Method and system for designing flat and urgent logistics network considering demand robust matching

Abstract

The application belongs to the technical field of emergency management, and specifically discloses a kind of flat emergency dual-purpose logistics network design method and system considering demand robust matching, comprising: constructing a fixed investment decision model;Constructing "flat emergency dual-purpose" logistics network operation decision model, the decision content of this model is network transportation decision of pre-disaster living materials and network transportation decision of post-disaster emergency materials respectively;Uncertain parameter emergency material demand, road loss condition and pre-disaster demand point demand for living materials are processed using Wasserstein uncertain set, so as to integrate the two models into a two-stage distributed robust optimization model based on Wasserstein distance;The robust optimization model is transformed into an equivalent model;The model is decomposed and linearly reconstructed, and the decomposed model is solved to obtain the final logistics network design result.The application can fully exert the synergistic advantages of "flat emergency dual-purpose" mode in improving emergency response capability and optimizing resource allocation.

Description

Technical Field

[0001] This invention belongs to the field of emergency management technology and relates to a multifunctional logistics network that considers "dual-use" warehousing facilities and robustly matches the warehousing and logistics needs under two different time and space scenarios. In particular, it relates to a design method for a dual-use logistics network that considers robust matching of needs. Background Technology

[0002] As urbanization continues, logistics networks not only need to efficiently transport daily necessities but also possess emergency response capabilities to sudden disasters. After a disaster, a large number of affected people desperately need emergency supplies such as water, food, and medicine. An efficient emergency logistics network is crucial for protecting the lives and property of the people. However, existing logistics networks have the following limitations: traditional logistics networks often only consider a single operational scenario, lacking overall planning for the logistics of daily necessities and emergency supplies, easily leading to low infrastructure utilization and uneven resource allocation; furthermore, due to the high uncertainty of the time, location, and scale of disasters, existing logistics networks struggle to balance response speed and resource allocation, making it difficult to provide timely, flexible, and efficient solutions.

[0003] In existing technologies, the concept of "dual-use" (normal and emergency) logistics is gradually becoming an important development direction for optimizing logistics networks. To promote the realization of this concept, the "Guidelines for Resilient Urban Planning and Land Policy with Combined Normal and Emergency Functions" proposes two key tasks for material support: first, to formulate action plans and project lists for material support scenario facilities; and second, to strengthen the planning and layout of "dual-use" public infrastructure nodes and encourage the exploration of diverse "dual-use" models. However, current domestic research on "dual-use" logistics is mostly at the conceptual level, lacking specific model design and verification analysis. Secondly, since disasters may cause road damage and exacerbate demand uncertainty, optimizing material transportation strategies considering disaster-affected road conditions has also become a research focus. Scholars such as Yin Yunqiang and Sun Huali have studied the emergency material distribution decision-making problem of joint road repair in response to the actual rescue needs of earthquakes. In addition, strengthening the construction of critical roads before a disaster is also an important measure to improve network resilience. By reinforcing key road sections in advance, the degree of damage caused by disasters to the network can be effectively reduced, and the need for post-disaster road repair can be reduced.

[0004] To address the differences and complexities between normal and emergency scenarios, the design of a "dual-purpose" logistics network needs to achieve robust demand matching under both routine and emergency conditions, and to cope with multiple uncertainties through effective modeling. Among existing optimization techniques, two methods characterize uncertainty based on the quantity and type of relevant demand information: stochastic programming and robust optimization. However, due to the extreme assumptions of stochastic programming and robust optimization, it is difficult to describe parameter uncertainty using limited historical data and uncertainty sets. Distributed robust optimization, due to its advantages in uncertainty modeling, can improve the robustness of the solution and reduce conservatism by being driven by historical data. Currently, the widely used types of uncertainty sets are moment-based uncertainty sets and statistical distance-based uncertainty sets. Moment-based uncertainty sets are difficult to adjust, and the resulting decisions may be conservative; Wasserstein distance-based uncertainty sets only require a limited amount of sampled data and are suitable for handling multiple uncertain parameters. Therefore, the following problems remain unresolved: 1) Although the construction of "dual-use" warehousing facilities has received policy support, existing research is mostly at the conceptual level and lacks systematic planning research; 2) Previous studies have insufficient methods for handling multiple uncertainties in different time and space scenarios, making it difficult to reliably guarantee the comprehensive matching of "dual-use" needs. Summary of the Invention

[0005] To address the aforementioned shortcomings or improvement needs of existing technologies, this invention provides a design method and system for a dual-purpose logistics network that considers robust demand matching for both normal and emergency use. It explores a dual-purpose model with the government as the decision-maker, aiming to design a multi-functional logistics network that considers dual-purpose warehousing facilities and robustly matches warehousing and logistics demands under two different spatiotemporal scenarios. This approach aims to coordinate normal and emergency demands, enhance social resilience, and optimize resource allocation.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for designing a dual-purpose logistics network considering robust demand matching is proposed, comprising the following steps:

[0007] Step 1: Construct a fixed investment decision-making model. The decision-making content of this model includes the selection of warehousing facility construction, pre-allocation of emergency supplies, storage capacity of living supplies, and road reinforcement construction decisions.

[0008] Step 2: Construct a "dual-use" logistics network operation decision model. The decision-making content of this model includes network transportation decisions for pre-disaster living supplies and network transportation decisions for post-disaster emergency supplies.

[0009] Step 3: The Wasserstein uncertainty set is used to process the uncertain parameters of emergency material demand, road damage, and pre-disaster demand for living materials, so as to integrate the fixed investment decision model and the "dual-use" logistics network operation decision model into a two-stage distributed robust optimization model based on Wasserstein distance.

[0010] Step four: Perform equivalent transformation on the corresponding robust optimization model;

[0011] Step 5: The semi-infinite optimization problem after robust equivalence transformation is linearly reconstructed through model decomposition, and the decomposed model is solved. The final logistics network design result is obtained through iterative optimization.

[0012] As a further preferred option, in step one, the objective function of the fixed investment decision model is constructed based on minimizing the total cost of facility construction, emergency material reserves, and road reinforcement construction.

[0013] Preferably, the objective function of the fixed investment decision model includes:

[0014]

[0015] In the formula, F is the set of candidate facility points; f i 0 The fixed cost of constructing facility i as a "dual-use" storage point; x i Indicates whether facility i is selected as a "dual-use" storage point; f i 1 The fixed cost of constructing facility i as an emergency supplies storage point; g i Indicates whether facility i is selected as an emergency supplies storage point; f i 2 The fixed cost of constructing facility i as a storage point for daily necessities; y i H1 indicates whether facility i is selected as a storage point for living supplies; H2 represents the set of emergency supplies types. This represents the unit storage cost of emergency supplies h for facility i; L represents the emergency supplies storage capacity h of facility i; L represents the path set; c ij R represents the reinforcement cost of path (i,j); ij Indicates whether path (i,j) should undergo road reinforcement construction; This represents the expected cost of the "dual-use" logistics network operation decision-making model.

[0016] Preferably, in the fixed investment decision model, each storage location can only construct one type of storage facility.

[0017]

[0018] If the storage site chooses to build a "dual-purpose" storage facility, it can store both daily necessities and emergency supplies simultaneously. If it chooses to build a daily necessities storage facility, it can only store daily necessities. If it chooses to build an emergency supplies storage facility, it can only store emergency supplies. This constraint includes:

[0019]

[0020] H1 represents the set of types of daily necessities; The storage capacity h of living supplies for facility i is represented by M, which is a constant.

[0021] Preferably, the costs of warehousing facility construction and emergency supplies pre-configuration shall not exceed the total budget constraints for facility construction and emergency supplies reserves, including:

[0022]

[0023] G1 represents the total budget for infrastructure construction and emergency supplies reserves;

[0024] Preferably, the cost of road reinforcement does not exceed the total budget constraint for road reinforcement construction, including:

[0025]

[0026] G2 represents the total budget for road construction.

[0027] As a further preferred embodiment, in step two, the objective constraint function of the "dual-use" logistics network operation decision model includes:

[0028]

[0029] In the formula, This represents the unit transportation cost of emergency supplies (h). The pre-disaster flow of the path (i,j) for the supply of daily necessities h; This represents the unit transportation cost of daily necessities (h). Let (i,j) represent the post-disaster flow of emergency supplies h along the path; W = P∪F represents all possible nodes; P represents the set of population demand points; This represents the unit shortage penalty cost of demand point i for daily necessities h. This indicates the shortage of daily necessities h at demand point i; This represents the unit shortage penalty cost of emergency supplies h at demand point i; This indicates the shortage of emergency supplies h at demand point i;

[0030] Preferably, in the "dual-use" logistics network operation decision model, the pre-disaster road traffic flow constraints during the operation of the daily necessities network include:

[0031]

[0032] Preferably, the network flow balance constraints for the transportation of essential supplies to each network node before a disaster include:

[0033]

[0034] In the formula, a ij β represents the pre-disaster capacity of road (i,j); ij The proportion of increased capacity after road reinforcement; For the pre-disaster demand point i's demand for living supplies h, r ij Determine whether to perform road reinforcement construction for path (i,j);

[0035] Preferably, during the operation of emergency supplies networks in disaster periods, post-disaster road traffic flow restrictions include:

[0036]

[0037] Preferably, the network flow balance constraints for emergency material transportation at each network node after a disaster include:

[0038]

[0039] in, Let (i,j) be the loss coefficient of road (i,j). The demand for emergency supplies h is based on the post-disaster demand point i.

[0040] As a further preferred option, step three includes:

[0041] Let the vector of uncertain parameters be... Given N Historical data Set a reference experience distribution Used to estimate the true probability distribution in Indicates that the unit mass is concentrated in The Dirac function;

[0042] Uncertain set Defined as the distribution that approximates the empirical distribution at the Wasserstein distance. All distribution families:

[0043]

[0044] In the formula, Let be the set of supported probability distributions on the space Ξ;

[0045] The Wasserstein distance is used to represent the statistical distance of the uncertain set:

[0046]

[0047] in, express probability distribution for probability distribution for and The joint probability distribution and Representing random variables respectively about and about marginal distribution, For random variables and The statistical distance on the space Ξ, the norm ||·|| is defined using the following...

[0048] As a further preferred option, according to Uncertain set Represented as:

[0049]

[0050] When the Wasserstein distance ρ equals 0, the estimate of the true probability distribution is the reference empirical distribution, and the model simplifies to a stochastic programming model.

[0051] When the Wasserstein distance ρ is greater than the support space Ξ of the uncertain parameter vector, the model takes the worst estimate of the uncertain parameters, and the model will degenerate into a robust optimization model.

[0052] As a further preferred embodiment, in step three, the two-stage distributed robust optimization model includes:

[0053]

[0054] Where, Δ DRO It is a two-stage distributed robust optimization model. for The worst-case expectation problem. In order to investigate the issue.

[0055] As a further preferred embodiment, step four, the equivalent transformation of the robust optimization model, includes:

[0056] For any policy variables s, r, e in a fixed investment decision model, if When the feasible region of the "dual-use" logistics network operation decision model is bounded, the robust optimization model is transformed into:

[0057]

[0058] λ≥0

[0059] Where, Δ DRO It is a two-stage distributed robust optimization model.

[0060] As a further preferred embodiment, step five, which involves linearly reconstructing the semi-infinite optimization problem after robust equivalence transformation through model decomposition, includes:

[0061] By introducing an auxiliary variable σ, the semi-infinite optimization problem is decomposed into a main problem and a series of subproblems;

[0062] Preferably, the main problem is defined as:

[0063]

[0064] Among them, Ω n (s,r,e,λ) is a subproblem;

[0065] The subproblem is defined as follows:

[0066]

[0067] Among them, for the internal max-min problem in the subproblem, the duality theorem is used to transform the "normal and emergency use" logistics network operation decision model into a dual problem for solution.

[0068] As a further preferred embodiment, in step five, the solution of the decomposed model, through iterative optimization to obtain the final logistics network design result, includes:

[0069] The row and column generation algorithm is used to determine the number of iterations ψ. The formulas for calculating the lower and upper bounds of each iteration include:

[0070]

[0071] Where LB is the lower bound of the iteration and UB is the upper bound of the iteration. For the current iteration, Let n be the number of all candidate solutions, n = 1, 2, ..., N;

[0072] When (UB-LB) / UB≤gap, the algorithm converges to the defined tolerance level gap and outputs the optimal solution.

[0073] According to another aspect of the present invention, a dual-purpose logistics network design system considering robust demand matching is also provided, comprising:

[0074] The first main control module is used to build a fixed investment decision model. The decision-making content of this model includes the selection of warehousing facility construction, pre-configuration of emergency supplies, storage capacity of living supplies, and road reinforcement construction decisions.

[0075] The second main control module is used to build a "dual-use" logistics network operation decision model. The decision content of this model is the network transportation decision of pre-disaster living materials and the network transportation decision of post-disaster emergency materials.

[0076] The third main control module is used to process the uncertain parameters of emergency material demand, road loss situation and pre-disaster demand points for living materials using Wasserstein uncertainty set, so as to integrate the fixed investment decision model and the "normal and emergency use" logistics network operation decision model into a two-stage distributed robust optimization model based on Wasserstein distance.

[0077] The fourth main control module is used to perform equivalent conversion on the corresponding robust optimization model;

[0078] The fifth main control module is used to linearly reconstruct the semi-infinite optimization problem after robust equivalence transformation through model decomposition, solve the decomposed model, and obtain the final logistics network design result through iterative optimization.

[0079] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0080] 1. This invention calculates decision-making results under different Wasserstein distance values ​​ρ. Overall, as the Wasserstein distance ρ increases, the objective function value and fixed costs show an upward trend. A suitable Wasserstein distance value ρ can be selected based on risk preference at the fluctuation point of the first difference of the fixed cost to balance construction cost-effectiveness and risk resistance. Furthermore, as ρ increases, the corresponding number of warehouse construction sites, road reinforcement construction sites, emergency material reserves, and living material capacity also increase.

[0081] 2. The "dual-use" logistics network of the present invention can effectively reduce the operating cost of the logistics network through resource sharing and functional integration; the "dual-use" logistics network can also reduce the transportation distance of emergency supplies from warehouses to the demand locations by increasing the storage and distribution of emergency supplies.

[0082] 3. The "dual-use" logistics network design model of this invention is quite sensitive to the construction cost of "dual-use" warehousing facilities, and this sensitivity is more pronounced under higher values ​​(ρ). In practical operation, a long-term operational perspective can help in deciding whether to choose the "dual-use" logistics model.

[0083] 4. The method of this invention can complete the calculation within an acceptable time range (24-48 hours) for engineering project planning, and the model and algorithm can be applied to conventional logistics network design problems. Attached Figure Description

[0084] Figure 1 This is a design block diagram of a "dual-purpose" logistics network design method that considers robust demand matching according to the present invention.

[0085] Figure 2 This is a schematic diagram of the transition between the "normal" and "urgent" time networks in this invention.

[0086] Figure 3 This is a flowchart illustrating how the final logistics network design result is obtained through iterative optimization in this invention.

[0087] Figure 4 This is a schematic diagram of the decision results of the example in this invention under different Wasserstein distance values ​​ρ;

[0088] Figure 5 This is a schematic diagram of the optimized logistics network design results under two different modes: "dual-use for both normal and emergency situations" and "separation of normal and emergency situations" in this invention.

[0089] Figure 6 This is a schematic diagram illustrating the evaluation results of the "dual-purpose" logistics network in this invention;

[0090] Figure 7 This is a schematic diagram showing the convergence status and execution time of the algorithm in this invention;

[0091] Figure 8 This is a schematic diagram of a calculation example in this invention with 30 network nodes. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0093] The current "dual-use" model is still in the exploratory stage. Different models can be proposed based on the development needs of different regions, daily operations, and emergency needs. Considering that emergency material storage is the foundation for realizing the material support function of "dual-use" public infrastructure, this invention explores a "dual-use" model with the government as the decision-making body. The goal is to design a multi-functional logistics network that considers "dual-use" warehousing facilities and robustly matches the warehousing and logistics needs under two different time and space scenarios, thereby coordinating normal and emergency needs, enhancing social resilience, and optimizing resource allocation.

[0094] To achieve the above objectives, the technical solution provided by this invention is as follows: a "dual-purpose" logistics network is designed based on a two-stage distributed robust optimization model. The first stage of the model optimizes decisions regarding warehouse location selection, emergency material pre-configuration, and road reinforcement construction. The second stage constructs an uncertainty set using Wasserstein distance to characterize the uncertainties of pre-disaster demand for living supplies, post-disaster demand for emergency supplies, and road damage. Based on this, the network transportation planning for both routine and emergency scenarios is comprehensively optimized to ensure the efficiency and reliability of the logistics network. To address the nonlinearity of the problem, the model is reconstructed using an equivalent linear model, and then the Column-and-Constraint Generation (CC&G) algorithm is used to solve the proposed two-stage distributed robust optimization model. Finally, numerical experiments are conducted based on a research case to analyze the model's applicability and propose relevant management decision-making suggestions.

[0095] like Figure 1 As shown, the "dual-use" warehousing facilities are designed to function as: in normal times, they serve as a storage and distribution center for daily necessities, ensuring the supply and stabilizing the prices of daily necessities; in times of emergency, they serve as an emergency material support function, used for allocating and storing reserve materials.

[0096] like Figure 2 As shown, this invention integrates and optimizes the following four aspects: 1) determining the construction of "dual-purpose" storage facilities, emergency storage facilities, or living supplies storage facilities among candidate warehouse locations; 2) determining the amount of emergency supplies or the storage capacity of living supplies at each storage location; 3) determining the road reinforcement construction decisions between each node; and 4) planning the network transportation of living supplies before a disaster and emergency supplies after a disaster. To more clearly describe the applicable scenarios of the model proposed in this study, the following assumptions are made:

[0097] Assumption 1: "Dual-purpose" warehousing facilities can simultaneously store urban daily necessities and emergency supplies, and the maximum storage capacity of the same warehousing facility construction site is the same;

[0098] Assume that the living supplies storage point can only store living supplies, and the emergency supplies storage point can only store emergency supplies;

[0099] Hypothesis 3 states that after road reinforcement construction, not only can the disaster-bearing capacity of roads be improved after a disaster, but the road transport capacity of the logistics network can also be improved before a disaster.

[0100] Assumption 4 assumes that, in order to facilitate the connection with transportation load and material demand, the capacity or demand of living materials and emergency materials will be converted into weight statistics.

[0101] Because it is difficult to determine the penalty cost of shortages of supplies in practice, daily necessities... and emergency supplies The shortage penalty cost is typically set as: 1) Additional procurement cost. In the event of a disaster emergency or insufficient supply of living materials, the shortage is replenished through additional procurement; 2) Deprivation cost. When it is difficult to replenish materials through procurement in a shortage situation, the shortage penalty cost can be set to a larger number, i.e., it becomes the deprivation cost. Considering that it is necessary to meet the considered demand scenarios as much as possible in disaster preparedness, this invention adopts the latter to characterize this parameter.

[0102] Based on the above technical settings, a two-stage distributed robust optimization model is constructed to realize a "dual-purpose" logistics network that can reliably match the needs of daily material operations with emergency material support.

[0103] Specifically, such as Figure 1 As shown in the figure, the present invention provides a "dual-purpose" logistics network design method that considers robust demand matching, characterized by the following steps:

[0104] Step 1: The first stage of the model executes fixed investment decisions, including the selection of warehousing facilities, the pre-allocation of emergency supplies, the storage capacity of living supplies, and the decision on road reinforcement construction.

[0105] Step 2: In the second stage, the model executes "dual-use" logistics network operation decisions, which include decisions on the network transportation of pre-disaster living supplies and post-disaster emergency supplies.

[0106] Step 3: Because the previously determined modeling method cannot handle uncertain parameters. Especially the demand for emergency supplies and road damage situation The amount of historical disaster data available is usually very limited, making it impossible to obtain their true probability distribution. Therefore, the Wasserstein uncertainty set is used to determine the uncertain parameters. Process it.

[0107] Step 4: Represent the two-stage stochastic programming model as a two-stage distributed robust optimization model using the Wasserstein uncertainty set.

[0108] Step 5: Worst-case expectation Involves probability distribution The infinite-dimensional optimization cannot be solved directly, so the model needs to be transformed into an equivalent form, i.e., a robust equivalent transformation.

[0109] Step 6: Linearly reconstruct the semi-infinite optimization problem after robust equivalence transformation through model decomposition.

[0110] Step 7: Use a row and column generation algorithm to solve the decomposed model, and obtain the final result through iterative optimization.

[0111] Based on any of the above embodiments or a combination of multiple embodiments, in step 1, the objective function of the first stage is as shown in formula (1):

[0112]

[0113] The objective function aims to minimize the total cost of facility construction, emergency material reserves, and road reinforcement, where F represents the set of candidate facility locations; f i 0 The fixed cost of constructing facility i as a "dual-use" storage point; x i The variable is 0-1, indicating whether facility i is selected as a "dual-use" storage point; f i 1 The fixed cost of constructing facility i as an emergency supplies storage point; g i The variable is 0-1, indicating whether facility i is selected as an emergency supplies storage point; f i 2 The fixed cost of constructing facility i as a storage point for daily necessities; y i H1 is a 0-1 variable, indicating whether facility i is selected as a storage point for living supplies; H2 represents the set of emergency supplies types. This represents the unit storage cost of emergency supplies h for facility i; L represents the emergency supplies storage capacity h of facility i; L represents the path set; c ij R represents the reinforcement cost of path (i,j); ij Indicates whether path (i,j) should undergo road reinforcement construction; This represents the expected cost of the second phase.

[0114] Each storage point can only construct one type of storage facility, as shown in formula (2):

[0115]

[0116] If the storage point chooses to build a "dual-purpose" storage facility, it can store both daily necessities and emergency supplies at the same time. If it chooses to build a daily necessities storage facility, it can only store daily necessities. If it chooses to build an emergency supplies storage facility, it can only store emergency supplies. The constraints are shown in formulas (3) to (5):

[0117]

[0118] H1 represents the set of types of daily necessities; M represents the storage capacity of living supplies h for facility i; M represents a large number.

[0119] The cost of warehousing facility construction and emergency material pre-configuration shall not exceed the total budget constraint for facility construction and emergency material reserves, as shown in formula (6):

[0120]

[0121] G1 represents the total budget for infrastructure construction and emergency supplies reserves.

[0122] The cost of road reinforcement shall not exceed the total budget constraint for road reinforcement construction, as shown in formula (7):

[0123]

[0124] G2 represents the total budget for road construction.

[0125] The range constraints for the decision variables in the first stage are shown in formulas (8) to (11):

[0126]

[0127] Based on any of the above embodiments or a combination of multiple embodiments, the objective function of the second stage described in step 2 is as shown in formula (12):

[0128]

[0129] The objective function aims to minimize the transportation costs of the logistics network, where... This represents the unit transportation cost of emergency supplies (h). The pre-disaster flow of the path (i,j) for the supply of daily necessities h; This represents the unit transportation cost of daily necessities (h). Let (i,j) represent the post-disaster flow of emergency supplies h along the path; W = P∪F represents all possible nodes; P represents the set of population demand points; This represents the unit shortage penalty cost of demand point i for daily necessities h. This indicates the shortage of daily necessities h at demand point i; This represents the unit shortage penalty cost of emergency supplies h at demand point i; This indicates the shortage of emergency supplies h at demand point i.

[0130] When the daily necessities network is in operation, the pre-disaster road flow restriction constraints are shown in formula (13): the pre-disaster network flow balance constraints for the transportation of daily necessities at each network node are shown in formula (14):

[0131]

[0132] Where a ij β represents the pre-disaster capacity of road (i,j); ij The proportion of increased capacity after road reinforcement; This indicates the pre-disaster demand point i for daily necessities h.

[0133] During the operation of the emergency supplies network during a disaster, the post-disaster road traffic flow restriction constraints are shown in formula (15); the post-disaster network flow balance constraints for emergency supplies transportation at each network node are shown in formula (16).

[0134]

[0135] Among them This represents the loss coefficient of road (i,j); This indicates the demand of disaster-stricken point i for emergency supplies h.

[0136] The constraints on the values ​​of the decision variables in the second stage are shown in formulas (17) to (20):

[0137]

[0138] Based on any of the above embodiments or combinations of embodiments, in step 3, let the vector of the uncertain parameters be... Given N Historical data Set a reference experience distribution Used to estimate the true probability distribution in Indicates that the unit mass is concentrated in The Dirac function. Uncertain set. Defined as the distribution that approximates the empirical distribution at the Wasserstein distance. All distribution families are shown in Equation (21):

[0139]

[0140] Among them Let represent the set of supported probability distributions on space Ξ, denote the threshold of statistical distance, and also serve as a robust control parameter for controlling the size of the uncertainty set.

[0141] The statistical distance of the uncertain set is represented by the Wasserstein distance, as shown in formula (22):

[0142]

[0143] Among them express probability distribution for probability distribution for and The joint probability distribution and Representing random variables respectively about and about The marginal distribution. For random variables and The statistical distance on the spatial Ξ. The norm ||·|| is defined using...

[0144] according to Definition, As shown in formula (23):

[0145]

[0146] When the Wasserstein distance ρ equals 0, the estimate of the true probability distribution is the reference empirical distribution, and the model simplifies to a stochastic programming model. When the Wasserstein distance ρ is greater than the support space Ξ of the uncertain parameter vector, the model takes the worst estimate of the uncertain parameters, and the model will degenerate into a robust optimization model.

[0147] Based on any of the above embodiments or combinations of multiple embodiments, step 4 can express the previous two-stage optimization model as a two-stage sub-Bruker optimization model, as shown in formula (24):

[0148]

[0149] In equation (24) Called The worst-case scenario expectation problem. It is the value function used to obtain the optimal value of the objective function in the second stage, also known as the recourse problem.

[0150] Based on any or a combination of the above embodiments, step 5, which transforms the distributed robust optimization model into a semi-infinite optimization problem, involves giving any first-stage decision variables s, r, e. When the second-stage model is bounded, formula (24) can be transformed into formulas (25) to (26):

[0151]

[0152] λ≥0 (26)

[0153] The specific proof process is as follows:

[0154] Regarding the worst mean in formula (24) Perform the following transformations:

[0155]

[0156] Where, Π represents and The joint probability distribution and Let these be the marginal distributions of the two random variables. for hour Based on the law of total probability, the conditional distribution of the equations (27) to (28) can be rewritten as equations (29) to (30):

[0157]

[0158] Finding the dual of formulas (29) to (30), we get:

[0159]

[0160] Therefore, formula (24) can be transformed into formulas (25) to (26).

[0161] Based on any of the above embodiments or combinations of embodiments, the linear reconstruction described in step 6 requires the introduction of an auxiliary variable σ to decompose the two-stage distributed robust optimization model into a master problem and a series of sub-problems. The master problem (MP) is defined as follows:

[0162]

[0163] Where, Ω n (s,r,e,λ) is defined as a subproblem (SP):

[0164]

[0165] For the internal max-min problem existing in the subproblem, the second-stage model (12) to (20) can be transformed into its dual problem for solution by using the duality theorem. Introducing auxiliary variables τ, θ, η, ε, the dual problem of the subproblem can be expressed by the following formula:

[0166]

[0167]

[0168] in:

[0169]

[0170] set up and They are respectively The maximum and minimum values, and They are respectively The maximum and minimum values, and b ij They are respectively The maximum and minimum values.

[0171] Theorem 1: When SP obtains the optimal solution, The optimal value will be in the set Taken from, The optimal value will be in the set Taken from, The optimal value will be in the set It was obtained from the middle.

[0172] The specific proof process is as follows:

[0173] For the subproblem:

[0174]

[0175] First of all, for According to and We will discuss two scenarios.

[0176] when hour:

[0177]

[0178] at this time, It exists only in the subproblem Ω n In the objective function (s,r,e,λ), and Ω n (s,r,e,λ) is about If it is a linear function, then its optimal value is...

[0179] when hour:

[0180]

[0181] Similarly, optimal value If we combine the two cases, then... Similarly, we can obtain and The optimal value:

[0182] Theorem 2 introduces the auxiliary variable π 1 ,π 2 ,ω 1 ,ω 2 ,α 1 ,α 2 ,τπ 1 ,τπ 2 ,θω 1 ,θω 2 ,εα 1 ,εα 2 The subproblem SP can be transformed into a linear model, as shown below:

[0183]

[0184] The specific proof process is as follows:

[0185] Based on Theorem 1, by introducing the auxiliary variable π 1 ,π 2 ,ω 1 ,ω 2 ,α 1 ,α 2 can and Represented as:

[0186]

[0187]

[0188] Ω in the above equation n Substituting (s,r,e,λ) into the equation, we get:

[0189]

[0190] The bilinear term in formula (59) is the product of the bivariate and the continuous variable. This can be achieved by introducing the auxiliary variable τπ 1 ,τπ 2 ,θω 1 ,θω 2 ,εα 1,εα 2 Linearization is applied to the nonlinear terms to improve solution efficiency. For example, the transformation method for nonlinear terms is as follows:

[0191]

[0192] transformation The conversion method is the same as that of .

[0193] Based on any of the above embodiments or a combination of multiple embodiments, such as Figure 3 As shown, in step 7, the row and column generation algorithm sets the iteration number as ψ, and the index of the candidate solution (i.e., the constraints and decision variables generated in each iteration) in the current iteration is ψ. gather Let n = 1, 2, ..., N, be the number of all candidate solutions. The formulas for the lower bound (LB) and upper bound (UB) for each iteration are as follows:

[0194]

[0195] When (UB-LB) / UB≤gap, the algorithm converges to the defined tolerance level gap, indicating that the worst-case scenario obtained by solving the subproblem is still feasible for the solution provided by the final main problem under the tolerance level gap.

[0196] The following is in conjunction with the appendix Figure 1-8 This paper provides a detailed description of an implementation example of a "dual-purpose" logistics network. It should be emphasized that the following description is merely exemplary and not intended to limit the scope or application of the invention.

[0197] Based on a two-stage distributed robust optimization model, this invention proposes a "dual-purpose" logistics network design method for both routine operations and disaster response. The specific implementation method of the invention is described in detail below.

[0198] Step 1: Determine the necessary parameters and data in advance.

[0199] (1) Warehouse capacity of candidate points; (2) Maximum total demand for emergency supplies; (3) Upper and lower bounds of the demand for supplies at each demand point; (4) Demand data for emergency supplies and daily necessities; (5) Fixed costs of warehousing facility construction; (6) Storage costs of emergency supplies such as water, food, and medicine; (7) Reinforcement cost per unit length of road; (8) Road capacity; (9) Damaged area; (10) Demand for each node; (11) Unit transportation cost of emergency supplies; (12) Unit transportation cost of daily necessities; (13) Increase in capacity of road reinforcement construction; (14) Coefficients of scarce supplies in the objective function; (15) Wasserstein distance value ρ; (16) Baseline value of uncertain parameters. (17) The ratio of the cost of "dual-use" warehousing facilities to the construction cost of emergency material warehousing facilities is represented by the cost control factor; (18) The values ​​of the demand for daily necessities and the demand for emergency materials under different risk scenarios are generated based on the benchmark values ​​of uncertain parameters and are represented by the risk factor; (19) Urban road data.

[0200] Step 2: Given the above conditions, write code to construct the model framework proposed in this method, and call the GUROBI optimization software to solve it, analyze the applicability of this model and propose relevant management decision-making suggestions.

[0201] Step 3: The results can be adjusted to a certain extent according to the actual situation.

[0202] To simplify the text of this application and avoid unnecessary detail, the specific solutions and formulas involved herein can be found in the invention content section of the preceding specification, and will not be repeated here.

[0203] The following is a detailed description based on an example:

[0204] Five cities (F0–F4) were selected as candidate facilities, and 15 cities (F0–F4 and D5–D14) were selected as demand points for numerical experiments. The network was constructed as follows: Figure 8 As shown, the following conditions are given:

[0205] (1) The warehouse capacity of candidate points is set to 3000-3200 tons; (2) The maximum total demand for emergency supplies is set to 1500 tons; (3) The upper and lower limits of the demand for supplies at each demand point are set to 200 and 0, respectively; (4) The demand data for emergency supplies and living supplies are set to be generated evenly within 90-110 tons (i.e., the baseline value is 100 tons); (5) The fixed cost of warehousing facility construction is set to 35-55 million yuan; (6) The storage cost of emergency supplies water, food, and medicine is set to {1,5,10} yuan / ton; (7) The cost of road reinforcement per unit length is set to 200,000 yuan / km; (8) The road capacity is set to be generated within the range of 800-1000 tons; (9) The damaged area is set to (10) The demand for each node is set to be generated in the range of 90 to 110 tons; (11) The unit transportation cost of emergency supplies is set to 0.005 million yuan / km / ton; (12) The unit transportation cost of living supplies is set to 0.002 million yuan / km / ton; (13) The capacity expansion ratio of road reinforcement construction is set to 0.5 times; (14) The coefficient of shortage materials in the objective function is set to the deprivation cost (i.e., a large number); (15) The Wasserstein distance value ρ∈{10,20,30,40,50,60,70,80,90,100,110,120}; (16) The baseline value of the uncertain parameter. (17) The cost control factors are set to {120%, 140%, 160%, 180%, 200%}; (18) The risk factors are set to 0%, 20%, 40%, 60%, 80%, 100%; (19) The urban road data are as follows:

[0206]

[0207]

[0208] Based on the given parameters, code was written to construct the model framework proposed in this method, and the GUROBI software was called to solve it.

[0209] For Example 1, the decision results of the example under different Wasserstein distance values ​​ρ were calculated, and the obtained reference values ​​were used to facilitate subsequent experimental analysis. Cross-validation was performed with different values ​​of ρ.

[0210] When ρ = 30, the fluctuation range of the first difference of subsequent fixed costs is relatively stable, indicating that the logistics network under this model parameter can cope well with multiple uncertainties in daily life and emergencies. Similarly, for consideration of higher disaster risks and disaster scale, ρ = 70 can be selected as a reference point.

[0211] The table below shows the decision results for ρ=30 and ρ=70, with an average calculation time of 7 minutes.

[0212]

[0213]

[0214] Note: X indicates that the storage point is a "dual-use" storage point.

[0215] As the table shows, with the increase of ρ, the corresponding number of warehouses to be built, the number of road reinforcement projects, the capacity for emergency supplies reserves, and the capacity for daily necessities also increase. Therefore, decision-makers can also make choices by referring to the specific calculation results.

[0216] The calculations yielded the following optimization results for the logistics network design under two different modes: "dual-use for both normal and emergency situations" and "separation of normal and emergency situations." Figure 4 As shown; the evaluation results of the "dual-use" logistics network are as follows: Figure 5 As shown:

[0217] from Figure 5 As can be seen, with ρ=30, DMP (Network Operational Performance) and EM (Emergency Response Time) are 33.27% and 33.92% respectively. The "dual-use" model has a high optimization rate, indicating its significant advantages through resource integration. The main reason is that the optimized "dual-use" network layout increases the distribution density of emergency supplies and reduces the transportation distance from warehouses to demand points, thereby shortening the delivery time of supplies. Figure 6 As shown, the optimization effects of DMP and EM decrease with increasing ρ, but they still maintain certain advantages. This indicates that the logistics network under the "dual-use" model has high network operation efficiency and emergency response capability.

[0218] The decision-making results under different costs for "dual-use" warehousing facilities are shown in the table below:

[0219]

[0220] like Figure 7 As shown, when ρ = 30 and the cost control factor is less than or equal to 160%, the decision results still include "dual-use" storage points; when ρ = 70 and the cost control factor is greater than or equal to 120%, the decision results do not include "dual-use" storage points. This indicates that the "dual-use" logistics network design model is quite sensitive to the construction cost of "dual-use" storage facilities, and this sensitivity is more pronounced at larger ρ values.

[0221] The robustness comparison results of the Sample Average Approximation (SSA) model and the distributed robust optimization model under different scenario settings are shown in the table below:

[0222]

[0223] As shown in the table above, when ρ = 30, the distributed robust optimization model can handle scenarios with a risk factor of less than 40% well. When ρ = 70, the distributed robust optimization model exhibits greater fault tolerance and can at least handle scenarios with a risk factor of less than 80%. However, the decision scheme obtained by sample average approximation is difficult to handle scenarios with a risk factor of more than 20%.

[0224] In summary, this invention comprehensively considers the coordination and matching between routine and emergency needs in logistics networks, as well as the uncertainty caused by increased road damage. It proposes a "dual-purpose" logistics network design method that considers robust demand matching, effectively improving upon the shortcomings of traditional methods. This invention can effectively reduce the operating costs of logistics networks and shorten the transportation distance of emergency supplies from warehouses to demand locations, and is applicable to conventional logistics network design problems.

[0225] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing a dual-purpose logistics network considering robust demand matching, characterized in that, Includes the following steps: Step 1: Construct a fixed investment decision-making model. The decision-making content of this model includes the selection of warehousing facility construction, pre-allocation of emergency supplies, storage capacity of living supplies, and road reinforcement construction decisions. Step 2: Construct a "dual-use" logistics network operation decision model. The decision-making content of this model includes network transportation decisions for pre-disaster living supplies and network transportation decisions for post-disaster emergency supplies. Step 3: The Wasserstein uncertainty set is used to process the uncertain parameters of emergency material demand, road damage, and pre-disaster demand for living materials, so as to integrate the fixed investment decision model and the "dual-use" logistics network operation decision model into a two-stage distributed robust optimization model based on Wasserstein distance. The two-stage distributed robust optimization model includes: ， in, It is a two-stage distributed robust optimization model. for The worst-case expectation problem. For the true probability distribution, It is an uncertain set. In order to pursue the issue; It is a set of candidate facility sites; Facilities Fixed costs for constructing a "dual-use" storage facility; Indication facilities Whether to select it as a "dual-use" storage point; Facilities Fixed costs for constructing an emergency supplies storage facility; Indication facilities Should it be selected as an emergency supplies storage point? Facilities Fixed costs for constructing a warehouse for storing daily necessities; For facilities Whether to select it as a storage point for daily necessities; This represents a collection of emergency supplies. Indication facilities The unit storage cost of emergency supplies; Indication facilities emergency supplies Storage capacity; Represents a set of paths; Representing a path The cost of strengthening construction; Representing a path Should road reinforcement construction be carried out? , and It is the vector corresponding to the variable. It refers to a vector with uncertain parameters; Step four: Perform an equivalent transformation on the robust optimization model: For any policy variable in a fixed investment decision model ,like When the feasible region of the "dual-use" logistics network operation decision model is bounded, the robust optimization model is transformed into: ， in, It is a two-stage distributed robust optimization model. Let be a vector of n uncertain parameters, where . For the support space of uncertain parameters, For robust control parameters, Let N be the Lagrange multiplier, N be the number of data samples, and H2 be the set of emergency supplies types. Step 5: The semi-infinite optimization problem after the equivalent transformation is linearly reconstructed through model decomposition, and the decomposed model is solved. The final logistics network design result is obtained through iterative optimization. In step five, the semi-infinite optimization problem after the equivalent transformation is linearly reconstructed through model decomposition, including: Introducing auxiliary variables The semi-infinite optimization problem is decomposed into a main problem and a series of subproblems; The main problem is defined as follows: ， in, For subproblems; The subproblem is defined as follows: ， Among them, for the internal max-min problem in the subproblem, the dual theorem is used to transform the "normal and emergency use" logistics network operation decision model into a dual problem for solution; In step five, the solution of the decomposed model, through iterative optimization, yields the final logistics network design result, including: The number of iterations is set using a row and column generation algorithm. The formulas for calculating the lower and upper bounds of each iteration include: ， Where LB is the lower bound of the iteration and UB is the upper bound of the iteration. For the current iteration, The number of all candidate solutions, , This refers to the current iteration number; when The algorithm converges to the defined tolerance level. When the time limit is reached, output the optimal solution.

2. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 1, characterized in that, In step one, the objective function of the fixed investment decision model is constructed based on minimizing the total cost of facility construction, emergency material reserves, and road reinforcement construction.

3. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 2, characterized in that, The objective function of the fixed investment decision model includes: In the formula, .

4. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 3, characterized in that, In the fixed investment decision-making model, each storage location can only construct one type of storage facility, which is a constraint. ， If the storage site chooses to build a "dual-purpose" storage facility, it can store both daily necessities and emergency supplies simultaneously. If it chooses to build a daily necessities storage facility, it can only store daily necessities. If it chooses to build an emergency supplies storage facility, it can only store emergency supplies. This constraint includes: ， in, This represents a collection of different types of daily necessities. Indication facilities daily necessities Storage capacity; It is a constant.

5. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 4, characterized in that, The costs of warehousing facility construction and emergency supplies pre-configuration shall not exceed the total budget constraints for facility construction and emergency supplies reserves, including: ， in, This indicates the total budget for facility construction and emergency supplies reserves; The cost of road reinforcement must not exceed the total budget constraint for road reinforcement construction, including: ， in, This indicates the total budget for road construction.

6. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 1, characterized in that, In step two, the objective constraint function of the "dual-use" logistics network operation decision model includes: ， In the formula, Indicates emergency supplies Unit transportation costs; Indicating daily necessities path Pre-disaster flow; Indicating daily necessities Unit transportation costs; Indicates emergency supplies path Post-disaster traffic; Indicates all optional nodes; Represents the set of population demand points; Indicate demand points daily necessities The unit shortage penalty cost; Indicate demand points daily necessities Shortage quantity; Indicate demand points emergency supplies The unit shortage penalty cost; Indicate demand points emergency supplies Shortage quantity.

7. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 6, characterized in that, In the aforementioned "dual-use" logistics network operation decision-making model, pre-disaster road traffic flow constraints during the operation of the daily necessities network include: ， The network flow balance constraints for the transportation of essential supplies to various network nodes before the disaster included: ， In the formula, Pre-disaster roads The capacity; The proportion of increased capacity after road reinforcement; Pre-disaster demand points For daily necessities demand, For path Should road reinforcement construction be carried out? When emergency supplies networks are in operation during disasters, post-disaster road traffic restrictions include: ， The network flow balance constraints for emergency supplies transportation at various network nodes after a disaster include: ， in, For roads The loss coefficient; Post-disaster demand points emergency supplies The demand.

8. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 1, characterized in that, Step three includes: Let the vector of uncertain parameters be... Given indivual Historical data Set a reference empirical distribution Used to estimate the true probability distribution ,in Indicates that the unit mass is concentrated in The Dirac function; Uncertain set Defined as the distribution that approximates the empirical distribution at the Wasserstein distance. All distribution families: ， In the formula, For space The set of probability distributions supported by the above; The Wasserstein distance is used to represent the statistical distance of the uncertain set: ， in, express probability distribution for probability distribution for and The joint probability distribution and Representing random variables respectively about and about marginal distribution, For random variables and In space Statistical distance on, norm The definition adopts Norm.

9. A method for designing a dual-purpose logistics network considering robust demand matching as described in claim 8, characterized in that, according to Uncertain set Represented as: ， When Wasserstein distance When the probability is equal to 0, the estimate of the true probability distribution is the reference empirical distribution, and the model simplifies to a stochastic programming model. When Wasserstein distance Support space greater than the uncertain parameter vector When the model obtains the worst-case estimate of the uncertain parameters, it will degenerate into a robust optimization model.

10. A system for designing a dual-purpose logistics network considering robust demand matching, used to implement the dual-purpose logistics network design method considering robust demand matching as described in any one of claims 1-9 by Ruan Li, characterized in that, include: The first main control module is used to build a fixed investment decision model. The decision-making content of this model includes the selection of warehousing facility construction, pre-configuration of emergency supplies, storage capacity of living supplies, and road reinforcement construction decisions. The second main control module is used to build a "dual-use" logistics network operation decision model. The decision content of this model is the network transportation decision of pre-disaster living materials and the network transportation decision of post-disaster emergency materials. The third main control module is used to process the demand for emergency supplies, road damage, and pre-disaster demand for living supplies using Wasserstein uncertainty sets, so as to integrate the fixed investment decision model and the "dual-use" logistics network operation decision model into a two-stage distributed robust optimization model based on Wasserstein distance. The fourth main control module is used to perform equivalent conversion on the corresponding robust optimization model; The fifth main control module is used to linearly reconstruct the semi-infinite optimization problem after the equivalent transformation through model decomposition, solve the decomposed model, and obtain the final logistics network design result through iterative optimization.

Images