CN115392821A - Punctualized material distribution method of single-load electric distribution vehicle adopting charging - Google Patents
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Abstract
The invention discloses a punctual material distribution method of a single-load electric distribution vehicle adopting charging, which comprises the following steps: obtaining production plan and material demand information of an automobile assembly line; establishing an information model of the electric distribution trolley; establishing a target function and a constraint condition of punctuality material distribution scheduling of a single-load electric distribution vehicle adopting charging; solving the material distribution scheduling model based on a branch pricing algorithm to obtain an optimal material distribution scheduling strategy; and the electric distribution vehicle executes the material distribution task of the station according to the scheduling strategy. Compared with the prior art, the method and the device consider the influence of the battery capacity limit of the electric delivery vehicle on the scheduling result, can accurately solve the optimal material delivery scheduling strategy of the electric delivery vehicle, and have the advantages of effectively reducing the number of delivery vehicles, improving the material delivery efficiency and stability and the like.
Description
Technical Field
The invention relates to the technical field of material distribution, in particular to a punctual material distribution method of a single-load electric distribution vehicle adopting charging.
Background
The mixed-flow assembly line produced by mixing multiple varieties and small batches can meet the requirements of market individuation and diversification and enhance the response speed of enterprises to the market, so that the mixed-flow assembly line is widely applied to the manufacturing industries mainly for assembling automobiles, household appliances and the like. Its corresponding process logistics system is an important subsystem of contemporary manufacturing.
The workshop material distribution system is an important component of an enterprise production system, and is also a subsystem forming an enterprise logistics system and is responsible for carrying out multi-variety and small-batch distribution on materials required by a production workshop. Whether the production materials can be delivered to a production place in a timely and accurate mode is the key for smooth operation of the production logistics system of an enterprise, and therefore, the on-time delivery of the materials is the premise and guarantee of smooth production of manufacturing enterprises.
The ideal material delivery requirements on the assembly line are: "the correct amount of the correct material is delivered to the correct place at the correct time and moment according to the correct conditions", the stock at the line edge is neither short of material nor piled up. Therefore, how to model and optimize the workshop logistics distribution system to realize the on-time material supply of the mixed flow production line is very important for the smooth operation of the assembly production line.
In the selection of transport means, the electric trolley has the advantages of no emission of polluted gas during running, low running noise and the like, so that the electric trolley is more suitable for material distribution of 'last kilometer' inside and outside a plant.
When solving the integer programming problem of electric trolley distribution, the branch pricing algorithm is widely applied due to the fast solving speed. The branch pricing algorithm searches all feasible solution spaces of the optimization problem with constraint conditions, continuously divides all feasible solution spaces into smaller and smaller branches, and calculates a lower bound or an upper bound for the value of a solution in each branch. After each branch, the branch with the boundary exceeding the known feasible solution value is cut, so that the search range can be narrowed, the search efficiency is improved, and the method is suitable for solving the material distribution problem of the vehicle. The prior art that employs a branch pricing algorithm to solve the delivery problem is as follows:
(1) A coordinated distribution route optimization method based on a branch pricing cutting algorithm (CN 114037180A) discloses a coordinated distribution route optimization method based on a branch pricing cutting algorithm, which comprises the following steps: s1, establishing a set division model, wherein the model is established on the basis of a feasible vehicle unmanned aerial vehicle cooperative distribution path (the feasible vehicle unmanned aerial vehicle cooperative path is a path which meets the time window, the requirement, the maximum service duration and the load of a vehicle/unmanned aerial vehicle) of a customer, and the total distribution cost is minimized on the basis of meeting the single service of each customer, wherein the total cost comprises the fixed use cost of the vehicle and the distribution cost of the vehicle unmanned aerial vehicle; and S2, solving the set division model by adopting an accurate algorithm based on branch pricing and cutting to obtain an optimal collaborative distribution route of the vehicle unmanned aerial vehicle.
(2) A distribution route optimization method based on vehicle-unmanned aerial vehicle cooperation (CN 114462693A) discloses a distribution route optimization method based on vehicle-unmanned aerial vehicle cooperation, which comprises the following steps: s1, establishing a mixed integer programming model for cooperative blood distribution of a vehicle unmanned aerial vehicle; s2, carrying out equivalent change on the mixed integer programming by adopting a logarithm-based method, and obviously reducing the number of binary variables by adding auxiliary linear constraint; and S3, dividing the mixed integer programming model into a Benders main problem and a Benders sub problem by adopting Benders weight representation, solving the Benders sub problem by adopting a branch pricing and cutting algorithm, and further optimizing the selection of the cluster center hospitals, the distribution of the non-cluster center hospitals and the vehicle driving route to obtain an optimized cluster center hospital selection and distribution strategy.
However, different from the constraints considered by the distribution problem of the unmanned aerial vehicle, the charging process of the electric distribution vehicle at the charging station needs to be considered after the electric trolley distribution is carried out on time and route optimization, so that the sub-problem is essentially an initial shortest path problem with resource constraint considering the battery capacity constraint and the time window constraint of the vehicle, and if a one-way label algorithm based on dynamic programming is adopted, a large number of labels are generated, and the solving speed is reduced; moreover, if the decomposition mode of the optimization model in the prior art is directly applied to the distribution problem of the electric trolley, the constraint number is still more, and the method is not an optimal solution.
Disclosure of Invention
In order to solve the problems in the prior art, the application provides the punctual material distribution method of the single-capacity electric distribution vehicle adopting charging, the influence of the battery capacity limitation of the electric distribution vehicle on the distribution result is considered, the optimal material distribution and distribution strategy of the electric distribution vehicle can be accurately solved, and the method has the advantages of effectively reducing the number of the distribution vehicles, improving the material distribution efficiency and stability and the like.
The technical scheme of the invention is as follows:
the punctual material distribution method of the single-load electric distribution vehicle adopting charging comprises the following steps:
s1, obtaining information of an automobile assembly line, including but not limited to: the method comprises the following steps of (1) producing a plan, material demand information of each station in a planning period, replenishment time window information, the distance from a material supermarket to an assembly station, and the time required by material loading and unloading;
s2, establishing an information model of the electric distribution vehicle, comprising the following steps: maximum load capacity, power level, power consumption rate;
s3, establishing a target function of the just-in-time material delivery scheduling of the single-load electric delivery vehicle adopting charging;
s4, determining the constraint conditions of the scheduling process, including: uniqueness constraint, task chain correlation constraint, time window constraint, vehicle constraint and electric quantity constraint;
s5, solving the material distribution scheduling model based on a branch pricing algorithm to obtain an optimal material distribution scheduling strategy; the material distribution strategy comprises a distribution task sequence executed by the electric distribution vehicle and the charging time of the electric distribution vehicle;
and S6, each electric distribution vehicle executes the material distribution task of the station according to the scheduling strategy.
Further, the electric distribution vehicle adopts point-to-point material distribution, namely: the electric distribution vehicle only carries the materials at the corresponding station, and distributes the materials from the material supermarket to the corresponding station and then returns to the material supermarket.
Further, the electric distribution vehicle is a single capacity vehicle, which has a limited battery capacity and requires access to a charging station during a planning period.
Further, the material delivery scheduling in step S3 is aimed at minimizing the number of electric delivery vehicles, and the objective function is:
wherein: y is k The variable is a binary variable, if the delivery task executed by the delivery vehicle k is 1, otherwise, the variable is 0; v is the set of delivery vehicles, k ∈ V.
Further, the constraint conditions of step S4 are as follows:
(1) The uniqueness constraint is as follows:
wherein: x is the number of ijk The variable is a binary variable, if the distributed vehicles k execute the tasks i and j successively, the variable is 1, otherwise, the variable is 0; n' distributing tasks and charging station sets; n +1 is a virtual node and represents the end point of the task chain;
(2) Task chain related constraints:
wherein: n is a distribution task set, N = {1, \8230;, N };0 is a virtual node and represents the starting point of the task chain;
(3) And (3) time window constraint:
τ ik +(2D i +LT+UT)-M·(1-x ijk )≤τ jk ,
τ ik +(2D i +g·(Q-u ik ))-M·(1-x ijk )≤τ jk ,
wherein: tau is ik A start time for executing task i for delivery vehicle k; d i The one-way time for the delivery vehicle to travel to the station corresponding to the task i; LT and UT are the loading time and the unloading time of the material box; m is a large positive integer; q is the battery capacity of the delivery vehicle; u. of ik The remaining capacity when the distribution vehicle k executes the task i; [ s ] of i ,l i ]A time window for dispatching task i; e is a charging station set, and E belongs to E; g is the charge rate;
(4) Vehicle restraint:
(5) Electric quantity constraint:
0≤u jk ≤u ik -2D i h-δw i d i D i +Q(1-x ijk ),
wherein: h is the electric quantity consumption rate in no load; delta is the increment of power consumption in unit time when the material with unit weight is increased; w is a i Is the unit material weight of the distribution task i; d is a radical of i Material demand for distribution task i.
Further, the step of the branch pricing algorithm in step S5 is as follows:
s5-1, decomposing the objective function and the constraint into a main problem and a pricing subproblem by adopting a Dantzig-Wolfe decomposition technology;
s5-2, relaxing integer constraint conditions of the main problem, and solving to obtain corresponding pair even variable values;
s5-3, updating corresponding coefficients of the pricing subproblems according to the dual variable values, and solving the pricing subproblems; adding to the main question if a column can be found that improves the main question target value;
s5-4, gradually iterating the main relaxation problem and the subproblems to find the optimal solution of the main relaxation problem;
and S5-5, if the solution of the main relaxation problem is an integer solution, ending the algorithm, otherwise, applying a branch strategy, and returning to the step S5-2.
Further, the objective function of the main question is:
the constraint conditions include:
wherein: ω is the scheduling strategy for a single delivery vehicle, described as the feasible delivery sequence for a single delivery vehicle meeting the constraints; c. C ω Cost for scheduling ω; z is a radical of formula ω The variable is a binary variable, if a scheduling strategy omega is selected in the optimal solution, 1 is selected, otherwise, 0 is selected; alpha (alpha) ("alpha") iω The scheduling strategy omega executes the distribution task i to be 1, otherwise, the distribution task i is 0;
will be in the model
Is changed into
Obtaining a linear relaxation main problem of the main problem; solving the main problem of linear relaxation by noting pi i And eta is the corresponding dual variable value.
Further, the objective function of the pricing subproblem is:
and solving the minimum pricing subproblem by adopting a label algorithm.
Further, in step S5-5, the step of branching the variable relaxing the score value of the main question by the branching policy is as follows:
s5-5-1, if the main problem is loosened and the optimal target value is not smaller than the current optimal integer solution, cutting off branches and ending, otherwise, executing the step S5-5-2;
s5-5-2, if the optimal solution of the main relaxation problem is an integer solution, replacing the current optimal solution with the optimal solution of the main relaxation problem, and then pruning and ending, otherwise, executing the step S5-5-3;
s5-5-3, if the optimal target value of the main relaxation problem is smaller than the current optimal integer solution, and the partial variable z ω If the decimal number is a decimal number, branching is performed.
Further, the branching step of step S5-5-3 is as follows:
s5-5-3-1, selecting branch variables
r * Scheduling policy omega for correspondence * The distribution route of (a);
s5-5-3-2, optionally a task node i and (j, i) e r * ；
S5-5-3-3, the arcs (j, i) on one branch are prohibited from being accessed, and the arcs except the arcs (j, i) on the other branch are prohibited from being accessed.
The beneficial technical effects of the invention are as follows:
(1) The invention combines the branch-and-bound algorithm with the column generation algorithm and is used for solving the problem of electric trolley distribution considering the battery capacity. The branch pricing algorithm adopted by the algorithm firstly decomposes an original problem into a main problem and a pricing subproblem based on a mixed integer programming model and a Dantzig-Wolfe decomposition technology, and then adopts a column generation algorithm to find a linear relaxation optimal solution of the main problem through gradual iteration between the main problem and the subproblem. Compared with the traditional sub-system solution algorithm, the relaxation optimal solution can provide a lower bound which is tighter than the relaxation of the original problem, so that a large-scale mixed integer programming model can be solved at a higher speed;
(2) Compared with the prior art, the Dantzig-Wolfe decomposition algorithm is adopted in the branch definition algorithm, the decomposition technology can be used for the algorithm of the large-scale linear programming problem, and the polyhedron set constraint is replaced by the single weighted constraint, so that the constraint number is reduced, the model is simplified, and the calculation efficiency is improved;
(3) The invention adopts a bidirectional label algorithm, overcomes the problems of the prior art and improves the speed of solving the pricing subproblem.
Drawings
FIG. 1 is a layout diagram of a punctuation material distribution system of an embodiment;
FIG. 2 is an overall flow diagram of the branch pricing algorithm of an embodiment.
In the drawings, the corresponding relationship between the component names and the reference numbers is as follows: 1. an article of manufacture; 2. assembling stations; 3. material preparation; 4. an electric delivery vehicle; 5. a delivery path; 6. a material supermarket; 7. charging station.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The punctuality material distribution method of the single-load electric distribution vehicle adopting charging is realized based on a point-to-point feeding system of a material supermarket. As shown in fig. 1, the point-to-point supermarket system for materials comprises a work in process 1, an assembly station 2, materials 3, an electric distribution vehicle 4, a distribution path 5, a supermarket for materials 6 and a charging station 7.
The material supermarket 6 is arranged beside an assembly line and used for supplying materials to the assembly stations 2, the electric distribution vehicle 4 is used for carrying out point-to-point material distribution on the materials of the material supermarket 6 along the distribution path 5, and when the electric distribution vehicle 4 is exhausted, the electric distribution vehicle can go to the charging station 7 for charging. In this embodiment, a replenishment task sequence of the electric distribution vehicle 4 for each station 2 can be designed by considering the punctuality material distribution method of the single-capacity electric distribution vehicle adopting charging.
The punctual material distribution method is based on a single-load electric distribution vehicle adopting charging and is used for carrying out point-to-point material distribution and dispatching on materials from a material supermarket to an assembly line station in an in-factory logistics stage, the rechargeable single-load electric distribution vehicle is adopted for distribution, the electric distribution vehicle only carries the materials of the corresponding station, and the materials are distributed to the corresponding station from the material supermarket and then return to the material supermarket. The electric distribution vehicle has a limited battery capacity and requires access to the charging station during the planning period. The method comprises the following steps:
s1, obtaining a production plan of an automobile assembly line, material demand information of each station in a planning period, replenishment time window information, a distance from a material supermarket to an assembly station, time required by material loading and unloading and the like.
S2, establishing an information model of the electric distribution trolley, which comprises the following steps: the maximum loading capacity of the electric distribution trolley, the electric quantity level of the electric distribution trolley and the power consumption rate of the electric distribution trolley.
S3, establishing an objective function of the punctuality material delivery scheduling of the single-load electric delivery vehicle adopting charging:
in the formula, y k The variable is a binary variable, if the delivery task executed by the delivery vehicle k is 1, otherwise, the variable is 0; v is a distribution vehicle set, and k belongs to V.
S4, determining a constraint condition of the scheduling process, including: uniqueness constraints, task chain correlation constraints, time window constraints, vehicle constraints, and power constraints.
(1) The uniqueness constraint is as follows:
in the formula, x ijk The variable is a binary variable, if the distributed vehicles k execute the tasks i and j successively, the variable is 1, otherwise the variable is 0; n' distribution task and charging station set; n +1 is a virtual node representing the end of the task chain.
(2) Task chain related constraints:
wherein, N is a distribution task set, N = {1, \8230 =, N }; and 0 is a virtual node and represents the starting point of the task chain.
(3) And (3) time window constraint:
τ ik +(2D i +LT+UT)-M·(1-x ijk )≤τ jk ,
τ ik +(2D i +g·(Q-u ik ))-M·(1-x ijk )≤τ jk ,
in the formula, τ ik A start time for executing task i for delivery vehicle k; d i The one-way time for the delivery vehicle to travel to the station corresponding to the task i; LT and UT are the loading time and the unloading time of the material box; m is a large positive integer; q is the battery capacity of the distribution vehicle; u. u ik The remaining capacity when executing task i for delivery vehicle k; [ s ] of i ,l i ]A time window for dispatching task i; e is a charging station set, and E belongs to E; g is the charge rate.
(4) Vehicle restraint:
(5) The electric quantity constraint is as follows:
0≤u jk ≤u ik -2D i h-δw i d i D i +Q(1-x ijk ),
wherein h is the electric quantity consumption rate in no load; delta is the increment of power consumption in unit time when the material with unit weight is increased; w is a i Is the unit material weight of the distribution task i; d is a radical of i Is the material demand of the distribution task i.
And S5, solving the material distribution scheduling model based on a branch pricing algorithm to obtain an optimal material distribution scheduling strategy. FIG. 2 is a flow chart of a branch pricing algorithm, the algorithm steps being as follows:
and S5-1, decomposing the objective function and the constraint into a main problem and a pricing subproblem by adopting a Dantzig-Wolfe decomposition technology. The main problems obtained after decomposition are as follows:
the objective function of the main problem is:
the constraint conditions include:
where ω is a scheduling strategy for a single delivery vehicle, describing the feasible delivery sequence for a single delivery vehicle at which the constraints are satisfied; c. C ω Cost for scheduling ω; z is a radical of ω If the optimal solution is a binary variable, selecting 1 if a scheduling strategy omega is selected, and otherwise, selecting 0; alpha is alpha iω Indicating that the scheduling policy ω executes the delivery task i as 1, otherwise as 0.
S5-2, relaxing the integer constraint conditions of the main problem, and solving to obtain corresponding dual variable values. Will be in the main question
Is changed into
I.e. the linear relaxation main problem that gets the main problem. Solving the linear relaxation main problem by adopting a linear programming solver, and recording pi i And eta is the corresponding dual variable value.
S5-3, updating the corresponding coefficient of the pricing subproblem according to the dual variable value to obtain an objective function of the pricing subproblem:
and solving the pricing subproblem by adopting a label algorithm. Any partial path ω from virtual node 0 to node i, i ∈ N', may be labeled
And (4) showing. Wherein the content of the first and second substances,
represents the sequence of tasks (0, \8230;, e, \8230;, i) visited when the path ω reached task node i;
representing a target value when the path omega reaches the task node i;
representing the residual electric quantity when the path omega reaches the task node i;
representing the charging times when the path omega reaches the task node i;
representing the time when the path omega reaches the task node i earliest;
and the times of executing the distribution task k when the path omega reaches the task node i, wherein the k belongs to the N.
The label at virtual node 0 is an initial label F ω0 ＝({0},0,Q,0,0,[0] N ). When the label of the task node i is expanded to the label of the task node j, the non-negative constraint of the electric quantity and the constraint of the time window need to be satisfied, and only the label satisfying the constraint can be further expanded, wherein the label recurrence formula is as follows:
When all the labels are expanded to the termination node n +1, finding the task sequence with the minimum pricing subproblem target value from all the obtained feasible task sequences, namely the task sequence is the optimal solution of the pricing subproblem. If the target value is negative, indicating that a column capable of improving the target value of the main problem is found and adding the column into the main problem of relaxation; otherwise, the relaxation main problem has already obtained the optimal solution.
And S5-4, gradually iterating the main relaxation problem and the subproblems to find the optimal solution of the main relaxation problem.
And S5-5, if the solution of the main relaxation problem is an integer solution, ending the algorithm, otherwise, applying a branch strategy, and returning to the step S5-2. In which a branch policy branches a variable that relaxes a main problem score value, there may be the following three cases:
the first condition is as follows: and if the optimal target value of the main relaxation problem is not less than the current optimal integer solution, pruning.
Case two: and if the optimal target value of the main relaxation problem is smaller than the current optimal integer solution and the optimal solution of the main relaxation problem is the integer solution, replacing the current optimal solution with the optimal solution of the main relaxation problem and pruning.
And a third situation: the optimal target value of the relaxation main problem is smaller than the current optimal integer solution, and the partial variable z ω If the decimal number is a decimal number, branching is performed. First, choose branch variables
r * For corresponding scheduling policy omega * The distribution route of (2); optionally selecting a task node i and (j, i) epsilon r * (ii) a Let the arcs (j, i) on one branch be prohibited from accessing, and arcs other than the arcs (j, i) on the other branch be prohibited from accessing.
And S6, each electric distribution vehicle executes the material distribution task of the station according to the scheduling strategy.
While the embodiments of the present invention have been disclosed above, it is not limited to the applications listed in the description and embodiments, but is fully applicable to various fields suitable for the present invention, and it will be apparent to those skilled in the art that various changes, modifications, substitutions and alterations can be made in the embodiments without departing from the principle and spirit of the present invention, and therefore the present invention is not limited to the specific details without departing from the general concept defined in the claims and the scope of equivalents thereof.
Claims (10)
1. The punctual material distribution method of the single-load electric distribution vehicle adopting charging is characterized by comprising the following steps:
s1, obtaining information of an automobile assembly line, including but not limited to: the method comprises the following steps of (1) producing a plan, material demand information of each station in a planning period, replenishment time window information, the distance from a material supermarket to an assembly station, and the time required by material loading and unloading;
s2, establishing an information model of the electric distribution vehicle, comprising the following steps: maximum load capacity, power level, power consumption rate;
s3, establishing a target function of the punctuality material distribution scheduling of the single-load electric distribution vehicle adopting charging;
s4, determining a constraint condition of the scheduling process, including: uniqueness constraint, task chain correlation constraint, time window constraint, vehicle constraint and electric quantity constraint;
s5, solving the material distribution scheduling model based on a branch pricing algorithm to obtain an optimal material distribution scheduling strategy; the material distribution strategy comprises a distribution task sequence executed by the electric distribution vehicle and the charging time of the electric distribution vehicle;
and S6, each electric distribution vehicle executes the material distribution task of the station according to the scheduling strategy.
2. The on-time material distribution method of a single-capacity electric distribution vehicle using charging according to claim 1, wherein the electric distribution vehicle uses point-to-point material distribution, that is: the electric distribution vehicle only carries the materials at the corresponding station, and distributes the materials from the material supermarket to the corresponding station and then returns to the material supermarket.
3. The method of claim 1, wherein the electric distribution vehicle is a single capacity vehicle having a limited battery capacity requiring access to a charging station during a planning period.
4. The on-time material distribution method for single-capacity electric distribution vehicles with electric charge as claimed in claim 1, wherein the material distribution schedule of step S3 aims at minimizing the number of electric distribution vehicles, and the objective function is:
wherein: y is k The variable is a binary variable, if the delivery task executed by the delivery vehicle k is 1, otherwise, the variable is 0; v is the set of delivery vehicles, k ∈ V.
5. The on-time material distribution method for a single-capacity electric distribution vehicle using charging according to claim 1, wherein the constraint conditions of step S4 are as follows:
(1) The uniqueness constraint is as follows:
wherein: x is the number of ijk The variable is a binary variable, if the distributed vehicles k execute the tasks i and j successively, the variable is 1, otherwise the variable is 0; n' distributing tasks and charging station sets; n +1 is a virtual node and represents the end point of the task chain;
(2) Task chain related constraints:
wherein: n is a distribution task set, N = {1, \8230;, N };0 is a virtual node and represents the starting point of the task chain;
(3) And (3) time window constraint:
τ ik +(2D i +LT+UT)-M·(1-x ijk )≤τ jk ,
τ ik +(2D i +g·(Q-u ik ))-M·(1-x ijk )≤τ jk ,
s i ≤τ ik ≤l i ,
wherein: tau is ik A start time for executing task i for delivery vehicle k; d i The one-way time for the delivery vehicle to travel to the station corresponding to the task i; LT and UT are the loading time and the unloading time of the material box; m is a large positive integer; q is the battery capacity of the distribution vehicle; u. of ik The remaining capacity when the distribution vehicle k executes the task i; [ s ] of i ,l i ]A time window for dispatching task i; e is a charging station set, and E belongs to E; g is the charge rate;
(4) Vehicle restraint:
(5) Electric quantity constraint:
0≤u jk ≤u ik -2D i h-δw i d i D i +Q(1-x ijk ),
0≤u jk ≤Q-2D i hx ijk ,
u 0k ＝Q,
wherein: h is the electric quantity consumption rate in no load; delta is the increment of power consumption in unit time when the material with unit weight is increased; w is a i Is the unit material weight of the distribution task i; d i Is the material demand of the distribution task i.
6. The on-time material distribution method for a single-capacity electric distribution vehicle using charging according to claim 1, wherein the branch pricing algorithm of step S5 comprises the following steps:
s5-1, decomposing the objective function and the constraint into a main problem and a pricing subproblem by adopting a Dantzig-Wolfe decomposition technology;
s5-2, loosening integer constraint conditions of the main problem, and solving to obtain corresponding pair of even variable values;
s5-3, updating corresponding coefficients of the pricing subproblems according to the dual variable values, and solving the pricing subproblems; if a column can be found that improves the main question target value, it is added to the main question;
s5-4, gradually iterating the main relaxation problem and the subproblems to find the optimal solution of the main relaxation problem;
and S5-5, if the solution of the main relaxation problem is an integer solution, ending the algorithm, otherwise, applying a branch strategy, and returning to the step S5-2.
7. The on-time material distribution method for a single-capacity electric distribution vehicle using a charge according to claim 6, wherein the objective function of the main problem is:
the constraint conditions include:
z ω ∈{0,1},
wherein: ω is a scheduling strategy for a single delivery vehicle, described as a feasible delivery sequence for the single delivery vehicle at which the constraints are satisfied; c. C ω Cost for scheduling ω; z is a radical of ω The variable is a binary variable, if a scheduling strategy omega is selected in the optimal solution, 1 is selected, otherwise, 0 is selected; alpha is alpha iω The scheduling strategy omega executes the distribution task i to be 1, otherwise, the distribution task i is 0;
will be z in the model ω ∈{0,1},
To z ω ≥0,
Obtaining a linear relaxation main problem of the main problem; solving the main problem of linear relaxation by noting pi i And eta is the corresponding dual variable value.
8. The method of claim 6, wherein the objective function of the pricing subproblem is:
and solving the minimum pricing subproblem by adopting a label algorithm.
9. The on-time material distribution method for a single-capacity electric distribution vehicle using charging according to claim 6, wherein:
in step S5-5, the step of branching the variable of the slack main question score value by the branching policy is as follows:
s5-5-1, if the optimal target value of the main relaxation problem is not less than the current optimal integer solution, cutting branches and ending, otherwise, executing the step S5-5-2;
s5-5-2, if the optimal solution of the main relaxation problem is an integer solution, replacing the current optimal solution with the optimal solution of the main relaxation problem, and then pruning and ending, otherwise, executing the step S5-5-3;
s5-5-3, if the optimal target value of the relaxation main problem is smaller than the current optimal integer solution, and the partial variable z ω If the number is small, branching is performed.
10. The on-time material distribution method for a single-capacity electric distribution vehicle using a charge according to claim 9, comprising:
the branching steps of step S5-5-3 are as follows:
s5-5-3-1, selecting branch variables
r * For corresponding scheduling policy omega * The distribution route of (a);
s5-5-3-2, optionally selecting a task node i and (j, i) epsilon r * ；
S5-5-3-3, the arcs (j, i) on one branch are prohibited from being accessed, and the arcs except the arcs (j, i) on the other branch are prohibited from being accessed.
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| CN115619082A (en) * | 2022-12-02 | 2023-01-17 | 天津大学 | Method and device for solving balance problem of man-machine cooperation mixed flow assembly line |
| CN116777063A (en) * | 2023-06-20 | 2023-09-19 | 广东工业大学 | Two-dimensional boxing method based on one-tool cutting constraint and branch pricing algorithm |
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| CN115619082A (en) * | 2022-12-02 | 2023-01-17 | 天津大学 | Method and device for solving balance problem of man-machine cooperation mixed flow assembly line |
| CN116777063A (en) * | 2023-06-20 | 2023-09-19 | 广东工业大学 | Two-dimensional boxing method based on one-tool cutting constraint and branch pricing algorithm |
| CN116777063B (en) * | 2023-06-20 | 2024-02-27 | 广东工业大学 | Two-dimensional boxing method based on one-tool cutting constraint and branch pricing algorithm |
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