基于时空网络的铁路空车调配动态优化模型

郑可心; 宋瑞; 李光晔

doi:10.3963/j.jssn.1674-4861.2021.02.018

基于时空网络的铁路空车调配动态优化模型

doi: 10.3963/j.jssn.1674-4861.2021.02.018

北京交通大学综合交通运输大数据应用技术交通运输行业重点实验室北京 100044

基金项目:

国家重点研发计划项目 2018YFB1201402

国家自然科学基金项目 62076023

中国国家铁路集团有限公司科技研究开发计划课题项目 P2019X004

详细信息

作者简介:
郑可心（1998—），硕士研究生. 研究方向：交通运输规划与管理.E-mail：19120973@bjtu.edu.cn

通讯作者:
宋瑞（1971—），博士，教授.研究方向：交通运输规划与管理.E-mail：rsong@bjtu.edu.cn

中图分类号: U292.3
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出版历程
- 收稿日期: 2020-10-03

An Optimization Model of Dynamic Allocation of Empty Railway Cars Based on Time-space Network

Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China

摘要

摘要: 为合理配置空车资源，研究了路局（公司）管内空车调配的动态优化问题。构建区分时段长度的时空网络，以准确描述车站作业能力的变化。借鉴运输问题（TP）的基本思想，通过引入空车供需约束，将动态空车调配问题转化为基于时空网络的多商品网络流问题。结合空车调配的特点，设置2组整数决策变量，将分界站排空与局（公司）管内配空分开考虑。设置0-1辅助变量构建车种代用约束。在此基础上，以总费用最小为目标，构建了空车调配动态优化的混合整数规划模型。以中国铁路昆明局集团有限公司管内空车调配为例，验证了模型的可行性与有效性。算例结果表明，与静态空车调配方法相比，构建的动态空车调配模型不仅降低了空车调配总成本，而且调配方案更加贴合实际。与现有动态空车调配方法相比，通过改变时空网络中时段的划分方式，降低了模型求解的复杂度，构建的模型在获取空车调配方案的同时能够更加直观的看出空车在不同时间的作业状态。
- 铁路运输 /
- 空车 /
- 动态优化 /
- 时空网络 /
- 车种代用 /
- 混合整数线性规划
Abstract: The paper studies the dynamic optimization of the empty car distribution within the railway administration (or company)to reasonably allocate empty cars. The time-space network with different periods is constructed to describe the changes in work capacities of railway stations. By referring to transportation problems, dynamic empty-car distribution is transformed into the multi-commodity network flow based on the time-space network by increasing the supply and demand constraints. Combining the characteristics of empty car distribution, the paper develops two sets of integer decision variables and considers discharging and assigning empty cars separately. 0-1 auxiliary variables are set to construct substitution constraints of car types. On this basis, a mixed-integer programming model for the dynamic optimization of empty-car distribution is constructed to minimize the total cost. The feasibility and effectiveness of the model are verified by taking empty-car distribution in Kunming railway administration as a case study. The results show that dynamic empty-car distribution is superior to static empty-car distribution in reducing the total cost and fitting the actual process. The complexity of solving the model is reduced by improving the time-space network compared with the existing methods of dynamic empty-car distribution. The model can obtain the scheme of empty-car distribution and check the operation status of empty cars at different times intuitively.
- railway transportation /
- empty cars /
- dynamic optimization /
- time-space network /
- model substitution of car types /
- mixed-integer linear programming

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图 1 时空网络的构建

Figure 1. Construction of the time-space network

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图 2 简化路网

Figure 2. Simplified road network

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图 3 时空网络

Figure 3. Time-space network

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图 4 空车调配方案

Figure 4. Solutions of empty-car distribution

下载: 全尺寸图片幻灯片

表 1 车站装车比重排序表

Table 1. List of loading proportions at stations

排序	单位名	装车比重/%	收人比重/%
1	王家营	10.141 7	13.212 8
2	读书铺	8.323 1	10.189 2
3	中谊村	07.906 2	07.504 2
4	昆明东	04.500 3	06.188 9
5	白塔村	04.462 2	06.509 7
6	红果	04.014 8	01.832 8
7	曲靖	03.803 3	04.188 6
8	柏果	03.650 0	02.317 4
9	宣威	03.245 9	01.709 2
10	盘关	03.057 3	00.320 4
11	平田	02.650 6	02.026 4
12	金马村	02.481 0	03.342 3
13	威舍	02.401 6	01.265 5
14	火铺	01.928 6	01.557 4
15	月亮田	01.818 0	01.933 3
16	大理东	01.743 4	05.253 4
17	禄丰	01.662 1	01.356 3
18	昆明西	01.654 7	01.915 6
19	陆良	01.653 8	01.655 6
20	珠江源	01.567 0	01.263 8

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表 2 空车需求站请求空车情况

Table 2. Requested conditions of stations demanding for empty cars

空车需求站	空车需求情况	货物种类	装运时间
柏果	罐车20车	石油	时段7
威舍	敞车30车	煤炭	时段8
陆良	敞车10车	煤炭	时段4
中谊村	棚车50车或敞车52车	粮食	时段5
大理东	敞车10车	煤炭	时段9
分界站宣威	棚车60车		时段8

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表 3 空车供给站有效空车数

Table 3. Effective number of empty cars of supply stations

空车供给站	有效空车数	卸空时段
红果	敞车80车、罐车30车	时段2
昆明东	敞车100车、棚车100车	时段2
读书铺	敞车50车、棚车60车	时段2
禄丰	敞车20车	时段5

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表 4 列车编组计划

Table 4. Formation of freight trains

发站	到站	列车种类	定期车次
昆明东	宣威	摘挂	22 608
宣威	曲靖	直通	22 617
曲靖	柏果	摘挂	45 307
红果	柏果	区段	45 305
曲靖	威舍	摘挂	45 316
昆明东	威舍	摘挂	37 008
昆明东	中谊村	摘挂	46 212
读书铺	禄丰	摘挂	51 781
读书铺	大理东	空车直达	51 981
禄丰	大理东	直通	51 987
读书铺	昆明东	区段	46 105
昆明东	宣威	直通	22 617

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表 5 模型求解结果

Table 5. Model solutions

供给节点	需求节点	空车数量/车	调配方案	车种
红果	柏果	20	C2-C3-C4-C5-C6-B7	罐车
红果	威舍	30	C2-C3-C4-C5-C6-G7-G8	敞车
昆明东	陆良	10	E2-H4	敞车
昆明东	中谊村	52	E2-I3-I4-I5	棚车
禄丰	大理东	10	J5-K8-K9	敞车
昆明东	宣威	48	E2-A4-A5-A6-A7-A8-A9	棚车
读书铺	宣威	12	F2-F3-F4-F5-F6-E7-A9	棚车

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表 6 不同策略下调配结果对比

Table 6. Result comparison under different strategies

策略		供给节点	需求节点	空车数量/车	车种	总成本/元
静态多阶段优化	阶段1	昆明东	陆良	10	敞车	100 450
		读书铺	中谊村	52	棚车
		红果	柏果	20	罐车
	阶段2	红果	威舍	30	敞车
		禄丰	大理东	10	敞车
		昆明东	宣威	60	棚车
		红果	柏果	20	罐车
动态优化		红果	威舍	30	敞车	99 560
		昆明东	陆良	10	敞车
		昆明东	中谊村	52	棚车
		禄丰	大理东	10	敞车
		昆明东	宣威	48	棚车
		读书铺	宣威	12	棚车

下载: 导出CSV

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