CN113627644A - Robust optimization method for multi-type intermodal transportation path under uncertain transportation price - Google Patents

Robust optimization method for multi-type intermodal transportation path under uncertain transportation price Download PDF

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CN113627644A
CN113627644A CN202110724623.3A CN202110724623A CN113627644A CN 113627644 A CN113627644 A CN 113627644A CN 202110724623 A CN202110724623 A CN 202110724623A CN 113627644 A CN113627644 A CN 113627644A
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张永
陈丹丹
周博见
窦闻
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Abstract

The invention provides a robust optimization method of a multi-mode intermodal transportation path under uncertain transportation prices, which comprises the steps of establishing a transportation path optimization model and constraint conditions of an objective function Z under certain conditions; then, converting into a target function under uncertain parameters, and constructing a model; and finally, obtaining a robust model, solving the robust model, analyzing the sensitivity of parameters, and determining the optimal solution of the model. The method comprises the steps of converting a multimodal transport path optimization basic model containing uncertain transport price parameters into a mixed integer linear programming model containing robust level regulation and control parameters by using a robust optimization theory, taking minimized transport cost as a target function, and solving the model and analyzing the sensitivity of the parameters to obtain an optimal path.

Description

Robust optimization method for multi-type intermodal transportation path under uncertain transportation price
Technical Field
The invention belongs to the technical field of multi-type intermodal transportation paths, and particularly relates to a robust optimization method of the multi-type intermodal transportation paths under the condition of uncertain transportation prices.
Background
For freight agency enterprises, planning of multi-mode intermodal transportation paths is a very important work, when path planning is carried out, transportation prices of different transportation modes on each transportation section in a transportation network are a key factor, the selection of the transportation modes and the transportation sections is influenced by the price, and the transportation efficiency and the transportation time are directly related to the transportation modes and the transportation sections.
The existing optimization researchers for the multimodal transportation path are numerous and mainly divided into two categories, namely path optimization under a determined condition and path optimization under an uncertain condition. The path optimization under the determined situation is mainly divided into single-objective optimization for minimizing transportation cost and transportation time and multi-objective path optimization for minimizing both transportation time and transportation cost, and in the multi-objective path optimization, some scholars consider the influence on the environment and add an environmental objective for minimizing carbon emission. In the path optimization under the uncertain condition, most research contents are concentrated on the aspects of uncertain transportation time and uncertain transportation demand, and the uncertain research on transportation prices is not much.
Disclosure of Invention
The purpose of the invention is as follows: in order to study the problem of transportation path optimization in situations where the transportation price is uncertain. Based on the current situation of optimization research of the multi-type intermodal transportation path, from the perspective of freight agent enterprises, the invention provides a robust optimization method of the multi-type intermodal transportation path under uncertain transportation prices, which comprises the following steps:
step (1): establishing a transport path optimization model and constraint conditions of an objective function Z under a determined condition, wherein the objective function Z is the minimum value of the sum of the total transport cost of a road section in actual transport and the total transfer cost generated when the freight transport mode conversion occurs in a multi-mode intermodal network node, and a formula 1-1 of the objective function Z is as follows:
Figure BDA0003138063870000011
wherein, A: a set of multimodal transport paths; m: a multimodal transportation mode set; tr: multi-type connectorTransporting the network transportation intermediate node; i. j: nodes in a multimodal transport network; k. l is a transportation mode in the multi-mode intermodal transportation network;
Figure BDA0003138063870000012
unit transportation cost of transportation mode m on route (i, j);
Figure BDA0003138063870000013
a decision variable having a value of 0 or 1, indicating whether the cargo is transported on the route (i, j) using the transport mode m;
Figure BDA0003138063870000014
transport distance of transport mode m on path (i, j), Q: the total amount of containers transporting goods in the network is ton;
Figure BDA0003138063870000021
a unit transit cost from transit mode k to transit mode I for node I in the transit network; y isi kl: a decision variable with a value of 0 or 1 represents whether the goods are converted from the transportation mode k to the transportation mode I at the transportation node I;
step (2): describing the transportation cost parameters under the condition that the transportation price is uncertain for the target function Z in the step (1), and adjusting a robust optimization model by setting the disturbance of a parameter gamma, wherein the value range of gamma is [0, n]N represents the total number of parameters of uncertain unit transportation cost in the network, when at most 1 unit transportation cost in the multimodal transportation network changes in the interval, and the remaining confirmed transportation cost is disturbed by one transportation cost
Figure BDA0003138063870000022
Then, the robust solution is still a feasible solution;
Figure BDA0003138063870000023
a mean or conventional value representing the unit transportation cost of the transportation mode m on the route (i, j);
Figure BDA0003138063870000024
an uncertainty level representing a unit transportation cost of the transportation mode m on the route (i, j);
and (3): when a robust optimization model is established, firstly, carrying out equivalent change on an original target function Z, converting uncertain parameters in the target function into uncertain parameters in a constraint, specifically, firstly, minimizing a target function min Z: conversion to the maximum objective function max (-Z); then set ZtrConverting the value to obtain the target function max Z through a conversion formulatr
Figure BDA0003138063870000025
Finally, adjusting through adjusting the parameter gamma and the problem G to obtain a final robust optimization model, wherein a formula 1-2 is as follows:
Figure BDA0003138063870000026
problem G
Figure BDA0003138063870000027
Wherein, S: representing a multi-mode intermodal transportation path set under uncertain conditions;
Figure BDA0003138063870000028
a decision variable representing the transportation of the goods on the path (i, j) using the transportation mode m under uncertain conditions;
Figure BDA0003138063870000029
aid decision variables for the transport of goods on the path (i, j) using the transport mode m,
Figure BDA0003138063870000031
and lambda is a variable and a parameter introduced by robustness;
and (4): and (4) determining the optimal solution of the model by solving the model in the step (3) and analyzing the sensitivity of the parameters.
In the step (1), the constraint condition of the objective function Z is as follows:
Figure BDA0003138063870000032
Figure BDA0003138063870000033
Figure BDA0003138063870000034
Figure BDA0003138063870000035
Figure BDA0003138063870000036
Figure BDA0003138063870000037
Figure BDA0003138063870000038
wherein, h: nodes in a multimodal transport network; o: starting a multi-type intermodal transportation network; d: a multi-mode intermodal transportation network terminal; i: connecting the node i and the forward and backward node set thereof;
Figure BDA0003138063870000039
a decision variable with a value of 0 or 1 indicating whether the cargo is transported on the route (h, i) using the transport mode m;
Figure BDA00031380638700000310
a decision variable with a value of 0 or 1 indicating whether the cargo is transported on the route (I, j) using the transport mode I;
Figure BDA00031380638700000311
a decision variable, valued as 0 or 1, indicating whether the cargo is transported on the route (h, i) using the transport mode k; mI: a set of transportation modes connecting the node i and the forward and backward nodes thereof;
Figure BDA00031380638700000312
a transport speed of the transport mode m on the path (i, j);
Figure BDA00031380638700000313
the unit transfer time for transferring the transport mode k to the transport mode I at the transport node I; t: total freight transit time limit; the formula 1-3 represents the balance of the inlet and outlet flow of the intermediate node of the multi-type intermodal network; formulas 1-4 and 1-5 represent the logical relationship of the multi-modal intermodal network nodes; formulas 1-6 show that for any intermediate node of the multi-mode intermodal network, the times of transportation mode conversion are not more than 1; formulas 1-7 indicate that only one mode of transportation can be used to transport containers on any section of the multimodal transportation; formulas 1-8 indicate that no transition in transport mode occurs for the start and end points of the multimodal transport network; equations 1-9 show that the overall multimodal transport time meets fixed upper limit requirements.
The parameter description in the step (2) specifically comprises the following steps: by setting the unit transportation cost on the route (i, j) of the transportation mode m
Figure BDA0003138063870000041
Is in a bounded and symmetrical interval;
Figure BDA0003138063870000042
wherein,
Figure BDA0003138063870000043
represents the mean value of the unit transportation cost on the path (i, j) of the transportation mode m,
Figure BDA0003138063870000044
an uncertainty level representing unit transportation cost, setting:
Figure BDA0003138063870000045
then set up
Figure BDA0003138063870000046
Representing a set of uncertain parameters in a robust optimization.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the method adopts a robust optimization theory to convert a multimodal transport path optimization basic model containing uncertain transport price parameters into a mixed integer linear programming model with minimized transport cost as a target function and robust horizontal regulation and control parameters, and obtains an optimal path by solving the model and analyzing the sensitivity of the parameters.
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Fig. 1 is a schematic diagram of a node network structure according to an embodiment of the present invention.
FIG. 2 shows the result of uncertain cost data at different robustness levels according to an embodiment of the present invention.
FIG. 3 is a graph of total transportation cost data results for different robustness levels according to an embodiment of the present invention.
Fig. 4 is a result of total transportation cost data under an uncertain road section set according to an embodiment of the present invention.
Fig. 5 is an uncertain cost data result under an uncertain road segment set according to an embodiment of the present invention.
FIG. 6 shows the result of uncertain cost data under different perturbation ranges according to an embodiment of the present invention.
Detailed Description
The following examples are given to further illustrate the embodiments of the present invention. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The invention provides a robust optimization method of a multi-type intermodal transportation path under uncertain transportation prices, which comprises the following steps:
step (1): establishing a transport path optimization model and constraint conditions of an objective function Z under a determined condition, wherein the objective function Z is the minimum value of the sum of the total transport cost of a road section in actual transport and the total transfer cost generated when the freight transport mode conversion occurs in a multi-mode intermodal network node, and a formula 1-1 of the objective function Z is as follows:
Figure BDA0003138063870000051
wherein, A: a set of multimodal transport paths; m: a multimodal transportation mode set; tr: the multi-mode intermodal network transports the intermediate node; i. j: nodes in a multimodal transport network; k. l is a transportation mode in the multi-mode intermodal transportation network;
Figure BDA0003138063870000052
unit transportation cost of transportation mode m on route (i, j);
Figure BDA0003138063870000053
a decision variable having a value of 0 or 1, indicating whether the cargo is transported on the route (i, j) using the transport mode m;
Figure BDA0003138063870000054
transport distance of transport mode m on path (i, j), Q: the total amount of containers transporting goods in the network is ton;
Figure BDA0003138063870000055
a unit transit cost from transit mode k to transit mode I for node I in the transit network; y isi kl: a decision variable with a value of 0 or 1, which indicates whether the goods are converted from the transportation mode k to the transportation at the transportation node iA input mode I;
step (2): describing the transportation cost parameters under the condition that the transportation price is uncertain for the target function Z in the step (1), and adjusting a robust optimization model by setting the disturbance of a parameter gamma, wherein the value range of gamma is [0, n]N represents the total number of parameters of uncertain unit transportation cost in the network, when at most gamma unit transportation cost in the multimodal transportation network changes in the interval, and the left determined transportation cost is disturbed by one transportation cost
Figure BDA0003138063870000056
Then, the robust solution is still a feasible solution;
Figure BDA0003138063870000057
a mean or conventional value representing the unit transportation cost of the transportation mode m on the route (i, j);
Figure BDA0003138063870000058
an uncertainty level representing a unit transportation cost of the transportation mode m on the route (i, j);
and (3): when a robust optimization model is established, firstly, carrying out equivalent change on an original target function Z, converting uncertain parameters in the target function into uncertain parameters in a constraint, specifically, firstly, minimizing a target function min Z: conversion to the maximum objective function max (-Z); then set ZtrConverting the value to obtain the target function max Z through a conversion formulatr
Figure BDA0003138063870000061
Finally, adjusting through adjusting the parameter gamma and the problem G to obtain a final robust optimization model, wherein a formula 1-2 is as follows:
Figure BDA0003138063870000062
problem G
Figure BDA0003138063870000063
Wherein, S: representing a multi-mode intermodal transportation path set under uncertain conditions;
Figure BDA0003138063870000064
a decision variable representing the transportation of the goods on the path (i, j) using the transportation mode m under uncertain conditions;
Figure BDA0003138063870000065
aid decision variables for the transport of goods on the path (i, j) using the transport mode m,
Figure BDA0003138063870000066
and lambda is a variable and a parameter introduced by robustness;
and (4): and (4) determining the optimal solution of the model by solving the model in the step (3) and analyzing the sensitivity of the parameters.
In the step (1), the constraint condition of the objective function Z is as follows:
Figure BDA0003138063870000067
Figure BDA0003138063870000068
Figure BDA0003138063870000069
Figure BDA00031380638700000610
Figure BDA0003138063870000071
Figure BDA0003138063870000072
Figure BDA0003138063870000073
wherein, h: nodes in a multimodal transport network; o: starting a multi-type intermodal transportation network; d: a multi-mode intermodal transportation network terminal; i: connecting the node i and the forward and backward node set thereof;
Figure BDA0003138063870000074
a decision variable with a value of 0 or 1 indicating whether the cargo is transported on the route (h, i) using the transport mode m;
Figure BDA0003138063870000075
a decision variable with a value of 0 or 1 indicating whether the cargo is transported on the route (I, j) using the transport mode I;
Figure BDA0003138063870000076
a decision variable, valued as 0 or 1, indicating whether the cargo is transported on the route (h, i) using the transport mode k; mI: a set of transportation modes connecting the node i and the forward and backward nodes thereof;
Figure BDA0003138063870000077
a transport speed of the transport mode m on the path (i, j); t isi kl: the unit transfer time for transferring the transport mode k to the transport mode I at the transport node I; t: total freight transit time limit; the formula 1-3 represents the balance of the inlet and outlet flow of the intermediate node of the multi-type intermodal network; formulas 1-4 and 1-5 represent the logical relationship of the multi-modal intermodal network nodes; formulas 1-6 show that for any intermediate node of the multi-mode intermodal network, the times of transportation mode conversion are not more than 1; formulas 1-7 indicate that only one mode of transportation can be used to transport containers on any section of the multimodal transportation; equations 1-8 indicate that for the start and end points of the multimodal transport network, no occurrences occurSwitching the transportation mode; equations 1-9 show that the overall multimodal transport time meets fixed upper limit requirements.
The parameter description in the step (2) specifically comprises the following steps: by setting the unit transportation cost on the route (i, j) of the transportation mode m
Figure BDA0003138063870000078
Is in a bounded and symmetrical interval;
Figure BDA0003138063870000079
wherein,
Figure BDA00031380638700000710
represents the mean value of the unit transportation cost on the path (i, j) of the transportation mode m,
Figure BDA00031380638700000711
an uncertainty level representing unit transportation cost, setting:
Figure BDA0003138063870000081
then set up
Figure BDA0003138063870000082
Representing a set of uncertain parameters in a robust optimization.
Example 1
In order to verify the validity of the above model, the following description and verification are made by specific examples. The system specifically comprises 35 network nodes and 69 transportation road sections, wherein three transportation modes of roads, railways and water transportation are involved in the network, and the specific structure is shown in figure 1.
The data in table 1 are obtained by obtaining the existing market of the Chinese transportation industry and making statistics on the transportation price and the transportation distance of railways, roads and water paths.
TABLE 1 cost and time of transshipment at each transportation node
Figure BDA0003138063870000083
Combining the current transportation situation, the average speed of railway freight is 65Km/h, the average speed of road freight is 85Km/h, the average speed of waterway freight is 25Km/h, the total freight time is limited to 60h, the freight volume is 1000 tons, the total transportation cost under determined regulation is 35721 yuan, the total transportation time is 41.32h, the transportation mode is all water transportation, and the transportation path is 1-4-5-13-16-21-27-28-35.
For the model provided by the invention, sensitivity analysis is carried out on the parameters, the sensitivity analysis of the parameters with different robustness levels is uncertain in cost and total transportation cost, and the result data is shown in FIGS. 2-3; analyzing the sensitivity of the uncertain road section set to analyze uncertain cost and total transportation cost, and obtaining result data shown in figures 4-5; the sensitivity analysis of the different perturbation ranges does not determine the cost, and the result data is shown in fig. 6.
According to the embodiment, a multi-type transport network calculation example comprising 35 transport nodes and 69 transport road sections is established, an optimal solution of a model is obtained by adopting an accurate solution, and through model solution and parameter sensitivity analysis, when transport price disturbance occurs in the multi-type transport network, the increase of the total transport cost can be found when the transport price disturbance occurs in the multi-type transport network. The higher the robustness level requirement, the higher the uncertain transportation costs of the multimodal transport network will be, leading to a higher increase in the total transportation costs, which also increases with the increase in the disturbance range. Compared with the change of the transportation scheme, the transportation network generally selects to increase the transportation cost to resist the disturbance of the transportation price, and the original transportation scheme is selected as much as possible to be more suitable.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (3)

1. A robust optimization method for a multimodal transportation route under uncertain transportation prices is characterized by comprising the following steps:
step (1): establishing a transport path optimization model and constraint conditions of an objective function Z under a determined condition, wherein the objective function Z is the minimum value of the sum of the total transport cost of a road section in actual transport and the total transfer cost generated when the freight transport mode conversion occurs in a multi-mode intermodal network node, and a formula 1-1 of the objective function Z is as follows:
Figure FDA0003138063860000011
wherein, A: a set of multimodal transport paths; m: a multimodal transportation mode set; tr: the multi-mode intermodal network transports the intermediate node; i. j: nodes in a multimodal transport network; k. l is a transportation mode in the multi-mode intermodal transportation network;
Figure FDA0003138063860000012
unit transportation cost of transportation mode m on route (i, j);
Figure FDA0003138063860000013
a decision variable having a value of 0 or 1, indicating whether the cargo is transported on the route (i, j) using the transport mode m;
Figure FDA0003138063860000014
transport distance of transport mode m on path (i, j), Q: the total amount of containers transporting goods in the network is ton;
Figure FDA0003138063860000015
node i in the transport network is transported from transport mode kThe unit transfer cost of the input mode l; y isi kl: a decision variable with a value of 0 or 1 represents whether the goods are converted from the transportation mode k to the transportation mode l at the transportation node i;
step (2): describing the transportation cost parameters under the condition that the transportation price is uncertain for the target function Z in the step (1), and adjusting a robust optimization model by setting the disturbance of a parameter gamma, wherein the value range of gamma is [0, n]N represents the total number of parameters of uncertain unit transportation cost in the network, when at most gamma unit transportation cost in the multimodal transportation network changes in the interval, and the left determined transportation cost is disturbed by one transportation cost
Figure FDA0003138063860000016
Then, the robust solution is still a feasible solution;
Figure FDA0003138063860000017
a mean or conventional value representing the unit transportation cost of the transportation mode m on the route (i, j);
Figure FDA0003138063860000018
an uncertainty level representing a unit transportation cost of the transportation mode m on the route (i, j);
and (3): when a robust optimization model is established, firstly, carrying out equivalent change on an original objective function Z, converting uncertain parameters in the objective function into uncertain parameters in a constraint, and specifically, firstly, converting a minimized objective function min Z into a maximized objective function max (-Z); then set ZtrConverting the value to obtain the target function max Z through a conversion formulatr
Figure FDA0003138063860000021
Finally, adjusting through adjusting the parameter gamma and the problem G to obtain a final robust optimization model, wherein a formula 1-2 is as follows:
Figure FDA0003138063860000022
problem G
Figure FDA0003138063860000023
Wherein, S: representing a multi-mode intermodal transportation path set under uncertain conditions;
Figure FDA0003138063860000024
a decision variable representing the transportation of the goods on the path (i, j) using the transportation mode m under uncertain conditions;
Figure FDA0003138063860000025
aid decision variables for the transport of goods on the path (i, j) using the transport mode m,
Figure FDA0003138063860000026
Figure FDA0003138063860000027
and lambda is a variable and a parameter introduced by robustness;
and (4): and (4) determining the optimal solution of the model by solving the model in the step (3) and analyzing the sensitivity of the parameters.
2. The robust optimization method of multimodal transportation routes under uncertainty of transportation prices according to claim 1, characterized by: in the step (1), the constraint condition of the objective function Z is as follows:
Figure FDA0003138063860000028
Figure FDA0003138063860000029
Figure FDA00031380638600000210
Figure FDA00031380638600000211
Figure FDA00031380638600000212
Figure FDA0003138063860000031
Figure FDA0003138063860000032
wherein, h: nodes in a multimodal transport network; o: starting a multi-type intermodal transportation network; d: a multi-mode intermodal transportation network terminal; i, connecting a node I and a forward and backward node set thereof;
Figure FDA0003138063860000033
a decision variable with a value of 0 or 1 indicating whether the cargo is transported on the route (h, i) using the transport mode m;
Figure FDA0003138063860000034
a decision variable with a value of 0 or 1 indicating whether the goods are transported on the route (i, j) using the transport mode l;
Figure FDA0003138063860000035
a decision variable, valued as 0 or 1, indicating whether the cargo is transported on the route (h, i) using the transport mode k; mI: a set of transportation modes connecting the node i and the forward and backward nodes thereof;
Figure FDA0003138063860000036
a transport speed of the transport mode m on the path (i, j); t isi kl: the unit transfer time for changing the transport mode k into the transport mode l at the transport node i; t: total freight transit time limit; the formula 1-3 represents the balance of the inlet and outlet flow of the intermediate node of the multi-type intermodal network; formulas 1-4 and 1-5 represent the logical relationship of the multi-modal intermodal network nodes; formulas 1-6 show that for any intermediate node of the multi-mode intermodal network, the times of transportation mode conversion are not more than 1; formulas 1-7 indicate that only one mode of transportation can be used to transport containers on any section of the multimodal transportation; formulas 1-8 indicate that no transition in transport mode occurs for the start and end points of the multimodal transport network; equations 1-9 show that the overall multimodal transport time meets fixed upper limit requirements.
3. The robust optimization method of multimodal transportation routes under uncertainty of transportation prices according to claim 2, characterized by: the parameter description in the step (2) specifically comprises the following steps: by setting the unit transportation cost on the route (i, j) of the transportation mode m
Figure FDA0003138063860000037
Is in a bounded and symmetrical interval;
Figure FDA0003138063860000038
wherein,
Figure FDA0003138063860000039
represents the mean value of the unit transportation cost on the path (i, j) of the transportation mode m,
Figure FDA00031380638600000310
an uncertainty level representing unit transportation cost, setting:
Figure FDA00031380638600000311
then set up
Figure FDA0003138063860000041
Representing a set of uncertain parameters in a robust optimization.
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CN114742502A (en) * 2022-04-14 2022-07-12 中国石油大学(北京) Finished oil pipeline conveying coordination optimization system

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