陳　雷　林柏梁　溫旭紅　王　龍　李　建

(1北京交通大學(xué)交通運輸學(xué)院, 北京 100044)(2中國鐵路經(jīng)濟規(guī)劃研究院, 北京 100038)

低碳運輸下陸路運輸系統(tǒng)貨流轉(zhuǎn)移及流量分配綜合優(yōu)化

陳雷1林柏梁1溫旭紅1王龍2李建1

(1北京交通大學(xué)交通運輸學(xué)院, 北京 100044)(2中國鐵路經(jīng)濟規(guī)劃研究院, 北京 100038)

摘要:基于公路網(wǎng)和鐵路網(wǎng)在貨物運輸過程中的不同特點,研究了可以實現(xiàn)低碳交通運輸目標的陸路運輸系統(tǒng)貨流轉(zhuǎn)移及流量分配的綜合優(yōu)化問題,并構(gòu)建了相應(yīng)的0-1規(guī)劃模型．該模型以包含碳排放成本在內(nèi)的陸路運輸總成本最小化為目標函數(shù),約束條件設(shè)置為節(jié)點的轉(zhuǎn)移能力限制、公路運輸弧段和鐵路運輸弧段的通過能力限制以及鐵路網(wǎng)流量分配的樹形徑路特點等.通過算例對該模型進行驗證．結(jié)果表明:鑒于鐵路運輸在成本和碳排放方面的優(yōu)勢,公路網(wǎng)貨流轉(zhuǎn)移至鐵路后,可使包含碳排放成本在內(nèi)的陸路運輸系統(tǒng)總成本大大降低;通過對鐵路網(wǎng)貨流進行重新分配,優(yōu)化了鐵路貨流的運輸路徑,提高了鐵路運輸能力的利用率．

關(guān)鍵詞:陸路運輸系統(tǒng);綜合優(yōu)化;貨流轉(zhuǎn)移;流量分配;碳排放

隨著全球經(jīng)濟的快速發(fā)展,溫室氣體污染日趨嚴重,發(fā)展綠色交通運輸已經(jīng)成為各國政府的共識．陸路運輸系統(tǒng)承擔(dān)了較大比例的貨物發(fā)送量和周轉(zhuǎn)量,且產(chǎn)生了大量的碳排放．在陸路運輸系統(tǒng)中,公路方式的單位碳排放量通常是鐵路的數(shù)倍之多,若將公路貨流轉(zhuǎn)移至鐵路運輸必然可以節(jié)約大量能源、減少交通運輸業(yè)的碳排放量,對緩解日益嚴重的溫室效應(yīng)具有重要意義．

目前,關(guān)于考慮碳排放的貨流轉(zhuǎn)移研究主要體現(xiàn)為綜合運輸和多式聯(lián)運兩大類[1-6]．在貨流分配方面,眾多學(xué)者對公路網(wǎng)貨流分配[7-8]和鐵路網(wǎng)貨流分配[9-16]進行了研究．然而,直接針對陸路運輸系統(tǒng)內(nèi)貨流轉(zhuǎn)移的研究比較少見．陸路運輸系統(tǒng)內(nèi)貨流轉(zhuǎn)移和流量分配是相互影響的,對兩者進行綜合優(yōu)化的文獻更是罕見．因此,本文將陸路運輸系統(tǒng)內(nèi)貨流轉(zhuǎn)移及流量分配問題進行綜合優(yōu)化,以達到實現(xiàn)低碳交通運輸?shù)哪康模?/p>

1模型構(gòu)建

1.1假設(shè)條件

構(gòu)建模型時,首先進行如下假設(shè):① 借鑒多式聯(lián)運的思想對陸路運輸系統(tǒng)的貨運節(jié)點進行擴展,且假定陸路運輸系統(tǒng)內(nèi)公路網(wǎng)和鐵路網(wǎng)是平行的．② 不同于鐵路運輸?shù)奶囟◤铰?公路貨車司機對運輸路徑的選擇具有較高的自主性,且一般傾向于運輸距離較短的路徑,因此對于任意2個公路節(jié)點之間的貨流,假設(shè)其選擇最短徑路進行運輸．③ 借鑒多商品流思想,假設(shè)任意2個公路節(jié)點之間可能存在多種不同品類的貨流,并假設(shè)對于任何一股公路網(wǎng)貨流,不存在部分轉(zhuǎn)移的情況．④ 利用碳稅對碳排放成本進行描述．

1.2目標函數(shù)及約束條件

鑒于鐵路在運輸成本和碳排放方面的優(yōu)勢,本文擬通過將公路網(wǎng)貨流轉(zhuǎn)移至鐵路網(wǎng)的方式,達到降低陸路運輸系統(tǒng)碳排放的目標．具體就一股公路網(wǎng)貨流而言,在貨流起始節(jié)點至終到節(jié)點的運輸過程中,可以分為3個階段:① 該股公路網(wǎng)貨流需經(jīng)由公路運輸方式運輸至轉(zhuǎn)運節(jié)點;② 在轉(zhuǎn)運節(jié)點內(nèi)部,通過換裝等作業(yè)將貨物轉(zhuǎn)移至鐵路;③ 按照鐵路特有的貨運組織方式送達至終到節(jié)點．因此,本文將按照這3個階段分別對模型進行描述,最后給出綜合優(yōu)化模型．

1) 公路網(wǎng)貨流轉(zhuǎn)移時,首先需要選擇相應(yīng)的轉(zhuǎn)移節(jié)點,然后將這部分貨流經(jīng)由公路運輸至轉(zhuǎn)移節(jié)點．這一過程中公路網(wǎng)的運輸成本和運輸碳排放成本為

(1)

對于公路節(jié)點i與公路節(jié)點j之間的第k類原始貨流,最多可以在除終到公路節(jié)點j以外的其他節(jié)點中選擇一個進行流量轉(zhuǎn)移,這一約束條件可以表示為

(2)

轉(zhuǎn)移方案確定后,公路網(wǎng)實際貨流經(jīng)由最短路徑運輸至轉(zhuǎn)移節(jié)點．然而在轉(zhuǎn)移過程中,當某一股公路原始貨流在其近似平行徑路上節(jié)點進行轉(zhuǎn)移,恰好其近似平行徑路上各公路節(jié)點之間的貨流沒有轉(zhuǎn)移時,就會出現(xiàn)該股貨流近似平行徑路上2個公路節(jié)點的實際貨流量大于原始貨流量的情況．故流量轉(zhuǎn)移時,必須滿足其所經(jīng)由的公路運輸弧段的能力限制,即

(3)

2) 在轉(zhuǎn)運過程中,也將產(chǎn)生轉(zhuǎn)運成本和轉(zhuǎn)運碳排放成本,其計算公式為

(4)

Fi≤di?i∈V

(5)

式中,di為節(jié)點i所能承受的最大貨流轉(zhuǎn)移量．

3) 貨流轉(zhuǎn)移后,鐵路網(wǎng)的貨流結(jié)構(gòu)將發(fā)生變化,需對鐵路網(wǎng)流量進行再分配．該過程中的運輸成本和運輸碳排放成本為

(6)

(7)

(8)

此外,在貨流轉(zhuǎn)移后,鐵路網(wǎng)流量分配必須滿足弧段能力限制,即

(9)

綜上所述,以Z1,Z2和Z3的總和最小化為目標函數(shù),以式(1)～(9)為約束條件,即可構(gòu)建考慮碳排放的陸路運輸系統(tǒng)內(nèi)貨流轉(zhuǎn)移及流量分配綜合優(yōu)化模型,即

minZ=Z1+Z2+Z3

(10)

s.t.式(1)～(9)

2算例分析

利用本文所構(gòu)建的模型對文獻[6]中的算例數(shù)據(jù)進行求解,計算時所需參數(shù)也參考文獻[6]取值．基于Lingo11.0平臺進行編程計算,經(jīng)過9 398 s的計算過程,得到的最優(yōu)化方案目標函數(shù)為1.817×109元,公路網(wǎng)貨流的轉(zhuǎn)移方案見表1．

優(yōu)化計算得到的貨流轉(zhuǎn)移后鐵路網(wǎng)貨流運輸徑路見表2．

由表1和表2可以看出,共有82股公路網(wǎng)貨流轉(zhuǎn)移至鐵路網(wǎng),18股鐵路網(wǎng)貨流進行了繞道運輸,最終方案中轉(zhuǎn)移總量達2.047×107t．為了驗證所提模型的合理性,本文利用Lingo11.0軟件對文獻[6]中的算例進行計算,得到的全局最優(yōu)解與文獻[6]的計算結(jié)果相同,說明文獻[6]利用粒子群算法也得到了全局最優(yōu)解．對這2個計算結(jié)果進行對比可知:① 文獻[6]中算例的目標函數(shù)值為2.239×109元,本文算例的目標函數(shù)值較文獻[6]

表1　公路網(wǎng)流量轉(zhuǎn)移方案

表2　鐵路網(wǎng)貨流運輸徑路

中的目標函數(shù)值降低了4.22×108元,說明利用所提模型更能實現(xiàn)整個陸路運輸系統(tǒng)社會物流成本的降低．② 與文獻[6]相比,本文算例中通過鐵路網(wǎng)貨流的重新分配,吸納了更多的公路貨流進行轉(zhuǎn)移,使得由公路網(wǎng)轉(zhuǎn)移至鐵路網(wǎng)的貨物總量增加了6×105t,從而進一步提高了陸路運輸系統(tǒng)中鐵路運輸能力的利用率．

3結(jié)語

本文研究了考慮碳排放的陸路運輸系統(tǒng)內(nèi)貨流轉(zhuǎn)移及流量分配的綜合優(yōu)化問題．通過構(gòu)建綜合優(yōu)化模型對該問題進行了描述,并通過算例進行驗證．優(yōu)化結(jié)果顯示,鑒于鐵路運輸在成本和碳排放方面的巨大優(yōu)勢,公路網(wǎng)貨流轉(zhuǎn)移至鐵路后,降低了整個陸路系統(tǒng)的社會物流成本．此外,流量轉(zhuǎn)移后通過鐵路網(wǎng)貨流的重新分配,可進一步提高鐵路運輸能力的利用率．下一步的主要工作為尋求計算效率更高的啟發(fā)式算法并對大規(guī)模實際案例進行求解．

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Integrated optimization of transfer of freight flow in land transportation system and transportation flow assignment based on low carbon emissions

Chen Lei1Lin Boliang1Wen Xuhong1Wang Long2Li Jian1

(1School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China) (2China Railway Economic and Planning Research Institute, Beijing 100038, China)

Abstract:Based on the different characteristics of highway and railway freight transportations, the integrated optimization of transfer of freight flow in the land transportation system and the transportation flow assignment was studied to achieve the goal of low carbon transportation, and the corresponding 0-1 mathematic model was put forward. The objective function of the proposed model was to minimize the total cost of the land transportation system including the cost of carbon emission. The constraints of the model were set as the transfer capacity limitation of the railway nodes, the transportation capacity limitation of highway and railway transportation arcs, and the tree-type routing characteristics of railway transportation flow assignment and so on. A numerical case was given to solve the proposed model. The results show that due to the advantages of rail transport in terms of cost and carbon emission, the total cost of the land transport system, including the cost of carbon emission, is greatly reduced after the transfer of freight flow. In addition, through the reassignment of freight flow of railway network, the transport paths are optimized and the utilization rate of the railway is improved.

Key words:land transportation system; integrated optimization; transfer of freight flow; transportation flow assignment; carbon emission

doi:10.3969/j.issn.1001-0505.2016.03.036

收稿日期:2015-12-03.

作者簡介:陳雷(1989—)，男，博士，講師；林柏梁(聯(lián)系人)，男，博士，教授，博士生導(dǎo)師，bllin@bjtu.edu.cn.

基金項目:國家自然科學(xué)基金資助項目(51378056).

中圖分類號:U292.32

文獻標志碼:A

文章編號:1001-0505(2016)03-0671-04

引用本文: 陳雷,林柏梁,溫旭紅,等.低碳運輸下陸路運輸系統(tǒng)貨流轉(zhuǎn)移及流量分配綜合優(yōu)化[J].東南大學(xué)學(xué)報(自然科學(xué)版),2016,46(3):671-674. DOI:10.3969/j.issn.1001-0505.2016.03.036.