TWI872900B - Method for evaluating the reliability of stochastic cold chain network - Google Patents

Abstract

A method to evaluate the reliability of a stochastic cold chain network, which includes constructing a network topology of the stochastic cold chain network, analyzing all time factors of the network topology and listing all transportation paths, finding out all feasible flow vectors that meet the demand among multiple transportation paths, generating delivery vectors that includes converting each feasible flow into delivery vectors and obtaining the minimum delivery vector, obtaining network vectors by calculating the currently allocable travel time through the time factors and values ​​used in network topology to obtain the maximum travel time vector, combining the minimum delivery vector and the maximum travel time vector into a network vector, and obtaining the minimum network vector to calculate the network reliability accordingly.

Description

Method for evaluating the reliability of random cold chain networks

The present invention relates to the field of network reliability technology, and in particular to a method for evaluating the reliability of a random cold chain network.

Due to the development of technology and the change of generations, the logistics industry has become an indispensable part of daily life. In recent years, the competition among operators has become increasingly fierce. In order to open up the consumer market and increase corporate profits, all companies are moving towards reducing costs, shortening cargo delivery time, improving product quality, and customizing products. Therefore, the concept of cold chain is the current trend in the logistics industry. In the past, the reliability of the cold chain network was calculated based on the number of transport vehicles in each transport section being occupied by other customers and showing a multi-level state, and the travel time of each transport section was considered as a fixed constant. However, the above does not take into account that the travel time of each transport segment may also present multiple levels of status due to factors such as traffic volume, weather conditions, accidents, etc. If the travel time of each transport segment is evaluated with a fixed constant, it cannot reflect the actual travel time of each transport segment.

Related technologies such as network reliability calculation methods, cold chain distribution systems, and cargo transportation route arrangements have been disclosed in related knowledge and techniques. These related technologies are based on the characteristics of different systems. For example, a complex network has a variety of transportation tools, and different sub-networks are established for evaluation due to different required service times; the supply chain network focuses on the transportation of fragile goods and proposes a network reliability calculation method to meet this transportation quantity. These knowledge and techniques can also consider different influencing factors to plan and arrange cargo routes. For example, a cold chain network monitoring system is proposed to control product temperature and humidity and plan transportation routes; routes are planned through historical transportation routes; or transportation routes are optimized by considering the influence of random service time and fuel consumption.

Since the systems and methods provided by the prior art do not consider the perspective of the logistics company, and the performance indicators calculated do not consider the uncertainty of the number of transport vehicles and travel time in each transport route, and do not evaluate the possibility of the current network being able to complete the transportation demand within a given time and the number of transport vehicles required.

In order to improve the above-mentioned deficiencies of the prior art, the present invention proposes a method for evaluating the reliability of a random cold chain network. The random cold chain network is constructed as a network topology and stored in a readable medium. The method is calculated by a processor. The method includes the following steps: constructing the network topology of the random cold chain network, including inputting network nodes, multiple transport segments connecting individual network nodes, and the travel time of each transport segment; analyzing all time factors of the network topology and listing all transport paths; finding all feasible flow vectors that meet the demand in the multiple transport paths; generating a transport vector, including converting each transport segment into a single transport segment; The feasible flow vectors are converted into transport vectors, and the minimum transport vector is obtained; the network vector is obtained, including calculating the current allocable travel time through the time factor and value used in the network topology, finding the travel time vector that meets the allocable travel time, obtaining the transport path that meets the current conditions, obtaining the maximum travel time vector, combining the minimum transport vector and the maximum travel time vector into the network vector, and adjusting the value of the travel time part in the network vector to be a negative value; the minimum network vector is obtained, and the network reliability of the random cold chain network is calculated using the minimum network vector.

In one embodiment, the above method for evaluating the reliability of a random cold chain network further includes evaluating the network performance of the random cold chain network through the results of the network reliability and making corresponding management decisions according to the changes in the network reliability.

In one embodiment, the network nodes include nodes formed by suppliers, third-party logistics companies and retailers.

In one embodiment, the step of executing the above-mentioned step of finding all feasible flow vectors that meet the demand further includes: checking whether the number of transportation vehicles used in all transportation routes exceeds the maximum number of available transportation vehicles; and checking whether the transportation vehicles departing from the supplier can arrive within the given time and do not exceed the above-mentioned maximum number of available transportation vehicles.

In one embodiment, the step of obtaining the network vector further includes: for unused transport segments, setting them to the maximum travel time so that the probability corresponding to the travel time of the transport segment is one; deleting unreasonable network vectors in which the number of transport vehicles in the network vector does not correspond to the correct travel time.

In one embodiment, the time factor includes the unloading and loading time at the node.

In one embodiment, the feasible flow vector, under the condition of satisfying demand, represents the quantity of the product that will arrive at the retailer within the current number of transport vehicles and the specified time.

In one embodiment, the minimum transport vector is obtained by using a comparison rule of vector operations.

In one embodiment, the maximum travel time vector is obtained by using a comparison rule of vector operations.

In one embodiment, the minimum network vector is obtained by using a comparison rule of vector operations.

Here, the present invention will be described in detail with respect to specific embodiments of the invention and its viewpoints. Such description is to explain the structure or step flow of the present invention, which is for the purpose of explanation rather than to limit the scope of the patent application of the present invention. Therefore, in addition to the specific embodiments and preferred embodiments in the specification, the present invention can also be widely implemented in other different embodiments. The following is an explanation of the implementation of the present invention by means of specific specific embodiments. People familiar with this technology can easily understand the effectiveness and advantages of the present invention through the contents disclosed in this specification. Moreover, the present invention can also be used and implemented through other specific embodiments. The various details described in this specification can also be applied based on different needs, and various modifications or changes can be made without departing from the spirit of the present invention.

The invention is related to "computing technology". In order to assist the transportation industry, logistics companies and other industries in evaluating the feasibility of meeting customer needs and making decisions related to transportation routes, the invention hopes to construct a practical cold chain logistics transportation system into a stochastic cold chain network with multistate travel time (SCCNMT) with multistate travel time. The goods transported are mainly low-temperature refrigerated foods or pharmaceutical products that are highly time-sensitive. Suppliers, logistics companies and retailers are regarded as nodes, and the transportation route between two nodes is regarded as a transmission edge. The SCCN takes into account that the number of transport vehicles and travel time on a transport route may be in multiple levels due to factors such as the number of customer orders and traffic volume, weather conditions, and unexpected events. The previously disclosed prior art (including patents or literature) only explores the impact of a single multi-level state factor, and logistics companies can only use historical data and past experience as a basis for decision-making. Therefore, the present invention uses network analysis techniques to explore two multi-level state factors, the number of transport vehicles and travel time, and calculates a quantitative index to help logistics companies understand the delivery status of orders and evaluate the possibility of meeting the needs of all retailers under the given number of transport vehicles and time constraints for each transport route. The managers of logistics companies can also adjust the delivery time threshold and the delivery route in a timely manner based on this quantified performance indicator to meet the needs of all retailers, and use it as a basis for future related decisions to achieve intelligent and data-based transportation system management.

The invention takes into account the number of transport vehicles provided by logistics companies at different transport sections in the actual cold chain transport network, as well as the probability of travel time for each transport section, and uses the network reliability proposed by the application method as a data indicator for evaluating network performance. The network reliability provided by the invention can be used to evaluate the status of the cold chain network distribution of logistics companies, and to evaluate the performance that the cold chain network can currently provide in a digital way, and provide managers with the ability to consolidate the status of the cold chain network and control risks. In the cold chain network, each transport route will have multiple possibilities (i.e., multiple levels) in the number of transport vehicles that can be provided due to the impact of the scheduled orders; and the travel time of each transport route will be affected by the traffic volume and weather conditions, resulting in multiple levels. In addition, the cold chain network market will be highly volatile due to various external risks such as market demand and fuel prices. Therefore, in order to effectively maintain the performance of the cold chain network to meet the needs of retailers, the network reliability proposed by the present invention can be used as a data indicator to evaluate the status of the cold chain network, so as to manage the transportation time and configure the transportation vehicles, and achieve the goal of successfully delivering all the required transportation volumes to all retailers within the time. The present invention can provide a logistics company with a quantitative performance indicator. Based on this indicator, the managers of the logistics company can adjust the transportation route in a timely manner according to the needs of retailers, the number of available transportation vehicles, and the travel time of each transportation route, so as to effectively maintain the efficiency of cold chain network transportation in the face of ever-changing market conditions.

Multistate networks are systems in real life, such as transportation systems, communication systems, and supply chain systems. In a cold chain network, we regard suppliers, logistics companies, and retailers as nodes, and the transportation links connecting the nodes as transmission edges. When the network demand is given, we can calculate the probability of successfully transmitting traffic from the source to the destination within the time limit, that is, the reliability of the cold chain network.

The present invention develops an algorithm for evaluating the network reliability of a random cold chain network with multi-stage travel time (SCCNMT). Network reliability is defined as the probability that the random cold chain network with multi-stage travel time (SCCNMT) meets the needs of all retailers under time constraints.

The following lists the network model construction and the notations used in the algorithm of the random cold chain network with multi-stage travel time (SCCNMT) mentioned in the present invention and their related descriptions: N is a set of perfectly reliable nodes, including suppliers, third-party logistics companies and retail stores. s is the number of transmission edges from suppliers to third-party logistics centers. z is the number of transmission edges in the network. a _q is the qth transmission edge in the network, q = 1, 2, …, z . A is the set of transmission edges, represented by { a _q | q = 1, 2, …, z}. _M is the capacity of the transmission edge a _q , q = 1, 2, …, z . M is the maximum transmission edge capacity vector (arc-capacity vector), represented by ( M ₁ , M ₂ , …, M _z ). v _q is the travel time of the transmission edge a _q , q = 1, 2, …, z . The minimum travel time of a transmission edge a _q , q = 1, 2, …, z . The maximum travel time of an edge _aq , q = 1, 2, …, z . V The set of travel times for an edge _aq , denoted by { _vq | q = 1, 2, …, z }. G The random cold chain network with multi-order travel time (SCCNMT), which can be represented by the network topology G ≡ ( N , A , M , V ). _xq The number of vehicles currently used by edge _aq , q = 1, 2, .., z . X The transportation vector, denoted by ₍ x1 , x2 _, .., xz ). U The time required for a truck to unload goods at a logistics company and a retailer. L The time required for a truck to load goods at a logistics company and a retailer. P _The number of retailers. d ^k is the demand of the kth retailer, k = 1, 2, …, p . D is the demand vector of retailers, represented by ( d ¹ , d ² , …, d ^k ). w _k is the number of transportation paths from the supplier to the kth retailer, k = 1, 2, …, p . The oth transport route of the kth retailer, o = 1, 2, …, w _k : k = 1, 2, …, p . The flow on o = 1, 2, …, w _k : k = 1, 2, …, p . The flow vector F is denoted by. I time threshold. I ^* currently available time threshold. Ω the set of transport vectors that satisfy the maximum travel time demandΩ _min the set of minimum transport vectors. R _D the reliability of a random cold chain network (SCCNMT) under multi-order travel time that can satisfy the demand at the maximum travel time. V travel time vector, denoted by ( v ₁ , v ₂ , …, v _z ). Transmission edges (arcs) that meet the travel time vector. δThe set of travel time vectors that meet the travel time threshold. _δmaxThe set of maximum travel time vectors. _RTThe time reliability of each transport vehicle to successfully reach the destination within the travel time threshold. R _{D, TThe} network reliability of a random cold chain network (SCCNMT) under multi-stage travel time (SCCNMT) that can meet the demand within the travel time threshold. Associative operator. S network vector, represented by ( s ₁ , s ₂ , …, s _2z ). s _q , s _{z + q} the current number of transport vehicles and travel time of the transmission edge a _q in a multi-stage random cold chain network with travel time (SCCNMT), q = 1, 2, …, 2 z . ρ the set of network vectors that satisfy the demand within the travel time threshold. γ the set of minimum network vector candidates. γ _min the set of minimum network vectors. e _i is set to 1 for some _si and to zero for the rest, represented by (0, …, 0, 1, …, 0). Constructing the model of a random cold chain network with travel time (SCCNMT)

The above-mentioned random cold chain network with multi-stage travel time (SCCNMT) can be represented by the network topology G ≡ ( N , A , M , V ), where N is a set of perfectly reliable nodes including suppliers, third-party logistics companies and retailers, A = { a _q | q = 1, 2, …, z } represents the set of z transmission edges (arcs), and M = ( M ₁ , M ₂ , …, M _q ), where M _q represents the maximum capacity of each transmission edge. V represents the travel time of the transmission edge V = { v _q | q = 1, 2, …, z }, and each transmission edge has its own travel time v _q . Each transmission edge a _q has a number of identical transport vehicles (carriers). The transport vector X represents the number of transport vehicles that each transmission edge has, and _xq takes a value in the set {0, 1, 2, …, _Mq }. The number of available transport vehicles for each transmission edge in the cold chain network is random, because the transport vehicles of each transmission edge may be occupied by other orders, and the travel time will be affected by traffic flow and other factors. In order to evaluate the network reliability of the random cold chain network (SCCNMT) under multi-stage travel time, the above network topology model G needs to meet the following assumptions: I. The flow and time units of the random cold chain network (SCCNMT) under multi-stage travel time are both integers. II. No inventory service is provided. III. Only one kind of product is provided. IV. The capacity and travel time of any component are statistically independent. V. The flows in the network topology G satisfy the flow conservation laws. VI. The same type of transport vehicles are used throughout the transport process. Vector operations are calculated according to the following rules: (1) X ≥ Y : ( x ₁ , x ₂ , …, x _n ) ≧ ( y ₁ , y ₂ , …, y _n ) if and if _xi ≧ _yi , for i = 1, 2, …, n . (2) X ＞ Y : ( x ₁ , x ₂ , …, x _n ) ＞ ( y ₁ , y ₂ , …, y _n ) if and if X ≧ Y and _xi ＞ _yi , for i = 1, 2, …, n . Analysis of total delivery time

Cold chain products must go through multiple processes before they can be provided from suppliers to retailers. First, the products are transported to a third-party logistics company, where they undergo a first travel time. Once the products arrive at the third-party logistics company, they are unloaded and wait for loading. Unlike general supply chains that send products to warehouses and wait for orders, cold chain products cannot be stored in warehouses due to their short shelf life and must be delivered in a timely manner. Instead, cold chain products wait for all ordered products to arrive before being loaded for the next shipment. Then, the cold chain products undergo a second transport to reach the retailer. The service time of the entire cold chain network is shown in Figure 1.

In a random cold chain network with multi-stage travel time (SCCNMT), the present invention will further explore the time required for cold chain products to be transported to retailers, which can be divided into three parts. The first part is the travel time from the supplier to the third-party logistics company, denoted as _vq , considering all transportation sections from the supplier to the third-party logistics company. Ideally, the products will arrive together and be unloaded at the same time. However, due to the different travel time of each transportation section, the products that arrive earlier need a waiting time to wait for other products to arrive before unloading, and time point A represents the start of unloading. After the goods arrive at the third-party logistics company, these products do not need to be stored, but wait for all orders to be loaded before shipment. We use U and L to represent the loading and unloading time required for each truck. The second part only needs to consider one loading time and two unloading times between the retailer and the third-party logistics company, expressed as ( U + L ) + U. The third part is similar to the first part. Ideally, the products arrive at the retailer at the same time. However, due to the different travel times of each transportation route, some products arrive at the retailer earlier and need to wait for other products to arrive. Time point B represents the time when all products arrive at the retailer, and then _vq represents the travel time from the third-party logistics company to the retailer. Delivery vector and the probability distribution

In a random cold chain network with multi-level travel time (SCCNMT), there are multiple suppliers and retailers. The transportation path is Indicates that the number of available transport vehicles for each transport route is given by Indicates. Due to different conditions to be considered, we use s to represent the number of transmission edges from suppliers to third-party logistics companies, and z represents the total number of transmission edges in the random cold chain network with multi-order travel time (SCCNMT). In order to ensure that the order is fulfilled, we must consider the number of transport vehicles available for each transmission edge, which cannot exceed the number of currently available transport vehicles, that is, the number of trucks, which is expressed as a constraint condition (Mathematical Formula 1), . [Mathematical formula 1]

However, we can use constraints to ensure that the product can be delivered to the retailer within a certain time. In addition to considering capacity, we must also consider the delivery deadline. If the flow vector F satisfies the constraint (Equation 2), it means that the product will reach the retailer within the specified time given the current number of transport vehicles. in, . [Mathematical formula 2] In order to ensure that the product arrives within the target time, we need to know the available time and the required time. The required time is calculated by multiplying the maximum number of transport vehicles that can reach the retailer by the unloading time, expressed as The calculation of the available time takes into account the longest service time before the product arrives, assuming that both travel times pass through the largest and single logistics hub in the logistics, expressed as By dividing the required time by the available time, we can determine the number of vehicles required for each road.

In constraint 1 (Formula 1), we can get the number of transport vehicles used before transporting to the third-party logistics company, while constraint 2 (Formula 2) considers the number of transport vehicles used by the third-party logistics company afterwards. Both of these constraints must be less than the maximum capacity M _q . In constraints 1 and 2, we can get the flow vector F that satisfies both demand and time constraints. By using constraints (Formula 3) and (Formula 4), we can get the number of transport vehicles used by each transmission edge of the random cold chain network (SCCNMT) under multi-order travel time, and thus we can get the transportation vector X in sequence. , [Mathematical formula 3] , in, [Formula 4] Minimal delivery vector and network reliability

Demand reliability _RD is an indicator in the stochastic cold chain network with multi-stage travel time (SCCNMT), which represents the probability of successfully meeting the demand within the maximum travel time. The set of transport vectors is represented by Ω . (Mathematical formula 5) can be used to calculate demand reliability _RD , which represents the probability of all feasible solutions. Each transport vector X can use assumption IV to statistically calculate the probability independently. ,in }. [Mathematical formula 5]

However, due to the large number of solutions in Ω , it may be inefficient and challenging to find all the delivery vectors X in the network. Therefore, it is simpler and more efficient to find the minimum delivery vector (MDV), which is the lower bound vector Ω _min belonging to the delivery vector set Ω . In order to obtain the minimum delivery vector (MDV), we need to go through the following steps and present the comparison process of how to get Ω _min in Table 1. [Table 1]: Comparison process of getting Ω _min Line 1: Assume that there are γ transport vectors X in Ω and set I = Ω _min = ( I is a stack storing the minimum transport vector (MDV) index) Line 2: For i = 1 to γ with Line 3: For j = i +1 to γ with Line 4: If , _Xi is not a minimum transport vector (MDV) and belongs _to Ωmin Line 5: Else _Xi belongs _to Ωmin , And go to Line 6 Line 6: END Line 7: Line 8: END

Each minimum transportation vector (MDV) represents the lower bound of the random cold chain network (SCCNMT) under the multi-order travel time. Therefore, if we get γ MDVs, we can use (Equation 6) to get the probability of a union set, which can be regarded as the probability of satisfying the demand with the maximum travel time, that is, the demand reliability _RD . . [Mathematical formula 6]

Various methods can be used to calculate the probability of a union set, including the inclusion-exclusion principle, state space decomposition, sum of disjoint products, and recursive sum of disjoint products (RSDP). In this invention, we use the recursive disjoint sum method (RSDP) to obtain the demand reliability, which represents the probability of meeting the time constraint. Algorithm for calculating demand reliability R _D

In order to evaluate the demand reliability of a random cold chain network (SCCNMT) with multi-order travel time, an algorithm for calculating the demand reliability R _D , namely the first algorithm (Algorithm I), will be proposed in the following paragraphs. The first algorithm (Algorithm I) is used to calculate the demand reliability (demand reliability R _D ): Input: Step 0: Analyze all time factors and list all transportation routes Step 1: Find all feasible flow vectors F according to the requirements and check whether they exceed the maximum capacity M _q of the corresponding transmission edge. All feasible vectors F that meet the requirements can be obtained by (Mathematical Formula 7), [Mathematical formula 7] 1.1) Check whether the maximum capacity of each transmission edge exceeds the number of vehicles that can be used under the constraints of (Mathematical formula 8), , q =1, 2, …, z. [Mathematical formula 8] 1.2) Check whether the trucks from the third-party logistics company can arrive at the given time within the specified time and the number of trucks used is less than the maximum capacity limit condition, that is, (Mathematical formula 9), , q = s +1, s +2, …, z , where [Mathematical formula 9] Step 2: Generate the transport vector X = ( _x1 , _x2 , …, _xz ) according to the following procedure. 2.1) Convert each F into the transport vector X before the third-party logistics company using (Mathematical formula 10): [Mathematical formula 10] 2.2) Using (Mathematical formula 11), transform each F into the transportation vector X after the third-party logistics company, while considering the time limit , in, . [Mathematical formula 11] 2.3) Obtain the transport vector X in Ω through steps 2.1 and 2.2, and eliminate other non-minimum transport vectors (non-MDVs) (in Ω ) calculated using the method in Table 1. Step 3: Assume that The minimum transport vectors (MDVs) are used to calculate the demand reliability R _D of the random cold chain network (SCCNMT) under multi-order travel time using the recursive non-intersecting sum method (RSDP), which can be obtained by: [Equation 12] Output: Demand reliability _RD . Travel time reliability

In the above paragraphs, we considered the maximum time by considering demand reliability. Here, we will further consider the important factor of multi-state travel time. Travel time has randomness due to traffic volume and weather conditions. Therefore, treating this factor as a constant in previous studies will lead to an overestimation of network reliability. The following paragraphs aim to calculate the time reliability _RT , which represents the time reliability of each transport vehicle to successfully reach the destination within the travel time threshold.

After incorporating multi-order travel times, the travel time of each transmission edge will follow its own probability distribution, which is different from previous studies that treat travel time as a constant value. Each possible arrival time corresponds to a probability, as shown in Table 2. For example, at transmission edge a ₁ , a travel time of 20 minutes corresponds to a probability of 0.5, meaning there is a 50% chance of arriving within that time. [Table 2]: Example of probability distribution of multi-order travel time for transmission edge a ₁ Travel time Arrival probability 10 0.1 20 0.5 25 1

However, since each transmission edge has its own travel time distribution, the probability of reaching a specific destination within a certain time can be calculated based on the transportation path given by the multi-order travel time. In order to calculate the travel time of each transmission edge, we need to recalculate the time threshold I. The product must be unloaded and loaded at the third-party logistics company and then unloaded again at the retailer. Therefore, the travel time threshold can be subtracted from these service times, and the resulting I* can be used to calculate the travel time vector based on the transportation path, . [Formula 13]

Each transport edge has its own arrival time distribution, and the travel time of each path must be at its minimum and maximum value In the network, the travel time constraint is used to allocate the travel time I* to all transport routes, taking into account the paths used in each route and Add them up. , q = 1, 2, …, z . [Equation 14] Finally, we can get the travel time vector V , which represents the travel time used by each transmission edge in the random cold link network with multi-order travel time (SCCNMT). The travel time vector V can be obtained using equation (15). For the transmission edges that meet the travel time threshold, we denote them as v' _q . For the remaining unused transmission edges, we directly set their travel time to the maximum travel time . , o = 1, 2, …, w _k ; k = 1, 2, …, p ; q = 1, 2, …, z [Formula 15]

The symbol δ represents the set of all travel time vectors that meet the travel time threshold. In order to avoid complex and inefficient calculations, similar to the description in the previous paragraph, we also adopt the comparison process shown in Table 3 to obtain the set of maximum travel time vectors δ _max . Therefore, if there are ρ maximum travel time vectors in the set δ _max , the time reliability _RT can be calculated using (Mathematical Formula 16), indicating that each transport vehicle can successfully reach the destination at the travel time threshold in the random cold chain network (SCCNMT) under multi-order travel time. This calculation can be performed using the second algorithm (Algorithm II) provided by the present invention. [Equation 16] [Table 3]: Comparison process for obtaining δ _max Line 1: Assume that there are ρ transport vectors X in δ and set I = δ _max = ( I is a stack storing the indices of the travel time upper limit vector) Line 2: For i = 1 to ρ with Line 3: For j = i +1 to γ with Line 4: If , _Vi is not the upper limit of travel time and belongs to δ _max Line 5: Else V _i belongs to δ _max , and go to Line 6 Line 6: END Line 7: Line 8: END

Algorithm II is used to calculate time reliability:

An algorithm for calculating the temporal reliability _RT , namely Algorithm II, will be proposed in the following paragraphs. The algorithm is as follows: Input: Step 1: Calculate the available travel time threshold I* by taking into account loading and unloading: . [Equation 17] Step 2: Find the maximum travel time vectors. 2.1) Obtain the feasible travel time vector V = ( v ₁ , v ₂ ,…, v _z ) of the constraint condition (Equation 18) to identify the transmission edges that meet the travel time threshold. For unused transmission edges, set their travel time to the maximum travel time. , o = 1, 2, …, w _k ; k = 1, 2, …, p ; q = 1, 2, …, z [Equation 18] 2.2) The maximum travel time vector is obtained by the comparison process in Table 3. Step 3: Assuming there are ρ maximum travel time vectors, the recursive non-intersecting sum method (RSDP) is used to calculate the time reliability _RT of the random cold chain network (SCCNMT) under multi-order travel time, which can be obtained by the following method: [Formula 19] Output: Time reliability _RT .

In the previous section on the calculation of demand reliability R _D , we calculated the demand reliability R _D for meeting the demand, but we only considered the maximum travel time of the transport link. Since travel time is multi-state, we further calculate the time reliability R _T for meeting multi-state travel time. Here we multiply the two probabilities to obtain the network reliability R _{D , T} considering multi-state capacity and travel time. By multiplying the demand reliability by the time reliability, we obtain an estimate that represents the network reliability under the two multi-state factors. The network reliability R _{D , T} considering capacity and travel time can be estimated using (Equation 20), . [Mathematical formula 20]

According to an embodiment of the present invention, FIG. 2 is used to illustrate the entire algorithm for estimating the network reliability RD _{, T} , that is, by integrating the first algorithm and the second algorithm, the network reliability RD _{, T} can be estimated quickly using (Mathematical Formula 20).

The above algorithm, integrating the first and second algorithms, can quickly calculate the reliability of a network with multiple levels of transport vehicle numbers and travel time. However, the above algorithm does not consider the correlation between feasible travel time and the number of transport vehicles (numbers of carriers). Therefore, it is proposed to make appropriate modifications to the above algorithm to calculate the accurate reliability of a network with multiple levels of transport vehicle numbers and travel time.

To calculate the exact network reliability, the feasible travel time corresponding to each transport path in the transport vector is considered here, generating a new network vector S. The network vector S is a multi-state factor, representing two factors of the stochastic cold chain network under multi-order travel time (SCCNMT), namely the number _of transport vehicles and travel time. Therefore, the network vector S = ( s1 _, s2 , …, s2z ), where _sq = _xq and _{sq + z} = _vq (for q ₌ 1, 2, …, z ), represents the combination of the transport vector X and the travel time vector V. In addition, the symbol Represents the associative operator for combining two vectors. For example, given X = (0, 3, 0, 3, 0, 0, 0, 2, 2, 2) and V = (35, 45, 35, 35, 35, 45, 30, 30, 40, 40), X ⊕ V yields the combined vector (0, 3, 0, 3, 0, 0, 0, 2, 2, 2, 35, 45, 35, 35, 35, 45, 30, 30, 40, 40). Like the network vector S , X ⊕ V is the combination of the transport vector X and the travel time vector V. In other words, S = ( X ⊕ V ). However, when considering the relationship between feasible travel time and the number of transport vehicles, some unreasonable network vectors will be deleted. For example, the network vector S = (0, 3, 0, 3, 0, 0, 0, 2, 2, 2, 35, 45, 35, 35, 35, 45,30, 30, 40, 40) is unreasonable and should be deleted because s1 is currently 0, indicating _that no transport vehicle is transported through _the transmission edge a1 , so the corresponding travel time s11 _on a1 should be considered _as the maximum value 45 instead of 35.

However, network vectors S have both lower and upper bounds, which makes it difficult to compute their joint probabilities and perform comparisons. To illustrate, let us consider two transport vectors: X1 = ( ₁ , 1, 1) and X2 = (2, 2, 2), and the corresponding travel time vectors V1 = ₍ 10, 10, 10) _and V2 ₌ (5, 5, 5). By combining these transport vectors with the travel time vector, we obtain two network vectors, S ₁ = X ₁ ⊕ V ₁ = (1, 1, 1, 10, 10, 10) and S ₂ = X ₂ ⊕ V ₂ = (2, 2, 2, 5, 5, 5). In this example, although the relationship between X ₁ and X ₂ , and V ₁ and V ₂ , can be understood, there is no way to directly compare S ₁ and S _2. In order to calculate network reliability using the same method as in the previous related paragraphs, such as the first and second algorithm related paragraphs, it is necessary to adjust the travel time v _q to a negative value. This adjustment allows comparing (1, 1, 1, -10, -10, -10) to (2, 2, 2, -5, -5, -5), yielding the relation S ₁ ＜ S ₂ . Thus, the travel time vectors are adjusted from upper bound vectors to lower bound vectors, transforming the entire network vector S into a lower bound vector.

The rest requires further adjustments. The travel time needs to be multiplied by a negative sign to obtain negative travel time before it can be used. This probability table is used to obtain the lower bound vector. In addition, due to the current negative travel time, the constraints used in the previous paragraphs related to the first and second algorithms also need to be adjusted. The modified constraints are expressed as (Mathematical Formula 21) to (Mathematical Formula 24). In the constraints (Mathematical Formula 21) and (Mathematical Formula 22), the available time needs to be calculated, so the maximum value of the two travel times is taken. In this case, the negative travel time is handled by taking the absolute value. , q = s +1, s +2, …, z , where [Mathematical formula 21] , q = s +1, s +2, …, z . [Equation 22]

For the constraint (Equation 23), the entire mathematical expression needs to be changed to account for negative travel time. In the constraint (Equation 24), the maximum value was originally taken from the unused transmission edge (arc), but due to the negative sign, the minimum value is now considered. , q = 1, 2, …, z . [Equation 23] , q = 1, 2, …, z . [Equation 24]

The network vector is composed of the transport vector and the travel time vector. After adjustment, it becomes the lower bound vector of the random cold link network with multi-order travel time (SCCNMT). The vector S equals ( X ⊕ V ) and is called the network vector. The network reliability can be expressed as RD _{, T} = Pr{ S | X meets the demand, and V is feasible within the travel time threshold}. Let ρ represent the set of those network vectors, _and the minimum vector in ρ is called the minimum network vector (MNV). The minimum network vector (MNV) can calculate the network reliability more efficiently.

In particular, let X be the minimum transport vector, and V is feasible under X and is taken as the adjusted maximum travel time vector, then the network vector S = ( X ⊕ V ) may be the minimum network vector (MNV). Let γ denote those network vectors S with the unreasonable vectors removed, i.e., the case of _sq = 0, but _{sq + z} is not the minimum value, which is considered as the candidate set of the minimum network vector (MNV).

By comparing the vectors in the set γ , the set γ _min is defined to store all these residual vectors. The set γ is the set of all candidates for the minimum network vector (MNV). γ _min is the set of the minimum network vector (MNV) that can meet the demand within the travel time threshold of the random cold chain network (SCCNMT) under multi-level travel time.

If γ _min stores θ minimum network vectors (MNVs), called S ₁ , S ₂ , …, S _θ , then the exact network reliability can be expressed as Calculation. Algorithm III

Algorithm III is used to calculate the exact network reliability R _{D, T} : Input: Step 0: Convert travel times to negative travel times and adjust their probabilities accordingly. List all transport routes. Step 1: Find all feasible flow vectors F according to the requirements and check whether they exceed the maximum capacity M _q of the corresponding transmission edge. 1.1) All feasible vectors F that meet the requirements can be obtained by (Mathematical Formula 25), , k = 1, 2, …, p . [Mathematical formula 25] 1.2) Check whether the maximum capacity of each transmission edge exceeds the number of vehicles that can be used under the constraints of (Mathematical formula 26), , q = 1, 2, …, z. [Mathematical formula 26] 1.3) Check whether the trucks from the third-party logistics company can arrive at the given time within the specified time and the number of trucks used is less than the maximum capacity constraint, that is, (Mathematical formula 27), , q = s +1, s +2, …, z , where [Mathematical formula 27] Step 2: Generate the transport vector X = ( _x1 , _x2 , …, _xz ) according to the following procedure. 2.1) Convert each F into the transport vector X before the third-party logistics company using (Mathematical formula 28): [Mathematical formula 28] 2.2) Considering the time limit, use (Mathematical formula 29) to transform each F into the transportation vector X after the third-party logistics company, and consider the time limit at the same time . [Mathematical formula 29] Let a set Ω store all transport vectors. 2.3) Use the method in Table 1 to obtain all minimum transport vectors (MDVs) and store them in the set Ω _min . Step 3: Generate the network vector S = ( s ₁ , s ₂ , …, s _2z ) through the following process. 3.1) Calculate the feasible travel time threshold I * by considering the time of loading and unloading goods from the time threshold ^I , . [Mathematical formula 30] 3.2) Based on the transportation route _{of the currently used transportation vehicle, obtain the feasible travel time vector V = (v1 ,} v2 , … _{, vz} ) . , q = 1, 2, …, z . [Mathematical formula 31] All the obtained travel time vectors are stored in a set δ . 3.3) All the maximum travel time vectors are obtained using the vector comparison method in Table 1 and stored in the set δ _max . 3.4) Combine the transportation vector and the travel time vector to form a network vector using (Mathematical formula 32). [Mathematical formula 32] 3.5) Delete unreasonable network vectors S, such as the number of transport vehicles that cannot be matched to the travel time, and store the remaining network vectors in the set γ . Step 4: Apply the vector comparison method in Table 1 to obtain all minimum network vectors (MNVs) and store them in the set γ _min . Assuming that there are θ minimum network vectors (MNVs) in the set γ _min , the exact network reliability R _{D, T} of a random cold link network (SCCNMT) under multi-order travel time is calculated by (Mathematical formula 33) using the recursive non-intersecting sum method (RSDP). [Equation 33] Output: Accurate network reliability R _{D, T} .

This invention will use a simple numerical example to illustrate the process of calculating the reliability of a random cold chain network. This invention can also be used in other practical networks containing two multi-order factors. This case uses network topology 10 to construct a network, as shown in Figure 3. Its network nodes include two suppliers, two third-party logistics companies and three retailers, and there are ten transportation segments as transmission edges (arcs) to connect different nodes. The number of available trucks on each transmission edge presents multiple states due to reservations by other customers. The available number and corresponding probability are shown in Table 4. Other time factors and values used in the transportation process are listed in Table 5, and Table 6 shows the travel time and arrival probability of each transportation segment. [Table 4]: Probability table of the number of transportation vehicles provided by each transportation segment Transport section Number of transport vehicles Probability a ₁ , a ₂ , a ₃ , a ₄ 0 1 2 3 0.01 0.01 0.01 0.97 a ₅ , a ₆ , a ₇ , a ₈ 0 1 2 3 0.01 0.02 0.02 0.95 a ₉ , a ₁₀ 0 1 2 3 0.02 0.02 0.01 0.95 [Table 5]: Time factors used in the network Time Factor Average time (minutes) Loading time 20 Unloading time 15 [Table 6]: Travel time and arrival probability table for each transport route Transport section Travel time (minutes) Arrival probability Transport section Travel time (minutes) Arrival probability a ₁ , a ₂ , -35 -37 -40 -45 0.8 0.1 0.05 0.05 a ₇ , a ₈ -20 -25 -27 -30 0.8 0.05 0.1 0.05 a ₃ , a ₄ -27 -30 -32 -35 0.7 0.2 0.05 0.05 a ₉ , a ₁₀ -30 -33 -35 -40 0.7 0.225 0.05 0.025 a ₅ , a ₆ , -35 -37 -40 -45 0.9 0.05 0.025 0.025

In order to achieve the feasibility of delivering each retailer's required vehicle quantity of 2 vehicles on time within the time limit of 130 minutes, the complete calculation steps are presented as follows: Step 1. Analyze all time factors and list all transportation routes P k o. According to the network graph, find all the transport paths: P 1 1 = { a ₁ , a ₅ }, P 1 2 = { a ₃ , a ₅ }, P 1 3 = { a ₂ , a ₈ }, P 1 4 = { a ₄ , a ₈ }, P 2 1 = { a ₁ , a ₆ }, P 2 2 = { a ₃ , a ₆ }, P 2 3 = { a ₂ , a ₉ }, P 2 4 = { a ₄ , a ₉ }, P 3 1 = { a ₁ , a ₇ }, P 3 2 = { a ₃ , a ₇ }, P 3 3 = { a ₂ , a ₁₀ }, and P 3 4 = { a ₄ , a _{10 }.} }, and adjust the travel time to a negative value. Step 2. Find all feasible flow vectors that meet the demand F = . [Mathematical formula 34] 2.1) Check whether the number of vehicles used in all transport sections exceeds the maximum number of available vehicles. [Mathematical formula 35] 2.2) Check whether the truck from the third-party logistics company can arrive within the given time. [Equation 36] Step 3. Generate a transport vector X = ( x ₁ , x ₂ , …, x ₁₀ ) according to the following steps, which represents the number of transport vehicles used in each transport segment in the network. 3.1) Convert each feasible flow vector into a transport vector X = ( x ₁ , x ₂ , x ₃ , x ₄ , x ₅ , x ₆ , x ₇ , x ₈ , x ₉ , x ₁₀ ). [Mathematical formula 37] 3.2) Use the comparison rule in the transportation vector operation, refer to Table 1, and obtain the minimum transportation vector (MDV). Step 4. Obtain the network vector S = ( s ₁ , s ₂ , …, s ₂₀ ). 4.1) Refer to the unloading and loading times in Table 5 to calculate the current allocatable travel time I ^* I ^* = 135 - (20 + 2 × 15) = 135 - (20 + 30) = 85 [Mathematical formula 38] 4.2) Find the travel time vector V = ( v ₁ , v ₂ , …, v ₁₀ ) that meets the allocatable travel time, and obtain all transportation routes that meet the current conditions. For unused transportation segments, set them to the minimum travel time and do not consider their probability. [Mathematical formula 39] 4.3) Using the comparison rules in the travel time vector operation, refer to Table 3 to obtain the maximum travel time vector. 4.4) Combine the minimum transport vector and the maximum travel time vector into a network vector, and use the network vector to represent the multi-order factors in this network. 4.5) Delete the unreasonable network vector in which the number of transport vehicles in the network vector does not correspond to the correct travel time. Step 5. Using the comparison rules in the vector operation, refer to Tables 1 and 3, obtain the minimum network vector, and use the minimum network vector to calculate the network reliability. [Mathematical formula 40] Step 6. The network reliability calculated through the above steps is 0.7567. The calculated network reliability is expressed in the cold chain network. Under the current number of transport vehicles and the travel time of each transport route, the probability of successfully transporting the demand of each retailer is 0.7567. The network reliability can be provided to the manager as a performance indicator for evaluating network performance, and corresponding management decisions can be made according to the changes in network reliability, such as setting standard transportation time or transportation route selection, and transportation volume allocation, etc., using digital management methods to effectively reduce the risk cost brought about by market changes, and further formulate appropriate management methods.

According to the description of the relevant paragraphs about the third algorithm and the actual numerical examples of applying the algorithm, the flowchart of the method for evaluating the reliability of a random cold chain network proposed by the present invention is summarized with reference to FIG4. The present invention considers the number of transport vehicles provided by the logistics company in different transport sections and the probability of travel time for each transport section for the random cold chain network, and uses the third algorithm mentioned above, and uses the processor 505 (refer to FIG5) to access the algorithm and execute the calculation to calculate the network reliability and thereby evaluate the network performance. Among them, the method for evaluating the reliability of the random cold chain network includes using the processor 505 (refer to Figure 5) to execute the following steps: Step S40: Constructing the random cold chain network as a network topology, including inputting network nodes composed of suppliers, third-party logistics companies and retailers, multiple transportation segments (transmission edges) connecting the above network nodes, and the travel time of each transportation segment; Step S41: Analyzing all time factors on the above network topology and listing all transportation segments according to the above network topology, adjusting the travel time value to a negative value and adjusting the arrival probability of the transportation vehicle of each transportation segment accordingly; Step S42: Find all feasible flow vectors that meet the demand; this step includes (1) checking whether the number of vehicles used by all transport segments (transmission edges or transport paths) exceeds the maximum number of available vehicles; and (2) checking whether the vehicles departing from the third-party logistics center company can arrive within the given time and do not exceed the maximum number of transport vehicles (vehicles); Step S43: Generate a transport vector, which represents the number of transport vehicles used by each transport segment (transmission edge) in the network. This step includes (1) converting each feasible flow vector into a transport vector; and (2) using the comparison rules in vector operations to obtain the minimum transport vector (MDV); Step S44: Obtaining a network vector, including (1) considering the unloading and loading time, calculating the currently allocable travel time; (2) finding the travel time vector for allocating travel time, obtaining a transport route that meets the current conditions, and setting the unused transport route to the minimum travel time without considering its probability; (3) using the comparison rule in vector operation to obtain the maximum travel time vector; (4) combining the minimum transport vector and the maximum travel time vector into a network vector, and using the network vector to represent the multi-order factors in this network; (5) deleting unreasonable network vectors in which the number of transport vehicles in the network vector does not correspond to the correct travel time; Step S45: using the comparison rule in vector operation to obtain the minimum network vector, and using the minimum network vector to calculate the network reliability; Step S46: Evaluate network performance through the above network reliability results, and make corresponding management decisions based on changes in network reliability.

The present invention mainly proposes a method for evaluating the performance of a cold chain network. The method is aimed at the number of available transport vehicles provided by the network in each transport segment, and the travel time of each transport segment is in a multi-level state. The minimum transport vector (MDV) and the maximum travel time vector ( δ _max ) for the network to successfully deliver the demand to each retailer under the time limit are calculated, and the network reliability is further evaluated. The network reliability is defined as the probability that the number of transport vehicles currently provided by the network can successfully deliver the demand of each retailer within the time limit. Based on the assessed network reliability, before each delivery begins, we can use the network reliability to assess whether the number of transport vehicles and travel time can meet the demand, so as to reduce the risk of delivery failure during actual delivery, and carefully assess the path that will affect the delivery on time to avoid the product not being delivered within the time limit. Therefore, this network reliability can be provided to the managers of the logistics company as a management indicator, as a data indicator for evaluating network performance.

Please refer to FIG5, which shows a schematic diagram of a device 500 for evaluating the reliability of a random cold chain network under multi-order travel time in an embodiment of the present invention. As shown in the figure, the reliability calculation device 500 for evaluating the reliability of a random cold chain network under multi-order travel time of the present invention may at least include an input device 501, a memory 503, a processor 505, and an output device 507. Among them, the input device 501 is electrically connected to the memory 503. The input device 501 may include various input interfaces of a computer device or a file receiving device. The input device 501 can receive the nodes and transmission edge architecture of the stochastic cold chain network under multi-state travel time (SCCNMT) 5031 (i.e., the SCCNMT network topology 5031) and store it in the memory 503. The memory 503 can store the algorithms of the network reliability calculation method developed for the above-mentioned random cold chain network with multi-order travel time (SCCNMT) 5031, including a first algorithm 5032, a second algorithm 5033 and a third algorithm 5034, wherein the third algorithm 5034 can calculate the accurate network reliability ( RD _{, T} ) by using the process steps disclosed in the above-mentioned embodiment.

In a preferred embodiment, the memory 503 may include a read-only memory, a flash memory, a disk, or a cloud database.

In a preferred embodiment, the processor 505 is electrically connected to the memory 503. The processor 505 includes a central processing unit, an image processor, a microprocessor, etc., and may include a multi-core processing unit or a combination of multiple processing units. The processor 505 can access the random cold chain network with multi-order travel time (SCCNMT) 5031 in the memory and the third algorithm 5034 for reliability calculation method to perform network reliability estimation.

In a preferred embodiment, the result of the calculation by the processor 505 can be output by the output device 507. The output device 507 can be a display for presenting the calculation result, such as an LCD, LED or OLED display screen, or a wired/wireless network transmission device to transmit the calculation result to a remote user.

The above is a preferred embodiment of the present invention. Those skilled in the art should understand that it is used to illustrate the present invention, not to limit the scope of the patent rights claimed by the present invention. The scope of patent protection shall be determined by the scope of the attached patent application and its equivalent field. Those skilled in the art in this field, without departing from the spirit or scope of the patent, shall make changes or modifications, which are equivalent changes or designs completed under the spirit disclosed by the present invention, and shall be included in the scope of the patent application below.

10: Network topology S40, S41, S42, S43, S44, S45, S46: Steps 500: Device for predicting system reliability 501: Input device 503: Memory 505: Processor 507: Output device 5031: SCCNMT network topology 5032: First algorithm 5033: Second algorithm 5034: Third algorithm

[Figure 1] is a schematic diagram showing the service time of the entire cold chain network proposed by the present invention.

[FIG. 2] shows the entire algorithm for illustrating the estimated network reliability according to a preferred embodiment of the present invention.

[Figure 3] shows the network topology adopted according to the embodiment of the present invention.

[FIG. 4] is a flow chart showing a method for evaluating the reliability of a random cold chain network according to an embodiment of the present invention.

[FIG. 5] is a schematic diagram showing a device for evaluating the reliability of a random cold chain network under multi-order travel time according to an embodiment of the present invention.

S40,S41,S42,S43,S44,S45,S46: Steps

Claims (10)

A method for evaluating the reliability of a random cold chain network, wherein the random cold chain network is constructed as a network topology and stored in a readable medium, and is calculated by a processor, and the method comprises the following steps: Constructing the network topology, including inputting network nodes, a plurality of transport segments connecting individual network nodes, and the travel time of each of the plurality of transport segments; Analyzing all time factors of the network topology and listing all transport paths, adjusting the value of the travel time to a negative value, so as to convert the entire network vector into a lower bound vector; Finding all feasible flow vectors that meet the demand in the plurality of transport segments; Generating a transport vector, including converting each of the above feasible flow vectors into a transport vector, and obtaining the minimum transport vector; Obtaining the network vector, including calculating the currently allocable travel time through the time factors and values used in the network topology, finding the travel time vector that meets the allocable travel time, and obtaining the maximum travel time vector, combining the minimum transport vector and the maximum travel time vector into the network vector, and adjusting it to the lower bound vector of the random cold link network under multi-order travel time; Obtaining the minimum network vector, and using the minimum network vector to calculate the network reliability of the random cold link network. The method for evaluating the reliability of a random cold chain network as described in claim 1 further includes evaluating the ability of the random cold chain network to meet transportation demands and time thresholds based on the results of the network reliability and making corresponding management decisions based on changes in the network reliability. A method for evaluating the reliability of a random cold chain network as described in claim 2, wherein the network nodes include a plurality of nodes consisting of a plurality of suppliers, a plurality of third-party logistics companies, and a plurality of retailers. The method for evaluating the reliability of a random cold chain network as described in claim 3, wherein the step of performing the above-mentioned step of finding all feasible flow vectors that meet the demand further includes: Checking whether the number of transport vehicles used by all the plurality of transport routes exceeds the maximum number of available transport vehicles; and Checking whether the transport vehicle departing from the supplier can arrive within a given time and does not exceed the above-mentioned maximum number of available transport vehicles. The method for evaluating the reliability of a random cold link network as described in claim 3, wherein the step of obtaining the network vector further includes: For the unused multiple transport segments, set them to the maximum travel time without considering their probability; Delete the unreasonable network vector in which the number of transport vehicles in the network vector does not correspond to the correct travel time. A method for evaluating the reliability of a random cold chain network as described in claim 3, wherein the time factor includes the unloading and loading time at the node. A method for evaluating the reliability of a random cold chain network as described in claim 3, wherein the feasible flow vector represents the quantity of products that will arrive at the retailer within the specified time using the current number of transport vehicles, provided that demand is met. A method for evaluating the reliability of a random cold link network as described in claim 1, wherein the minimum transport vector is obtained by using a comparison rule of vector operations. A method for evaluating the reliability of a random cold link network as described in claim 1, wherein the maximum travel time vector is obtained by using a comparison rule of vector operations. A method for evaluating the reliability of a random cold link network as described in claim 1, wherein the minimum network vector is obtained by using a comparison rule of vector operations.