Logistics planning toughness MILP optimization method in emergency scene

Abstract

The invention discloses a logistics planning toughness MILP optimization method for an emergency scene, and the method comprises the specific steps: 1, defining an emergency material transportation parameter system, and fusing a vehicle dynamic starting point, a goods yard supply capability, a demand priority weight, and a road network blocking variable; and 2, constructing a mixed integer linear programming model, coupling a timeliness objective function and a toughness constraint, and integrating path connectivity, time window limitation and a redundant path rehearsal mechanism. And step 3, converting the objective function through the auxiliary variable, and realizing collaborative optimization of the transportation efficiency and robustness in the most unfavorable scene by the inner layer and the outer layer. And 4, solving the model to generate a dynamic scheduling scheme, outputting a vehicle path plan, a goods yard loading strategy and a distribution time sequence, and ensuring reliable delivery of high-priority goods and materials in a golden time window. According to the method, the anti-interference capability of the emergency logistics system in a dynamic disaster environment can be remarkably improved, and the timeliness guarantee rate of key material transportation and the toughness level of a scheduling scheme are improved by optimizing scheduling multi-resource coordination, path redundancy design and time-sensitive demand matching. Compared with an existing method, the method is more scientific, foresight and robust, can be widely applied to the fields of post-disaster emergency management, resource scheduling optimization and the like, and provides a scientific basis for emergency decision making.

Description

Technical Field

[0001] The present invention belongs to the field of emergency logistics scheduling technology, and specifically relates to an emergency logistics timeliness optimization method under dynamic resilience modeling based on mixed integer linear programming (MILP). It is particularly suitable for modeling and solving high-timeliness and high-resilience material transportation tasks in complex environments such as natural disaster relief, public health event response and military conflicts. Background Art

[0002] Traditional emergency logistics research has focused on path planning or static resource allocation, improving scheduling efficiency through single-objective optimization (e.g., shortest path, lowest cost). However, such approaches struggle to cope with the combined effects of multiple uncertainties in complex scenarios. Reality has shown that a single optimization objective can no longer meet the rigid requirements of emergency logistics' "golden 72 hours" response time. Multi-objective collaborative modeling is urgently needed to address scheduling challenges in dynamic environments.

[0003] Existing technologies have the following limitations: First, the models fail to fully couple timeliness and resilience, failing to balance transportation efficiency and system robustness in dynamic environments; second, the optimization objective is singular, failing to incorporate material demand priorities, time-degradation effects, and path redundancy design into a unified framework; and third, they lack effective modeling for the coordinated scheduling of multiple factors in large-scale road networks. These issues make existing methods difficult to ensure the timely and reliable delivery of critical materials in extreme scenarios. A MILP modeling approach that balances timeliness optimization with resilience design is urgently needed. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a resilient optimization model for the transportation of emergency materials that can cope with complex dynamic road networks, sudden demand time constraints and multi-resource collaborative scheduling. By constructing a scheduling model with multiple factors coupled, it ensures that high-priority materials are delivered efficiently within the time window and minimizes the impact of the most unfavorable environment on transportation efficiency.

[0005] To achieve the above objectives, the MILP optimization method for ensuring the timeliness of emergency logistics under dynamic resilience modeling of the present invention includes the following steps:

[0006] Step 1: Define the process and parameter representation of emergency supplies transportation.

[0007] Specifically, in a typical scenario of emergency transportation, the vehicle set K is distributed at the nodes of the road network (given by the parameter R = {r k} defines the vehicle starting point), it is necessary to base on the material supply capacity of the freight yard node set O (defined by B os Indicates whether the freight yard o supplies material s) and the vehicle loading capacity C ks , dynamically assign a loading point to each vehicle k. The vehicle starts from the starting point r kDeparture, select the freight yard node to load the matching materials, and then transport them to the distribution node set D. The demand for material s at each distribution point d is Q ds and priority weight W ds Significant differences, such as the need for emergency medicine (high W ds ) must be satisfied first within the time window H, while low-priority materials can be delayed appropriately. During transportation, the road network edge set E may be damaged by disasters (through the decision variable z i Identifies whether the edge is blocked), resulting in the actual distance matrix dis ij Dynamic changes. Vehicle path planning depends on the binary variable x kij Indicates whether vehicle k uses edge (i, j) and combines it with the time variable t ki Ensure that the arrival time of each node does not exceed H. In addition, the loading operation of the vehicle at the freight yard o (by u kos Identification) must satisfy inventory constraint B os , and the load capacity m kds Vehicle capacity C ks Restrictions are imposed, and ultimately the precise matching of demands is ensured through unloading quantity constraints.

[0008] Step 2: Based on the parameter representation in step 1, a mixed integer programming model of the problem is established; the mixed integer programming model includes the objective function and various constraints in the transportation of emergency supplies.

[0009] Step 2.1: Define the decision variables for the emergency supplies transportation process;

[0010] Step 2.2: Establish the objective function of emergency material transportation;

[0011]

[0012] Where X is all decision variables except the opponent variable z;

[0013] Step 2.3: Establish flow balance constraints;

[0014]

[0015] Step 2.4: Establish net flow constraints;

[0016]

[0017] Step 2.5: Establish outflow constraints at the starting point;

[0018]

[0019] Step 2.6: Establish the endpoint out-degree constraint;

[0020]

[0021] Step 2.7: Create an endpoint unique constraint;

[0022]

[0023] Step 2.8: Establish access and service relationship constraints;

[0024]

[0025] Step 2.9: Establish service verification constraints;

[0026]

[0027] Step 2.10: Create yard assignment constraints;

[0028]

[0029] Step 2.11: Establish yard access constraints;

[0030]

[0031] Step 2.12: Establish inventory limit constraints;

[0032]

[0033] Step 2.13: Establish loading capacity constraints;

[0034]

[0035] Step 2.14: Establish requirements satisfaction constraints;

[0036]

[0037] Step 2.15: Establish capacity constraints;

[0038]

[0039] Step 2.16: Establish edge restriction constraints;

[0040]

[0041] Step 2.17: Establish path connectivity constraints;

[0042]

[0043] Step 2.18: Establish time propagation constraints;

[0044]

[0045] Step 2.19: Establish the starting time constraint;

[0046]

[0047] Step 2.20: Establish timing requirements constraints;

[0048]

[0049] Step 2.21: Establish time limit constraints;

[0050]

[0051] Step 3: Process the objective function;

[0052] Specifically: introduce auxiliary variable f, let This formula limits the lower bound of the objective function, which is equivalent to the optimal value of the inner layer minimization problem;

[0053] The outer maximization problem is transformed into max f.

[0054] Step 4: Solve the mixed integer programming model to obtain the solution for emergency material transportation scheduling;

[0055] Specifically: solve the mixed integer programming model to obtain the value of the decision variable for emergency material transportation scheduling, and use the decision variable x kij Determine the transportation path for each vehicle k; through the variable u kos Determine the cargo yard o that vehicle k needs to visit and the type of materials s it loads, using the variable m kds Determine the specific quantity of material s that vehicle k unloads at delivery point d.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The present invention achieves a significant improvement in emergency transportation efficiency under multi-resource collaborative optimization and complex road network scenarios by constructing a dynamic resilient scheduling model. Its core value lies in the deep integration of the timeliness guarantee of high-priority materials and the robustness optimization of road network damage: through dynamic path connectivity constraints and broken edge preview mechanism, it ensures that the initial plan can still maintain the availability of critical paths under extreme interference such as edge blocking; based on the objective function and time window constraints of weighted time integral, it gives priority to ensuring the delivery rate of high-weight materials such as emergency medicines within the golden time window; combined with the freight yard-vehicle matching constraints and flow balancing mechanism, it realizes cross-dimensional dynamic collaboration of people, vehicles, goods and warehouses, and effectively solves the scheduling failure problem of traditional methods in scenarios of material type matching, vehicle capacity restrictions and uneven inventory distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1This is a flowchart of a MILP optimization method for ensuring timeliness of emergency logistics under dynamic resilience modeling in an embodiment of the present invention;

[0059] Figure 2 Schematic diagram of an optimal vehicle route taking resilience into consideration in an embodiment of the present invention;

[0060] Figure 3 This is a schematic diagram of the vehicle route obtained by directly solving the model without considering toughness in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention is described in detail below with reference to the accompanying drawings and embodiments. A MILP optimization method for ensuring the timeliness of emergency logistics under dynamic resilience modeling, such as Figure 1 As shown, the following steps are included: Step 1: Define the process and parameter representation of emergency material transportation.

[0062] Specifically, in a typical scenario of emergency transportation, the vehicle set K is distributed at the nodes of the road network (given by the parameter R = {r k} defines the vehicle starting point), it is necessary to base on the material supply capacity of the freight yard node set O (defined by B os Indicates whether the freight yard o supplies material s) and the vehicle loading capacity C ks , dynamically assign a loading point to each vehicle k. The vehicle starts from the starting point r k Departure, select the freight yard node to load the matching materials, and then transport them to the distribution node set D. The demand for material s at each distribution point d is Q ds and priority weight W ds Significant differences, such as the need for emergency medicine (high W ds ) must be satisfied first within the time window H, while low-priority materials can be delayed appropriately. During transportation, the road network edge set E may be damaged by disasters (through the decision variable z i Identifies whether the edge is blocked), resulting in the actual distance matrix dis ij Dynamic changes. Vehicle path planning depends on the binary variable x kij Indicates whether vehicle k uses edge (i, j) and combines it with the time variable t ki Ensure that the arrival time of each node does not exceed H. In addition, the loading operation of the vehicle at the freight yard o (by u kos Identification) must satisfy inventory constraint B os , and the load capacity m kds Vehicle capacity C ks Restrictions are imposed, and ultimately the precise matching of demands is ensured through unloading quantity constraints.

[0063] Step 2: Based on the parameter representation in step 1, a mixed integer programming model of the problem is constructed; the mixed integer programming model includes the objective function and various constraints in the transportation of emergency supplies.

[0064] Step 2.1: Define the decision variables for the emergency supplies transportation process;

[0065] x kij ∈{0,1}: binary variable indicating vehicle k uses edge (i,j);

[0066] z ij ∈{0,1}: a binary variable indicating whether the edge (i,j) is broken;

[0067] Node sort position (integer variable);

[0068] u kos ∈{0,1}: vehicle k loads cargo s at freight yard o;

[0069] y ki ∈{0,1}: whether vehicle k chooses i as the destination;

[0070] The number of vehicles k unloading cargo s at the delivery point d;

[0071] The time variable of vehicle k at node i;

[0072] δ kd ∈{0,1}: whether vehicle k serves delivery point d;

[0073] γ kd ∈{0,1}: service flag of delivery point d;

[0074] σ ks ∈{0,1}: whether vehicle k is transporting cargo s;

[0075] ξ ij ∈{0,1}: whether the edge (i,j) is connected;

[0076] objective function value;

[0077] Edge distance after destruction;

[0078] Step 2.2: Establish the objective function of emergency material transportation;

[0079]

[0080] Where X represents all decision variables except the opponent variable z. This function characterizes the cumulative effect of the destination material demand satisfaction rate on time and reflects the priority of demand.

[0081] Step 2.3: Establish flow balance constraints;

[0082]

[0083] The constraint states that for each vehicle k and all non-origin and end nodes (i.e., nodes other than the freight yard, delivery point, or vehicle origin), the number of incoming edges to the vehicle equals the number of outgoing edges. This ensures path continuity and prevents vehicle flow interruptions at intermediate nodes.

[0084] Step 2.4: Establish net flow constraints;

[0085]

[0086] The constraint means that for a freight yard or distribution node d, if vehicle k does not choose d as the destination (i.e., y kd =0), the flow in and out of the node must be balanced; if the node is selected as the end point (y kd =1), allowing the existence of net flow. The relationship between binary variables and flow is linearized using the Big M method.

[0087] Step 2.5: Establish outflow constraints at the starting point;

[0088]

[0089] The constraint means that each car k must start from its starting point r k Start from the specified starting point and there is only one outgoing edge.

[0090] Step 2.6: Establish the endpoint out-degree constraint;

[0091]

[0092] The constraint means that if node i is selected as the destination of vehicle k (y ki =1), then the number of outgoing edges is 0; otherwise, normal flow is allowed. No more movement after the forced end point.

[0093] Step 2.7: Create an endpoint unique constraint;

[0094]

[0095] The constraint means that each vehicle k must and can only choose one destination node, ensuring that the path has a clear end point.

[0096] Step 2.8: Establish access and service relationship constraints;

[0097]

[0098] The constraint means that if vehicle k transports materials to delivery point d (∑ s m kds >0), then the node (δ kd=1), and the path contains an edge entering d. Enforce the causal relationship between transportation and path access.

[0099] Step 2.9: Establish service verification constraints;

[0100]

[0101] The constraint means that if vehicle k visits the delivery point d (the path contains an edge entering d), it must deliver goods to this point (∑m kds >0). Avoid wasting resources by empty access.

[0102] Step 2.10: Create yard assignment constraints;

[0103]

[0104] The constraint means that if vehicle k transports material s(σ ks =1), then it must be loaded from at least one yard o that supplies s (u kos =1). Ensure that the materials are sourced legally.

[0105] Step 2.11: Establish yard access constraints;

[0106]

[0107] The constraint means that if vehicle k is assigned to load goods from yard o, then its path must include an edge entering o. This enforces the completion of the loading operation.

[0108] Step 2.12: Establish inventory limit constraints;

[0109]

[0110] Constraint means that the freight yard o can only assign vehicles to load the types of materials it actually supplies (defined by B os Avoid assigning to a yard that has no inventory.

[0111] Step 2.13: Establish loading capacity constraints;

[0112]

[0113] Constraint means that vehicle k can only carry the type of goods allowed by its capacity (given by C ks Control). Prevent loading of cargo types it cannot carry.

[0114] Step 2.14: Establish requirements satisfaction constraints;

[0115]

[0116] The constraint means that the total amount of materials s received by the distribution point d must not exceed its demand Q ds . Avoid excessive distribution and waste of resources.

[0117] Step 2.15: Establish capacity constraints;

[0118]

[0119] The constraint means that the total amount of each type of material transported by vehicle k must not exceed its loading capacity.

[0120] Step 2.16: Establish edge restriction constraints;

[0121]

[0122] The constraint means that at most Z one-way road edges are allowed to be destroyed (controlled by zij), simulating the most unfavorable damage scenario of the road network.

[0123] Step 2.17: Establish path connectivity constraints;

[0124]

[0125] The constraint means that if there is a broken edge in the shortest alternative path of edge (i, j), the actual distance dis ij is set to the maximum value M (by ξ ij Mark whether it is connected).

[0126] Step 2.18: Establish time propagation constraints;

[0127]

[0128] The constraint means that the time t2kj when the vehicle arrives at node j must be later than the time at the previous node i plus the travel time, ensuring that the time recursion conforms to physical logic.

[0129] Step 2.19: Establish the starting time constraint;

[0130]

[0131] The constraint means that after the vehicle starts from the starting point rk, the time it takes to reach the first node is calculated based on the distance and speed. Initialize the time variable.

[0132] Step 2.20: Establish timing requirements constraints;

[0133]

[0134] The constraint means that if a vehicle is transporting goods to delivery point d, the time it visits the freight yard o must be earlier than the time it arrives at d. This enforces the order of "loading first, then delivery".

[0135] Step 2.21: Establish time limit constraints;

[0136]

[0137] The constraint means that the arrival time of all nodes must not exceed the time window length H. This ensures that the task is completed within the timeliness requirement.

[0138] Step 3: Process the objective function;

[0139] Specifically: introduce auxiliary variable f, let This formula limits the lower bound of the objective function and is equivalent to the optimal value of the inner layer minimization problem.

[0140] The outer maximization problem is transformed into max f.

[0141] Step 4: Solve the mixed integer programming model to obtain the solution for emergency material transportation scheduling; Specifically: solve the mixed integer programming model to obtain the value of the decision variable for emergency material transportation scheduling, and use the decision variable x kij Determine the transportation path for each vehicle k; through the variable u kos Determine the cargo yard o that vehicle k needs to visit and the type of materials s it loads, using the variable m kds Determine the specific quantity of material s that vehicle k unloads at delivery point d.

[0142] In this implementation, Gurobi 12.0.1 is used for solving the problem on an AMD Ryzen 7 5700U with Radeon Graphics CPU @ 1.80 GHz, 16 GB RAM, and Windows 10 operating system.

[0143] The MILP was tested and validated on a typical case with and without considering toughness. The model was solved using Gurobi 12.0.1.

[0144] The road network connection relationship and the location of vehicles, freight yards and destinations are shown in Figure 2 and Figure 3 The timeliness duration H is set to 15 hours, the maximum number of blocked roads is set to 15, and the types of goods are set to 3. The vehicle movement parameters, vehicle cargo capacity parameters, freight yard parameters, and destination demand parameters are shown in Tables 1, 2, 3, 4, and 5, respectively.

[0145] Table 1 Vehicle position and speed parameters:

[0146] Table 2 Vehicle cargo capacity parameters:

[0147] Table 3 Freight yard parameters:

[0148] Table 4 Destination demand parameters:

[0149] Table 5 Delivery task priority weights:

[0150] The experimental results are as follows Figure 2 、 Figure 3 As shown in Tables 6, 7 and 8.

[0151] Table 6 Optimal task assignment scheme for resilience-optimized vehicles:

[0152] Table 7 Optimal vehicle task assignment scheme without considering toughness:

[0153] Table 8 Comparison of optimal values with and without considering the resilience solution:

[0154] From the comparison of the optimal values of the two schemes, it can be seen that the emergency material distribution scheme has stronger robustness when considering resilience. Although the objective function value is slightly lower under normal circumstances, it can still maintain a high level when encountering road damage, especially when key sections are blocked. It is more instructive for emergency material transportation scheduling decisions in complex environments.

Claims

1. A resilient MILP optimization method for logistics planning in emergency scenarios, characterized by: The following steps are involved: Step 1: Define the process and parameter representation of emergency material transportation, including the vehicle set K, the freight yard node set O, the distribution node set D, the material type set S, the vehicle initial position R = {r k }、Cargo yard supply capacity B os 、Vehicle loading capacity C ks , the demand quantity Q of the distribution point ds , Material priority weight W ds , time window H, and dynamic road network blocking variable z ij ; Step 2: Based on the parameters of step 1, a mixed integer linear programming model is constructed, including an objective function and constraints; the objective function is a weighted time-efficiency integral: , and the constraints include flow balance constraint, net flow constraint, path connectivity constraint, time propagation constraint, yard assignment constraint, and broken edge restriction constraint; Step 3: Linearize the objective function, introduce the auxiliary variable f, and transform the original objective function into a two-level optimization problem: the outer layer is transformed into max f; Step 4: Solve the linearized mixed integer programming model and output the vehicle path planning x kij , cargo yard loading operation kos , unloading volume at distribution point m kds , realizing the coordinated optimization of anti-destruction and timeliness in the transportation and dispatch of emergency materials.

2. The method according to claim 1, characterized in that The constraints in step 2 specifically include: Traffic balance constraint: The number of incoming and outgoing edges of a vehicle at non-start and end nodes is equal; Net flow constraint: The inflow and outflow of the freight yard or distribution node is combined with the terminal selection variable y through the big M method. kd association; Path connectivity constraint: Dynamically adjust the actual distance dis based on whether the alternative path is blocked ij , ensuring connectivity of critical paths; Time propagation constraint: arrival time t through a node ki and travel time calculations, enforcing timeliness within the time window H; Freight yard assignment constraints: Vehicles can only load designated materials from freight yards with supply capabilities, and the loading volume does not exceed inventory B os and vehicle capacity C ks .

3. The method according to claim 1, characterized in that The step 2 further comprises: Material priority weight constraint: delivery time t of high-weight materials kd Occupy higher priority in the objective function; Broken edge restriction constraint: limits the number of edges Z allowed to be blocked in the dynamic road network to simulate the most unfavorable damage scenario.

4. The method according to claim 1, wherein The decision variables defined in step 2 include: Path selection variable x kij ∈{0,1}, road network blocking variable z ij ∈{0,1}, freight yard loading variable u kos ∈{0,1}, unloading quantity variable m kds , time variable t ki .

5. The method according to claim 1, wherein In step 4, the Gurobi solver is used to solve the MILP model, and the robustness of the invulnerability optimization scheme in the road network blocking scenario is verified through experiments.

6. The method according to claim 2, characterized in that The path connectivity constraint is implemented by the following formula: ij =Dis ij +M·ξ ij , where ξ ij ∈{0,1} marks whether the edge (i,j) fails due to the blocking of the alternative path, and M is a maximum constant.

7. The method according to claim 1, characterized in that The step 2 further comprises: Service verification constraints: If a vehicle visits a delivery point d, it must transport a certain amount of supplies to avoid empty loads; Timing requirement constraints: Force vehicles to visit the freight yard earlier than the delivery point to ensure the "load first, then deliver" logic.

8. The method according to claim 1, characterized in that The objective function in step 2 is linearized to transform the two-level optimization problem into a single-level linear programming, thereby reducing the complexity of the solution.

9. The method according to claim 1, characterized in that The dynamic road network blocking variable zij is used to preview the damage scenario of the critical path and optimize the anti-destruction performance of the initial path solution.

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