Keywords: Transportation network, Hazardous materials, Risk index, Routing, Network optimization.

Transcription

1 IUST Intenatonal Jounal of Engneeng Scence, Vol. 19, No.3, 2008, Page Chemcal & Cvl Engneeng, Specal Issue A ROUTING METHODOLOGY FOR HAARDOUS MATIALS TRANSPORTATION TO REDUCE THE RISK OF ROAD NETWORK Afshn Shaat Mohaymany & Masoud Khodadadyan Abstact: The shpments of hazadous mateals (HAMATs) nduce vaous sks to the oad netwok. Today, one of the majo consdeatons of tanspotaton system manages s HAMATs shpments, due to the nceasng demand of these goods (because t s moe used n ndusty, agcultue, medcne, etc.), and the sng numbe of ncdents that ae assocated to hazadous mateals. Ths pape pesents a tool fo HAMATs tanspotaton authotes and plannes that would educe the sk of the oad netwok by dentfyng safe and economc outes fo HM tansshpment. Usng the poposed lnea ntege pogammng model, the HM management system could detemne an optmal assgnment fo all ogn destnaton pas fo vaous hazadous mateals n a tanspotaton netwok and so educe the vulneablty due to HAMATs eleases such as populaton and envonmental vulneablty. The model s mplemented and evaluated fo the hazadous mateals outng wthn Fas, Yazd, Isfahan, and Chahamaha-o-Bakhtya povnces of Ian. The banchand-bound algothm s appled to solve the model usng the Lngo softwae package. Keywods: Tanspotaton netwo Hazadous mateals, Rsk ndex, Routng, Netwok optmzaton. 1. Intoducton 1 Today, hazadous mateals (HM) such as explosves, flammable lquds, toxc gases and nfectous substances ae beng wdely used n dffeent felds such as ndusty, agcultue and medcne. In most cases, the poducton ste s fa fom the consumpton ste and so the goods must be tanspoted to the consumpton ste fom the poducton ste. Due to the hazadous natue of these substances, safety measues must be povded fo them dung all poducton, stoage and tanspotaton pocess. The hstoy of HM accdents and the elease emphaszes the mpotance of ths subject. Rsk analyss, the locaton of facltes, outng and schedulng ae the man poblems n tanspotaton of such substances. In outng poblem, on one hand, HAMATs shpment must be economc enough to have the potental to attact nvestment and on the othe hand, some safety measues Receved by the edto Aug, 17, 2007; fnal evsed fom June, 24, A. Shaat Mohaymany, Assstant Pofesso, Depatment of Cvl Engneeng, Ian Unvesty of Scence and Technology, Tehan, Ian. [email protected]. M. Khodadadyan, MS of Tanspotaton Engneeng, Depatment of Cvl Engneeng, Ian Unvesty of Scence and Technology, Tehan, Ian. [email protected]. must be povded to educe the sk of HAMATs tanspotaton. Snce 1980, many eseaches have undetaken studes n ths feld and many methods have been pesented fo outng the shpment of these substances. Routng of these mateals s a tadeoff between cost and sk fo each O-D pa. These studes can be categozed based on the dependency of the netwoks on tme (tme-ndependent o tme-dependent netwoks) o the objectve functons of the models (one-objectve o mult-objectve models). In tme-ndependent (tme-nvaant) netwoks, t s assumed that the featues of netwok lnks such as tavel tme and sk ae constant. But n tme-dependent (tmevayng) netwoks, these featues ae vaable. Fo nstance, n tme-dependent netwoks, the tavel tme on the lnk depends on the length of lnk and the tme of day due to the vaaton of the taffc condtons of the netwok. Theefoe, n such netwoks, sk and tavel tme ae andom vaables wth a pobablty dstbuton functon. In one-objectve models, the shotest path algothm has been used. In these models, dependng on the objectve functon, the ntended attbute s consdeed to be the label of lnks. Fo example, Kaa & Vete (2004)

2 58 A Routng Methodology fo Hazadous Mateals Tanspotaton to Reduce the Rsk of Road Netwok [1], pesented a two-phased model n whch the objectve of the fst phase (publc secto) s to mnmze the populaton sk and that of second phase (pvate secto) s to mnmze the tavel length. Smlaly Caotenuto et al. (2007) [2] have used populaton sk as the lnk label. The dffeence between mult-objectve models poposed n the lteatue s that whethe o not a utlty functon has been used to combne the objectves. In the models whee a utlty functon has been used, the multobjectve model educes to a one-objectve model whch could be solved by the shotest path algothm. In ths case, the selected path s vey senstve to the change n paametes of the utlty functon. Fo example, Ashtakala & Eno (1996) [3] have ncluded n the objectve functon, the weghted combnaton of nomalzed populaton and envonmental sk. Lkewse, the utlty functon based on a model ntoduced by Haghan and Chen (2003) [4] s to mnmze the weghted combnaton of thee objectves: O-D tavel tme, vulneable populaton on the oute and that on ntemedate nodes. Howeve, models that have not used utlty functon povde a set of paeto-optmal paths (non-domnated paths). Non-domnated paths ae a set of paths that none of them have any advantage o pefeence ove othes based on all the objectves. In such cases, t s up to the decson make to select the pefeed altenatve. Fo example, the model poposed by Penwah et al. (2000) [5] consdes optmal nondomnated paths based on the least specal populaton sk and least tavel tme. The objectves that have been used n the paeto-optmal solutons as eflected n the Huang and Fey method [6] nclude tavel tme, pobablty of elease accdents, populaton s specal populaton s envonmental s pvate secto cost, damages esultng fom delayed emegency esponse teams, and secuty sk. The objectve of Meng s model s to dentfy non-domnated paths between an ogndestnaton pa n a tme-vayng netwok based on tavel tme and othe ctea such as vulneable populaton [7]. The Attbutes of the model poposed by Mlle- Hooks & Mahmassan (1998) [8] ae tavel tme and vulneable populaton and ts objectve s to detemne the optmal path n a tme-vayng netwok based on a tadeoff between cost and sk. In the model devsed by Nozck and Tunqut, the numbe of objectves s optonal [9]. In ths study the tavel tme and vulneable populaton have been consdeed as andom vaables. In geneal, the factos that affect the outng of hazadous mateals can be categozed nto two pats; the fst categoy ae those elated to the sk consdeatons and depends on vulneable elements ncludng populaton s specal populaton s envonmental sk and popety sk. The second pat s elated to the economc consdeatons and ncludes tavel cost, tavel length and tavel tme. Specal populatons goups such as schools, hosptals and shoppng centes ae goups that may be patculaly senstve to hazadous mateals eleases, may be dffcult to evacuate, and ae hghly concentated, o ae outdoos [10]. It s clea that economc measues ae dependent upon each othe and because of ths, only one of them s appled n the optmzaton poblem, whle seveal sk measues fom the fst categoy may be appled. 2. Rsk Consdeaton Ths pape uses Eq. (1) fo sk assessment: R = P C (1) Whee R s the sk of lnk, P s the occuence pobablty of the elease accdent on lnk and C s the measue of elease accdent consequence on lnk. Snce sk on the whole oute s equal to the sum of the sks of ts contbutng lnks, the sk of a oute s specfed as follows [11]: () = P C TR. ; (2) Whee TR() s the sk on oute. In addton, accodng to Eq. (3), HM ncdent pobablty has been used to calculate the occuence pobablty of a HM accdent. (Moe detals can be found n [12].) P = P( A) = Rate( A). l (3) Whee P s the occuence pobablty of a HM accdent on lnk, P(A) s the HM ncdent pobablty, Rate(A) s the ate of HM ncdent on lnk (fo pe mllon vehcle-km) and l s the length of lnk (km). The vulneable components that have been consdeed n ths study nclude those of populaton and envonment (C ). To detemne the amount of populaton and envonment exposue, the mpact adus method s used as follows [10]: IA., c = 2d c l (4) PV., c = IA, c PD (5) EV., c = IA, c ED (6) Whee IA,c s the mpact aea along lnk due to shpment of HM class c on lnk (km 2 ), d c s the mpact dstance of HM class c (km), l s the length of lnk (km), PV,c s the populaton exposue on lnk fo the shpment of HM class c (people), PD s the populaton densty on lnk (people/km 2 ), EV s the envonmental esouce exposue on lnk fo the shpment of HM class c (km 2 ) and ED s the densty of envonmental esouce on lnk fo the shpment of HM class c (km 2 /km 2 ). In ode to mpove the capabltes of the model, some smplfyng assumptons have been used based on avalable data. The applcaton of these hypothess esults n the calculaton of elatve sk athe than absolute sk. As the am of ths study s to detemne the

3 Afshn Shaat Mohaymany & Masoud Khodadadyan 59 optmal assgnment of HM tucks and n othe wods the am s to compae some altenatve outes and fnd a pefeable opton, the applcaton of elatve sk would be acceptable. 3. Cost Consdeatons Thee s anothe cteon that mattes n HAMATs outng othe than safety ctea (sk ctea), and that s the cost of tanspotaton. It s obvous that sk and cost measues ae two compettve and opposte ctea. Abkowtz et al. (1991) [13] showed that f outng model s only based on sk facto, the length of the obtaned oute would be at least twce the shotest oute, whch can not be accepted fom an economcal pont of vew. In eale studes, tavel cost, tavel tme and tavel length have been consdeed as the cost of tanspotaton n HAMATs outng models. In ths study, tavel tme has been consdeed as tanspotaton cost. It s assumed that ths measue s a tme-ndependent vaable. It s obvous that when the length and aveage tavel speed on each lnk s specfed, the tavel tme on that lnk can be calculated. 4. Poblem Fomulaton Consde a tanspotaton netwok N(V,A) whee V s the set of netwok nodes and A s the set of netwok lnks such that the lnks ( є A) posses populaton and envonmental sk lmtatons. Ths netwok has thee dffeent types of nodes: ogn nodes, destnaton nodes and ntemedate nodes. The am s to shp a defnte quantty of vaous HAMATs between seveal O-D pas. In othe wods, O-D matx fo dffeent knds of HAMATs s defnte and specfed. Thee ae some altenatve outes to tanspot these mateals fom ogns to destnatons. The poblem s to detemne the optmal assgnment of tuck flow wthn ths tanspotaton netwok that mnmzes the weghted combnaton of objectves. The lnea ntege pogammng poblem s expessed by Eq. (7). Whee, u, u and u T ae espectvely the utlty of objectves; populaton s envonmental sk and tavel tme n the netwok (0 u 1),, and T ae espectvely populaton s envonmental sk and tavel tme of the netwo and mn ae espectvely the mum and mnmum populaton sk n the netwo and mn ae espectvely mum and mnmum envonmental s T and mn T ae espectvely mum and mnmum tavel tme, N,c s the numbe of tucks cayng HM class c on lnk n oute fom O-D pa k (decson vaable), N.,c s the numbe of tucks cayng HM class c on oute fom O-D pa N..,c s the demand of (numbe of tucks cayng) HM class c fom O-D pa,c and,c ae espectvely the base populaton and envonmental sk on lnk due to passng HM class c on that lnk (o the populaton and envonmental sk on lnk due to passng a tuck of HM class c on that lnk), T,. s the tavel tme on lnk, and ae espectvely the mum allowable (uppe-bound) populaton and envonmental sk on unt-length lnks, l s the length of lnk and δ,. s the bnay paamete of lnk-ncdence. The decson vaable that s the numbe of tucks cayng HM class c on lnk on oute fom O-D pa k and (N,c ) s theefoe an ntege vaable. { } ( S ) Max u, u, u subject to 1) 2) 3) u u : T = = T T mn T T mn mn 4) = N. c, c, c k 5) = N. c, c, c k 6) = N. T k, T c,,. c k 7) N = N ; c, k c,.., c., c 8) N.. l ; c,, c 9) N.. l ; 10) u T c k c k N = c, c, c, k, N., c δ,. = 1 = ;, c, k, k, 0 δ,. = 0 N Intege ;, c, k, Equaton (8) has been used to combne all thee objectves nto a utlty functon and convet the multobjectve functon nto a sngle-objectve functon. Max U = w u + w u + w u (8) Whee U s the total netwok utlty (0 U 1), u, u and u T ae espectvely the utlty of objectves; populaton s envonmental sk and tavel tme n the netwok (0 u 1) and w, w and w T ae espectvely the weght of objectves. Theefoe, the objectve functon model has been defned as the mzaton of the total netwok s utlty (U). Ths measue s made up of a weghted combnaton T T (7)

4 60 A Routng Methodology fo Hazadous Mateals Tanspotaton to Reduce the Rsk of Road Netwok of utltes of populaton s envonmental sk and tavel tme at the netwok level. Equaton (9) has been used to calculate any one of those utltes [14]. u = (9) mn Whee u s the utlty of objectve,, and mn ae espectvely cuent, mnmum and mum values of objectve. The values of utlty measues ae between 0 and 1. Also, the weghtng system has two chaactestcs; the sum of these weghts s equal to 1 and each weght s between 0 and 1. Theefoe, the total utlty measue value wll be between 0 and 1. 0 u 1, 0 w 1, 3 = 1 w = 1 0 U 1 (10) Weghtng systems ae detemnate by decson makes. The uppe and lowe lmts of the utlty functon wll help the analyst to ntepet the model's esults. Ths advantage of utlty functons n the fom of Eq. (9) s the eason of ts applcaton. Constants 1, 2 and 3 ae the utlty of dffeent objectves. Constants 4, 5 and 6 ae the thee objectves at the netwok level. The sk of the netwok s the sum of the sks of all lnks. Constant 7 epesents the fact that thee ae seveal paths between evey O-D pa to whch the O-D tuck demand should be assgned. Constants 8 and 9 ae espectvely the allowed populaton and envonmental sk lmtatons fo lnks. These lmtatons ae detemned by the decson makes. These lmtatons togethe wth mnmzng elated sks at the netwok level may ase the queston on whethe they ovelap one anothe. It can be noted that pncpally they ae nethe opposte to each othe no synthetc o ovelapped by each othe. In othe wods, optmzng a measue does not necessaly mean consdeng the lmts of that allowed measue. On the othe hand, n ths model, a combnaton of objectves s used as the utlty functon, and the model does not mnmze each sngle objectve. It s theefoe necessay to ente constants n the model to consde these lmts. Constant 10 defnes the flow n the oute. It s obvous that the flow on each lnk that belongs to a oute connectng any O-D pa s equal to the flow n that oute. In othe wods, f lnk belongs to oute connectng O-D pa k (δ,. =1), all the flow n oute s assgned to that lnk. In addton, f the decson-make s nteested n addng a constant as the mnmum lnk flow (tuck), a constant as N,c N',c could be added to the model n whch N',c s the mnmum allowed numbe of passng tucks cayng HM class c on lnk n oute connectng O-D pa k. It s obvous that such constant would put a futhe lmt to the feasble egon o n othe wods t deceases the feasblty of solvng the poblem. To calculate the mum and mnmum values of each objectve, a model wth the followng geneal fom must be solved: ( M) Objectve Functon subject to : 1) N = N ; c, k k, c, k,.., c., c 2) N.. l ; c k k, c, c, 3) N.. l ; c k k, c, c, k, k,,.,,. 1 k N c δ = 4) Nc, = ;, c, k, k, 0 δ,. = 0 N Intege ;, c, k, (11) Poblem M s dvded nto sx sub-models that ae pesented n table 1, based on objectve functons. 5. Applcaton Flowchat In geneal, the applcaton flowchat of the HAMATs tanspotaton outng poblem that s shown n Fg. 1 conssts of thee sectons: 5.1. Inputs Ths pat concens the model nput data and conssts of data about the tanspotaton netwo populaton dstbuton, envonmental esouces dstbuton, HAMATs nfomaton and decson make nfomaton Calculatons Thee opeatons ae conducted n ths secton. Fst, the feasble paths between evey O-D pa ae dentfed based on the tanspotaton netwo so δ,. s obtaned and the lnk labels ae detemned. The sx sub-models ae solved usng ths data so that all othe equed data fo the soluton of the majo poblem ae n hand. No Tab. 1. Sx sub-models Sub-model Maxmzaton netwok populaton sk Mnmzaton netwok populaton sk Maxmzaton netwok envonmental sk Mnmzaton netwok envonmental sk Maxmzaton netwok tavel tme Mnmzaton netwok tavel tme Objectve functon ( M 1)Max ( M 2) Mn ( M 3)Max ( M 4) Mn ( M 5)Max T ( M 6) Mn T

5 Afshn Shaat Mohaymany & Masoud Khodadadyan 61 1 If lnk belongs to oute fom O-D pa k δ,. = ;, (13) 0 Othewse w w w T. N., c, mn, mn, mn T T (, c,, c, T ),. ( δ ),. 6. Case Study The case study netwok s shown n Fg. 2. Ths study was undetaken n Fas, Yazd, Isfahan, and Chahamahal-o-Bakhtya povnces. Ths netwok has 73 lnks and 66 nodes, thee nodes of whch ae ogns and destnatons and othe 70 nodes ae ntemedate nodes. The netwok lnks ae numbeed fom 10 to 82. N, c,, T u, u, u T U Fg 1. Poblem soluton algothm 5.3. Outputs Ultmately, the man output of the poblem, whch s the decson vaable N,c s obtaned by solvng the majo poblem. In addton, othe outputs such as populaton s envonmental sk and tavel tme at the netwok level o lnk level and utltes ae calculated. Also t s necessay to explan the two followng tems: 5.4. Lnk s label Based on the populaton s envonmental sk and tavel tme n the objectve functon, the vecto label of any lnk of the netwok that conssts of thee elements can be defned as follows:,1,1, 2, 2.. (, c,, c, T,. ) = (,, T,. )...., c, c (12) The fst and second elements of the lnk label ae a vecto wth c elements. All elements of the lnk label ae fxed. To detemne fst and second elements of ths label, data such as accdent ate, lnk length, mpact dstance of HAMATs, populaton densty and envonmental esouces densty fo all netwok lnks ae equed Lnk-ncdence matx Evey oute s a chan of lnks that connect two nodes. To defne the feasble outes, a bnay paamete δ,. was used. Fg 2. Case study Netwok The netwok nodes have been chosen n such a way that the attbutes of any lnk ae constant. These attbutes nclude lnk type (speed), populaton densty [15] and envonmental esouce densty [16]. Theefoe, the nodes shown n Fg. 2 do not ndcate a populaton cente but ndeed pedomnates as at least one of the mentoned attbutes. The netwok lnks have been dvded nto types 1, 2 and 3; and tavel speeds of tucks n these lnks ae 40, 60 and 70 km/h, espectvely. O-D pas, as specfed n ths study, ae Shaz- Yazd (SY) and Isfahan-Shaz (IS). Theefoe, the ogns ae Shaz (S) and Isfahan (I) and the destnatons ae Yazd (Y) and Shaz (S). Two consdeed knds of hazadous mateals ae HM1 and HM2 wth mpact dstance of 0.8 and 0.5 km, espectvely. The demand matx s shown n table 2. Ths matx shows the demand of O-D pas n tems of the numbe of tucks fo both knds of HAMATs. Tab. 2. Demand matx (numbe of tucks) HAMAT SY IS HM HM Table 3 shows some of the lnks nfomaton n the netwok. In ths table, t s assumed that the dmenson of

6 62 A Routng Methodology fo Hazadous Mateals Tanspotaton to Reduce the Rsk of Road Netwok accdent ate on each lnk s accdent numbes/bllon vehcles-km. The level of avalable nfomaton was at the povncal and muncpal levels. Due to ths, the nfomaton about populaton densty whch was at the muncpal level s shown n moe detals than that of envonmental esouce densty. Thee ae 12 feasble paths n the netwok such that thee ae sx paths between evey O-D pa (R1, R2 R12). The outes between SY and IS ae shown n Fg. 3. In the next step, t s necessay to calculate the mpact aea, vulneable populaton, vulneable envonment and accdent pobablty of all netwok lnks fo two HAMATs. Snce these HAMATs ae n pospect, fo each lnk two quanttes ae obtaned fo vulneable populaton and vulneable envonment. Then, populaton base sk and envonmental base sk of all netwok lnks must be calculated. The base sk of a lnk s assocated to the passage of a sngle tuck wth a cetan class of HAMAT and t s calculated usng lnk accdent pobablty (lnk accdent ate multpled by lnk length) multpled by the vulneable aea (populaton and envonmental vulneablty). Populaton and envonmental base sks on a lnk show espectvely the expected values of vulneable populaton and envonment due to the passage of a tuck. Also, snce the length (h) and speed (km/h) of lnks ae known, the tavel tme (h) s calculable. Theefoe, by fa thee attbutes of the netwok lnks that ae equed as model nputs have been calculated; populaton base s envonmental base sk and tavel tme of netwok lnks. Tab. 3. Detals of lnks n netwok Lnk No. Lnk type L Accdent ate Pop. densty Env. densty km 10-9 /veh-km pop/km 2 km 2 /km The values of tavel tme, populaton sk and envonmental sk at two levels of the netwok lnks and the whole netwok ae a pat of model outputs. The tavel tme of a lnk o netwok coespondngly ndcates the tuck-hous taveled n a lnk o netwok. Populaton sk of a lnk o netwok coespondngly ndcates the expected numbe of dead people o those of njued due to one bllon tucks along the lnk o netwok. Envonmental sk of a lnk o netwok coespondngly ndcates the expected envonmental vulneablty (km 2 ) due to the passage of one bllon tucks along the lnk o netwok. It s obvous that by the dvson of lnk sk by the length of the ln the unt length sk of the lnk s obtaned. In ode to solve a model, t s necessay to nclude the data offeed by the decson-make. Ths data conssts of the weghtng system and sk lmtatons. In ths case study, we consde the decson-make data accodng to table 4. Tab. 4. Decson-make data w w w T Fst, t s pmaly necessay to solve the sx submodels fo decson-make data. At ths stage, weghtng systems have no effect and only the sk lmtaton must be consdeed (table 4).Table 5 shows the soluton esults of the sx sub-models. Tab. 5. Results of sx sub-models T mn mn T mn Based on the nputs, the esults of the mplemented model ae shown n Fg. 4 to Fg. 6. The LINGO softwae package s used to solve poblem (S) and sub-poblems (M). The solve employs the banch-and-bound algothm to solve those. Banch-and-bound s a systematc method fo mplctly enumeatng all possble combnatons of the ntege vaables. To analyse the above-mentoned optmzng case, two cases have been consdeed: Case I. The tavel tme based shotest path assgnment; In ths case, the total demand of each O-D pa s passed though ts shotest path. In othe wods, n ths case, sk lmtaton has not been consdeed and the shotest path between each pa has been used fo the shpment of HAMATs. Case II. Unfom assgnment; In ths case, the total demand of each O-D pa s dstbuted equally between the feasble paths. Smlaly n ths case, no sk lmtaton s appled. The values of populaton s envonmental sk and tavel tme n the netwok n any of these thee cases have been shown n table 6 and Fg. 7. Lkewse table 7 shows the used paths n any of thee cases.

7 Afshn Shaat Mohaymany & Masoud Khodadadyan 63 to these shotest paths; so the flow of HM tucks s hgh on these paths and the esultant sk on lnks belongng to these paths s nceased. In unfom assgnment, the netwok tavel tme nceases but the sevety of populaton and envonmental sks on lnks deceases. In unfom assgnment, the numbe of ctcal lnks s fewe than that of tavel tme shotest path assgnment. In the optmal assgnment (poposed n ths atcle), thee s no ctcal lnk but the netwok tavel tme s moe than that of shotest path assgnment. Although, t s stll less than the tavel tme n unfom assgnment. Fg 4. Routng of HAMATs n the netwok Fg 3. Feasble outes Shaz-Yazd and Isfahan- Shaz Tab. 6. Values of thee attbutes n the netwok n any of the thee cases Assgnment Netwok populaton sk Netwok envonmental sk Netwok tavel tme Tavel tme shotest path Unfom Optmal In geneal, t could be sad that as the allowable level of sk has not been consdeed n the shotest path assgnment, the whole demand has been assgned Fg 5. Populaton sk of unt length of lnk

8 64 A Routng Methodology fo Hazadous Mateals Tanspotaton to Reduce the Rsk of Road Netwok Fg 6. Envonmental sk of unt length of lnks 0 Netwok populaton sk (*10e5) Netwok envonmental sk (*10e5) Netwok tavel tme (tuck-h) Tavel tme shotest path assgnment Unfom assgnment Optmal assgnment Fg 7. Netwok populaton s Netwok envonmental sk and Netwok tavel tme at any of thee cases Tab. 7. The used netwok Paths at thee cases Shaz-Yazd Isfahan-Shaz Assgnment (SY) (IS) Tavel tme R6 R10 shotest path Unfom All outes All outes Optmal R1,R2, R6 R7, R8, R9, R10 Usng ths compason, the capablty of ths model n mnmzng the weghted combnaton of all thee objectves; populaton s envonmental sk and tavel tme of netwok has been clealy shown. 7. Concluson Based on ths eseach, t s evdent that the tanspotaton of HM tucks n oad netwoks could be optmzed. The applcaton of optmal outes contbutes to the sk mnmzaton and mzes the safety. In the pevous studes, the man objectve was to fnd the shotest path fo the shpment of demand between just one O-D pa. In addton, some othe dffeences between ths study and othe eseaches could be ponted out as the followng: A. Snce the am of these poblems s to tanspot HAMATs fom one ogn to one destnaton, the dectons of lnks on the netwok have been assumed based on ogn-destnaton decton. Theefoe, the model s ntoduced n a dectonal netwok. B. As the shotest path algothm has been used n these eseaches, the demand does not affect the selecton of the opton. C. As the demand has not been consdeed n these models, no lmtaton has been appled to the netwok lnks n the models. Theefoe, the whole demand s tansfeed on the fst shotest path and t s not necessay to fnd next paths. D. Seveal sk and cost attbutes have been assgned to the netwok lnks based on objectves of the model that some of them could vay wth tme of day. In compason wth the pevous studes, n ths eseach, the demand matx conssts of seveal O-D pas and dffeent classes of HAMATs. In ths netwo some lnks opeate bdectonal and theefoe the netwok s not a dectonal netwok. Futhemoe, t s assumed that the attbutes of netwok lnks ae tme ndependent. The applcaton of the poposed model makes assessment of the cuent HM flow pattens on oad netwoks possble. Ths can be accomplshed by both compang sk measues of netwok lnks n the exstng stuaton and the allowed sk and by compang them wth the optmal flow patten. Futhemoe, by optmzng the HAMATs assgnment, the ctcal lnks n the netwok can be detemned. The tem ctcal lnks means those lnks whch have appoached the specfed allowed sk. Ths model also allows the assessment of the ule and mpotance of any lnk and the altenatve outes fo flow of HM tucks n netwok elablty. Ths model, theefoe, contbutes consdeably to the pesent decson-makng and futue plannng undetaken by authotes to mpove the opeaton of the oad netwok based on HAMATs tanspotaton. Refeences [1] Kaa, B.Y., Vete, V., "Desgnng a Road Netwok fo Hazadous Mateals Tanspotaton", Tanspotaton Scence, Vol. 38, No. 2, 2004, PP [2] Caotenuto, P., Godan, S., Rccadell, S., "Fndng Mnmum and Equtable Rsk Routes fo Hazmat Shpments", Computes & Opeatons Reseach, Vol. 34, No. 5, 2007, PP [3] Ashtakala, B., Eno, L.A., "Mnmum Rsk Route Model fo Hazadous Mateals", Jounal of Tanspotaton Engneeng, Vol. 122, No. 5, 1996.

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