacity vector set C into subsets C' using the central axis. j With the remainder set C\C j subset C j Defined as: C j ={X|X∈C and x kj =u kj }, and C j The boundary is: the minimum capacity vector L j =(l1,l2,...,l kj-1 ,u kj ,l kj+1 ,...,l m ), Maximum capacity vector U j =(u1,u2,...,u kj- 1,u kj ,u kj+1 ,...,u m ).

6. The method for reliability assessment of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: The network maximum flow algorithm for the distance constraint only considers paths with a total length not exceeding the delivery distance threshold D when calculating the maximum flow from the source point to the sink point.

7. The method for assessing the reliability of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: The calculation formula for the probability Pr(C0) of the acceptable capacity vector set C0 is: in, and C represents the set of vectors with acceptable capacity. 0 The i-th edge a i The lower and upper bounds of the capacity range, For edge a i The capacity state is x i The probability of that time.

8. The method for reliability assessment of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: The reliability index R (d,D) This represents the probability that the fresh food logistics network can successfully deliver at least d units of fresh food from the source point s to the sink point t, provided that the delivery path length does not exceed the threshold D.

9. The method for reliability assessment of fresh food logistics networks considering delivery distance constraints according to claim 1, characterized in that: In step 3), the network obtained after adding the virtual edge is an extended network.

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