Face-time and urgent-time dual-purpose logistics network design method and system considering demand robust matching

Abstract

The invention belongs to the technical field of emergency management, and particularly discloses a method and a system for designing a level and urgent dual-purpose logistics network considering demand robust matching. Comprising the steps of constructing a fixed investment decision model; constructing a'peacetime and urgency dual-purpose 'logistics network operation decision-making model, wherein the decision-making contents of the model are respectively a network transportation decision-making of pre-disaster life materials and a network transportation decision-making of post-disaster emergency materials; a Wasserstein uncertain set is adopted to process uncertain parameter emergency material demands, road loss conditions and demands of pre-disaster demand points on living materials, so that the two models are integrated into a two-stage distributed robust optimization model based on a Wasserstein distance; performing peer-to-peer conversion on the robust optimization model; and performing decomposition linear reconstruction on the model, solving the decomposed model, and obtaining a final logistics network design result through iterative optimization. According to the invention, the cooperative advantages of the'peacetime and urgency dual-purpose 'mode in improvement of emergency response capability and optimization of resource configuration can be brought into full play.

Description

Technical Field

[0001] The present invention belongs to the field of emergency management technology, and relates to a composite functional logistics network that takes into account "dual-purpose" warehousing facilities, and robustly matches the warehousing and logistics needs in two different time and space scenarios. In particular, it relates to a design method for a dual-purpose logistics network that takes into account robust matching of needs. Background Art

[0002] With the continuous advancement of urbanization, logistics networks must not only ensure the efficient flow of daily necessities but also possess the emergency response capabilities to sudden disasters. After a disaster, large numbers of affected people are in dire need of emergency supplies such as water, food, and medicine. An efficient emergency logistics network is crucial for safeguarding 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 coordinated planning for both daily necessities and emergency logistics, which can lead to low infrastructure utilization and uneven resource utilization. Furthermore, due to the high uncertainty of the time, location, and scale of a disaster, existing logistics networks struggle to balance responsiveness with coordinated resource allocation, making it difficult to provide flexible and efficient solutions in a timely manner.

[0003] The concept of "dual-use" for both peacetime and emergency logistics is becoming a key development direction for optimizing logistics networks. To promote this concept, the "Guidelines for Resilient Urban Planning and Land Policy with Integrated Peacetime and Emergency Functions" proposes two key tasks for material support: first, developing an action plan and project list for facilities in these scenarios; second, strengthening the planning and layout of public infrastructure nodes for "dual-use" services, and encouraging the exploration of diverse "dual-use" models. However, current domestic research on "dual-use" services remains largely conceptual, lacking specific model design and validation analysis. Furthermore, because disasters can cause road damage and exacerbate demand uncertainty, optimizing material transportation strategies that consider disaster-prone road conditions has also become a research focus. Researchers Yin Yunqiang et al. and Sun Huali et al., focusing on the actual needs of earthquake rescue efforts, studied the decision-making problem of emergency material distribution combined with road repair. Furthermore, strengthening key roads before a disaster strikes is also an important measure to enhance network resilience. Preemptive reinforcement of key road sections can effectively mitigate damage to the network and reduce the need for post-disaster road repair.

[0004] Given the differences and complexity of both normal and emergency scenarios, the design of a dual-use logistics network must achieve robust demand matching in both routine and emergency situations, and address multiple uncertainties through effective modeling. Existing optimization techniques offer two approaches for characterizing uncertainty, depending on the amount and type of relevant demand information: stochastic programming and robust optimization. However, due to their extreme assumptions, stochastic programming and robust optimization make it difficult to describe parameter uncertainty using limited historical data and uncertainty sets. Distributed robust optimization, with its advantages in uncertainty modeling, can improve the robustness of solutions and reduce conservatism, driven by historical data. Currently, widely used uncertainty sets are those based on moment information and those based on statistical distance. Uncertainty sets based on moment information are difficult to adjust, resulting in potentially conservative decisions. Uncertainty sets based on Wasserstein distance require only a limited amount of sampled data and are suitable for processing multiple uncertain parameters. Therefore, the following problems remain unresolved: 1) Although the construction of "dual-use" storage facilities for peacetime and emergency purposes has received policy support, existing research mostly remains at the conceptual level and lacks systematic planning research; 2) Previous studies have insufficient methods for dealing with multiple uncertainties in different time and space scenarios, making it difficult to robustly ensure the comprehensive matching of "peacetime and emergency" needs. Summary of the Invention

[0005] To address the aforementioned shortcomings or improvements in existing technologies, this invention provides a design method and system for a dual-use logistics network that robustly matches demand. This system explores a "dual-use" model for both normal and emergency logistics, with the government as the decision-maker. The goal is to design a multifunctional logistics network that incorporates both normal and emergency storage facilities and robustly matches storage and logistics demands in two different spatial and temporal scenarios, thereby coordinating normal and emergency demands, enhancing social resilience, and optimizing 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 for both regular and emergency use, taking into account robust demand matching, is proposed, comprising the following steps:

[0007] Step 1: Build a fixed investment decision model. The decision-making content of this model includes the selection of storage facility construction, emergency material pre-allocation, storage capacity of daily necessities, and road strengthening construction decisions.

[0008] Step 2: Build a "dual-use" logistics network operation decision model. The decision content of this model is the network transportation decision of pre-disaster daily necessities and 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 the demand for daily necessities at demand points before the disaster, 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 the Wasserstein distance.

[0010] Step 4: 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 to obtain the final logistics network design result through iterative optimization.

[0012] As a further preferred embodiment, in step 1, the objective function of the fixed investment decision model is constructed based on minimizing the sum of the costs of facility construction, emergency material reserves, and road strengthening construction;

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

[0014]

[0015] Where F is the set of candidate facilities; f i 0 is the fixed cost of building facility i into a "dual-use" storage point; x i Indicates whether facility i is selected as a "dual-use" storage point; f i 1 is the fixed cost of building facility i as an emergency material storage point; g i Indicates whether facility i is selected as an emergency material storage point; f i 2 is the fixed cost of building facility i as a storage point for daily necessities; i is whether facility i is selected as a storage point for daily necessities; H2 represents the set of emergency supplies types; represents the unit storage cost of emergency supplies h at facility i; represents the storage volume of emergency supplies h at facility i; L represents the set of paths; c ij represents the strengthening construction cost of path (i, j); r ij Indicates whether the path (i, j) undergoes road strengthening construction; represents the expected cost of the “normal and urgent dual-use” logistics network operation decision model,

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

[0017]

[0018] If the storage point chooses to build a "dual-use" storage facility, it can store both daily necessities and emergency supplies. 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 include:

[0019]

[0020] Among them, H1 represents the set of types of daily necessities; represents the storage capacity of living supplies h at facility i; M is a constant;

[0021] Preferably, the cost of storage facility construction and emergency material pre-positioning does not exceed the total budget constraint for facility construction and emergency material reserves, including:

[0022]

[0023] Among them, G1 represents the total budget for facility construction and emergency material reserves;

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

[0025]

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

[0027] As a further preferred embodiment, in step 2, the objective constraint function of the "normal and urgent dual-use" logistics network operation decision model includes:

[0028]

[0029] Where, represents the unit transportation cost of emergency supplies h; represents the pre-disaster flow of path (i, j) of daily necessities h; represents the unit transportation cost of daily necessities h; represents the post-disaster flow of the path (i, j) of emergency supplies h; W = P∪F represents all optional nodes; P represents the set of population demand points; represents the unit shortage penalty cost of daily necessities h at demand point i; represents the shortage of daily necessities h at demand point i; represents the unit shortage penalty cost of emergency supplies h at demand point i; represents the shortage of emergency supplies h at demand point i;

[0030] Preferably, in the "dual-use" logistics network operation decision model, when the daily life material network is operating, the pre-disaster road flow restriction constraints include:

[0031]

[0032] Preferably, the network flow balance constraints for the transportation of daily necessities at each network node before the disaster include:

[0033]

[0034] Where a ij is the capacity of road (i, j) before the disaster; β ij The proportion of capacity increase after road strengthening; is the demand for daily necessities h at demand point i before the disaster, r ij Whether the path (i, j) undergoes road strengthening construction;

[0035] Preferably, when the emergency material network is in operation during a disaster, the post-disaster road flow restriction constraints include:

[0036]

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

[0038]

[0039] in, is the loss coefficient of road (i, j); is the demand for emergency supplies h at demand point i after the disaster.

[0040] As further preferred, step three includes:

[0041] Let the vector of uncertain parameters be Given N Historical data Setting the reference empirical distribution To estimate the true probability distribution in Indicates that the unit mass is concentrated in The Dirac function of

[0042] The uncertain set Defined as the Wasserstein distance close to the empirical distribution All distribution families of :

[0043]

[0044] Where, is the set of probability distributions supported on the space Ξ;

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

[0046]

[0047] in, express The probability distribution of for The probability distribution of for and The joint probability distribution of and Represent random variables about and about The marginal distribution of is a random variable and The definition of the statistical distance norm ||·|| on the space Ξ is taken as

[0048] As a further preferred embodiment, according to Uncertain Set Expressed as:

[0049]

[0050] When the Wasserstein distance ρ is equal to 0, the estimate of the true probability distribution is the reference empirical distribution, and the model is simplified 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 3, the two-stage distributed robust optimization model includes:

[0053]

[0054] Among them, Δ DRO It is a two-stage distributed robust optimization model. for The worst-case expectation problem, To pursue the issue.

[0055] As a further preferred embodiment, in step 4, performing equivalent conversion on the robust optimization model includes:

[0056] For any policy variables s, r, e in the fixed investment decision model, if When the feasible domain of the “normal and emergency dual-use” logistics network operation decision model is bounded, the robust optimization model is transformed into:

[0057]

[0058] λ≥0

[0059] Among them, Δ DRO A two-stage distributed robust optimization model.

[0060] As a further preferred embodiment, in step 5, linearly reconstructing the semi-infinite optimization problem after robust equivalence conversion through model decomposition includes:

[0061] The auxiliary variable σ is introduced to decompose the semi-infinite optimization problem into a main problem and a series of sub-problems;

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

[0063]

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

[0065] The sub-problem is defined as:

[0066]

[0067] Among them, for the internal max-min problem existing in the sub-problem, the "normal and urgent dual-use" logistics network operation decision model is transformed into a dual problem through the duality theorem for solution.

[0068] As a further preferred embodiment, in step 5, solving the decomposed model and obtaining the final logistics network design result through iterative optimization includes:

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

[0070]

[0071] Among them, LB is the lower bound of the iteration, UB is the upper bound of the iteration, is the candidate solution for the current iteration, is 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 system for designing a logistics network for both normal and urgent use, taking into account robust demand matching, is provided, comprising:

[0074] The first main control module is used to build a fixed investment decision-making model. The decision-making content of this model includes the selection of storage facility construction, pre-allocation of emergency supplies, storage capacity of daily necessities, and road strengthening 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 daily necessities and post-disaster emergency supplies.

[0076] The third main control module is used to process the uncertain parameters of emergency material demand, road damage, and pre-disaster demand for daily necessities 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.

[0077] The fourth main control module is used to perform peer-to-peer conversion on the 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 general, the above technical solutions conceived by the present invention have the following technical advantages compared with the existing technology:

[0080] 1. This invention calculates decision-making results for different Wasserstein distance values ρ. Overall, as the Wasserstein distance ρ increases, the objective function value and fixed costs tend to rise. An appropriate Wasserstein distance value ρ can be selected based on risk preferences at the fluctuation point of the first-order difference of fixed costs to balance construction cost-effectiveness and risk mitigation. Furthermore, as ρ increases, the number of corresponding storage points, road reinforcement construction, emergency supply reserves, and daily necessities also increase.

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

[0082] 3. The proposed dual-use logistics network design model is sensitive to the construction costs of dual-use storage facilities, and this sensitivity is more pronounced at higher ρ values. In practice, this model can be used to guide long-term operational decisions regarding the adoption of a dual-use logistics model.

[0083] 4. The method of the present invention can complete the calculation within the time range acceptable for engineering project planning (24-48 hours), and the model and algorithm can be applied to conventional logistics network design problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 This is a design block diagram of a "normal and urgent dual-purpose" logistics network design method that takes into account robust demand matching in the present invention;

[0085] Figure 2 This is a schematic diagram of the normal and emergency conversion between the "normal" time network and the "emergency" time network in the present invention;

[0086] Figure 3 This is a flow chart of obtaining the final logistics network design result through iterative optimization in the present invention;

[0087] Figure 4 Schematic diagram of the decision results of the example in the present invention under different Wasserstein distance values ρ;

[0088] Figure 5 This is a schematic diagram of the logistics network design optimization results under two different modes of "dual-use of normal and urgent" and "separation of normal and urgent" in the present invention;

[0089] Figure 6 This is a schematic diagram of the evaluation results of the "normal and urgent dual-purpose" logistics network in the present invention;

[0090] Figure 7 It is a schematic diagram of the convergence and execution time of the algorithm in the present invention;

[0091] Figure 8 This is a schematic diagram of a calculation example in which the number of network nodes is 30 in the present invention. DETAILED DESCRIPTION

[0092] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0093] The current "dual-use" model for emergency and peacetime use is still in its exploratory phase. Different models can be proposed based on the development, daily operational, and emergency needs of different regions. Considering that emergency material storage is fundamental to fulfilling the material support function of "dual-use" public infrastructure, this paper explores a "dual-use" model with the government as the decision-maker. The goal is to design a multifunctional logistics network that considers "dual-use" storage facilities and robustly matches storage and logistics needs in two different spatiotemporal scenarios, thereby coordinating emergency and peacetime needs, enhancing social resilience, and optimizing resource allocation.

[0094] To achieve the above objectives, the present invention provides a technical solution: a "dual-use" logistics network for both normal and emergency situations is designed based on a two-stage distributed robust optimization model. The first stage of the model optimizes decisions regarding warehouse site selection, emergency material pre-allocation, and road reinforcement. The second stage uses the Wasserstein distance to construct uncertainty sets to characterize the uncertainty of pre-disaster demand for daily necessities, post-disaster demand for emergency materials, and road damage. Based on this, network transportation planning for both daily and emergency scenarios is comprehensively optimized to ensure the efficiency and reliability of the logistics network. After performing an equivalent linear reconstruction of the model to account for the nonlinearity of the problem, the proposed two-stage distributed robust optimization model is solved using the Column-and-Constraint Generation (CC&G) algorithm. Finally, numerical experiments are conducted based on the case study of the July 20 rainstorm in Henan Province to analyze the model's applicability and provide relevant management decision-making recommendations.

[0095] like Figure 1 As shown, the functions of the "dual-purpose" storage facilities are set as follows: in peacetime, they serve as a storage and distribution base for daily necessities, used to ensure the supply and price stability of daily necessities; in emergencies, they play the role of emergency material guarantee and are used to allocate reserve materials.

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

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

[0098] Assumption 2: Daily necessities storage points can only store daily necessities, and emergency necessities storage points can only store emergency necessities;

[0099] Hypothesis 3: After road strengthening and construction, not only can the disaster-bearing capacity of roads be improved after disasters, but the road transportation capacity of logistics networks can also be increased before disasters;

[0100] Assumption 4: To facilitate the connection with transportation load and material demand, the capacity or demand of daily necessities and emergency supplies is converted into weight statistics.

[0101] Since it is difficult to determine the penalty cost of material shortage in practice, the cost of daily necessities and emergency supplies The shortage penalty cost is typically set as: 1) Additional procurement cost. In the event of a post-disaster emergency or daily necessities shortage, the missing supplies are replenished through additional procurement; 2) Deprivation cost. When replenishing supplies through procurement is difficult, the shortage penalty cost can be set to a larger number, effectively becoming a deprivation cost. Given the need to meet the needs of the considered scenario as much as possible during pre-disaster preparations, this paper adopts the latter parameter to characterize this parameter.

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

[0103] Specifically, such as Figure 1 As shown, an embodiment of the present invention provides a "normal and urgent dual-purpose" logistics network design method that considers robust demand matching, characterized by including the following steps:

[0104] Step 1: The first stage model performs fixed investment decisions, including the selection of storage facility construction, pre-allocation of emergency supplies, storage capacity of daily necessities, and road strengthening construction decisions.

[0105] Step 2: The second-stage model executes the "dual-use" logistics network operation decision, which includes the network transportation decision of pre-disaster daily necessities and the network transportation decision of post-disaster emergency supplies.

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

[0107] Step 4: The two-stage stochastic programming model is expressed as a two-stage distributed robust optimization model through the Wasserstein uncertainty set.

[0108] Step 5: Worst-case Expectations Involving probability distribution The infinite-dimensional optimization of cannot be solved directly, so the model needs to be transformed, that is, robust transformation.

[0109] Step 6: The semi-infinite optimization problem after robust equivalence transformation is linearly reconstructed through model decomposition.

[0110] Step 7: Use the row-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 first-stage objective function is as shown in formula (1):

[0112]

[0113] The objective function is to minimize the sum of the costs of facility construction, emergency material storage, and road strengthening construction, where F represents the set of candidate facility points; f i 0 is the fixed cost of building facility i into a "dual-use" storage point; x i is a 0-1 variable, indicating whether facility i is selected as a "dual-use" storage point; f i 1 is the fixed cost of building facility i as an emergency material storage point; g i is a 0-1 variable, indicating whether facility i is selected as an emergency material storage point; f i 2 is the fixed cost of building facility i as a storage point for daily necessities; i is a 0-1 variable, indicating whether facility i is selected as a storage point for daily necessities; H2 represents the set of emergency supplies types; represents the unit storage cost of emergency supplies h at facility i; represents the storage volume of emergency supplies h at facility i; L represents the set of paths; c ij represents the strengthening construction cost of path (i, j); r ij Indicates whether the path (i, j) undergoes road strengthening construction; represents the expected cost of the second stage.

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

[0115]

[0116] If the storage point chooses to build a "dual-use" storage facility, it can store both daily necessities and emergency supplies. 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] Among them, H1 represents the collection of types of daily necessities; It represents the storage capacity of living supplies h of facility i; M represents a larger number.

[0119] The cost of storage facility construction and emergency material pre-allocation must 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 facility construction and emergency material reserves.

[0122] The cost of strengthening roads does not exceed the total budget constraint of road strengthening construction as shown in formula (7):

[0123]

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

[0125] The value range constraints of 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 second-stage objective function described in step 2 is shown in formula (12):

[0128]

[0129] The objective function is to minimize the transportation cost of the logistics network, where represents the unit transportation cost of emergency supplies h; represents the pre-disaster flow of path (i, j) of daily necessities h; represents the unit transportation cost of daily necessities h; represents the post-disaster flow of the path (i, j) of emergency supplies h; W = P∪F represents all optional nodes; P represents the set of population demand points; represents the unit shortage penalty cost of daily necessities h at demand point i; represents the shortage of daily necessities h at demand point i; represents the unit shortage penalty cost of emergency supplies h at demand point i; It represents the shortage of emergency supplies h at demand point i.

[0130] When the daily necessities network is in operation, the road flow restriction constraint before the disaster is as shown in formula (13): The network flow balance constraint of the daily necessities transportation of each network node before the disaster is as shown in formula (14):

[0131]

[0132] Among them a ij represents the capacity of road (i, j) before the disaster; β ij The proportion of capacity increase after road strengthening; It represents the demand of demand point i for daily necessities h before the disaster.

[0133] When the emergency material network operates during a disaster, the post-disaster road flow restriction constraint is shown in formula (15); the network flow balance constraint for the transportation of emergency materials at each network node after the disaster is shown in formula (16):

[0134]

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

[0136] The value constraints 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 a combination of multiple embodiments, in step 3, the vector of uncertain parameters is Given N Historical data Setting the reference empirical distribution To estimate the true probability distribution in Indicates that the unit mass is concentrated in Dirac function of the uncertainty set Defined as the Wasserstein distance close to the empirical distribution All distribution families of , as shown in formula (21):

[0139]

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

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

[0142]

[0143] Among them express The probability distribution of for The probability distribution of for and The joint probability distribution of and Represent random variables about and about The marginal distribution of . is a random variable and The statistical distance in space Ξ. The definition of the norm ||·|| takes

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

[0145]

[0146] When the Wasserstein distance ρ is equal to 0, the estimate of the true probability distribution is the reference empirical distribution, and the model is simplified 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 a combination of multiple embodiments, the previous two-stage optimization model described in step 4 can be expressed as a two-stage distributed robust optimization model, as shown in formula (24):

[0148]

[0149] In formula (24) called Worst-case expectation problem. It is the value function used to obtain the optimal value of the second-stage objective function, also known as the recourse problem.

[0150] Based on any of the above embodiments or a combination of multiple embodiments, the distributed robust optimization model is transformed into a semi-infinite optimization problem in step 5, that is, by giving any first-stage decision variables s, r, e, When the feasible region of 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] For the worst mean value in formula (24) Perform the following conversion:

[0155]

[0156] Where π represents and The joint probability distribution of and are the marginal distributions of the two random variables respectively. Let for hour Based on the total probability formula, formulas (27) to (28) can be rewritten as formulas (29) to (30):

[0157]

[0158] By finding the duality of formulas (29) to (30), we can obtain:

[0159]

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

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

[0162]

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

[0164]

[0165] For the internal max-min problem in the subproblem, the second-stage model (12) to (20) can be transformed into its dual problem by the duality theorem and solved. Auxiliary variables τ, θ, η, ε are introduced. The dual problem of the subproblem can be expressed as follows:

[0166]

[0167]

[0168] in:

[0169]

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

[0171] Theorem 1: When SP obtains the optimal solution, The optimal value of will be in the set Take it from The optimal value of will be in the set Take it from The optimal value of will be in the set Take it from the middle.

[0172] The specific proof process is as follows:

[0173] For the sub-problems:

[0174]

[0175] First, for Can be based on and The discussion is divided into two situations.

[0176] when hour:

[0177]

[0178] at this time, Only exists in the subproblem Ω n (s, r, e, λ) in the objective function, and Ω n (s,r,e,λ) is about The optimal value of a linear function is

[0179] when hour:

[0180]

[0181] Similarly, The optimal value of Combining the two cases, The same logic applies and The optimal value of:

[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 sub-problem SP can be transformed into a linear model as follows:

[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 , you can and Expressed as:

[0186]

[0187]

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

[0189]

[0190] The bilinear term in formula (59), that is, the product of the binary variable and the continuous variable By introducing the auxiliary variable τπ 1 ,τπ 2 ,θω 1 ,θω 2 ,εα 1,εα 2 The nonlinear terms are linearized to improve the solution efficiency. For example, the nonlinear term transformation is as follows:

[0191]

[0192] Conversion The conversion method is the same as .

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

[0194]

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

[0196] The following is combined with Figure 1-8 It should be emphasized that the following description is only illustrative and is not intended to limit the scope of the present invention and its application.

[0197] Based on a two-stage distributed robust optimization model, the present invention proposes a "dual-use" logistics network design method for daily operations and disaster response with composite functions. 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 at candidate points; (2) Maximum total demand for emergency supplies; (3) Upper and lower bounds of material demand at each demand point; (4) Demand data for emergency supplies and daily necessities; (5) Fixed costs for storage facility construction; (6) Storage costs for emergency supplies such as water, food, and medicine; (7) Unit length strengthening cost of roads; (8) Road capacity; (9) Damaged interval; (10) Demand at each node; (11) Unit transportation cost of emergency supplies; (12) Unit transportation cost of daily necessities; (13) Increased capacity ratio of road strengthening construction; (14) Coefficient of the number of shortage materials in the objective function; (15) Wasserstein distance value ρ; (16) Reference value of uncertain parameters (17) The ratio of the cost of "dual-use" storage facilities to the construction cost of emergency material storage facilities is expressed as a cost control factor; (18) The values of the demand for daily necessities and emergency materials under different risk scenarios are generated based on the benchmark values of uncertain parameters and are expressed as risk factors; (19) Urban road data.

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

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

[0202] In order to simplify the text of this application and reduce its length, the specific schemes and formulas involved here can be found in the invention content section of the previous specification and will not be repeated here.

[0203] The following is a detailed description based on the embodiments:

[0204] Five cities (F0~F4) were selected as facility candidate points, 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, given the following conditions:

[0205] (1) The warehouse capacity of candidate points is set to 3,000 to 3,200 tons; (2) The maximum total demand for emergency supplies is set to 1,500 tons; (3) The upper and lower limits of the material demand for each demand point are set to 200 and 0; (4) The demand data for emergency supplies and daily necessities are set to be generated uniformly within 90 to 110 tons (i.e., the baseline value is 100 tons); (5) The fixed cost of storage facility construction is set to 35 million to 55 million yuan; (6) The storage cost of emergency supplies such as water, food, and medicine is set to {10,000,000 yuan / ton; (7) The road unit length reinforcement cost is set to 200,000 yuan / kilometer; (8) The road capacity is set to be generated in the interval of 800 to 1,000 tons; (9) The damaged section is set to =set to 0.6~0.8 (the baseline value is 0.7); (10) the demand for each node is set to be generated in the range of 90~110 tons; (11) the unit transportation cost of emergency supplies is set to 0.005 million yuan / km / ton; (12) the unit transportation cost of daily necessities is set to 0.002 million yuan / km / ton; (13) the capacity increase ratio of road strengthening construction is set to 0.5 times; (14) the coefficient of the shortage material in the objective function is set to the deprivation cost (i.e., a larger 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 values of the cost control factor are {120%, 140%, 160%, 180%, 200%}; (18) The risk factor is set to 0%, 20%, 40%, 60%, 80%, 100%; (19) The urban road data are as follows:

[0206]

[0207]

[0208] Based on the given parameter conditions above, write code to build the model framework proposed by this method, and call GUROBI software for solution.

[0209] For Example 1, the decision results of the example under different Wasserstein distance values ρ were calculated and the reference values were obtained to facilitate subsequent experimental analysis. Different ρ values were set for cross-validation.

[0210] When ρ = 30, the fluctuation range of the first-order difference value of subsequent fixed costs is relatively stable, indicating that the logistics network can better cope with the multiple uncertainties of daily and emergency situations under this model parameter. Similarly, for considerations of higher disaster risks and disaster scales, ρ = 70 can be selected as a reference point.

[0211] The following table shows the decision results when 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 "normal and emergency" storage point.

[0215] As can be seen from the table, as ρ increases, the number of storage points, road reinforcement construction, emergency supplies reserves, and daily necessities capacity also increase. Therefore, decision makers can also make choices based on the specific calculation results.

[0216] The results of logistics network design optimization under two different modes, namely "dual use of normal and urgent" and "separation of normal and urgent", are as follows: Figure 4 The evaluation results of the “normal and emergency dual-use” logistics network are shown in Figure 5 As shown:

[0217] from Figure 5 As can be seen from the figure, when ρ = 30, DMP (network operation efficiency) and EM (emergency response time) are 33.27% and 33.92% respectively. The optimization rate of the "dual-use" model is relatively high, indicating that it has shown significant advantages through resource integration. The main reason is that the optimized "dual-use" network layout has increased the distribution density of emergency supplies, reduced the transportation mileage from the warehouse to the demand point, and thus shortened the delivery time of supplies. Figure 6 As shown in Figure 2, as ρ increases, the optimization effects of DMP and EM decrease, but they still maintain a certain advantage. This shows that the logistics network under the "dual-use" mode has higher network operation efficiency and emergency response capabilities.

[0218] After calculation, the decision results under different costs of "normal and emergency dual-use" storage facilities are obtained, as shown in the following table:

[0219]

[0220] like Figure 7 As shown in the figure, 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, the cost control factor is greater than or equal to 120%, and the decision results do not include "dual-use" storage points. This shows that the "dual-use" logistics network design model is more sensitive to the construction cost of "dual-use" storage facilities, and this is more obvious when ρ is larger.

[0221] After calculation, the robustness comparison results of the Sample Average Approximation (SSA) model and the distributed robust optimization model under different scenario settings are obtained, as shown in the following table:

[0222]

[0223] As can be seen from the above table, when ρ = 30, the distributed robust optimization model can well cope with scenarios with risk factors less than 40%. When ρ = 70, the distributed robust optimization model shows greater fault tolerance and can at least cope with scenarios with risk factors below 80%. However, the decision solution obtained by the sample average approximation is difficult to cope with scenarios with risk factors greater than 20%.

[0224] In summary, this paper comprehensively considers the coordinated matching of daily and emergency needs in logistics networks and the uncertainty of increasing road damage, proposing a "dual-use" logistics network design method that robustly matches demand, effectively addressing the shortcomings of traditional methods. This method can effectively reduce logistics network operating costs and shorten the transportation distance of emergency supplies from warehouses to demand locations, and is applicable to conventional logistics network design problems.

[0225] It will be easily understood by those skilled in the art 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 in the scope of protection of the present invention.

Claims

1. A method for designing a dual-purpose logistics network for both normal and urgent use, considering robust demand matching, characterized by: The following steps are involved: Step 1: Build a fixed investment decision model. The decision-making content of this model includes the selection of storage facility construction, emergency material pre-allocation, storage capacity of daily necessities, and road strengthening construction decisions. Step 2: Build a "dual-use" logistics network operation decision model. The model's decision content is the network transportation decision of pre-disaster daily necessities and post-disaster emergency supplies. Step 3: Use the Wasserstein uncertainty set to process the uncertain parameters of emergency material demand, road damage, and pre-disaster demand for daily necessities at demand points. This allows the fixed investment decision model and the "dual-use" logistics network operation decision model to be integrated into a two-stage distributed robust optimization model based on the Wasserstein distance. Step 4: Perform equivalent transformation on the corresponding robust optimization model; Step 5: The semi-infinite optimization problem after robust equivalence transformation is linearly reconstructed through model decomposition, and the decomposed model is solved to obtain the final logistics network design result through iterative optimization.

2. A method for designing a dual-purpose logistics network for demand robust matching according to claim 1, characterized in that: In step 1, the objective function of the fixed investment decision model is constructed based on minimizing the sum of the costs of facility construction, emergency material storage, and road strengthening construction; Preferably, the objective function of the fixed investment decision model includes: Where F is the set of candidate facilities; f i 0 is the fixed cost of building facility i into a "dual-use" storage point; x i Indicates whether facility i is selected as a "dual-use" storage point; f i 1 is the fixed cost of building facility i as an emergency material storage point; g i Indicates whether facility i is selected as an emergency material storage point; f i 2 is the fixed cost of building facility i as a storage point for daily necessities; i is whether facility i is selected as a storage point for daily necessities; H2 represents the set of emergency supplies types; represents the unit storage cost of emergency supplies h at facility i; represents the storage volume of emergency supplies h at facility i; L represents the set of paths; c ij represents the strengthening construction cost of path (i, j); r ij Indicates whether the path (i, j) undergoes road strengthening construction; represents the expected cost of the "normal and urgent dual-use" logistics network operation decision model, Preferably, in the fixed investment decision model, each storage point can only construct one type of storage facility constraint: If the storage site chooses to build a "dual-use" storage facility, it can store both daily necessities and emergency supplies. 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 include: Among them, H1 represents the set of types of daily necessities; represents the storage capacity of living supplies h at facility i; M is a constant; Preferably, the cost of storage facility construction and emergency material pre-positioning does not exceed the total budget constraint for facility construction and emergency material reserves, including: Among them, G1 represents the total budget for facility construction and emergency material reserves; Preferably, the cost of strengthening the road does not exceed the total budget constraint for road strengthening construction, including: Among them, G2 represents the total budget for road construction.

3. The method for designing a dual-purpose logistics network for emergency and normal operations considering robust demand matching according to claim 1, characterized in that: In step 2, the objective constraint function of the "normal and urgent dual-use" logistics network operation decision model includes: Where, represents the unit transportation cost of emergency supplies h; represents the pre-disaster flow of path (i, j) of daily necessities h; represents the unit transportation cost of daily necessities h; represents the post-disaster flow of the path (i, j) of emergency supplies h; W = P∪F represents all optional nodes; P represents the set of population demand points; represents the unit shortage penalty cost of daily necessities h at demand point i; represents the shortage of daily necessities h at demand point i; represents the unit shortage penalty cost of emergency supplies h at demand point i; represents the shortage of emergency supplies h at demand point i; Preferably, in the "dual-use" logistics network operation decision model, when the daily life material network is operated, the pre-disaster road flow restriction constraints include: Preferably, the network flow balance constraints for the transportation of daily necessities at each network node before the disaster include: Where a ij is the capacity of road (i, j) before the disaster; β ij The proportion of capacity increase after road strengthening; is the demand for daily necessities h at demand point i before the disaster, r ij Whether the path (i, j) undergoes road strengthening construction; Preferably, when the emergency material network is in operation during a disaster, the post-disaster road flow restriction constraints include: Preferably, the network flow balance constraints for emergency material transportation at each network node after a disaster include: in, is the loss coefficient of road (i, j); is the demand for emergency supplies h at demand point i after the disaster.

4. The method for designing a dual-purpose logistics network for emergency and normal operations considering robust demand matching according to claim 1, characterized in that: Step three includes: Let the vector of uncertain parameters be Given N Historical data Setting the reference empirical distribution To estimate the true probability distribution in Indicates that the unit mass is concentrated in The Dirac function of The uncertain set Defined as the Wasserstein distance close to the empirical distribution All distribution families of : Where, For space The set of probability distributions supported on ; Wasserstein distance is used to represent the statistical distance of uncertain sets: in, express The probability distribution of for The probability distribution of for and The joint probability distribution of and Represent random variables about and about The marginal distribution of is a random variable and In space The statistical distance on , the definition of norm ||·|| takes 1-norm.

5. The method for designing a dual-purpose logistics network for emergency and normal operations considering robust demand matching according to claim 4, characterized in that: according to Uncertain Set Expressed as: When the Wasserstein distance ρ is equal to 0, the estimate of the true probability distribution is the reference empirical distribution, and the model is simplified 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.

6. The method for designing a dual-purpose logistics network for demand robust matching according to claim 1 is characterized in that: In step 3, the two-stage distributed robust optimization model includes: Among them, Δ DRO It is a two-stage distributed robust optimization model. for The worst-case expectation problem, To pursue the issue.

7. The method for designing a dual-purpose logistics network for emergency and normal operations considering robust demand matching according to claim 1, characterized in that: In step 4, the equivalent conversion of the robust optimization model includes: For any policy variables s, r, e in the fixed investment decision model, if When the feasible domain of the "dual-use" logistics network operation decision model is bounded, the robust optimization model is transformed into: Among them, Δ DRO A two-stage distributed robust optimization model.

8. The method for designing a dual-purpose logistics network for emergency and normal operations considering robust demand matching according to claim 1, characterized in that: In step 5, the semi-infinite optimization problem after robust equivalence conversion is linearly reconstructed through model decomposition, including: The auxiliary variable σ is introduced to decompose the semi-infinite optimization problem into a main problem and a series of sub-problems; Preferably, the main problem is defined as: Among them, Ω n (s,r,e,λ) is a subproblem; The sub-problem is defined as: Among them, for the internal max-min problem existing in the sub-problem, the "normal and emergency dual-use" logistics network operation decision model is transformed into a dual problem through the duality theorem for solution.

9. The method for designing a dual-purpose logistics network considering robust demand matching according to claim 1, characterized in that: In step 5, solving the decomposed model and obtaining the final logistics network design result through iterative optimization includes: The row and column generation algorithm is used to set the number of iterations ψ. The calculation formulas for the lower and upper bounds of each iteration include: Among them, LB is the lower bound of the iteration, UB is the upper bound of the iteration, and is the candidate solution under the current iteration. is the number of all candidate solutions, n = 1, 2, ..., N; When (UB-LB) / UB≤gap, the algorithm converges to the defined tolerance level gap and outputs the optimal solution.

10. A system for designing a dual-purpose logistics network for both normal and emergency situations, taking into account robust demand matching, characterized by: include: The first main control module is used to build a fixed investment decision-making model. The decision-making content of this model includes the selection of storage facility construction, pre-allocation of emergency supplies, storage capacity of daily necessities, and road strengthening construction decisions; The second main control module is used to build a "dual-use" logistics network operation decision-making model. The decision-making content of this model is the network transportation decision of pre-disaster daily necessities and post-disaster emergency supplies. The third main control module uses Wasserstein uncertainty sets to process the uncertain parameters of emergency supply demand, road damage, and pre-disaster demand for daily necessities at demand points. This allows the fixed investment decision model and the "dual-use" logistics network operation decision model to be integrated into a two-stage distributed robust optimization model based on Wasserstein distance. The fourth main control module is used to perform peer-to-peer conversion on the robust optimization model; 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.

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