CN108288114B - Emergency material scheduling method based on primitive dual theory - Google Patents
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Abstract
The invention provides an emergency material scheduling method based on an original dual theory, which is characterized by comprising the following steps: step I1., determining the allocation and transportation time and allocation and transportation cost from each supply point to each demand point, and acquiring an allocation and transportation time and cost matrix; step I2, determining the maximum value of the minimum element in each row and each column of elements in the dispatching time matrix as the current candidate optimal solution; step I3, establishing a minimum cost flow network model related to the current alternative optimal solution; step I4., determining the maximum flow by solving the optimal solution of the model based on the dual principle; step I5., judging whether the flow reaches the given value, if so, finding the optimal matching scheme; otherwise, updating the current alternative optimal solution and model by the principle of value-added minimum, and returning to the step I4; step II, according to the optimal matching scheme, in combination with the cost matrix, seeking the optimal allocation and transportation scheme which is the maximum transportation amount in the shortest time and enables the total cost to be the minimum; and III, carrying out emergency material allocation and transportation according to the optimal allocation and transportation scheme.
Description
Technical Field
The invention belongs to the technical field of material scheduling, and particularly relates to an emergency material scheduling method based on an original dual theory.
Technical Field
In general, conventional material distribution requires a minimum total project distribution cost. In some emergency situations, such as emergency rescue and relief work, emergency medical treatment, etc., the first consideration is to transfer emergency materials to different places with different demands in the shortest time, and the second requirement is to minimize the total transfer and transportation cost of the project.
Because the problem of emergency material allocation and transportation is a typical multi-target planning, the current main methods for solving the problem are of two types: firstly, directly solving a multi-target planning problem by adopting a traditional interactive algorithm, a fuzzy planning method, a genetic algorithm and the like; and secondly, converting the multi-target planning problem of the emergency material allocation and transportation into the traditional transportation problem, and seeking an optimal solution by utilizing a method for solving the traditional transportation problem. When the emergency dispatching problem involves more supply points and disaster-affected points, the calculation scale of the problem is rapidly enlarged, and the traditional interactive algorithm, the fuzzy planning method and the genetic algorithm all have the problems that the calculation scale is increased, the calculation time is obviously increased, and the like. In addition, the problem scale can be artificially enlarged by converting the general unbalanced emergency material allocation and transportation problem with unequal supply and demand into the balanced material allocation and transportation problem, the algorithm process for solving the traditional transportation problem is complex, and the method is not favorable for checking whether the obtained solution is the optimal solution or not.
Disclosure of Invention
The invention is carried out to solve the problems, and aims to provide an emergency material dispatching method based on an original dual theory, which can quickly obtain an optimal scheme for dispatching and transporting emergency materials, effectively improve dispatching and transporting efficiency, reduce cost and optimize resource allocation.
In order to achieve the purpose, the invention adopts the following scheme:
the invention provides an emergency material scheduling method based on an original dual theory, which is characterized by comprising the following steps of:
step I, determining an optimal matching scheme from each emergency material demand point to an emergency material supply point in the shortest time, wherein the optimal matching scheme comprises the following steps:
step I1., determining allocation and transportation time and unit material allocation and transportation cost from each emergency material supply point to each emergency material demand point, and acquiring an allocation and transportation time matrix and an allocation and transportation cost matrix;
step I2, determining the maximum value of the minimum element in each row and each column of elements in the dispatching time matrix as the current candidate optimal solution;
step I3, establishing a minimum cost flow network model of the emergency material allocation and transportation related to the current optimal solution of the alternative materials;
step I4., determining the maximum flow in the current network by using the optimal solution of the minimum cost flow model established based on the dual principle;
step I5., judging whether the flow reaches a given value (the given value is the number of the emergency material receiving points), if the flow reaches the given value, finding the optimal matching scheme which completes the emergency material allocation and transportation in the shortest time; otherwise, updating the current alternative optimal solution according to the minimum value-added principle, updating the constructed minimum cost flow model for emergency material allocation and transportation, and returning to the step I4;
step II, seeking the maximum transportation amount which can be dispatched from an emergency material supply point to an emergency material demand point in the shortest time according to the optimal matching scheme obtained in the step I5 and by combining a dispatching cost matrix, and taking the scheme which enables the total transportation cost to be minimum as the optimal dispatching scheme;
and III, carrying out emergency material allocation and transportation according to the optimal allocation and transportation scheme determined in the step II.
The emergency material scheduling method based on the original dual theory provided by the invention can also have the following characteristics: as shown in fig. 2, step I3 includes the following sub-steps:
step I3-1, constructing a bipartite graph of supply points and demand points of emergency materials, wherein only the transportation time t from the supply point I e M (I1, 2.. multidot. m.M is a supply point set) to the demand point j e N (j 1, 2.. multidot.n is a supply point set) is reserved in the bipartite graphij＜t*(t*An edge that is the current candidate optimal solution);
step I3-2, construct a virtual start point s and a virtual end point t, add edges (s, I),
and edge
(j，t)，
Step (ii) ofI3-3. parameter for defining edge is (c)ij，uij) Wherein c isijRepresenting the cost, u, of unit material transport from location i to location jijIs the capacity of the edge; opposite sides (s, i),
let csi＝0，usiN (n is the number of emergency material receiving points); opposite side (i, j), i belongs to M, j belongs to N, and uij1 is ═ 1; opposite side (j, t), j ∈ N, let cjt＝0，ujt＝1。
The emergency material scheduling method based on the original dual theory provided by the invention can also have the following characteristics: as shown in fig. 2, step I4 includes the following sub-steps:
step I4-1, order
(A is the set of edges in the minimum cost flow model); label source s with (0, + ∞); the point S ═ { S } < u > M,
when the flow v' is 0; note the book
Is set as
Backward edge set
Step I4-2: firstly, pair
Get
If not, if theta cannot be determined, the current flow is the maximum flow of the original network, and the optimal scheme of emergency material allocation and transportation is found;
order to
Step I4-3.pi-pj＝tijThen (i, j) is e.g. R;
step I4-4. for I e S, as (I, j) e R,
and xijWhen j is 0, the label (i, 1) is given; s ═ tauj }; such as (j, i) e R,
and xijIf > 0, j is marked (-i, 1);
② pair
At this time, the maximum flow in the network is allowed, and then the step I4-2 is returned; otherwise, if t epsilon is S, finding the amplifiable chain mu in R, and then executing the step I4-4;
increasing the flow
The flow becomes: v' + 1;
when the augmentation chain cannot be found, the maximum flow in the network is reached, and the optimal allocation and transportation scheme of the materials is found; otherwise, keeping the label of the source point s, deleting the labels of all the other nodes, updating the current alternative optimal solution, and adding the value T in the current minimum cost flow network1And then returns to the edge corresponding to the unit flow rate costReturning to the step I4-2.
The emergency material scheduling method based on the original dual theory provided by the invention can also have the following characteristics: in step I5, updating the current candidate optimal solution rule according to the minimum value-added rule is:
T1＝T1+min{Tij-T1|tij＞T1，i＝1，2，...，m；j＝1，2，...，n}，
in the formula, tijIs the transportation time from the emergency material supply point i to the emergency material demand point j.
The emergency material scheduling method based on the original dual theory provided by the invention can also have the following characteristics: step II comprises the following substeps: step II1, redefining relevant parameters of each side in the network corresponding to the optimal matching scheme according to the following rules: let the supply quantity of the material supply point i be ai，1, 2, m, the demand of the material demand point j is bjN. the parameters defining an edge are (c)ij，uij) Wherein c isijRepresenting the cost, u, of unit material transport from location i to location jijIs the capacity of the edge; opposite side (s, i)
Let csi＝0，usi＝aiOpposite side (i, j), i belongs to M, j belongs to N, and u belongs toij＝min(ai，bj) (ii) a Opposite side (j, t), j ∈ N, let cjt＝0，ujt＝bj(ii) a And step II2, solving the optimal solution of the network model in the step II1 by using a dual principle, determining the minimum cost maximum flow in the current network, and further determining the optimal dispatching scheme.
The emergency material scheduling method based on the original dual theory provided by the invention can also have the following characteristics: the solution method of step II2 is consistent with step I4.
Action and Effect of the invention
The invention constructs a minimum cost flow network model corresponding to the determined shortest time by determining the shortest time which can finish the allocation and transportation of all materials at present, and seeks the minimum cost maximum flow in the current network on the basis. When the flow in the network does not reach the given value, the shortest time for completing the emergency material allocation and transportation at present is adjusted according to the minimum value-added principle, and the process is repeated until the minimum cost maximum flow in the network is sought. In the iteration process, the information of the previous iteration is fully utilized in the next iteration, so that the method can greatly improve the calculation efficiency. And when the problem that the material demand quantity is different from the material supply quantity is sought, the method does not need to convert the problem into the traditional production and marketing balance problem, cannot artificially enlarge the scale of the problem, can greatly reduce the calculation time for obtaining the optimal allocation and transportation scheme, and has strong practicability. Particularly, when large-scale material distribution and transportation are carried out, the method can quickly seek the optimal scheme.
Drawings
Fig. 1 is a flowchart of an emergency material scheduling method based on primitive dual theory according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating the solution of the minimum cost flow model for emergency material distribution and transportation according to the present invention based on dual theory (corresponding to steps I1 to I4);
FIG. 3 is a diagram of an initial minimum network flow model in an embodiment of the invention;
FIG. 4 is a schematic diagram of the process of seeking a minimum time in an embodiment of the present invention;
fig. 5 is a schematic diagram of a process of seeking to minimize the total dispatching cost when the maximum amount of emergency materials can be dispatched in the shortest time according to the embodiment of the invention.
Detailed Description
The emergency material scheduling method based on the primitive dual theory according to the present invention will be described in detail with reference to the accompanying drawings.
< example >
Assuming earthquake disaster happens in a certain area, two villages B exist1，B2In case of disaster, 3 different cities A are required1，A2，A3And (5) emergency dispatching and transporting disaster relief materials. Known as A1，A2，A3The adjustable material quantity is respectively 6t, 5t and 7 t; b is1，B2Required material distributionThe transportation time (unit: h) from each city to each village and the unit material allocation and transportation cost (unit: thousand yuan) are respectively 7t and 8t, which are shown in the following table (in the table, x | y has the meaning as follows: x represents the transportation time, and how to organize and allocate and transport the disaster relief materials to B in the shortest time1，B2And at the same time, the cost for transferring the maximum material in the shortest time is required to be the minimum.
Watch 1
As shown in the first table, the left side number of the 'I' in the table represents the transportation time from the emergency material supply point to the emergency material demand point, and the right side number of the 'I' represents the unit material transportation cost from the emergency material supply point to the emergency material demand point.
As shown in fig. 1, the emergency material scheduling method based on the primitive dual theory provided in this embodiment includes the following steps:
step I, determining an optimal matching scheme from each emergency material demand point to an emergency material supply point in the shortest time:
step I1., acquiring an emergency material allocation and transportation time matrix and a unit emergency material allocation and transportation cost matrix according to table 1;
time matrix of allocation and transportation
Allocating and transporting unit material cost matrix:
and step I2, determining an initial alternative optimal solution. According to the dispatching time matrix, the initial candidate optimal solution T1＝max{min(18，20)，min(21，18)，min(22，19)，min(18，21，22)，min(20，18，19)}＝19.
And step I3, as shown in the figure 3, establishing a minimum cost flow network model of the emergency material allocation and transportation related to the current optimal solution of the alternative.
Step I4. solves the least cost maximum flow in step I3 using a dual principle based approach. The solving process for obtaining the shortest time for dispatching the emergency materials in the embodiment is shown in fig. 4.
Step I5. finds the scheme for dispatching emergency supplies in the shortest time because there are two emergency supply receiving points, and the corresponding minimum cost flow chart has a flow rate of 2, which is equal to the number of supply receiving points. Namely supply point a1To receiving point B1To emergency supplies, supply points A2To receiving point B2And (5) adjusting emergency materials. The minimum time used at this time was 18 hours.
Step II, determining that the most emergency materials can be dispatched to the emergency material receiving point in the shortest time and the cost is the least, wherein the specific mode is as follows: according to the allocation and transportation emergency material allocation and transportation scheme within the shortest time obtained in the step I5, in combination with the allocation and transportation unit material cost matrix, a scheme that minimizes the total transportation cost within the shortest time is sought as an optimal allocation and transportation scheme, and the process is shown in fig. 5.
To this end, a minimum cost maximum flow of 2 has been obtained. Therefore, the minimum time for the emergency supplies to be dispatched from the supply points to each demand point in the minimum time is 18 hours. In the shortest time, the maximum emergency material quantity can be dispatched and transported, and the scheme of making the lowest point of total cost be material supply point A1To material receiving point B1Transporting the material 6t from the material supply point A2To material receiving point B25t of materials are transported, and the minimum transportation cost is 4 multiplied by 6+5 multiplied by 5 which is 49 thousand yuan.
And III, carrying out emergency material allocation and transportation according to the optimal allocation and transportation scheme determined in the step II.
The above embodiments are merely illustrative of the technical solutions of the present invention. The emergency material dispatching method based on the primitive dual theory according to the present invention is not limited only to the contents described in the above embodiments, but is subject to the scope defined by the claims. Any modification or supplement or equivalent replacement made by a person skilled in the art on the basis of this embodiment is within the scope of the invention as claimed in the claims.
Claims (3)
1. An emergency material scheduling method based on an original dual theory is characterized by comprising the following steps:
step I, determining an optimal matching scheme from each emergency material demand point to an emergency material supply point in the shortest time, wherein the optimal matching scheme comprises the following steps:
step I1., determining allocation and transportation time and unit material allocation and transportation cost from each emergency material supply point to each emergency material demand point, and acquiring an allocation and transportation time matrix and an allocation and transportation cost matrix;
step I2, determining the maximum value of the minimum element in each row and each column of elements in the dispatching time matrix as the current candidate optimal solution;
and step I3, establishing a minimum cost flow network model of the emergency material allocation and transportation related to the current optimal solution of the alternative:
step I3-1, constructing a bipartite graph of an emergency material supply point and an emergency material demand point, wherein only the transportation time t from the supply point I to the demand point j is reserved in the bipartite graphij＜t*Where i ∈ M, i ═ 1, 2.. M, M is the set of supply points, j ∈ N, j ═ 1, 2.. N, N is the set of demand points, t ∈ M, i ═ 1, 2.. N, N is the set of demand points*The current alternative optimal solution is obtained;
step I3-2, construct virtual start point s and virtual end point t, add edge
And edge
Step I3-3. defining the parameters of the edge as (c)ij，uij) Wherein c isijRepresenting the cost, u, of unit material transport from location i to location jijIs the capacity of the edge; opposite side
Let csi＝0，usiN is the number of emergency material receiving points; opposite side (i, j), i belongs to M, j belongs to N, and uij1 is ═ 1; opposite side (j, t), j ∈ N, such thatcjt＝0，ujt＝1；
Step I4., determining the maximum flow in the current network by using the optimal solution of the minimum cost flow model established based on the dual principle;
step I5., judging whether the flow reaches a given value, if the flow reaches the given value, finding the optimal matching scheme which completes the emergency material allocation and transportation in the shortest time; otherwise, updating the current alternative optimal solution according to the minimum value-added principle, updating the constructed minimum cost flow model for emergency material allocation and transportation, and returning to the step I4; updating the current alternative optimal solution rule according to the minimum value-added principle as follows:
T1＝T1+min{tij-T1|tij＞T1，i＝1，2，...，m；j＝1，2，...，n}，
in the formula, tijThe transportation time from an emergency material supply point i to an emergency material demand point j is shown;
step II, seeking the maximum transportation amount which can be dispatched from an emergency material supply point to an emergency material demand point in the shortest time according to the optimal matching scheme obtained in the step I5 and by combining a dispatching cost matrix, and taking the scheme which enables the total transportation cost to be minimum as the optimal dispatching scheme;
and III, carrying out emergency material allocation and transportation according to the optimal allocation and transportation scheme determined in the step II.
2. The original dual theory-based emergency material scheduling method according to claim 1, wherein: wherein, step I4 includes the following sub-steps:
step I4-1, order
A is an edge set in the minimum cost flow model; the source point S is labeled (0, + ∞); the point S ═ { S } < u > M,
when the flow v' is 0; note the book
Is set as
Backward edge set
Step I4-2: firstly, pair
Get
If not, if theta cannot be determined, the current flow is the maximum flow of the original network, and the optimal scheme of emergency material allocation and transportation is found;
order to
Step I4-3.pi-pj＝tijThen (i, j) is e.g. R;
step I4-4. for I e S, as (I, j) e R,
and xijWhen j is 0, the label (i, 1) is given; s ═ tauj }; such as (j, i) e R,
and xijIf > 0, j is marked (-i, 1);
②
at this time, the maximum flow in the network is allowed, and then the step I4-2 is returned; otherwise, if t epsilon is S, finding the amplifiable chain mu in R, and then executing the step I4-4;
increasing the flow
The flow becomes: v' + 1;
when the augmentation chain cannot be found, the maximum flow in the network is reached, and the optimal allocation and transportation scheme of the materials is found; otherwise, keeping the label of the source point S, deleting the labels of all the other nodes, updating the current alternative optimal solution, and adding the value T in the current minimum cost flow network1Then returns to step I4-2.
3. The original dual theory-based emergency material scheduling method according to claim 1, wherein: wherein, step II comprises the following substeps:
step II1, redefining relevant parameters of each side in the network corresponding to the optimal matching scheme according to the following rules:
let the supply quantity of the material supply point i be aiI is 1, 2,.. m, and the demand of the material demand point j is bjN. the parameters defining an edge are (c)ij，uij) Wherein c isijRepresenting the cost, u, of unit material transport from location i to location jijIs the capacity of the edge; opposite side
Let csi＝0，usi＝aiOpposite side (i, j), i belongs to M, j belongs to N, and u belongs toij＝min(ai，bj) (ii) a Opposite side (j, t), j ∈ N, let cjt＝0，ujt＝bj；
And step II2, solving the optimal solution of the network model in the step II1 by using a dual principle, determining the minimum cost maximum flow in the current network, and further determining the optimal dispatching scheme.
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| (m,n,k)指派问题的最小费用流模型及其算法;胡勇文等;《数学的实践与认知》;20170930;第1-3节 * |
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Effective date of registration: 20240218 Address after: No. B501-2, 5th Floor, Building B, High tech Entrepreneurship Service Center, No. 2 Zhuri Road, High tech Zone, Xiangyang City, Hubei Province, 441004 Patentee after: Hubei taodaji supply chain Co.,Ltd. Country or region after: China Address before: 441053 No. 296, Longzhong Road, Xiangcheng District, Xiangyang City, Hubei Province Patentee before: HUBEI University OF ARTS AND SCIENCE Country or region before: China |