A vehicle dispatching method considering tiered freight rate subsidies

Abstract

The present invention discloses a vehicle scheduling method considering step-rate subsidies, which belongs to the field of logistics and transportation technology, and includes: S1: using the acquired customer order and geographic location information and vehicle constraint information as input information; S2: constructing a vehicle scheduling model for multi-vehicle allocation and path planning considering step-rate subsidies based on mixed integer programming; S3: reconstructing the vehicle scheduling model based on mixed integer programming into a main problem model and a sub-problem model; S4: using an optimized branch-and-bound algorithm to solve the main problem model of the vehicle scheduling model to obtain a target result, and using the target result to obtain a vehicle scheduling plan with the lowest cost, so as to perform multi-vehicle allocation and driving path planning. The present invention uses an improved branch-and-price algorithm to solve the main problem of the vehicle scheduling model, and performs multi-vehicle allocation and driving path planning according to the target result, thereby improving vehicle scheduling efficiency and reducing logistics costs.

Description

Technical Field

[0001] The present invention belongs to the technical field of logistics and transportation, and more specifically, relates to a vehicle dispatching method taking into account tiered freight rate subsidies. Background Art

[0002] Vehicle routing is the core of logistics and distribution, and is also the foundation and important module for the establishment of logistics and distribution information systems. The quality of vehicle routing has a great impact on the efficiency of logistics and distribution. Currently, there are generally a variety of limited-number and different-capacity vehicle models in logistics and distribution, which need to be used to complete the delivery and service of customer orders within the time window specified by the customer, which forms the classic multi-vehicle routing problem.

[0003] Currently, a large number of corporate logistics distribution is carried out by outsourced carriers. The unit prices of transportation for different customers in the corresponding areas vary depending on the transportation area. In transportation settlement, it is common that when the order quantity does not reach the minimum quantity under the corresponding transportation mode, corresponding transportation subsidies are required. At the same time, since the minimum quantity will also change due to the different number of vehicle transportation during the transportation and distribution settlement process, a freight rate settlement mechanism that considers tiered freight rate subsidies has been created. More specifically, for high-value, highly regulated logistics such as tobacco and medicine, their distribution characteristics require that there is a limit on the number of customers transported by a single vehicle.

[0004] However, the vehicle scheduling algorithms in the prior art are mostly heuristic algorithms, whose convergence needs to be verified, and they are prone to fall into local optimal solutions and cannot guarantee the optimal solution to the driving path planning problem, which leads to low vehicle scheduling efficiency and high logistics costs. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a vehicle scheduling method taking into account the tiered freight rate subsidy, which aims to use an improved branch pricing algorithm to solve the main problem of the vehicle scheduling model, thereby improving the vehicle scheduling efficiency and reducing the logistics cost, thereby solving the technical problems of low vehicle scheduling efficiency and high logistics cost in the prior art.

[0006] To achieve the above object, according to one aspect of the present invention, a vehicle dispatching method considering tiered fare subsidies is provided, comprising:

[0007] S1: taking the acquired customer order, geographic location information and vehicle constraint information as input information;

[0008] S2: Construct a vehicle scheduling model based on mixed integer programming with multi-vehicle allocation and path planning considering tiered fare subsidies;

[0009] S3: Reconstruct the vehicle scheduling model based on mixed integer programming into a main problem model and a sub-problem model;

[0010] S4: using an optimized branch and bound algorithm to solve the main problem model of the vehicle scheduling model to obtain a target result; using the target result to obtain a vehicle scheduling solution with the lowest cost to perform multi-vehicle allocation and driving path planning.

[0011] In one embodiment, in step S1:

[0012] The customer order and geographic location information includes: the geographic location, order quantity, service time window and unit transportation cost of each customer waiting for delivery; the location information of the distribution center and each customer, and the path length information; the maximum allowed customer transportation volume of the vehicle, and the standard transportation weight related to the transportation node;

[0013] The vehicle constraint information includes: all customer orders must be satisfied within the customer's time window [a i , b i ]; early arrival requires waiting; vehicle loading does not exceed vehicle capacity; the number of vehicles used is less than the total number of vehicle models; the maximum allowed customer transport volume of the path shall not be greater than k max ;

[0014] Among them, vehicle types are sorted and coded according to capacity. The smaller the capacity, the higher the sorting and the smaller the coded ID. The larger the capacity, the higher the sorting and the larger the coded ID.

[0015] In one embodiment, the vehicle scheduling model based on mixed integer programming in step S3 is as follows:

[0016]

[0017]

[0018] Among them, formula (1.1) indicates that the objective function is to minimize the total cost; formula (1.2) and formula (1.3) together calculate the distribution cost considering the tiered freight rate subsidy; formula (1.4) represents the vehicle capacity constraint, ensuring that the amount allocated to each vehicle is less than its vehicle capacity Q m ; Formula (1.5) represents the order allocation constraint, ensuring that each order is assigned a vehicle; Formula (1.6) is the vehicle number constraint, ensuring that the number of vehicles of each type does not exceed the provided quantity |Z m |; Formula (1.7) represents the maximum number of allowed transport points for a vehicle, ensuring that each vehicle transport point does not exceed k max ; Formulas (1.8) and (1.9) are used to connect variables; Formulas (1.10)-(1.12) represent the operation time constraints to ensure time feasibility; Formulas (1.13) and (1.14) represent the variable range.

[0019] In one embodiment, the main problem model is as follows:

[0020]

[0021] Formula (1.15) represents minimizing the total cost; Formula (1.16) represents ensuring that each order is delivered; Formula (1.17) represents the specific vehicle number constraint, ensuring that the number of corresponding models is less than the number of existing vehicles; Formula (1.18) is the variable range constraint;

[0022] Among them, Ω m represents the set of feasible transportation path solutions for vehicle type m; c mr represents the cost of the effective transport path r for vehicle type m, ω ir is a 0-1 variable. If vehicle type m has transportation path r, then x mr is 1, ψ mr is a 0-1 decision variable. If vehicle type m has transportation path r, then x mr is 1;

[0023] The sub-problem model is as follows:

[0024]

[0025]

[0026] In formula (1.19), u i The dual variable of the customer-related constraints (1.16) of the main problem; v m The dual variable of the vehicle-related constraints (1.17) of the main problem; is a 0-1 decision variable, 1 if customer i is transported by vehicle type m, and 0 otherwise; is a 0-1 decision variable, which is 1 when a vehicle of model m is transporting from customer i to customer j, and 0 otherwise.

[0027] In one embodiment, the step S4 comprises:

[0028] S4-1: Initialize node information, set the global upper bound to positive infinity, and the active node set Δ active is empty;

[0029] S4-2: The heuristic method HVARP obtains the initial solution Best of the main problem;

[0030] S4-3: Use the initial solution Best to initialize the root node of the restricted main problem RMP node tree And add this node to the active node set Δ active ;

[0031] S4-4: Use the column generation process CG to calculate the lower bound of the problem

[0032] S4-5: Determination Δ active Is it empty? If so, jump to S4-10, otherwise, the next step;

[0033] S4-6: Select active node set Δ active The node δ with the smallest lower bound is removed from the set Δ active Delete from;

[0034] S4-7: Determine the lower bound δ of node δ lb Is it better than Best? If not, go to S4-5, otherwise go to the next step;

[0035] S4-8: Determine whether the node δ is an integer solution. If so, set the solution δ of the current node to Best and go to step S4-5. Otherwise, go to the next step.

[0036] S4-9: Generate two new nodes δ through branching process BB 1 and δ 2 , the column generation process CG calculates its lower bound and And add the two nodes to the active node set Δ active , jump to S4-5;

[0037] S4-10: Obtain the optimal solution, output the target result, and the algorithm ends.

[0038] In one embodiment, the step S4-2 comprises:

[0039] HVARP-1: Initialization return set Δ HVARP ←NULL, Θ←NULL, Θ′←NULL, k←1;

[0040] HVARP-2: According to the customer's time window [a i , b i ], sort in ascending order;

[0041] HVARP-3: The reduced mass q i Less than standard weight Customers of are added to the set to be merged Θ, and other customers are added to the set to be processed Θ′;

[0042] HVARP-4: Determine whether Θ is empty. If so, go to step HVARP-8, otherwise go to the next step.

[0043] HVARP-5: Calculate the savings of any two customers i and j in Θi&j , select i,j customers whose time window is feasible and whose saving value is the largest and greater than 0 to generate temporary path r temp , delete customers i, j from the set Θ; if no customer with a savings value greater than 0 can be found, add Θ to the set Θ′ and clear Θ;

[0044] HVARP-6: Determine temporary path r temp Does the customer's discounted quality q exist in i Less than standard weight If it does not exist, then the path r temp Add the path set Ω and go to step HVARP-4; otherwise, go to the next step;

[0045] HVARP-7: k←k+1, traverse the set Θ, and find the value that matches r temp The combination can satisfy the time window constraint and save value The largest customer i forms a new path r′ temp , delete customer i from the set Θ, and r temp ←r′ temp , go to step HVARP-6; if no customer meeting the conditions is found, then the path r temp Add the path set Ω and go to step HVARP-5;

[0046] HVARP-8: Arrange the paths in the path set Ω in ascending order according to path capacity, and the vehicles are also arranged in ascending order according to vehicle capacity;

[0047] HVARP-9: Determine whether the path set Ω is empty. If so, go to step HVARP-11, otherwise go to the next step;

[0048] HVARP-10: Assign the first feasible vehicle m to the path r of Ω in turn. After the assignment is completed, add To the set Δ HVARP ; At the same time, delete the path r from the set and update the remaining vehicle information, and go to step HVARP-9;

[0049] HVARP-11: Determine whether Θ′ is empty. If so, go to step HVARP-13, otherwise go to the next step;

[0050] HVARP-12: Calculate any two customers i and j in Θ′ in turn, select the time window that is feasible and has the largest path capacity to generate a temporary path r temp Delete customers i and j from the set Θ′; if no feasible customer combination can be found, generate a path r for the remaining customers in Θ′ in the form of single-point transportation, add them to the set Ω, clear Θ′, and go to step HVARP-11;

[0051] HVARP-13: Sort the paths in the path set Ω in descending order according to path capacity, and the vehicles are also sorted in descending order according to vehicle capacity;

[0052] HVARP-14: Determine whether the path set Ω is empty. If so, go to step HVARP-16, otherwise go to the next step;

[0053] HVARP-15: Assign the first feasible vehicle m to the path r of Ω in turn. After the assignment is completed, add To the set Δ HVARP ; At the same time, the path r is deleted from the set and the remaining vehicle information is updated, and then the step HVARP-15 is transferred;

[0054] HVARP-16: Algorithm ends, returns result set Δ HVARP .

[0055] In one embodiment, the step S4-4 comprises:

[0056] CG-1: Construct the restricted master problem model RMP;

[0057] CG-2: Directly solve the relaxed constrained master problem LP-RMP using a pre-defined solver;

[0058] CG-3: Use the heuristic method HA to obtain the solution of the subproblem h , and obtain its target value rc h ;

[0059] CG-4: Determine rc h Is it less than 0? If it is less than 0, then s h Add to collection Δ cg , proceed to the next step, otherwise go to step CG-6;

[0060] CG-5: Judgment set Δ cg Is the size greater than 20? If so, go to step CG-1, otherwise go to the next step;

[0061] CG-6: Execute the exact solution algorithm EA to obtain the solution of the subproblem e , and obtain its target value rc e ;

[0062] CG-7: Determine rc e Is it less than 0? If it is satisfied, add solution s e To the set Δ cg Go to step CG-1, otherwise go to the next step;

[0063] CG-8: The optimal solution of the main problem has been reached, the solver solution is returned, and the algorithm ends.

[0064] In one embodiment, step CG-3 comprises:

[0065] HA-1: Initialize return set Δ ha is empty, k←k max , m←0, size←20;

[0066] HA-2: Calculate the standard weight of customer i separately Virtual cost under

[0067] HA-3: Virtual Cost Add to collection separately middle;

[0068] HA-4: Determine k = 0. If it is satisfied, go to step HA-10; otherwise, select Traverse and select k customers to get the set

[0069] HA-5: If If it is not empty, then take out a customer list l k ={i0, i1, i2, ..., i k}, arranged in ascending order according to the time window to form path r k , and change the customer list from On the contrary, if is empty, then k←k-1, go to step HA-4;

[0070] HA-6: Determine path r k Is the time window feasible? If not, go to step HA-5; otherwise, calculate the smallest available vehicle model. make

[0071] HA-7: If m≤|M|, calculate Otherwise, go to step HA-5;

[0072] HA-8: If Go to step HA-9, otherwise m←m+1, go to step HA-7;

[0073] HA-9: If |Δ ha |<size, then add To the set Δ ha , m←m+1, go to step HA-7, otherwise go to the next step;

[0074] HA-10: End the algorithm and return Δ ha .

[0075] In one embodiment, step CG-6 comprises:

[0076] EA-1: Initialize the return set Δ ea is empty, k←k max , m←0, rc max ←+∞, size←20;

[0077] EA-2: Calculate the standard weight of customer i separately Virtual cost under

[0078] EA-3: Virtual Costs Add to collection separately middle;

[0079] EA-4: Determine k = 0. If it is satisfied, go to step EA-12. Otherwise, select Traverse and select k customers to get the set And according to Sort in ascending order;

[0080] EA-5: If If it is not empty, then take out a customer list l k ={i0, i1, i2, ..., i k}, change the customer list from , and arrange them in ascending order according to the time window to form path r k , on the contrary, if is empty, then k←k-1, go to step EA-4;

[0081] EA-6: Determine path r k Is the time window feasible? If it is feasible, go to step EA-8; if not, calculate the composition r k Full list of customers

[0082] EA-7: Traversal Determine whether there is a path r′ k Satisfy the time window constraint, if it exists, then r k ←r′ k , otherwise go to step EA-5;

[0083] EA-8: Calculate the smallest available vehicle model make

[0084] EA-9: If m ≤ |M|, calculate Otherwise, go to step EA-5;

[0085] EA-10: If Go to step EA-11, otherwise m←m+1, go to step EA-9;

[0086] EA-11: If |Δ ha |<size, then add To the set Δ ha ,renew m←m+1, go to step EA-9; otherwise, go to the next step;

[0087] EA-12: If Then in the set Δ ha Delete rc max A corresponding solution, and add To the set Δ ha , and update m←m+1, go to step EA-9; otherwise, m←m+1, go to step EA-9;

[0088] EA-13: End the algorithm and return Δ ea .

[0089] In one embodiment, the branch process BB in step S4-9 includes:

[0090] BB-1: Count the arcs (i, j) contained in the solution of the current node δ and add them to the set Δ bb ;

[0091] BB-2: Δ bb Calculate the flow of all arcs in Where R ij is the set of paths containing arc(i, j);

[0092] BB-3: Select the arc (i, j) with the flow closest to 0.5 as the branch item f′ ij ;

[0093] BB-4: Generate node δ 1 , the cost of using the arc (i, j) in this node is infinite, generating node δ 2 ; Among all arcs in this section that contain nodes i and j, the usage cost is infinite except for arc (i, j);

[0094] BB-5: Algorithm ends, return to node δ 1 and δ 2 .

[0095] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0096] 1. The present invention converts the actual mixed road network into an abstract node-road network by acquiring input information such as customer data and geographic location; then constructs a vehicle scheduling model for multi-vehicle type allocation and path planning considering tiered fare subsidies based on mixed integer programming; and reconstructs the mixed integer programming vehicle scheduling model into a main problem model and a sub-problem model; designs an accurate branch pricing algorithm for the vehicle scheduling model, realizes its use in different tiered fare scenarios, improves vehicle scheduling efficiency, reasonably arranges vehicle types and plans optimal routes, thereby reducing logistics costs.

[0097] 2. The present invention adopts a combination of flow branching and heuristic and precise solution methods, which effectively improves the solution efficiency while ensuring the optimal solution, thereby improving the vehicle dispatching efficiency. The present invention can provide the best dispatching solution for large-scale mixed fleet distribution enterprises or systems that adopt tiered freight rate subsidies, while ensuring customer satisfaction, reducing logistics costs and achieving optimal dispatching. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 It is a flow chart of a vehicle dispatching method considering tiered freight rate subsidies provided by the present invention;

[0099] Figure 2 is a curve diagram showing the change of cost with demand in an embodiment of the present invention;

[0100] Figure 3 is a specific flow chart of solving the main problem model in step S4 in an embodiment of the present invention;

[0101] Figure 4 is a specific flow chart of the heuristic method HVARP in an embodiment of the present invention;

[0102] Figure 5 It is a specific flow chart of the column generation process CG in an embodiment of the present invention;

[0103] Figure 6 This is a specific flow chart of branch process BB in an embodiment of the present invention;

[0104] Figure 7 is a specific flow chart of the heuristic method HA in an embodiment of the present invention;

[0105] Figure 8 It is a specific flow chart of the accurate solution algorithm EA in the embodiment of the present invention;

[0106] Fig. 9 Schematic diagram of a scheduling scheme in an embodiment of the present invention. DETAILED DESCRIPTION

[0107] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain 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 can be combined with each other as long as they do not conflict with each other.

[0108] like Figure 1 As shown, this embodiment provides a vehicle dispatching method considering tiered fare subsidies, which mainly includes four steps:

[0109] S1: taking the acquired customer order, geographic location information and vehicle constraint information as input information;

[0110] S2: Construct a vehicle scheduling model based on mixed integer programming with multi-vehicle allocation and path planning considering tiered fare subsidies;

[0111] S3: Reconstruct the vehicle scheduling model based on mixed integer programming into a main problem model and a sub-problem model;

[0112] S4: using an optimized branch and bound algorithm to solve the main problem model of the vehicle scheduling model to obtain a target result; using the target result to obtain a vehicle scheduling solution with the lowest cost to perform multi-vehicle allocation and driving path planning.

[0113] In one embodiment, the customer order and geographic location information includes: the geographic location, order quantity, service time window and unit transportation cost of each customer waiting for delivery; the location information of the distribution center and each customer, and the path length information; the maximum allowed customer transportation volume of the vehicle, and the transportation standard weight related to the transportation node;

[0114] The vehicle constraint information includes: all customer orders must be satisfied within the customer's time window [a i , b i ]; early arrival requires waiting; vehicle loading does not exceed vehicle capacity; the number of vehicles used is less than the total number of vehicle models; the maximum allowed customer transport volume of the path shall not be greater than k max ;

[0115] Among them, vehicle types are sorted and coded according to capacity. The smaller the capacity, the higher the sorting and the smaller the coded ID. The larger the capacity, the higher the sorting and the larger the coded ID.

[0116] For example, suppose that company A has n customers with known locations and needs that need to be shipped from the shipping warehouse depot, and each customer has a service time window (early arrivals need to wait, and late arrivals are not allowed). In order to meet customer needs, the company first outsources the logistics distribution task to logistics company B. The logistics company has a mixed fleet of multiple vehicles with a limited number of models. It is known that this logistics company has different freight unit prices for different regions, that is, different transportation unit prices for customers, and this logistics company has a minimum weight stage guarantee system. When the converted weight of the customer's transported items does not reach the established standard weight, it is charged according to the standard weight. At the same time, due to the special industry of company A, the value of the goods is large and requires strong supervision, requiring that a single vehicle shall not transport more than 3 customers. Logistics company B also sets three different conversion standard weights of 12, 10, and 5 based on this. Now company A needs to jointly decide on vehicle model allocation and vehicle route planning, so that the distribution system can meet customer needs while minimizing logistics costs.

[0117] In one embodiment, in the mixed integer programming model, if the vth vehicle of type m is used m The vehicle transportation path is r = (i0, i1, i2, ...., i k ), then the delivery cost of customer i considering the subsidy is: where p i is the unit shipping cost for the customer, d 0i is the distance from the distribution center to the customer, q i The order quantity for the customer, is the standard transportation weight corresponding to path r, such as Figure 2 The figure shows the curve of the cost of transporting a customer i under three standard weights as the demand changes.

[0118] In one embodiment, the mixed integer programming model is as follows, and its parameters and symbol definitions are shown in Table 1:

[0119]

[0120]

[0121] Among them, formula (1.1) indicates that the objective function is to minimize the total cost; formula (1.2) and formula (1.3) together calculate the distribution cost considering the tiered freight rate subsidy; formula (1.4) represents the vehicle capacity constraint, ensuring that the amount allocated to each vehicle is less than its vehicle capacity Q m ; Formula (1.5) represents the order allocation constraint, ensuring that each order is assigned a vehicle; Formula (1.6) is the vehicle number constraint, ensuring that the number of vehicles of each type does not exceed the provided quantity |Z m|; Formula (1.7) represents the maximum number of allowed transport points for a vehicle, ensuring that each vehicle transport point does not exceed k max ; Formulas (1.8) and (1.9) are used to connect variables; Formulas (1.10)-(1.12) represent the operation time constraints to ensure time feasibility; Formulas (1.13) and (1.14) represent the variable range.

[0122]

[0123]

[0124] Table 1

[0125] In one embodiment, the master problem model MP includes the following formula:

[0126]

[0127] Formula (1.15) represents minimizing the total cost; Formula (1.16) represents ensuring that each order is delivered; Formula (1.17) represents the specific vehicle number constraint, ensuring that the number of corresponding models is less than the number of existing vehicles; Formula (1.18) is the variable range constraint; where, Ω m represents the set of feasible transportation path solutions for vehicle type m, c mr represents the cost of the effective transport path r for vehicle type m, ω ir is a 0-1 variable. If vehicle type m has transportation path r, then x mr is 1, ψ mr is a 0-1 decision variable. If vehicle type m has transportation path r, then x mr is 1. Among them is to minimize the total cost; to ensure that each order is delivered; is the specific number of vehicles constraint, ensuring that the number of corresponding models is less than the number of existing vehicles; is the variable range constraint.

[0128] Furthermore, the sub-problem model includes the following formula:

[0129]

[0130] The parameters and symbols are defined as shown in Table 1. i The dual variable of the customer-related constraints of the main problem; v m The dual variables of the vehicle-related constraints of the main problem; is a 0-1 decision variable, 1 if customer i is transported by vehicle type m, and 0 otherwise; is a 0-1 decision variable, which is 1 when a vehicle of model m is transporting from customer i to customer j, and 0 otherwise.

[0131] Furthermore, the process of solving the main problem model is as follows: Figure 3As shown, it mainly includes the following steps:

[0132] S4-1 initializes node information, sets the global upper bound to positive infinity, and the active node set Δ active is empty;

[0133] S4-2 The heuristic method HVARP obtains the initial solution Best of the problem;

[0134] S4-3 Use the initial solution Best to initialize the root node of the restricted main problem RMP node tree And add this node to the active node set Δ active ;

[0135] S4-4 Use the column generation process CG to calculate the lower bound of the problem

[0136] S4-5 Judge Δ active Is it empty? If so, jump to S4-10, otherwise, the next step;

[0137] S4-6 Select active node set Δ active The node δ with the smallest lower bound is removed from the set Δ active Delete from;

[0138] S4-7 Determine the lower bound δ of node δ lb Is it better than Best? If not, go to S4-5, otherwise go to the next step;

[0139] S4-8 determines whether the node δ is an integer solution. If so, the solution δ of the current node is set to Best and the process goes to step S4-5. Otherwise, the process goes to the next step.

[0140] S4-9 generates two new nodes δ through branch process BB 1 and δ 2 , the column generation process CG calculates its lower bound and And add the two nodes to the active node set Δ active , jump to S4-5.

[0141] S4-10 obtains the optimal solution, outputs the result, and the algorithm ends.

[0142] Furthermore, the heuristic method HVARP in step S4-2 has the following process: Figure 4 The steps include:

[0143] HVARP-1 Initialization Return Set Δ HVARP ←NULL, Θ←NULL, Θ′←NULL, k←1;

[0144] HVARP-2 is based on the customer's time window [a i , b i ], sort in ascending order;

[0145] HVARP-3 will convert the mass q i Less than standard weight Customers of are added to the set to be merged Θ, and other customers are added to the set to be processed Θ′;

[0146] HVARP-4 determines whether Θ is empty. If so, go to step HVARP-8, otherwise go to the next step;

[0147] HVARP-5 calculates the savings value Save of any two customers i and j in Θ in turn i&j , select i,j customers whose time window is feasible and whose saving value is the largest and greater than 0 to generate temporary path r temp , delete customers i, j from the set Θ. If no customer with a savings value greater than 0 can be found, add Θ to the set Θ′ and clear Θ;

[0148] HVARP-6 determines the temporary path r temp Does the customer's discounted quality q exist in i Less than standard weight If it does not exist, then the path r temp Add the path set Ω and go to step HVARP-4; otherwise, go to the next step;

[0149] HVARP-7k←k+1, traverse the set Θ, and find the temp The combination can satisfy the time window constraint and save value The largest customer i forms a new path r′ temp , delete customer i from the set Θ, and r temp ←r′ temp , go to step HVARP-6; if no customer meeting the conditions is found, then the path r temp Add the path set Ω and go to step HVARP-5;

[0150] HVARP-8 sorts the paths in the path set Ω in ascending order according to path capacity, and the vehicles are also sorted in ascending order according to vehicle capacity;

[0151] HVARP-9 determines whether the path set Ω is empty. If it is empty, go to step HVARP-11, otherwise go to the next step;

[0152] HVARP-10 assigns the first feasible vehicle m to the path r of Ω in turn. After the assignment is completed, add To the set Δ HVARPAt the same time, the path r is deleted from the set, and the remaining vehicle information is updated, and then the process goes to step HVARP-9;

[0153] HVARP-11 determines whether Θ′ is empty. If so, go to step HVARP-13, otherwise go to the next step;

[0154] HVARP-12 calculates any two customers i and j in Θ′ in turn, selects a temporary path r with a feasible time window and the largest path capacity temp Delete customers i and j from the set Θ′. If no feasible customer combination can be found, generate a path r for the remaining customers in Θ′ in the form of single-point transportation, add them to the set Ω, clear Θ′, and go to step HVARP-11;

[0155] HVARP-13 sorts the paths in the path set Ω in descending order according to the path capacity, and the vehicles are also sorted in descending order according to the vehicle capacity;

[0156] HVARP-14 determines whether the path set Ω is empty. If it is empty, go to step HVARP-16, otherwise go to the next step;

[0157] HVARP-15 assigns the first feasible vehicle m to the path r of Ω in turn. After the assignment is completed, add To the set Δ HVARP At the same time, the path r is deleted from the set, and the remaining vehicle information is updated, and then the process goes to step HVARP-15;

[0158] The HVARP-16 algorithm ends and returns the result set Δ HVARP .

[0159] In one embodiment, HVARP-7 The calculation formula is where r′={i,r temp}; In one embodiment, when judging the feasibility of the time window of path r′, it is necessary to sort all customers in r′ according to the time window, and then judge in order whether their time windows are feasible; further, the column generation process CG in the solution of the main problem model is as follows Figure 5 The steps include:

[0160] CG-1 constructs the restricted master problem model (RMP);

[0161] CG-2 uses a commercial solver to directly solve the relaxed restricted master problem (LP-RMP);

[0162] CG-3 uses the heuristic method HA to obtain the solution of the subproblem h , and obtain its target value rc h;

[0163] CG-4 judge rc h Is it less than 0? If it is less than 0, then s h Add to collection Δ cg , proceed to the next step, otherwise go to step CG-6;

[0164] CG-5 judgment set Δ cg Is the size greater than 20? If so, go to step CG-1, otherwise go to the next step;

[0165] CG-6 executes the exact solution algorithm EA to obtain the solution of the subproblem e , and obtain its target value rc e ;

[0166] CG-7 judge rc e Is it less than 0? If it is satisfied, add solution s e To the set Δ cg Go to step CG-1, otherwise go to the next step;

[0167] The CG-8 main problem has reached the optimal solution, and the solver solution result is returned, ending the algorithm.

[0168] In one embodiment, the restricted master problem model is a model constructed by the initial feasible solution in the form of the master problem model, and the relaxed restricted master problem is to replace the formula in the RMP model with 0≤ψ mr ≤1

[0169] Furthermore, the branch process BB in the solution of the main problem model is as follows: Figure 6 The steps include:

[0170] BB-1 counts the arcs (i, j) contained in the solution of the current node δ and adds them to the set Δ bb ;

[0171] BB-2 to Δ bb Calculate the flow of all arcs in Where R ij is the set of paths containing arc(i, j);

[0172] BB-3 selects the arc (i, j) with the flow closest to 0.5 as the branch item f′ ij ;

[0173] BB-4 generates node delta 1 , the cost of using the arc (i, j) in this node is infinite, generating node δ 2 Among all arcs in this section that contain nodes i and j, the usage cost is infinite except for arc (i, j).

[0174] BB-5 algorithm ends, returns to node δ 1 and δ 2 .

[0175] Furthermore, the heuristic method HA in the column generation process CG has the following process: Figure 7 The steps include:

[0176] HA-1 Initialization Return Set Δ ha is empty, k←k max , m←0, size←20;

[0177] HA-2 calculates the standard weight of customer i separately Virtual cost under

[0178] HA-3 will virtualize the cost Add to collection separately middle;

[0179] HA-4 determines k = 0. If it is satisfied, go to step HA-10. Otherwise, Traverse and select k customers to get the set

[0180] HA-5 If it is not empty, then take out a customer list l k ={i0, i1, i2, ..., i k}, arranged in ascending order according to the time window to form path r k , and change the customer list from On the contrary, if is empty, then k←k-1, go to step HA-4;

[0181] HA-6 judgment path r k Is the time window feasible? If not, go to step HA-5; otherwise, calculate the smallest available vehicle model. make

[0182] HA-7 If m≤|M|, calculate Otherwise, go to step HA-5;

[0183] HA-8 Go to step HA-9, otherwise m←m+1, go to step HA-7;

[0184] HA-9 if |Δ ha |<size, then add To the set Δ ha , m←m+1, go to step HA-7, otherwise go to the next step;

[0185] HA-10 ends the algorithm and returns Δ ha .

[0186] In one embodiment, size represents the size of the result set returned by the heuristic method HA. In actual use, an appropriate value can be selected by performing orthogonal experiments according to different problems. The solution can be realized by using the dictionary order method, and only the customer content is considered in the solution process without considering the order relationship between customers, that is, the customer list {i0, i1, i2} and {i2, i1, i0} represent the same customer list. You can choose Arranging in ascending order helps to speed up the acquisition of the optimal solution. In one embodiment, from the actual use effect, k is from k max Start decreasing to 0 than k increases from 0 to k max , the target value can be obtained to be smaller, which is more conducive to solving the main problem.

[0187] Furthermore, the exact solution algorithm EA in the column generation process CG has the following process: Figure 8 The steps include:

[0188] EA-1 initializes the returned set Δ ea is empty, k←k max , m←0, rc max ←+∞, size←20;

[0189] EA-2 Calculate the standard weight of customer i Virtual cost under

[0190] EA-3 will virtualize the cost Add to collection separately middle;

[0191] EA-4 determines k = 0. If it is satisfied, go to step EA-12. Otherwise, select Traverse and select k customers to get the set And according to Sort in ascending order;

[0192] EA-5 If it is not empty, then take out a customer list l k ={i0, i1, i2, ..., i k}, change the customer list from , and arrange them in ascending order according to the time window to form path r k, on the contrary, if is empty, then k←k-1, go to step HA-4;

[0193] EA-6 Determination Path r k Is the time window feasible? If it is feasible, go to step EA-8; if not, calculate the composition r k Full list of customers

[0194] EA-7 Traversal Determine whether there is a path r′ k Satisfy the time window constraint, if it exists, then r k ←r′ k , otherwise go to step EA-5;

[0195] EA-8 calculates the smallest available vehicle model make

[0196] EA-9 If m ≤ |M|, calculate Otherwise, go to step EA-5;

[0197] EA-10 Go to step EA-11, otherwise go to the next step; m←m+1, go to step EA-9;

[0198] EA-11 If |Δ ha |<size, then add To the set Δ ha ,renew m←m+1, go to step EA-9; otherwise, go to the next step;

[0199] EA-12 Then in the set Δ ha Delete rc max A corresponding solution, and add To the set Δ ha , and update m←m+1, go to step EA-9; otherwise, m←m+1, go to step EA-9;

[0200] EA-13 ends the algorithm and returns Δ ea .

[0201] In order to make the process, technical solution and advantages of this algorithm clearer, the technical solution of this algorithm will be clearly and completely described below with examples.

[0202] Assume that enterprise A has 10 customers with known locations and needs that need to be shipped from the shipping warehouse (numbered 0), and each customer has a service time window (early arrivals need to wait, and late arrivals are not allowed). In order to meet customer needs, the enterprise now outsources the logistics distribution task to logistics enterprise B, which has a mixed fleet of multiple vehicles. This fleet has two types of vehicles, with a number of 10 and 6 respectively, and a capacity of 30 and 20 respectively. It is known that this logistics enterprise has different freight unit prices for different regions, that is, different transportation unit prices for customers. See Table 2 for detailed information, and Table 3 for distance conditions.

[0203] At the same time, due to the special industry of Company A, the value of goods is large and requires strong supervision, requiring that a single vehicle cannot transport more than 3 customers. Logistics Company B has a minimum weight stage guarantee system. When the converted weight of the customer's goods does not reach the established standard weight, it will be charged according to the standard weight. Logistics Company B also sets three different conversion standard weights 12, 10, and 5 based on this. Now Company A needs to make joint decisions on vehicle model allocation and vehicle route planning so that the distribution system can meet customer needs while minimizing logistics costs.

[0204]

[0205] Table 2

[0206] d0 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 d0 0 15.2 18 22.3 25 20.6 11.1 21.2 26.2 32 25.4 c1 15.2 0 32.5 14.5 32.2 32.2 24.8 21 31.5 17.8 15.5 c2 18 32.5 0 34.4 20.2 23.8 16.4 36.2 36 47.4 43.2 c3 22.3 14.5 34.4 0 25 42.7 33.5 35.3 45 15 29.1 c4 25 32.2 20.2 25 0 41.2 31.6 46 50.5 40 47.1 c5 20.6 32.2 23.8 42.7 41.2 0 10 20.6 13.9 50 33.5 c6 11.1 24.8 16.4 33.5 31.6 10 0 20.6 19.8 42.4 30.4 c7 21.2 21 36.2 35.3 46 20.6 20.6 0 12.2 36.4 14.1 c8 26.2 31.5 36 45 50.5 13.9 19.8 12.2 0 48.1 26.2 c9 32 17.8 47.4 15 40 50 42.4 36.4 48.1 0 25 c10 25.4 15.5 43.2 29.1 47.1 33.5 30.4 14.1 26.2 25 0

[0207] Table 3

[0208] The 25 solutions obtained by branching are used as the initial solutions for node 1, and column generation is used to solve the relaxed restricted main problem L-RMP of this node. During the solution process, a column is added once, and a total of 8 solutions are added.

[0209] r 31 =(0, 10, 1, 11) using vehicle type 2 as the corresponding variable ψ 231 Cost 231 =532.886

[0210] r 32 =(0, 7, 6, 1, 11) The model number is 2, corresponding to the variable ψ 232 Cost 232 =263.835

[0211] r 33 =(0, 8, 10, 11) using vehicle type as 1 corresponding to variable ψ 133 Cost 133 =641.302

[0212] r 34 =(0, 7, 6, 1, 11) The model number is 2, corresponding to the variable ψ 234 Cost234 =263.835

[0213] r 35 =(0, 8, 1, 11) Use vehicle type as 1 corresponding to variable ψ 135 Cost 135 =344.32

[0214] r 36 =(0, 7, 8, 10, 11) using vehicle type 2 as the corresponding variable ψ 236 Cost 236 =745.124

[0215] r 37 =(0, 8, 1, 11) using vehicle type 2 as the corresponding variable ψ 237 Cost 237 =344.32

[0216] r 38 =(0, 7, 8, 1, 11) The vehicle type is 1 and the corresponding variable is ψ 138 Cost 238 =448.141

[0217] Finally, the optimal objective value of the relaxed constrained master problem L-RMP is obtained: 2497.8262; the optimal solution is: ψ 13 =ψ 14 =ψ 19 =ψ 25 =ψ 211 =ψ 225 =1, others = 0; at this time, the solutions of L-RMP are all integer solutions, which satisfies the original RMP problem and obtains the optimal solution of the original problem. There is no need to continue calculating node 2. The optimal solution is finally obtained:

[0218] r3=(0,3,11) The model used is 1 cost c 13 =124.657

[0219] r4=(0,4,11) The model used is 1 cost c 14 =259.825

[0220] r5=(0,5,11) The model used is 2, cost c 25 =514.7116

[0221] r9=(0,9,11) The model used is 1 cost c 19 =625.664

[0222] r 11 =(0, 2, 7, 8, 11) The model used is 2, cost c 211 =420.657

[0223] r 25 =(0, 6, 10, 1, 11) The model used is 2, cost c 225 =552.311

[0224] At this time, the corresponding scheduling solution is Fig. 9 shown.

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

Claims

1. A vehicle dispatching method considering tiered freight rate subsidies, characterized in that: include: S1: taking the acquired customer order, geographic location information and vehicle constraint information as input information; The customer order and geographic location information includes: the geographic location, order quantity, service time window and unit transportation cost of each customer waiting for delivery; the location information of the distribution center and each customer, and the path length information; the maximum allowed customer transportation volume of the vehicle, and the transportation standard weight related to the transportation node; The vehicle constraint information includes: all customer orders must meet the customer's time window [a i , b i ]; early arrival requires waiting; vehicle loading does not exceed vehicle capacity; the number of vehicles used is less than the total number of vehicle types; a single vehicle has no more than k transport points on the transport route max ; Among them, vehicle types are sorted and coded according to capacity. The smaller the capacity, the higher the sorting and the smaller the coded ID. The larger the capacity, the lower the sorting and the larger the coded ID. S2: Based on mixed integer programming, a vehicle scheduling model with multi-vehicle allocation and path planning considering tiered fare subsidies is constructed as follows: Among them, formula (1.1) indicates that the objective function is to minimize the total cost; formula (1.2) and formula (1.3) together calculate the distribution cost considering the tiered freight rate subsidy; formula (1.4) represents the vehicle capacity constraint, ensuring that the amount allocated to each vehicle is less than its vehicle capacity Q m ; Formula (1.5) represents the order allocation constraint, ensuring that each order is assigned a vehicle; Formula (1.6) is the vehicle number constraint, ensuring that the number of vehicles of each type does not exceed the provided quantity |Z m |; Formula (1.7) represents the maximum number of allowed transport points for a vehicle, ensuring that each vehicle transport point does not exceed k max ; Formulas (1.8) and (1.9) are used to connect variables; Formulas (1.10)-(1.12) represent the operation time constraints to ensure time feasibility; Formulas (1.13) and (1.14) represent the variable range; V is the set of transport nodes, V = {0, 1, ....., n, n+1}, A is the edge set, arc(i, j) ∈ A, V0 is the set of customer nodes, V0 = V\{0, n+1}, M is the set of vehicle types, Z m is a set of vehicles of model m; i, j represent transportation nodes, i, j∈V, 0 represents the starting point, n+1 represents the end point; m represents the model, m=1, 2, ..., |M|; Q m Indicates the loading capacity of vehicle type m, and the loading capacity increases as the subscript increases; p i is the unit freight rate of customer i; q i is the demand of customer i, [a i , b i ] is the time window when customer i starts serving, k max is the maximum number of transport nodes a single vehicle is allowed to visit, s i represents the service time of customer i, represents the transfer time of model m from customer i to customer j; V for M models m The start time of service for vehicle transport customer i, Indicates that order i is assigned to vehicle v m Calculated weight for shipping; V represents the M model m If the vehicle transports customer i, it is 1, otherwise it is 0; V for M models m 1 when the vehicle is transferred from customer i to customer j, otherwise 0; S3: Reconstructing the vehicle scheduling model based on mixed integer programming into a main problem model and a sub-problem model; S4: using an optimized branch and bound algorithm to solve the main problem model of the vehicle scheduling model to obtain a target result, and using the target result to obtain a vehicle scheduling solution with the lowest cost to perform multi-vehicle allocation and driving path planning.

2. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 1, characterized in that: The main problem model is as follows: Formula (1.15) represents minimizing the total cost; Formula (1.16) represents ensuring that each order is delivered; Formula (1.17) represents the specific vehicle number constraint, ensuring that the number of corresponding models is less than the number of existing vehicles; Formula (1.18) is the variable range constraint; Among them, Ω m represents the set of feasible transportation path solutions for vehicle type m; c mr represents the cost of the effective transport path r for vehicle type m, ω ir is a 0-1 variable. If customer i is in path r, then ω ir is 1, ψ mr is a 0-1 decision variable. If the vehicle type is m and the transportation path is r, then ψ mr is 1; The sub-problem model is as follows: In formula (1.19), u i The dual variable of the customer-related constraints (1.16) of the main problem; v m The dual variable of the vehicle-related constraints (1.17) of the main problem; is a 0-1 decision variable, 1 if customer i is transported by vehicle type m, and 0 otherwise; is a 0-1 decision variable, which is 1 when a vehicle of model m is transporting from customer i to customer j, and 0 otherwise.

3. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 1, characterized in that: In step S4, an optimized branch and bound algorithm is used to solve the main problem model of the vehicle scheduling model to obtain a target result, including: S4-1: Initialize node information, set the global upper bound to positive infinity, and the active node set Δ active is empty; S4-2: The heuristic method HVARP obtains the initial solution Best of the main problem; S4-3: Use the initial solution Best to initialize the root node of the restricted main problem RMP node tree And add this node to the active node set Δ active ; S4-4: Use the column generation process CG to calculate the lower bound of the problem S4-5: Determination Δ active Is it empty? If so, jump to S4-10, otherwise, the next step; S4-6: Select active node set Δ active The node δ with the smallest lower bound is removed from the set Δ active Delete from; S4-7: Determine the lower bound δ of node δ lb Is it better than Best? If not, go to S4-5, otherwise go to the next step; S4-8: Determine whether the node δ is an integer solution. If so, set the solution δ of the current node to Best and go to step S4-5. Otherwise, go to the next step. S4-9: Generate two new nodes δ through branching process BB 1 and δ 2 , the column generation process CG calculates its lower bound and And add the two nodes to the active node set Δ active , jump to S4-5; S4-10: Obtain the optimal solution, output the target result, and the algorithm ends.

4. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 3 is characterized in that: The step S4-2 comprises: HVARP-1: Initialization return set Δ HVARP ←NULL, Θ←NULL, Θ′←NULL, k←1; HVARP-2: According to the customer's time window [a i , b i ], sort in ascending order; HVARP-3: The reduced mass q i Less than standard weight Customers of are added to the set to be merged Θ, and other customers are added to the set to be processed Θ′; HVARP-4: Determine whether Θ is empty. If so, go to step HVARP-8, otherwise go to the next step. HVARP-5: Calculate the savings of any two customers i and j in Θ i&j , select i,j customers whose time window is feasible and whose saving value is the largest and greater than 0 to generate temporary path r temp , delete customers i, j from the set Θ; if no customer with a savings value greater than 0 can be found, add Θ to the set Θ′ and clear Θ; HVARP-6: Determine temporary path r temp Does the customer's discounted quality q exist in i Less than standard weight If it does not exist, then the path r temp Add the path set Ω and go to step HVARP-4; otherwise, go to the next step; HVARP-7: k←k+1, traverse the set Θ, and find the value that matches r temp The combination can satisfy the time window constraint and save value The largest customer i forms a new path r′ temp , delete customer i from the set Θ, and r temp ←r′ temp , go to step HVARP-6; if no customer meeting the conditions is found, then the path r temp Add the path set Ω and go to step HVARP-5; HVARP-8: Arrange the paths in the path set Ω in ascending order according to path capacity, and the vehicles are also arranged in ascending order according to vehicle capacity; HVARP-9: Determine whether the path set Ω is empty. If so, go to step HVARP-11, otherwise go to the next step; HVARP-10: Assign the first feasible vehicle m to the path r of Ω in turn. After the assignment is completed, add To the set Δ HVARP ; At the same time, delete path r from the set and update the remaining vehicle information, and go to step HVARP-9; HVARP-11: Determine whether Θ′ is empty. If so, go to step HVARP-13, otherwise go to the next step; HVARP-12: Calculate any two customers i and j in Θ′ in turn, select the time window that is feasible and has the largest path capacity to generate a temporary path r temp Delete customers i and j from the set Θ′; if no feasible customer combination can be found, generate a path r for the remaining customers in Θ′ in the form of single-point transportation, add them to the set Ω, clear Θ′, and go to step HVARP-11; HVARP-13: Sort the paths in the path set Ω in descending order according to path capacity, and the vehicles are also sorted in descending order according to vehicle capacity; HVARP-14: Determine whether the path set Ω is empty. If so, go to step HVARP-16, otherwise go to the next step; HVARP-15: Assign the first feasible vehicle m to the path r of Ω in turn. After the assignment is completed, add To the set Δ HVARP ; At the same time, the path r is deleted from the set and the remaining vehicle information is updated, and then the step HVARP-15 is transferred; HVARP-16: Algorithm ends, returns result set Δ HVARP .

5. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 3, characterized in that: The step S4-4 comprises: CG-1: Construct the restricted master problem model RMP; CG-2: Directly solve the relaxed constrained master problem LP-RMP using a pre-defined solver; CG-3: Use the heuristic method HA to obtain the solution of the subproblem h , and obtain its target value rc h ; CG-4: Determine rc h Is it less than 0? If it is less than 0, then s h Add to collection Δ cg , proceed to the next step, otherwise go to step CG-6; CG-5: Judgment set Δ cg Is the size greater than 20? If so, go to step CG-1, otherwise go to the next step; CG-6: Execute the exact solution algorithm EA to obtain the solution of the subproblem e , and obtain its target value rc e ; CG-7: Determine rc e Is it less than 0? If it is satisfied, add solution s e To the set Δ cg Go to step CG-1, otherwise go to the next step; CG-8: The optimal solution of the main problem has been reached, the solver solution is returned, and the algorithm ends.

6. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 5, characterized in that: The step CG-3 comprises: HA-1: Initialize return set Δ ha is empty, k←k max , m←0, size←20; HA-2: Calculate the standard weight of customer i separately Virtual cost under HA-3: Virtual Cost Add to collection separately middle; HA-4: Determine k = 0. If it is satisfied, go to step HA-10; otherwise, select Traverse and select k customers to get the set HA-5: If If it is not empty, then take out a customer list l k ={i0, i1, i2, ..., i k }, arranged in ascending order according to the time window to form path r k , and change the customer list from On the contrary, if is empty, then k←k-1, go to step HA-4; HA-6: Determine path r k Is the time window feasible? If not, go to step HA-5; otherwise, calculate the smallest available vehicle model. make HA-7: If m≤|M|, calculate Otherwise, go to step HA-5; HA-8: If Go to step HA-9, otherwise m←m+1, go to step HA-7; HA-9: If |Δ ha |<size, then add To the set Δ ha , m←m+1, go to step HA-7, otherwise go to the next step; HA-10: End the algorithm and return Δ ha .

7. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 5, characterized in that: The step CG-6 comprises: EA-1: Initialize the return set Δ ea is empty, k←k max , m←0, rc max ←+∞, size←20; EA-2: Calculate the standard weight of customer i separately Virtual cost under EA-3: Virtual Costs Add to collection separately middle; EA-4: Determine k = 0. If it is satisfied, go to step EA-12. Otherwise, select Traverse and select k customers to get the set And according to Sort in ascending order; EA-5: If If it is not empty, then take out a customer list l k ={i0, i1, i2, ..., i k }, change the customer list from , and arrange them in ascending order according to the time window to form path r k , on the contrary, if is empty, then k←k-1, go to step EA-4; EA-6: Determine path r k Is the time window feasible? If it is feasible, go to step EA-8; if not, calculate the composition r k Full list of customers EA-7: Traversal Determine whether there is a path r′ k Satisfy the time window constraint, if it exists, then r k ←r′ k , otherwise go to step EA-5; EA-8: Calculate the smallest available vehicle model make EA-9: If m ≤ |M|, calculate Otherwise, go to step EA-5; EA-10: If Go to step EA-11, otherwise m←m+1, go to step EA-9; EA-11: If |Δ ha |<size, then add To the set Δ ha ,renew m←m+1, go to step EA-9; otherwise, go to the next step; EA-12: If Then in the set Δ ha Delete rc max A corresponding solution, and add To the set Δ ha , and update m←m+1, go to step EA-9; otherwise, m←m+1, go to step EA-9; EA-13: End the algorithm and return Δ ea .

8. The vehicle dispatching method considering the step-rate subsidy as claimed in claim 3, characterized in that: The branch process BB in step S4-9 includes: BB-1: Count the arcs (i, j) contained in the solution of the current node δ and add them to the set Δ bb ; BB-2: Δ bb Calculate the flow of all arcs in Where R ij is the set of paths containing arc(i, j); BB-3: Select the arc (i, j) with the flow closest to 0.5 as the branch item f′ ij ; BB-4: Generate node δ 1 , the cost of using the arc (i, j) in this node is infinite, generating node δ 2 ; Among all arcs in this section that contain nodes i and j, the usage cost is infinite except for arc (i, j); BB-5: Algorithm ends, return to node δ 1 and δ 2 .

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