Routing Hazmat Multimodal Transportation Based on CVaR Assessment

Transcription

1 207 Asia-Pacific Engineering and Technology Conference (APETC 207) ISBN: outing azmat Multimodal Transportation Based on CVa Assessment Liping Liu, ongxue Du, Shuxia Li, Tun Fan and Yifan Wu ABSTACT Multimodal plays a more significant role in long distances transportation of hazardous materials, while there haven t been systemic risk evaluation methods to hazmat multimodal transportation. Considering that the risk of hazmat transportation has the characteristics of low probability and high consequence, this paper studies how CVa applied to the routing optimization of hazmat multimodal transportation while CVa could better compute the tail loss of risk. We build a multimodal hazmat transportation risk assessment model in this paper, and prove its effectiveness by a computational study. esults show that the proposed model can provide a CVa optimal transportation path to hazmat multimodal transportation in realistic. INTODUCTION In recent years, the demand for hazmat has a rapid growth. Apparent in 200, two-chlorine demand reached tons, in spite of the influence of the financial crisis of 2008, compared with tons in 2005, and grew by almost half []. At present, the multimodal transport system has also been gradually perfected. For example, Jincheng trans logistics is one of the largest international logistics enterprises in China, has built from inland China to the surrounding countries. Under the background of the increasingly perfect transportation network, how to design the lowest risk path is what we should pay more attention to. Considering the risk of hazmat transportation has obvious fat tail (low probability and high consequences), this paper applies CVa to risk assessment of hazmat multimodal transportation, where CVa is seen as risk measurement tools to optimize the portfolio of financial market, can better capture the investment risk in extreme Liping Liu, ongxue Du *, Shuxia Li, Tun Fan, Yifan Wu * Institute of Operation and Supply Chain Management, esearch Center of Virtual Business, Department of Management Science and Engineering, School of Business, East China University of Science and Technology, S, China Corresponding author: ongxue Du, @qq.com, Yifan Wu, yifanwu@ecust.edu.cn 208

2 market conditions, and compute the tail loss. In recent years it has been applied to the risk assessment in all walks of life. EVIEWS The liquid process of hazmat transportation makes it difficult to forecast the risk. Scholars have studied in many fields with obective of minimizing transportation cost or risk, considering constrains of time or transportation modes selection at the same time [2]. According to statistics, in 2007, million tons of dangerous goods by the multimodal transport system in America [3]. Shuai et al. summarize literatures in recent years, points out that the railway and multimodal transport are lower risk of transport modes, and points out that establishing adaptive multimodal transport risk assessment model based on CVa is the research direction of the future [4]. CVa was first used in the financial sector to optimize portfolio [5]. Based on the good nature of CVa used in a financial portfolio, Kwon et al. [6] mainly studied the application of Va and CVa in hazmat transport, assume the probability of risk occurrence and consequences as a function of time. The above literatures laid a solid foundation to the study of CVa optimization in hazmat transport. Solving CVa model is now a difficult problem, Meng et al. [7] studied Multistage dynamic CVa problem, and equal the whole decision-making process as CVa overla. Meng et al. [8] presented Sample mean smoothing approximation method to solve the single and mixed CVa optimal problems, can be extended to solve other smooth function, combined with smooth method and sample mean approximation method. MODEL BUILDING Model of Single Transportation Mode of azmat Based on CVa Assumes the continuous random variables, the probability density function indicated as p( ) and the loss function indicated as f ( x, ); so, the cumulative distribution function could be described as follows when f ( x, ) less than a constant y, ( x, y) p( ) d y () f ( x, ) y y ( x) min y : ( x, y) y (x) represents a Va value. At the same time, considering the following function, ( x) ( ) f( x, ) p( ) d (3) (2) f ( x, ) y ( x) ( x) represents a CVa value. For convenient calculation, consider the following equivalent problem. But in real life, the fundamental of risk measurement is each section from origin to destination. Therefore, the established model is discrete. F ( x, y) y f x, y p( )d (4) 209

3 Defined G ( N, E) as transportation networks, N is the set of nodes to connect traffic lines; and E is the set of traffic lines. For a certain origin-destination (OD)pair, there are many connecting paths l L, each path l consists of many l segments A, the consequences of risk occurrence is C and the corresponding probability of risk-happening is p ; The conditional value at risk can be expressed as (6). x indicates whether choose a path for transport. st.. F ( xy, ) y c y px (5) l min CVa min F( x, y) y P [c y] x {x : x, x, x x,x {0,}, (i, ) A} i io, N in, D N in (6) l A (7) isk Assessment Model of Multimodal Transport Based on the CVa Model assumptions and parameters introduction. There is a pair of OD in the traffic network, there is highway or railway can be chosen between two cities, supplier will take risk as the main consideration to path choices. A multimodal transportation network G (N,E), and N (N,N,N ) is the set that combine each traffic line; is the set nodes that both are highways, N is the set nodes that both are railways, N is the set of transit nodes; Only transportation mode conversion occurs, there will be risk occurrence. Otherwise, even if there is a pass by of transit nodes k N, no transfer risk will happen. E (E,E ) is the set of road lines and rail lines. variables C m m P Table. Decerebration of the parameters. explanation Confidence, on behalf of the supplier's risk aversion level The consequences of different transportation modes (person / segment) The probability of risk occurrence of transportation modes y0 The risk threshold of Select path l under the condition of CVa * x m Y k Model building and calculation method 0- variables, whether to select the mode of transport for the road 0- variables, whether to select a point to transport Considering highway, railway transport risk and transhipment risk, build following models: l min CVa y0 P [C y0] x [C 0] [C 0] Y P y x Pk k y k l l l (, i ) E (, i ) E kn (8) x : x, i O; xi, id; x xi 0, io, D, x 0, i, N x 0,,, xi i O D x 0, i, N (0) (9) 2020

4 x x Y (E,E ), N, i i x x Y (E,E ), N, i () i (2) transformation of trafficmode, k N Y k 0 otherwise 2 (3) (8) is obective for path l at a certain confidence level for a certain OD pair; and [ x] max( x,0),where(9)(0) is the constraint of decision variables, ensure the continuity of transport; ()(2)ensure that only in the event of transport mode changes, there will be transhipment risk. (3) is the choice decision variable of the transit point, equal to when be chosen as a transit centre, otherwise 0.In the obective function, because the value is uncertain, the obective function is a stochastic nonlinear function, which is more difficult to solve. And because the ml l optimal meet y 0 ( C, C k ), and arrange all segments of the path l in descending l l order, which are defined asc 0, C, C 2... C n, Ck is the k th minimum value among(c,c k ), ml l C0 0. y0( C, C k) is the stable values set, the obective function becomes a linear function, the optimal CVa value for path l ust as follows, l min CVa min y0 P [C y0] x [C 0] [C 0] Y 0 { 0,...C } P y x Pk k y y C C k m l l l (, i ) E (, i ) E kn (4) The optimal CVa value for each OD pair is as (4), the obective function is a nonlinear function and cannot be solved by existing software. After the known range of y0 values, it can be transformed into a linear function. l CVa min{cva l L} (5) COMPUTATION ANALYSIS Numerical Example Analysis As shown in Figure, with nine points, twelve lines. Assuming an OD pair exists. Each segment has two data, the length and the consequences of the risk. The length refers to the actual distance between cities, l ~(40,90), l ~ (50,200).The risk 2 value is calculated as: C C *Len ; C.The probability of risk-happen for road and rail are p and P ; and Pk p Through cplex2.0 calculation, it will give the optimal path directly from the data. ail lines oad lines Transfer yards Figure. distribution network. 202

5 Table 2. the length of each segment and the value of risk. Segment Segment length (Miles) Average density (person / km 2 ) isk Value (person / segment) (rail) (rail) (rail) (rail) Table 3. isk values for each transit yard. Transit yard Average density (person / km 2 ) isk Value B D F Under , solved with cplex2.0, we can get CVa* ; and the optimal path is, A(O) B 4 E 7 F 0 I(D).From this small scale numerical example, results show the feasibility of CVa to the application in intermodal transportation problem, we can also get the corresponding optimal transportation path. Numerical Example Analysis Based on China's Middle-eastern Transportation network As is shown in Figure2, 20 administrative centres can be connected by highway, rail is not surely connected. Select nine transportation centres with larger traffic flow as transit yards. Choose different OD pairs, the risk consequences of the traffic lines is computed as c len ; The risk consequence of transit yard choose to the population in two kilometres ck 4 k; and the population density refer to the average population density in every province; The probability of risk 6 6 occurrence could be described as ; 0.60 ; pk ; p len p len Figure 2. Transport network diagram of Middle-Eastern China. 2022

6 Table 4. Traffic node list. Administrative Whether transit Administrative Whether transit Being Yes Fuzhou No(destination) Tianin No Nanchang No Shiazhuang No Jinan Yes Taiyuan No Zhengzhou Yes Shenyang Yes Wuhan Yes Changchun No Changsha No Shanghai No Chongqing Yes Naning No Guiyang No angzhou No Xian Yes efei Yes Yinchuan No(origin) Make an example of Yinchuan in Ningxia province, Fuzhou in Fuian province as an OD pair, after solving by cplex2.0, we can get CVa*= , and the computation time is no more than 5 seconds; finally, the route obtained is as follows: road rail rail rail rail road Yinchuan Xian Taiyuan Jinan Naning Shanghai Fuzh ou CONCLUSIONS Multimodal transport is the effective ways to increase social transport efficiency, reduce society transportation cost, and integrate various mode of transportation advantage. Especially for the transport of hazardous materials, both the endurances of transportation time and risk factor are important. This article applied CVa to establish risk assessment model, in the future research, we will pay attention to the time connection and provide a more effective and comprehensive reference for the suppliers. ACKNOWLEDGEMENTS This research was supported by the National Natural Science Foundation of China (NSFC) for the proects of Transportation mode and transportation route optimization of hazardous materials multimodal transportation based on dynamic risk (No ),(No ) and (No ),(No ), (No ), and (No ), and also by umanities and Social Sciences Youth Fund from Ministry of Education for the proect of esearch on dynamic risk assessment for transport of dangerous chemicals (No.2YJC63020) and the Special Fund from China Scholarship Council, and the Special Fund from the Central Collegiate Basic Scientific esearch Bursary. EFEENCE [] Xin Zhang. The present situation and development trend of chloride methane industry in our country [J]. Journal of China Agrochemicals, 20 (7): [2] Saat M.., Werth C.J., Schaeffer D., et al. Environmental risk analysis of hazardous material rail transportation [J]. Journal of hazardous materials, 204, 264: [3] Erkut E., Tandra S.A., Verter V. Transportation :andbooks in operations research and management science [M]. Amsterdam: Elsevier, 2007:

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