A Method for Evaluating the Reliability of a Stochastic Logistics Distribution Network Considering Carbon Emission Constraints

Abstract

The present invention relates to a method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints, belonging to the field of logistics technology. The method comprises the following steps: S1: input basic data; S2: solve the flow vector F that meets the demand by the enumeration method; S3: calculate the carbon emissions corresponding to each flow vector F by using the carbon emission formula; S4: verify whether the flow vector F meets the capacity constraint and the carbon emission constraint; S5: convert the feasible flow vector into a candidate minimum capacity vector; S6: find the minimum capacity vector; S7: calculate the reliability of the stochastic logistics distribution network under the carbon emission constraint. The present invention can evaluate and verify whether the service efficiency and service quality of the logistics distribution network meet the reliability requirements.

Description

Technical Field

[0001] The present invention belongs to the technical field of logistics, and relates to a method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints. Background Art

[0002] Based on this stochastic property, a large number of studies regard the logistics distribution network as a multi-state stochastic flow network, and each edge in the network has independent, finite, non-negative integer-valued stochastic capacities, and the values of these capacities usually follow a certain probability distribution according to the historical data of service providers. Specifically, the reliability of a logistics distribution network refers to the probability that the network can transport the demand of d units of goods from the supply place to the demand place.

[0003] The reliability of a stochastic logistics distribution network considering carbon emission constraints refers to the probability that the network can successfully transport the demand of d units of goods to the destination and the carbon emissions generated during the transportation do not exceed the given upper limit TE, and this reliability index is denoted by R d,TE for representation.

[0004] Calculating R d,TE The simplest method is the exhaustive method. This method first needs to enumerate each capacity vector that satisfies the constraints in the capacity vector space one by one, and then accumulate and sum the probabilities of each state vector. This probability sum is the reliability value. Although the enumeration method is simple and easy to understand, its time complexity is very high and it is not suitable for large-scale logistics distribution networks. Therefore, by using the concept of the shortest path in graph theory and introducing the minimum capacity vector that satisfies the carbon emission constraints to calculate R d,TE can significantly improve the solution efficiency. The minimum capacity vector that satisfies the carbon emission constraints means that under this capacity vector, the network can transport the demand of d units of goods to the destination and the total carbon emissions generated during the transportation do not exceed the given upper limit TE, while under any other capacity vector smaller than this capacity vector, the network cannot satisfy the above two conditions simultaneously. After obtaining the minimum capacity vector that satisfies the carbon emission constraints, R d,TE can be calculated by the disjoint sum method. Therefore, finding the minimum capacity vector that satisfies the carbon emission constraints is the main goal of this method. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints. It is necessary to find the minimum capacity vector that satisfies the carbon emission constraints under the given capacity distribution conditions, and then calculate the network reliability using the disjoint sum formula.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] A method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints, the method comprising the following steps:

[0008] S1: Input basic data;

[0009] S2: Solve the flow vector F that meets the requirements by the enumeration method;

[0010] S3: Calculate the carbon emissions corresponding to each flow vector F using the carbon emission formula;

[0011] S4: Verify whether the flow vector F meets the capacity constraint and the carbon emission constraint;

[0012] S5: Convert the feasible flow vector into a candidate minimum capacity vector;

[0013] S6: Find the minimum capacity vector:

[0014] S7: Calculate the reliability of the stochastic logistics distribution network under the carbon emission constraint.

[0015] Optionally, in the S1, the basic data includes the commodity demand d; all the shortest paths from the supply place s to the destination t: p1, p2,..., p m , where m represents the total number of the shortest paths from the supply place s to the destination t; the capacity probability distribution and the transportation distance l of each edge i (1 ≤ i ≤ n), where n represents the total number of transportation edges; the fuel consumption rates when the vehicle is empty and fully loaded: s 0 and s 1 ; the carbon emission factor e and the carbon emission upper limit TE.

[0016] Optionally, the S2 is specifically:

[0017] Assume that the commodity demand at the destination t is d, in units of vehicles. When transporting d units of commodities from the supply place s to the destination t, find all the flow vectors F = (f1, f2,..., f m ) that meet the demand d according to the following two conditions:

[0018]

[0019] where j = 1, 2,..., m

[0020] where f j represents the flow on the shortest path p j , that is, the number of transportation vehicles on the shortest path p j , 1 ≤ j ≤ m; p j represents the jth shortest path connecting the supply place s and the destination t, represents the sum of the commodity flows on all the shortest paths, represents the maximum capacity of the shortest path p j , assume that each edge has k i capacity states, use Represents a i The maximum capacity of.

[0021] Optionally, the S3 is specifically:

[0022] s 0 and s 1 respectively represent the fuel consumption rate when the vehicle is unloaded and fully loaded. The carbon emission formula indicates that the actual fuel consumption rate p of the vehicle = s 0 +q×(s 1 -s 0 ) / c, where q and c respectively represent the weight of the transported goods and the maximum load of the vehicle; when taking full vehicle transportation, the fuel consumption rate on each transportation edge a i is Assume that logistics service providers all take full vehicle transportation and the vehicle types are the same. Then the carbon emission of the transportation edge a i is determined by the number of vehicles consumed by the commodity flow passing through a i . The carbon emission of the transportation edge a i is regarded as a function of the commodity flow on the minimum path. The total carbon emission is calculated by summing up the carbon emissions on each transportation edge; the variables e and l i are respectively used to represent the carbon emission factor of the vehicle and the distance of the transportation edge a i ; the carbon emission g i on each transportation edge a during the commodity distribution process i and the total carbon emission E(F) of the logistics distribution network are calculated by the following relational expressions:

[0023] where i = 1, 2,..., n

[0024]

[0025] Optionally, the S4 is specifically:

[0026] The capacity vector X = (x1, x2,..., x n ) represents the current capacity state of the network, where x i represents the capacity state of the transportation edge a i , and takes integer values between the minimum capacity 0 and the maximum capacity , represents the maximum capacity vector of the network; use TE to represent the carbon emission upper limit. The flow vector F is a feasible flow vector if the flow vector F satisfies the following capacity constraint and carbon emission constraint:

[0027] where i = 1, 2,..., n

[0028] E(F) ≤ TE

[0029] Among them represents the commodity flow through edge a i of the commodity flow, representing the capacity consumed by the commodity flow through edge a i Verify whether each flow vector F satisfies the above constraints one by one, and obtain a feasible flow vector.

[0030] Optionally, the S5 is specifically:

[0031] Convert all feasible flow vectors F into corresponding candidate minimum capacity vectors X=(x1, x2,..., x n ) according to the following relational expression:

[0032]

[0033] Optionally, the S6 is specifically:

[0034] Verify each candidate minimum capacity vector one by one. According to the relationship between the minimum capacity vector and the candidate minimum capacity vector, use the comparison method for verification. Let X be the candidate minimum capacity vector. If there is no other candidate minimum capacity vector Y such that X≥Y, then X is the minimum capacity vector; use the comparison method to verify all candidate minimum capacity vectors obtained in S5 one by one to obtain all minimum capacity vectors.

[0035] Optionally, the S7 is specifically:

[0036] According to the obtained minimum capacity vector, calculate the probability that the logistics distribution network can successfully transport d units of commodity demand from the supply place to the destination and the carbon emissions generated during the transportation do not exceed the given upper limit TE through the disjoint sum algorithm, that is, the network reliability R d,TE .

[0037] The beneficial effect of the present invention is that it can evaluate and verify whether the service efficiency and service quality of the logistics distribution network meet the reliability requirements.

[0038] Other advantages, objectives and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in preferred detail below in conjunction with the drawings, where:

[0040] Figure 1 is the method flow chart of the present invention;

[0041] Figure 2 The network diagram of the specific embodiment. Specific implementation manner

[0042] The following uses specific specific examples to illustrate the implementation manners 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 implementation manners. Various details in this specification can also 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 diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0043] Among them, the attached drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and should not be construed as a limitation to the present invention; in order to better illustrate the embodiments of the present invention, some components in the attached drawings will be omitted, enlarged or reduced, which does not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the attached drawings may be omitted.

[0044] In the attached 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 there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the attached drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the attached drawings are only for illustrative purposes and should not be construed as a limitation to the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0045] The present invention provides a method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints. The method flow chart is as Figure 1 shown, and includes the following steps:

[0046] 1) Input basic data.

[0047] The basic data includes the commodity demand d; all the minimum paths from the supply place s to the destination t: p1, p2,..., p m , where m represents the total number of minimum paths from the supply place s to the destination t, and p j (1 ≤ j ≤ m) represents the j-th minimum path; the capacity probability distribution and transportation distance l of each edge i (1 ≤ i ≤ n), where n represents the total number of transportation edges; the fuel consumption rates when the vehicle is empty and fully loaded: s 0and s 1 ; the carbon emission factor e and the carbon emission ceiling TE.

[0048] 2) Solve the flow vector F that meets the requirements by the enumeration method.

[0049] Suppose the network needs to deliver goods with a demand of d (unit: vehicle) from the supply place s to the destination t via different distribution centers or transfer nodes, and find all flow vectors that meet the demand d by enumerating one by one. Here, the vector F = (f1, f2,..., f m ) composed of the commodity flows through each minimal path in the network is called the flow vector, where m represents the total number of minimal paths from the supply place s to the destination t, and f j (1 ≤ j ≤ m) represents the flow through the minimal path p j . The so-called minimal path refers to a set of edges that form a path from the supply place to the demand place, and if any element in the set is removed, the remaining ones cannot form a path from the supply place to the demand place. Based on this, p j represents the j-th minimal path connecting the supply place s and the demand place t in the network. Since any flow in the network follows the flow conservation law, that is, the total flow does not increase or decrease during distribution and transportation, the total flow flowing into a point is equal to the total flow flowing out of this point (except for the supply place and the demand place). Therefore, find all flow vectors F = (f1, f2,..., f m ) according to the following two conditions:

[0050]

[0051] where j = 1, 2,..., m

[0052] where represents the total commodity flow through all minimal paths in the network, represents the maximum capacity of the minimal path p j , indicates that the flow on each minimal path cannot exceed the demand and the path maximum capacity limit, and all flows are non-negative. In addition, each service provider on each edge has k i (1 ≤ i ≤ n) capacity states, then represents the maximum capacity on a i .

[0053] 3) Calculate the carbon emissions corresponding to each flow vector F using the carbon emission formula.

[0054] To more comprehensively reflect the impact of commodity flow on network carbon emissions, parameters such as vehicle fuel consumption rate and load factor are used to determine network carbon emissions. The carbon emission calculation formula mainly includes the following two steps: (1) Calculate the fuel consumption per unit distance during vehicle transportation using the load factor and fuel consumption rates at empty and full loads; (2) Determine the total network carbon emissions by combining the carbon emission factor and distance. s 0 and s 1 are used to represent the fuel consumption rates of the vehicle at empty and full loads respectively. Combining the load situation, the carbon emission formula gives the actual fuel consumption rate of the vehicle: p = s 0 + q×(s 1 - s 0 ) / c, where q and c represent the weight of the transported goods and the maximum load of the vehicle respectively. When using full vehicle transportation, the fuel consumption rate on each transportation edge a i under the flow vector F is Moreover, since logistics service providers all use the same type of vehicle for transportation, the carbon emissions of transportation edge a i are determined by the number of vehicles consumed by the commodity flow passing through a i . Therefore, the carbon emissions of transportation edge a i can be regarded as a function of the commodity flow on the minimal path, and the total network carbon emissions are calculated by summing up the carbon emissions on each transportation edge. e and l i (1 ≤ i ≤ n) are used to represent the carbon emission factor of the corresponding vehicle and the distance of transportation edge a i respectively. Therefore, the carbon emissions g i on transportation edge a i during commodity distribution and the total carbon emissions E(F) of the logistics distribution network can be calculated by the following relational expressions:

[0055] where i = 1, 2, …, n

[0056]

[0057] 4) Verify whether the flow vector F satisfies the capacity constraint and carbon emission constraint.

[0058] The capacity vector X = (x1, x2, …, x n ) represents the current capacity state of the network, where x i (1 ≤ i ≤ n) represents the actual capacity of transportation edge a i , and takes integer values between the minimum capacity 0 and the maximum capacity . is used to represent the maximum capacity vector of the network. Using TE to represent the carbon emission upper limit, if the flow vector F satisfies the following capacity constraint and carbon emission constraint, then the flow vector F is called a feasible flow vector:

[0059] where \(i = 1, 2, \ldots, n\)

[0060] \(E(F)\leq TE\)

[0061] where represents the total commodity flow through edge \(a\) i That is, the capacity consumed by the commodity flow through edge \(a\) i Therefore, the relational expression represents that the capacity consumed by the commodity flow through the transportation edge \(a\) i cannot exceed the maximum capacity of \(a\) i . Combining the total carbon emissions in step 3), \(E(F)\leq TE\) indicates that under the flow vector \(F\), the total network carbon emissions cannot exceed the given carbon emission upper limit \(TE\). By verifying these constraint conditions, all feasible flow vectors that satisfy the capacity and carbon emission constraints can be obtained;

[0062] 5) Convert the feasible flow vector into a candidate minimum capacity vector.

[0063] According to the relationship between flow and capacity, all feasible flow vectors \(F\) are converted into the corresponding candidate minimum capacity vectors \(X=(x_1, x_2, \ldots, x\) n ) through the following relational expression:

[0064]

[0065] 6) Find the minimum capacity vector.

[0066] Since the minimum capacity vector must be a candidate minimum capacity vector, but a candidate minimum capacity vector is not necessarily a minimum capacity vector, each candidate minimum capacity vector needs to be verified one by one. According to the relationship between the two, the comparison method can be used for verification. Assume that \(X\) is a candidate minimum capacity vector. If there is no other candidate minimum capacity vector \(Y\) such that \(X\geq Y\), then \(X\) is the minimum capacity vector; perform comparison operations on all candidate minimum capacity vectors to obtain all minimum capacity vectors;

[0067] 7) Calculate the reliability of the stochastic logistics distribution network under carbon emission constraints.

[0068] According to the obtained minimum capacity vector, use the disjoint sum algorithm to calculate the probability that the logistics distribution network can successfully transport \(d\) units of commodity demand from the supply place to the destination and the carbon emissions generated during transportation do not exceed the given carbon emission upper limit \(TE\), that is, the reliability value \(R\) of the stochastic logistics distribution network under carbon emission constraints d,TE .

[0069] The present invention will be described in detail below with reference to specific embodiments:

[0070] A specific embodiment is as followsFigure 2 As shown in Figure 2 , after abstracting a logistics distribution network, the network in Figure 2 is obtained. This network consists of 4 nodes and 6 transportation edges. Among them, node s represents the supply place, intermediate nodes 1 and 2 represent the distribution centers, and node t represents the demand place. Table 1 gives the capacity probability distribution and section distance of each edge in the network. Table 1 gives the capacity distribution and transportation distance of each edge in the network; there are 4 minimum paths from the supply place s to the demand place t in the network, which are p1 = {a1, a2}, p2 = {a1, a3, a6}, p3 = {a5, a4, a2}, and p4 = {a5, a6}. Suppose there are 6 large equipment items that need to be transported from the supply place s to the destination t, each equipment weighs 2 tons, and the maximum load of the transport vehicle providing the service is 4 tons. Therefore, the demand d = 3 (unit: vehicle), that is, the equipment of 3 vehicles needs to be transported to the destination t. At the same time, it is measured that the fuel consumption rate s Figure 2 of the vehicle when fully loaded is 0.5 L / km, the carbon emission factor e = 3.15 kg / L, and the carbon emission constraint TE = 110 kg. According to the relationship between flow and carbon emissions, Table 2 gives the fuel consumption rate and carbon emission function expressions of each transportation edge respectively. 1 =0.5L / km, carbon emission factor e = 3.15kg / L, carbon emission constraint TE = 110kg. According to the relationship between flow and carbon emissions, Table 2 gives the fuel consumption rate and carbon emission function expressions of each transportation edge respectively.

[0071] Table 1 Capacity probability distribution and transportation distance of each edge

[0072]

[0073] Table 2 Figure 1 Fuel consumption rate and carbon emission function of each edge in Figure 1

[0074] side <![CDATA[s i (F)]]> <![CDATA[g i (F)]]> <![CDATA[a1]]> <![CDATA[0.5(f1 + f2)]]> <![CDATA[9.45(f1 + f2)]]> <![CDATA[a2]]> <![CDATA[0.5(f1 + f3)]]> <![CDATA[12.6(f1 + f3)]]> <![CDATA[a3]]> <![CDATA[0.5f2]]> <![CDATA[11.025f2]]> <![CDATA[a4]]> <![CDATA[0.5f3]]> <![CDATA[15.75f3]]> <![CDATA[a5]]> <![CDATA[0.5(f3 + f4)]]> <![CDATA[14.175(f3 + f4)]]> <![CDATA[a6]]> <![CDATA[0.5(f2 + f4)]]> <![CDATA[9.45(f2 + f4)]]>

[0075] Next, use the method of the present invention to calculate the probability that this logistics distribution network can transport 3 units of equipment demand to the destination and the total carbon emissions do not exceed the given carbon emission upper limit TE = 110 kg.

[0076] According to the method steps of the present invention, the solution process is as follows:

[0077] 1) Input basic data. Specifically, it includes demand d = 3, minimum paths: p1 = {a1, a2}, p2 = {a1, a3, a6}, p3 = {a5, a4, a2}, p4 = {a5, a6}, the capacity probability distribution and transportation distance of each edge are shown in Table 1, where the transportation distances are: l1 = 6, l2 = 8, l3 = 7, l4 = 10, l5 = 9, l6 = 6, the fuel consumption rate s 1 of the vehicle when fully loaded is 0.5 L / km, the carbon emission factor e = 3.15 kg / L, and the carbon emission constraint TE = 110.

[0078] 2) Use the enumeration method to solve the flow vector F that meets the demand.

[0079] Find all flow vectors \(F=(f_1,f_2,\cdots,f m )\) that meet Requirement 3 through the following relationship:

[0080] \(f_1 + f_2 + f_3 + f_4 = 3\)

[0081] \(0\leq f_1\leq3\)

[0082] \(0\leq f_2\leq1\)

[0083] \(0\leq f_3\leq3\)

[0084] \(0\leq f_4\leq1\)

[0085] Use the enumeration method to obtain the flow vectors that meet Requirement 3 as: \(F_1=(0,0,2,1)\), \(F_2=(0,1,1,1)\), \(F_3=(0,1,2,0)\), \(F_4=(1,0,1,1)\), \(F_5=(1,0,2,0)\), \(F_6=(1,1,0,1)\), \(F_7=(1,1,1,0)\), \(F_8=(2,0,0,1)\), \(F_9=(2,0,1,0)\), \(F 10 =(2,1,0,0)\), \(F 11 =(3,0,0,0)\).

[0086] 3) Calculate the carbon emissions corresponding to each flow vector \(F\) using the carbon emission formula. Taking \(F_1=(0,0,2,1)\) as an example, \(g_1 = 9.45\times(0 + 0)=0\), \(g_2 = 12.6\times(0 + 2)=25.2\), \(g_3 = 11.025\times0 = 0\), \(g_4 = 15.75\times2 = 31.5\), \(g_5 = 14.175\times(2 + 1)=99.225\), \(g_6 = 9.45\times(0 + 1)=9.45\). Therefore, the total network carbon emissions \(E(F_1)=108.675\) under the flow vector \(F_1\). Finally, calculate the total network carbon emissions under the remaining flow vectors: \(E(F_2)=96.075\), \(E(F_3)=114.975\), \(E(F_4)=88.2\), \(E(F_5)=107.1\), \(E(F_6)=75.6\), \(E(F_7)=94.5\), \(E(F_8)=67.725\), \(E(F_9)=86.625\), \(E(F 10 )=74.025\), \(E(F 11 )=66.15\).

[0087] 4) Verify whether the flow vector \(F\) meets the capacity constraint and the carbon emission constraint.

[0088] Judge whether the flow vector \(F\) generated in step 3) meets the maximum capacity constraint \(H=(4,4,4,3,4,1)\) of the transportation edge through the following constraint, and judge whether the total carbon emissions of the logistics distribution network under each flow vector \(F\) do not exceed the carbon emission upper limit of 110.

[0089] f1 + f2 ≤ 4

[0090] f1 + f3 ≤ 4

[0091] f2 ≤ 4

[0092] f3 ≤ 3

[0093] f3 + f4 ≤ 4

[0094] f2 + f4 ≤ 1

[0095] E(F i ) ≤ 110

[0096] After calculation, a total of 8 feasible flow vectors that satisfy the maximum capacity constraint and carbon emission constraint are finally obtained: F1 = (0, 0, 2, 1), F4 = (1, 0, 1, 1), F5 = (1, 0, 2, 0), F7 = (1, 1, 1, 0), F8 = (2, 0, 0, 1), F9 = (2, 0, 1, 0), F 10 =(2, 1, 0, 0), F 11 =(3, 0, 0, 0).

[0097] 5) Convert the feasible flow vectors into candidate minimum capacity vectors.

[0098] Convert the obtained 8 feasible flow vectors F into the corresponding candidate minimum capacity vectors X according to the following relational expressions:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] Convert the 8 feasible flow vectors obtained in step 4) into the corresponding candidate minimum capacity vectors respectively, that is: X1 = (0, 2, 0, 2, 3, 1), X2 = (1, 2, 0, 1, 2, 1), X3 = (1, 3, 0, 2, 2, 0), X4 = (2, 2, 1, 1, 1, 1), X5 = (2, 2, 0, 0, 1, 1), X6 = (2, 3, 0, 1, 1, 0), X7 = (3, 2, 1, 0, 0, 1), X8 = (3, 3, 0, 0, 0, 0).

[0106] 6) Find the minimum capacity vectors.

[0107] Perform a comparison operation on the candidate minimum capacity vectors obtained in step 5) to obtain 7 minimum capacity vectors: X1 = (0, 2, 0, 2, 3, 1), X2 = (1, 2, 0, 1, 2, 1), X3 = (1, 3, 0, 2, 2, 0), X5 = (2, 2, 0, 0, 1, 1), X6 = (2, 3, 0, 1, 1, 0), X7 = (3, 2, 1, 0, 0, 1), X8 = (3, 3, 0, 0, 0, 0).

[0108] 7) Calculate the reliability of the stochastic logistics distribution network under carbon emission constraints.

[0109] According to the known capacity probability distribution in Table 1, substitute the 7 minimum capacity vectors obtained in step 6) into the disjoint sum formula. It can be calculated that the probability that the logistics distribution network can successfully transport 3 units of equipment demand from the supply place s to the demand place t and the carbon emissions generated during transportation do not exceed the given carbon emission upper limit TE = 110 kg is 0.8782, that is, the network reliability R 3,110 = 0.8782.

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints, characterized in that: The method comprises the following steps: S1: Input basic data; S2: Solve the flow vector F that meets the requirements by the enumeration method; Specifically, S2 is as follows: Let the demand for goods at destination \(t\) be \(d\) in units of vehicles. When transporting \(d\) units of goods from supply location \(s\) to destination \(t\), find all flow vectors \(F=(f_1,f_2,\ldots,f\) m ) that satisfy the demand \(d\) according to the following two conditions: where j = 1, 2, …, m where f j represents the flow on the shortest path p j , that is, the number of transport vehicles on the shortest path p j , 1 ≤ j ≤ m; p j represents the j-th shortest path connecting the supply point s and the destination t represents the sum of the commodity flows on all shortest paths represents the maximum capacity of the shortest path p j . Suppose each edge has k i capacity states, denoted by as the maximum capacity of a i ; S3: Calculate the carbon emissions corresponding to each flow vector F by using the carbon emission formula; Specifically, S3 is as follows: s 0 and s 1 respectively represent the fuel consumption rates of the vehicle when it is unloaded and fully loaded. The carbon emission formula indicates that the actual fuel consumption rate p of the vehicle = s 0 +q×(s 1 -s 0 ) / c, where q and c respectively represent the weight of the transported goods and the maximum load of the vehicle; when using full vehicle transportation, under the flow vector F, the fuel consumption rate on each transportation edge a i is Assume that logistics service providers all use full vehicle transportation and the vehicle types are the same. Then the carbon emissions of transportation edge a i are determined by the number of vehicles consumed by the commodity flow passing through a i . The carbon emissions of transportation edge a i are regarded as a function of the commodity flow on the minimal path. The total carbon emissions are calculated by summing up the carbon emissions on each transportation edge; the variables e and l i are respectively used to represent the carbon emission factor of the vehicle and the distance of transportation edge a i ; during the commodity distribution process, the carbon emissions g i on each transportation edge a i and the total carbon emissions E(F) of the logistics distribution network are calculated by the following relational expressions: where i = 1, 2, …, n S4: Verify whether the flow vector F meets the capacity constraint and the carbon emission constraint; Specifically, S4 is as follows: The capacity vector X = (x1, x2, …, x n ) represents the current capacity state of the network, where x i represents the capacity state of the transportation edge a i , and takes integer values between the minimum capacity 0 and the maximum capacity ; represents the maximum capacity vector of the network; Let TE denote the carbon emission cap. The flow vector F is a feasible flow vector if the flow vector F satisfies the following capacity constraint and carbon emission constraint: where i = 1, 2, …, n E(F) ≤ TE Among them represents the commodity flow through edge a i The commodity flow through edge a i The capacity consumed by the commodity flow. Verify whether each flow vector F satisfies the above constraint conditions one by one to obtain a feasible flow vector; S5: Convert the feasible flow vector into a candidate minimum capacity vector; S6: Search for the minimum capacity vector: S7: Calculate the reliability of the stochastic logistics distribution network under the carbon emission constraint.

2. The reliability evaluation method of a stochastic logistics distribution network considering carbon emission constraints according to claim 1, characterized in that: In the above S1, the basic data includes the commodity demand d; all the shortest paths from the supply place s to the destination t: p1, p2, …, p m , where m represents the total number of the shortest paths from the supply place s to the destination t; the capacity probability distribution and the transportation distance l of each edge i , where 1 ≤ i ≤ n and n represents the total number of transportation edges; the fuel consumption rates when the vehicle is empty and fully loaded: s 0 and s 1 ; the carbon emission factor e and the carbon emission upper limit TE.

3. A reliability evaluation method for a stochastic logistics distribution network considering carbon emission constraints according to claim 1, characterized in that: Specifically, S5 is as follows: Convert all feasible flow vectors F into corresponding candidate minimum capacity vectors X = (x1, x2, …, x n ) according to the following relationship: where i = 1, 2, …, n.

4. A method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints according to claim 3, characterized in that: Specifically, S6 is as follows: Verify each candidate minimum capacity vector one by one. According to the relationship between the minimum capacity vector and the candidate minimum capacity vector, use the comparison method for verification. Let X be the candidate minimum capacity vector. If there does not exist another candidate minimum capacity vector Y such that X ≥ Y, then X is the minimum capacity vector; use the comparison method to verify each of the candidate minimum capacity vectors obtained in S5 one by one to obtain all the minimum capacity vectors.

5. A method for evaluating the reliability of a stochastic logistics distribution network considering carbon emission constraints according to claim 4, characterized in that: Specifically, S7 is as follows: According to the obtained minimum capacity vector, the probability that the logistics distribution network can successfully transport d units of commodity demand from the supply place to the destination through the disjoint sum algorithm, and the carbon emissions generated during the transportation do not exceed the given upper limit TE, that is, the network reliability R d,TE .

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