A method for evaluating reliability of a logistics supply network considering storage capacity of line-side warehouse nodes

Abstract

This invention relates to a reliability assessment method for logistics supply networks that considers the storage capacity of line-side warehouse nodes, belonging to the fields of industrial engineering and logistics technology. This method aims to solve the problem of distorted assessment results caused by existing technologies neglecting the buffer adjustment capabilities of line-side warehouse nodes and the capacity limitations of transportation channels. The technical solution is as follows: First, a multi-state logistics network model including supplier nodes, line-side warehouse nodes, and production workstation nodes is constructed; then, all feasible flow vectors are generated based on flow conservation and line-side warehouse storage capacity constraints; next, it is verified whether each flow vector satisfies the capacity constraints of each transportation edge in the network; then, the feasible flow vectors are transformed into candidate minimum capacity vectors and screened using a comparison method to obtain all minimum capacity vectors; finally, the reliability probability that the network can meet production needs is calculated. This invention improves the accuracy and realism of reliability assessment of industrial production material supply systems and can effectively reflect the supply value of line-side warehouses in the actual logistics system.

Description

Technical Field

[0001] This invention belongs to the field of industrial engineering and logistics technology, and relates to a method for assessing the reliability of a logistics supply network that considers the storage capacity of line-side warehouse nodes. Background Technology

[0002] In modern Industry 4.0 and intelligent manufacturing systems, the stability of material transportation is crucial for ensuring the continuous operation of production lines. A typical industrial production logistics supply network usually consists of raw material supplier nodes, intermediate transfer nodes, production station nodes, and logistics channels connecting them. Due to various uncertainties, the transportation capacity of logistics channels fluctuates randomly, thus the overall network's transportation capacity is also random. Therefore, this network is often modeled as a multi-state flow network for research, where network reliability is defined as the probability of transporting materials that meet production needs from suppliers to production stations.

[0003] In the field of network reliability analysis, methods based on minimum paths and minimum capacity vectors are commonly used to compress the state space of complex networks to improve computational efficiency. However, existing logistics supply network reliability assessment techniques are often based on two types of simplification assumptions that do not conform to actual industrial scenarios.

[0004] The first type is the assumption of fixed supply capacity. This assumption holds that material supply capacity is concentrated only at the source node, i.e., the supplier, while intermediate transshipment nodes are regarded merely as forwarding points without supply capacity. This completely ignores the buffering, regulating, and emergency supply functions of line-side warehouse nodes, which are widely present in actual industrial scenarios.

[0005] The second category involves simplistic assumptions in determining storage capacity. While some improved models consider the storage function of intermediate nodes, their judgment rules are often overly simplistic, such as simply comparing the total warehouse storage capacity with the total production demand. This static judgment based on total quantity ignores the network topology and the transportation capacity limitations of specific logistics channels. Even if the line-side warehouse has sufficient storage, if the specific transport channel leading to the production station is faulty or has insufficient capacity, the transportation task still cannot be completed.

[0006] Therefore, existing technologies cannot accurately assess the reliability of industrial logistics supply networks when intermediate transshipment nodes have limited storage capacity and transportation channels experience random capacity fluctuations. This can easily lead to misjudgments of production risks and make it difficult to meet the needs of lean manufacturing for refined management of supply chain robustness. Summary of the Invention

[0007] In view of this, the purpose of the present invention is to provide a method for evaluating the reliability of a logistics supply network that takes into account the storage capacity of line-side warehouse nodes.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A method for assessing the reliability of a logistics supply network that considers the storage capacity of line-side warehouse nodes includes the following steps: S1: Construct an industrial production logistics supply network model and initialize parameters: Establish a multi-state logistics supply network G ( N , A ); Among them, the node set N Include o Supplier nodes , u Individual warehouse nodes At least one pure transit node and a production workstation node T edge set A Include n transport side ; For the i Strip edge It has A discrete capacity state, the capacity state ranging from minimum capacity 0 to maximum capacity. Take the integer value between; The storage capacity of each line-side warehouse node forms a vector. The capacity consumption coefficient per unit quantity of material at the transport side is Production workstation nodes T The material requirements are d ; Define supplier nodes To the production workstation node T The set of minimal paths MP is ,in Indicates the number of MPs in the minimum path; Define lineside warehouse node To the production workstation node T The set of minimal paths MP is ,in Indicates the number of MPs in the minimum path; S2: Generate a set of flow vectors that satisfy storage capacity and demand constraints: According to the law of flow conservation, traverse and search all flow vectors that satisfy formulas (1) and (2). ; in, Indicates supplier node MP flows through its minima to the production station nodes. T The flow vector, Indicates supplier node Through its first j The flow rate of the minimum path MP; Indicates the line-side warehouse node MP flows through its minima to the production station nodes. T The flow vector, Indicates the line-side warehouse node Through its first k The flow rate of the minimum path MP; (1) (2) S3: Verify feasible flow vectors based on capacity consumption coefficient: For each flow vector obtained in S2 F According to formula (3), it is verified whether it satisfies the requirements of each transport edge in the network. Capacity constraints; if the flow vector F If the flow vector satisfies formula (3), then the flow vector is determined. F It is a feasible flow vector; (3) in, Representing an edge Maximum capacity; S4: Transform feasible flow vectors into candidate minimum capacity vectors: For each feasible flow vector selected in S3... F According to formula (4), it is transformed into a candidate minimum capacity vector. ,in Representing an edge In capacity vector X The components in; (4) S5: Use a comparison method to screen for the smallest capacity vector: Consider all candidate smallest capacity vectors obtained in S4. X The comparison method is used for verification; if there is no other candidate minimum capacity vector... Y satisfy and Then the candidate minimum capacity vector X It is a vector with minimal capacity; S6: Calculate the reliability of the logistics supply network Substituting all the minimum capacity vectors obtained from S5 into the disjoint sum formula, we can calculate the storage capacity vector of the given line-side warehouse. Z and demand d Under these conditions, the logistics supply network can successfully transport materials to production workstation nodes. T probability .

[0009] Furthermore, in S1, the transport edge Ther Each capacity state is represented as ,in ,and .

[0010] Furthermore, in S1, the supplier node quantity o The line-side warehouse node is greater than or equal to 1. quantity u Greater than or equal to 1.

[0011] Furthermore, in S3, the verification process of formula (3) is to determine the flow vector. F On each edge Does the total demand capacity generated by this not exceed that side? Maximum available capacity .

[0012] Furthermore, in S4, the meaning of formula (4) is for each edge Allocate a vector that can carry the flow vector F Minimum discrete capacity state of required flow .

[0013] Furthermore, in S5, the comparison method is specifically defined as follows: for two capacity vectors and , If and only if for all i =1,2,..., n They all .

[0014] Furthermore, in S6, the reliability of the logistics supply network... The calculation formula is the non-intersection formula.

[0015] Furthermore, the pure transit node It lacks material storage and supply functions.

[0016] The beneficial effects of this invention are as follows: First, this method breaks through the limitation of traditional reliability assessments where supply capacity is fixed at the source node, explicitly incorporating line-side warehouse nodes into the supply system, thus truly reflecting their actual value in material buffering and emergency replenishment. Second, this method overcomes the shortcomings of existing technologies that judge whether supply meets demand solely through simple total quantity comparisons. By comprehensively considering network topology, random capacity fluctuations of each logistics channel, and the storage capacity limit of line-side warehouses, it achieves refined modeling of logistics supply capacity. Finally, this method significantly improves the accuracy and realism of reliability assessments for industrial production material supply systems, effectively identifying supply disruption risks caused by the combined effects of transportation bottlenecks and storage limitations. This provides a more reliable theoretical basis and assessment tool for optimizing supply chain configuration and supporting lean production and intelligent manufacturing decisions.

[0017] 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

[0018] 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 method flow of the present invention; Figure 2 This is a network topology diagram of a specific embodiment of the present invention. Detailed Implementation

[0019] 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.

[0020] 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.

[0021] 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.

[0022] This invention provides a method for assessing the reliability of a logistics supply network that considers the storage capacity of line-side warehouse nodes. The flowchart of the method is as follows: Figure 1 As shown, the method specifically includes the following steps: Step 1: Construct an industrial production logistics supply network model and initialize parameters.

[0023] Establish a multi-state logistics supply network G ( N , A ), where the set of nodes N Includes supplier nodes (Source point), line-side warehouse node (Intermediate storage point), pure transit node and production workstation nodes T (Remittance Point); edge set A Representing logistics and transportation channels, there are a total of n For the transport side, for the first i Strip edge Its transportation capacity has Various capacity states, among which Representing an edge The r Each capacity state ranges from minimum capacity 0 to maximum capacity. The maximum capacity vector of the network is represented by M = (taking integer values ​​between these ranges). , ,…, ); Supplier Node The set of minimal paths to production station node T is represented as follows: ,in Indicates supplier node Minimum number of paths to production workstation nodes, line-side warehouse nodes The set of minimum paths to the production workstation node is ,in Indicates the line-side warehouse node Minimal number of paths to production workstation nodes; Define the number of supplier nodes as o Define the number of nodes in the line-side warehouse as u And the vector composed of the storage capacities of each line-side warehouse node is ,in For the first i The storage capacity of each line-side warehouse node, and the capacity consumption coefficient per unit quantity of material are: The capacity consumption coefficient of a unit material at any transport edge is defined as follows: .

[0024] Step 2: Generate a set of flow vectors that satisfy the storage capacity constraint and workstation requirement constraint.

[0025] Set production workstation nodes T The material requirements are d Supplier nodes To the production workstation node T The j a very narrow path The material flow rate is expressed as ( j =1,2,…, μ e Then the supplier node To the production workstation node T All flow vectors can be represented as Similarly, the line-side warehouse node. To the production workstation node T The k a very narrow path The material flow rate is ( k =1,2,…, β g Its flow vector is represented as Based on the law of conservation of flow, we iterate through all flow vectors that satisfy the following conditions. : Workstation demand constraint: The sum of the material quantity transported by all suppliers through their minimum paths and the material quantity transported by the line-side buffer nodes through their minimum paths equals the demand. d ;

[0026] in, This represents the total amount of material delivered by all supplier nodes to production workstation nodes through their minimum paths. This represents the total amount of material delivered from all line-side warehouse nodes to production workstation nodes via their minimum paths. This constraint ensures that the total material supply from supplier nodes and line-side warehouse nodes must meet the production needs of the workstations.

[0027] Storage capacity constraint: any line-edge warehouse node To production workstation nodes T The material being transported does not exceed its storage capacity. .

[0028]

[0029] This constraint ensures that the total amount of material supplied by the line-side warehouse node does not exceed its storage capacity.

[0030] Step 3: Verify feasible flow vectors based on capacity consumption coefficients.

[0031] For the flow vector obtained in step 2 F Calculate the flow vector along each transport edge in the network. The total transport capacity occupied by the edge, if the total transport capacity occupied is less than or equal to that edge Maximum transport capacity If the flow vector satisfies the physical constraints, then the flow vector is called a flow vector. F It is a feasible flow vector:

[0032] in, It is the capacity of a unit of material consumed at any transport edge. This refers to the traffic provided by all supplier nodes to the production workstation nodes on the transport side. Summary above This refers to the flow of traffic provided by all line-side warehouse nodes to production workstation nodes at the transportation edge. Summary above It is the edge Maximum capacity.

[0033] Step 4: Transform the feasible flow vector into a candidate minimum capacity vector. X .

[0034] For each edge Its capacity vector X Components in The value is taken as the edge in the flow vector. F The minimum discrete capacity state level required under the action. All feasible flow vectors selected in step 3 are represented by the following relationship. F Transform into candidate minimum capacity vector :

[0035] Step 5: Use the comparison method to filter vectors with minimal capacity.

[0036] Since a candidate minimum capacity vector is not necessarily a minimum capacity vector, each candidate minimum capacity vector needs to be verified individually. A comparison method is used, assuming... X If there are no other candidate minimum capacity vectors, then... Y ,satisfy and ,but X The candidate minimum capacity vectors are obtained in step 4 by comparing them one by one to obtain all the minimum capacity vectors.

[0037] Step 6: Calculate network reliability metrics.

[0038] Calculate the reliability R of the logistics supply network that satisfies the storage capacity constraints and workstation demand constraints of the line-side warehouse nodes. d Substitute all the minimum capacity vectors obtained from step 5 into the disjoint sum formula to calculate the storage capacity of the warehouse along the given line. Under certain conditions, the probability that the network can successfully transport materials with a demand of d to the production workstation node is the reliability R of the logistics supply network that satisfies the constraints of the storage capacity of the line-side warehouse node and the workstation demand. d .

[0039] Example 1 A specific implementation example Figure 2 As shown, an abstraction of a logistics supply network yields... Figure 2 The network consists of 6 nodes and 9 transport edges, where nodes v1 and v2 represent two suppliers, and nodes t1 and t2 represent two other suppliers. Each node represents one of two line-side warehouses and one pure transshipment node, with node T representing a production workstation. Table 1 shows the capacity state and corresponding probability distribution of each edge in the network. Figure 2 It can be concluded that there are a total of 8 minimal paths from all suppliers and line-side warehouses to the production station, namely: ={a1,a7}, ={a2,a8}, ={a3,a9}, ={a4,a7}, ={a5,a8}, ={a6,a9}, ={a7}, ={a8}. Assume the storage capacities of the two line-side warehouses are z1=2 and z2=2 respectively, and the capacity consumption coefficient of a unit material on any transport side is ω=0.6.

[0040] Table 1 Figure 2 Capacity state and probability distribution of the middle edge

[0041] The following uses the method of the present invention to calculate the probability that the logistics supply network can successfully transport materials with a workstation demand of d=4 from the supplier or lineside warehouse to the production workstation.

[0042] According to the method steps of this invention, the solution process is as follows: 1) Construct an industrial production logistics supply network model and initialize its parameters. Specifically, this includes finding the minimum paths from all supplier nodes and line-side warehouse nodes to production workstation nodes. ={a1,a7}, ={a2,a8}, ={a3,a9}, ={a4,a7}, ={a5,a8}, ={a6,a9}, ={a7}, ={a8}. Workstation requirement d=4, line-side warehouse storage capacity z1=2, z2=2, unit capacity consumption coefficient ω=0.6.

[0043] 2) Generate a set of flow vectors that satisfy both storage capacity and demand constraints. Find all flow vectors F = ( ) that satisfy the demand d. ): ≤2, ≤2, =4 A total of 314 flow vectors are generated from the above conditions, as shown in the first column of Table 2.

[0044] 3) Verify the feasible flow vector based on the capacity consumption coefficient. Check whether the flow vector F obtained in step 2) satisfies the capacity constraint condition: 0.6× ≤2, 0.6× ≤3, 0.6× ≤2, 0.6× ≤2, 0.6× ≤3, 0.6× ≤2, 0.6×( + + ) ≤3, 0.6×( + + ) ≤1, 0.6×( + ) ≤3, After filtering, a total of 163 feasible flow vectors that meet the conditions were obtained, as shown in the second column of Table 2.

[0045] 4) Transform the feasible flow vectors into candidate minimum capacity vectors X. Transform all feasible flow vectors F selected in step 3) into corresponding candidate minimum capacity vectors X = (x1, x2, x3, x4, x5, x6, x7, x8, x9): x1=b 1r ,ifb 1r ≥ 0.6× >b 1r-1 r=1,2,…,π1 x2=b 2r ,ifb 2r ≥ 0.6× >b 2r-1 r=1,2,…,π2 x3=b 3r ,ifb 3r ≥ 0.6× >b 3r-1 r=1,2,…,π3 x4=b 4r ,ifb 4r ≥ 0.6× >b 4r-1 r=1,2,…,π4 x5=b 5r ,ifb 5r ≥ 0.6× >b 5r-1 r=1,2,…,π5 x6=b 6r ,ifb 6r ≥ 0.6× >b 6r-1 r=1,2,…,π6 x7=b 7r ,ifb 7r ≥ 0.6×( + + ) >b 7r-1 r=1,2,…,π7 x8=b 8r ,ifb 8r ≥ 0.6×( + + ) >b 8r-1 r=1,2,…,π8 x9=b 9r ,ifb 9r ≥ 0.6×( + ) >b 9r-1 r=1,2,…,π 9。

[0046] The conversion results are shown in column 3 of Table 2.

[0047] 5) Use the comparison method to select vectors with minimal capacity.

[0048] The candidate minimum capacity vectors obtained in step 4) were verified one by one using the comparison method. A total of 19 minimum capacity vectors that meet the conditions were obtained, as shown in column 4 of Table 2.

[0049] 6) Calculate the reliability R of the logistics supply network that satisfies the storage capacity constraints and workstation demand constraints of the line-side warehouse nodes. d .

[0050] The network reliability R4 was calculated to be 0.96238 using the disjoint sum algorithm. That is, the logistics supply network has a probability of 0.96238 of successfully transporting 4 units of material from the supplier or line-side warehouse to the production station.

[0051] Table 2 shows the calculation results for the minimum capacity vector.

[0052] 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 assessing the reliability of a logistics supply network considering the storage capacity of line-side warehouse nodes, characterized in that: Includes the following steps: S1: Construct an industrial production logistics supply network model and initialize parameters: Establish a multi-state logistics supply network G ( N , A ); Among them, the node set N Include o Supplier nodes , u Individual warehouse nodes At least one pure transit node and a production workstation node T edge set A Include n transport side ; For the i Strip edge It has A discrete capacity state, the capacity state ranging from minimum capacity 0 to maximum capacity. Take the integer value between; The storage capacity of each line-side warehouse node forms a vector. The capacity consumption coefficient per unit quantity of material at the transport side is Production workstation nodes T The material requirements are d ; Define supplier nodes To the production workstation node T The set of minimal paths MP is ,in Indicates the number of MPs in the minimum path; Define lineside warehouse node To the production workstation node T The set of minimal paths MP is ,in Indicates the number of MPs in the minimum path; S2: Generate a set of flow vectors that satisfy storage capacity and demand constraints: According to the law of flow conservation, traverse and search all flow vectors that satisfy formulas (1) and (2). ; in, Indicates supplier node MP flows through its minima to the production station nodes. T The flow vector, Indicates supplier node Through its first j The flow rate of the minimum path MP; Indicates the line-side warehouse node MP flows through its minima to the production station nodes. T The flow vector, Indicates the line-side warehouse node Through its first k The flow rate of the minimum path MP; (1) (2) S3: Verify feasible flow vectors based on capacity consumption coefficient: For each flow vector obtained in S2 F According to formula (3), it is verified whether it satisfies the requirements of each transport edge in the network. Capacity constraints; if the flow vector F If the flow vector satisfies formula (3), then the flow vector is determined. F It is a feasible flow vector; (3) in, Representing an edge Maximum capacity; S4: Transform feasible flow vectors into candidate minimum capacity vectors: For each feasible flow vector selected in S3... F According to formula (4), it is transformed into a candidate minimum capacity vector. ,in Representing an edge In capacity vector X The components in; (4) S5: Use a comparison method to screen for the smallest capacity vector: Consider all candidate smallest capacity vectors obtained in S4. X The comparison method is used for verification; if there is no other candidate minimum capacity vector... Y satisfy and Then the candidate minimum capacity vector X It is a vector with minimal capacity; S6: Calculate the reliability of the logistics supply network Substituting all the minimum capacity vectors obtained from S5 into the disjoint sum formula, we can calculate the storage capacity vector of the given line-side warehouse. Z and demand d Under these conditions, the logistics supply network can successfully transport materials to production workstation nodes. T probability .

2. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to claim 1, characterized in that: In S1, the transport edge The r Each capacity state is represented as ,in ,and .

3. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to claim 1, characterized in that: In S1, the supplier node quantity o The line-side warehouse node is greater than or equal to 1. quantity u Greater than or equal to 1.

4. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to claim 1, characterized in that: In S3, the verification process of formula (3) is to determine the flow vector. F On each edge Does the total demand capacity generated by this not exceed that side? Maximum available capacity .

5. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to claim 1, characterized in that: In S4, the meaning of formula (4) is for each edge Allocate a vector that can carry the flow vector F Minimum discrete capacity state of required flow .

6. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to claim 1, characterized in that: In S5, the comparison method is specifically defined as follows: for two capacity vectors and , If and only if for all i =1,2,..., n They all .

7. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to claim 1, characterized in that: In S6, the reliability of the logistics supply network The calculation formula is the non-intersection formula.

8. The logistics supply network reliability assessment method considering the storage capacity of line-side warehouse nodes according to any one of claims 1 to 7, characterized in that: The pure transit node It lacks material storage and supply functions.

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