Incorporating Uncertainty and Risk in Transportation Investment Decision Making: Detroit River International Crossing Case Study

Transcription

1 Icorporatig Ucertaity ad Risk i Trasportatio Ivestmet Decisio Makig: Detroit River Iteratioal Crossig Case Study Sabyasachee Mishra a*, Sehamay Khasabis b, Subrat Swai c a Natioal Ceter for Smart Growth Research ad Educatio, 054 Preikert Fieldhouse, Uiveity of Marylad, College Park, MD b Departmet of Civil ad Evirometal Egieerig, Waye State Uiveity, Detroit, MI c Departmet of Electrical, Computer ad Eergy Egieerig, Arizoa State Uiveity, Tempe, AZ Abstract Large scale trasportatio projects represet major ivestmets i costructio, operatio, ad maiteace of facilities over a exteded period. Typically, these ivestmets are irreveible i ature ad require log-term commitmet by the public at large relative to utilizatio, maiteace, ad operatio. Traditioal ecoomic aalysis techiques used to evaluate the feasibility of such projects are based upo the assumptio of future cash flows that are determiistic i ature. I reality, may of these projects are associated with sigificat ucertaities ad risks stemmig from a lack of kowledge about future cost ad beefit streams. There is ot a uified methodology i the literature to address ucertaity ad risk i trasportatio ivestmet decisio makig. The autho preset a framework for addressig ucertaity ad risk for large scale trasportatio ivestmets ivolvig joit participatio by the public ad private etity. Demad, * Correspodig Author: Tel.: ;fax: addresses: mishra@umd.edu (Sabyasachee Mishra), skhas@waye.edu (SehamayKhasabis), Subrat.Swai.@asu.edu (Subrat Swai) 0

2 fare/toll, ad demad resposive costs are cosidered i the ucertaity aalysis. A bi-level programmig is proposed, where the upper level costitutes the preferece of the policy maker, ad the lower level determies the user s respose to the policy. The ucertaity aalysis provides ecoomic feasibility of the project. A set of relaxatio policies is proposed to form various Owehip, Teure, ad Goverace (OTG) strategies reflectig the ature ad level of participatio by the public ad private etity. The ucertaity aalysis output serves as a iput to the risk aalysis. Mote Carlo Simulatio is used to address risks for feasible policy optios selected from ucertaity aalysis. The cocept of Value at Risk (VaR) is used to quatify risk. Fially, a methodology is proposed to itegrate ucertaity ad risk. The framework is tested o the proposed multibillio dollar iteratioal river crossig etitled as the Detroit River Iteratioal Crossig (DRIC) coectig the cities of Detroit i the US with Widsor i Caada. The aalysis provides isights to probable outcomes for this trasportatio ifrastructure ivestmet. This methodology ca be used as a tool for trasportatio ifrastructure ivestmet decisio makig process. Key words: ucertaity, bi-level programmig, mote carlo simulatio, value at risk, ivestmets 1

3 1. Itroductio Trasportatio ifrastructures are itegral parts of a atio s etwork coectivity. Large-scale trasportatio projects represet major ivestmets i costructio, operatio, ad maiteace of facilities over a exteded period. Typically, these ivestmets are irreveible i ature ad require log-term commitmet by taxpaye relative to their utilizatio, maiteace, ad operatio. Examples are mass-trasit systems, freeway corrido, subways, crossigs i the form of bridges ad tuels, high occupacy vehicle (HOV) laes, ad toll roads. A Natioal Trasportatio Statistics report suggests that total gross trasportatio ivestmet by the federal, state ad local govermets reached $80 billio i the US i the fiscal year 2003 (BTS 2008). Similarly expeditures i operatig, maitaiig ad admiisterig the atio s trasportatio facilities are over $200 billio aually. Projected federal, state ad local highway reveues are isufficiet to meet estimates of future highway requiremets (USDOT 2006). Lack of capital fuds to meet the eeds of the coutry may result i icreased private participatio i trasportatio ifrastructure projects (Roth 1996). The potetial of such projects to produce ecoomic beefits has become a icreasigly importat factor i the ivestmet decisio makig process. Some of these large ivestmets may ivolve the private eterprise i the costructio, operatio ad maiteace process alog with the federal, state ad local govermets. 2. Problem Statemet I traditioal ecoomic aalysis, future cash flows are assumed to be fully determiistic i ature. Thus, these are ot desiged to accout for ay risk ad ucertaity i the assessmet of 3

4 future retu. I reality, may of these ifrastructure projects are associated with sigificat ucertaities stemmig from lack of kowledge about future cost ad reveue streams. The term risk refe to situatios where the decisio maker ca assig mathematical probabilities to the radomess relative to future outcomes. I cotrast, the term ucertaity refe to situatios whe this radomess caot be expressed i terms of mathematical probabilities (Kight 1921). A sigificat research o ivestmet decisio makig uder ucertaity ad risk is reported i the fields of ecoomics ad fiacial maagemet that icludes a theoretical approach o capital ivestmet cosiderig the irreveibility of ivestmet decisios ad ucertaity of ecoomic eviromet (Dixit ad Pidyck 1994). Other relevat work o this topic icludes research o decisio-makig process, behavioral adjustmets, ad actual experiece of use ad policy make i a aget-based approach reflectig etwork maagemet ad fiacig policies (Zhag et al. 2008); o ivestmet decisio makig for a Build Operate ad Trasfer (BOT) problem usig a multi-objective geetic algorithm procedure ad a mea-variace model for BOT scheme uder demad ucertaity(che et al. 2003, Che et al. 2006); o capacity expasio usig demad ucertaity ad simulated aealig (Su ad Turquist 2007)ad o decisio makig uder ucertaity for highway developmet usig real optios approach (Zhao ad Kockelma 2006). The problem ivestigated i this research relates to a lack of uified approach i the curret literature i icorporatig ucertaity ad risk i trasportatio ivestmet decisio makig. This paper presets a aalytic framework to explore the implicatios of a joit owehip of a trasportatio ifrastructure project, with cost/reveue ad demad estimates fraught with sigificat ucertaities. A case study is also preseted to demostrate the applicatio of the framework. 4

5 The framework also explores various forms of joit owehip associated with the public ad private eterprise. There are a umber of reasos for the growig tred of private participatio i public projects. These iclude, the scarcity of fiscal resources at the public sector level, the perceptio that the private sector is more efficiet i maagig large projects, ad the advatage of joitly sharig risks ad ucertaities, thereby reducig exposure levels to fiacial losses for both etities. Joit owehip has become icreasigly popular i Europe, Australia ad more recetly i Asia, as it allows a part or the whole of the capital fuds from private resources i exchage of future reveues (Garber ad Hoel 2002, Khasabis et al. 2010). Joit owehip is geerally associated with three terms: Owehip, Teure ad Goverace (OTG). A OTG strategy ca be looked upo as a mechaism to pla, desig, implemet, operate, ad maitai a project by developig various combiatios of owehip, teure, ad goverace procedures, where: The term Owehip has embedded i it, the cocept of possessio ad title related to the property i questio. Depedig upo the ature of the joit project, its owehip may belog to the public etity, private etity, or both durig the cocessio period. Owehip may also chage at the ed of the cocessio period (Mera ad Njiru 1998). Teure refe to the status of holdig a possessio of a project for a specific period, ragig from few days to a umber of yea. For most joit owehip projects, teure is likely to coicide with the cocessio period; however, exceptios to this geeral rule may be ecoutered. Goverace refe to maagemet, policy ad decisio makig pertaiig to a orgaizatio with the itet of producig desired results. 5

6 The objective of the research is to propose a framework to icorporate ucertaity ad risk, ad to evaluate the proposed framework with a real-world case study. The methodology proposed i the paper is desiged for major trasportatio ifrastructure projects ivolvig public private participatio. The case study is applied to a iteratioal toll bridge. 3. A Combied Framework for Ucertaity ad Risk Aalysis The proposed framework to icorporate the cocept of ivestmet decisios uder ucertaity ad risk is illustrated i Figure 1 ad is categorized ito three steps; 1. Step 1: Ucertaity Aalysis 2. Step2: Risk Aalysis 3. Step 3: Itegratio of ucertaity ad risk Step-1: Ucertaity Aalysis Ucertaity aalysis is further divided ito three sub-steps: Step - 1.1: Policy Optios Step - 1.2: Bi-level Programmig for ucertaity aalysis Step - 1.3: Feasibility Aalysis Step 1.1 is a examiatio of the ivestmet policy optios recommeded by the relevat public agecies relatig to ew trasportatio projects that may represet various combiatios of rights ad resposibilities of public ad private agecies (FHWA 2010).At oe ed of the spectrum, the public etity may have all the major resposibilities with the private agecy playig a mior role. At the other ed, the roles may be reveed. Various other combiatios may form the itermediate rage. 6

7 I Step 1.2, a bi-level process is proposed as for evaluatio of the proposed policy optios. The policy maker (upper level) is assumed to have some udetadig of the road use likely respose (lower level) to a give strategy. However, the strategy set by the policy maker ca oly ifluece (but ot cotrol) the road use route choice. I other words, policy optios ad route choice decisios ca be represeted as a bi-level program, where, the upper level ivolves the policy maker s decisio to determie the toll value, while road use are assiged to the proposed facility at the lower level. I the bi-level process, the upper level may be subdivided ito three categories (1) private ivestor, (2) public ivestor, (3) road user. While the desiged toll value for all the three pepectives will be differet at the upper level, a user equilibrium assigmet problem is addressed at the lower level with a elastic demad feature desiged to cosider ucertaity i travel patter. I Step 1.3 ecoomic ad fiacial feasibility of various policy optios are examied. Policy regulatios such as costructio cost subsidy, cocessio period extesio, etc. ca be cosidered if ecessary. The relaxatios are embedded i a set of OTG strategies. The viability of the project uder differet strategies ca be tested usig a set of pre-specified criteria. Step - 2: Risk Aalysis Three sub-steps are proposed i the risk aalysis: Step 2.1: Idetificatio of risk variables Step 2.2: Settig up the simulatio process Step 2.3: Estimatio of Value at Risk (VaR) 7

8 Step-1.1 USDOT Policy Optios State Policy Optios Ivestmet Policies from Toll Facility Operato Survey Step-1.2 Bi-level programmig Fixed Cost ad Demad Resposive Variable Costs Ucertaity Aalysis (Step-1) Policy Decisio (Toll) Estimate Cash Flow Demad Assigmet Measures of Effectiveess for Policy Optios Cosider Ivestmet Optios: (OTG Strategies) Impose (or Relax) Policy Regulatios Step-1.3 Feasibility of Ecoomic ad Fiacial Regulatios No Yes Simulatio Cycle Step-2.2 Risk Aalysis (Step-2) Step-2.1 Risk Aalysis Process Idetify Project Risk Variables Set up Risk Model Assig Probabilities to Risk Variables Perform Simulatio No Start Simulatio Geerate Radom Numbe for Risk Variables Recalculate MOE Record Simulatio Result Desired # of Iteratios Performed Estimate VaR Step-2.3 Itegratio of Ucertaity ad Risk (Step-3) Itegrate the measures of ucertaity ad risk Yes Propose feasible strategies Ed Simulatio FIGURE 1 Proposed Methodology for Ucertaity ad Risk Aalysis 8

9 I step 2.1, variables associated with differet ivestmet optios are idetified. For example, i trasportatio ivestmets, possible risk variables are related to demad, fare, ad costs. Probabilities are assiged to the risk variables i a simulatio model. A umber of simulatio approaches ad risk measures are preseted i the literature (Jorio 1997). I step 2.2, various iteratios of the simulatio cycle are recorded. I step 2.3, the measure of risk is determied. Oe such measure is Value at Risk (VaR), that ca be used to deote the maximum expected loss over a give horizo at a give cofidece level for a specific policy optio. This step will eable the decisio maker avoid risky policy optios, ad focus more o those optios with modest risk exposure. Step 3: Itegratio of Ucertaity ad Risk I this step, Measures of Effectiveess (MOE) of ucertaity ad risk aalyses are combied. Policy optios associated with least ucertaity ad risk ca be proposed for further cosideratio. 3.1 Decisio Tool for Ucertaity Aalysis Sources of ucertaity i the trasportatio ifrastructure ivestmet ca arise from future costs ad reveues. Bulk of the cost elemet is from costructio cost icurred before the facility is opeed to traffic; other cost elemets such as regular ad periodic operatio ad maiteace costs deped o future travel demad. Reveue is directly depedet o travel demad ad toll. Ucertaities related to cost ad reveue are primarily geerated from travel demad. Ivestmets i major trasportatio ifrastructure are ofte complex, with a mix of public ad private fiace, with the respective agecies havig differet missios ad motivatios. The public sector may cosist of atioal, state ad local agecies with a social welfare pepective. 9

10 The public ad private etities are iterested i explorig optimal tollig strategies that may yield differet solutios (Hyma ad Mayhew 2008, Wog et al. 2005, Palma et al. 2006, Rouwedal ad Verhoef 2006). While the public etity s primary iterest is to maximize cosumer surplus 1 (social welfare), the private etity is iterested i maximizig profit. Sice the public sector is the evetual ower ad operator of the facility, it must esure that the facility attracts use ad serves the eeds of the commuity (Yag ad Meg 2000).Thus, the optimal toll must be viable to the ultimate ed use. Hece, i the ivestmet decisio makig process, three etities pepectives should be cosidered: (1) the private, (2) the public, ad (3) the user. Private Ivestor s Pepective The objective of the private ivestor is to maximize profit. The aual profit for demad ucertaity is the differece betwee beefit ad cost ad is preseted as followig (Che ad Subprasom 2007): P,x, B C (1) Where, P is the profit geerated i year, which is a fuctio of the demad (x) ad toll (). B ad C are correspodig reveue ad cost for year respectively. The reveue geerated is a fuctio of ucertai demad ad toll, while the cost ca be preseted i the form of capital ad operatio ad maiteace cost. The revised equatio 1 ca be represeted as: a a a,c a a P,x, x C O x (2) aa 1 The additioal value or beefit received over ad above the expeses actually made is kow as cosumer surplus. 10

11 where, is a parameter which coverts hourly lik flows to aual lik flow, x a, a C a,c, O a are the demad, toll charge, costructio cost ad operatio ad maiteace cost for year o lik a respectively. N is the aalysis period ad A is a set of ewly implemeted liks subjected to toll. The objective fuctio for profit maximizatio ca be formulated as: max. P,x, N (3),x, 0 (4) subject to: where, x, is determied from the lower level program ad suggests that the toll value ad the volume caot be egative. Public Ivestor s Pepective The proposed framework is based o the premise that the primary objective of the public etity is to maximize cosumer surplus, typically measured as the additioal moetary revalue over ad above the price paid (Wohl ad Hedrickso 1984). There are other social beefits such as improved traffic flow, evirometal beefits, higher safety etc., that may be derived from major ifrastructure projects. The public sector appea to be icreasigly iterested i reveue maximizatio decisios with trasportatio assets (Johso 2007). These are ot icorporated i the proposed framework ad the classical approach of maximizatio of cosumer surplus was used at the oly public beefit. The cosumer surplus ca be mathematically represeted as, q q d q (5)

12 where, is the cosumes surplus for the O-D pair r-s for the year, q is the demad betwee 1 O-D pair r-s for year, q pair r-s, ad is the ivee demad fuctio for the Origi-Destiatio (O-D) is the miimum travel cost betwee the O-D pair r-s. The fit term of the equatio 5 represets the user willigess to pay to travel from r-s ad the secod term is the amout user actually paid (or miimum travel cost to travel from r-s). The cosumer surplus is a measure from the public etity pepective used i a umber of studies i trasport etwork desig (Ukkusuri ad Patil 2009, Che ad Subprasom 2007, Yag ad Meg 2000, Zhag ad Ge 2004, Zhag ad Kumaraswamy 2001, Zhao ad Kockelma 2006). Patil 2009): Cosumer surplus for a O-D pair r-s for a improved case is give by (Ukkusuri ad The cosumer surplus for the total etwork ca be represeted as: q q d q (6) 1 0 The aual cosumer surplus i moetary terms ca be represeted as: q 1 q d q (7) 0 where, is a parameter which coverts time value to moetary terms, is the parameter that coverts hourly to aual demad. The savigs i cosumer surplus ca be defied as the differece betwee the cosumer surplus ad the cost of the project (Che ad Subprasom 2007, Yag ad Meg 2000). This ca be represeted as: 12

13 ,x, C (8) where, is the savigs i cosumer surplus. A higher cosumer surplus is better for the public ivestor. The public etity perceives the user beefit equivalet to a value which travele expect to receive from makig trips as measured by the gross amout paid by the travele i makig a trip. The objective fuctio for cosumer surplus maximizatio ca be formulated as: max.,x, (9) subject to:,x, 0 (10) where, x, is determied from the lower level program. Road User s Pepective If the implemetatio of project oly beefits a small sectio of travele i the study area, the the distributio will ot be called as equitable. Theil s idex, oe of the commoly used measures of iequality distributio, was used i this study because of its flexible structure (Theil 1967). Theil s idex, i its simplest form, ca be estimated as (Theil 1967): q s s s T b..l r q (11) where, r s q q is the travel demad of OD pair r-s i the th year, ) for the whole etwork, q is the total demad (i.e. is the cosumer surplus improvemet for OD pair r-s i the 13

14 th year, is the total cosumer surplus improvemet (i.e. r s ). If every zoe has same beefit the the Theil s idex is zero (perfect equality), ad if the beefit is cocetrated at oe (perfect iequality) zoe the the Theil s idex is l q. The lower the Theil s idex, the more equitable is the project. The objective fuctio for user iequality (betwee groups) miimizatio ca be formulated as: mi. T,x, b (12) subject to:,x, 0 where, x, is determied from the lower level program. While the upper level program determies the toll for various pepectives cosidered, the lower level determies the route choice of use for a desiged toll value subjected to ucertai demad. The lower level problem is a user equilibrium traffic assigmet with elastic demad (Sheffi 1985). xa xa q (13) 1 mi ta wdw ta w dw q wdw aaa 0 aa 0 0 x, subject to: fk q (14) k fk 0 (15) 14

15 q 0 (16) x f (17) a k a,k r s k a,k 1 if lik ais o path k betwee O-D r-s 0 Otherwise (18) The objective fuctio i expressio 13 miimizes the travel time of the etwork till equilibrium is achieved. The fit two terms are the lik performace fuctio of all o-tolled ad tolled liks i the etwork respectively. The third term is the ivee demad fuctio associated with the OD pair r-s, which is a decreasig fuctio of the OD travel times. Expressio 14 is a flow coservatio costrait to esure that flow o all paths coectig each OD pair has to equal the trip rate. Expressio 15 ad16 are o-egativity costraits to esure that the flow caot be egative. The defiitioal relatioship of lik flow from path flows is preseted i expressio 17 ad 18. The miimizatio problem i expressio 13 cosists of toll value ( ) which is a fuctio of a set of lik flows (x a, ) ad a set of OD demads (q, Flow i lower level is a fuctio of toll i the upper level (recall three policy pepectives specified i upper level). ). Demad Elasticity ad Ucertaity Additio of ew liks or improvemet of the road etwork will reduce the travel cost betwee origi ad destiatio. This improvemet ca result i icreasig demad betwee the correspodig OD pai. A expoetial demad fuctio ca be used to estimate the aual demad (Sheffi 1985). 15

16 q q exp (19) Where, q is the radom potetial demad betwee r-s, is the miimum travel cost betwee r-s which icludes the desiged toll value, is a positive costat, ad demad for year betwee the OD pair r-s. q is the realized travel Ucertaity i travel demad is icorporated through a radom samplig approach with a predefied mea ad variace. Radom umbe are geerated with predefied probability distributio fuctio (i.e. ormal distributio). This is performed exogeously from the lower level traffic assigmet(che ad Subprasom 2007) q q z (20) Where, q, are the mea ad stadard deviatio of radom potetial demad for OD pair r- s, ad z is a radom variable geerated from ormal distributio with mea zero ad uity variace. The lik travel time used i the lower level traffic assigmet problem is the Bureau of Public Roads fuctio, deoted as (Sheffi 1985): 4 0 x a ta xat a G a (21) where, t 0 a ad Ga is the free flow travel time ad capacity for lik a. 16

17 3.2 Decisio Tool for Risk Aalysis Risk is ofte defied as the probability of occurrece of a udesirable outcome (Jorio 1997). Risk aalysis cosists of simulatig the various iputs over the life of the project ad fidig the preset value. This process is repeated umber of times usig Mote Carlo Simulatio (MCS) to icorporate risks from multiple sources, both o reveues ad costs. The Measure of Effectiveess (MOE) thus obtaied reflects the effect of risk. I the proposed risk aalysis, the simulatio model employs pre-defied realizatios of toll, ad traffic volume to aalyze the effect of idecisive iputs o the output of the modeled system. Risk ca be quatified ad measured i differet ways (Mu 2006). Value at Risk (VaR) is oe such that ca be defied as the maximum expected loss over a target horizo, with a give level of cofidece (Jorio 1997). VaR describes the quatile of the projected distributios of gais ad losses over the target horizo. If α is the selected cofidece level, VaR correspods to the (1- α) lower tail level. For example for 90 percet cofidece level, VaR should be such that it exceeds 10 percet of the total umber of observatios i the distributio. 4. Case Study A proposed iteratioal bridge betwee the city of Detroit i the US ad the city of Widsor i Caada is selected as the case study. Surface trade betwee Southwester Otario ad Southeaster Michiga exceeded 200 billio i 2004 ad is expected to icrease by twofold by the year 2030(MDOT 2003). 70 percet of trade movemet betwee the US ad Caada is by trucks. Approximately 28 percet of surface tradig is by trucks for the crossigs betwee Southeast Michiga ad Southwest Otario(MDOT 2008). Majority of the trade is for the crossigs i the Detroit River area, coectig the city of Detroit i the US ad the city of 17

18 Widsor i Caada. This large trade volume has a sigificat positive effect o the local, regioal ad atioal ecoomies through cross-border employmet opportuities. The Cetral Busiess Districts (CBDs) of the cities of Detroit ad Widsor are curretly coected by four crossigs: (1) The Ambassador Bridge (AB), (2) The Detroit Widsor Tuel (DWT), (3) a Rail Tuel (RT), ad (4) The Detroit Widsor Truck Ferry (DWTF). Both AB ad DWT are across the Detroit river, built durig the late 1920s. AB is a privately owed fourlae suspesio structure, while DWT is a two-lae facility with height restrictio, joitly owed by the two cities ad operated by a private corporatio. The Blue Water Bridge (BWB) across the St. Clair River (100 km orth of Detroit) that coects Port Huro i the USA with Saria i Caada. BWB is a six lae arch structure built i 1938 ad reovated i 1999; ad is joitly owed by the two cities. The RT ad DWTF, both costructed uder the Detroit River, carry cargo betwee two cities. The Caada US Otario Michiga Trasportatio Partehip Study (Partehip Study) attempted to develop log-term strategies to provide safe ad efficiet movemet for people ad goods betwee Michiga ad Otario (MDOT 2008). Eve though the curret capacities of the Ambassador Bridge ad the Detroit-Widsor tuel adequately serve the traffic eeds durig most hou, o specific days durig peak periods, the systems operates at full capacity. Cosiderig log-term traffic growth ad the overall importace of the Detroit River crossigs o the regioal ecoomy, the eed for a third crossig seems immesely justified. As a result of umber of studies iitiated i early 2000 s ad curretly earig completio, the Michiga Departmet of Trasportatio (MDOT), ad the Otario Miistry of Trasportatio have idetified a bridge kow as X-10(B) as the most preferred alterative to built i the 18

19 viciity of the Ambassador Bridge (MDOT 2008). The alterative has bee referred to as the Detroit River Iteratioal Crossig (DRIC) i the case study (Figure 2). 5. Results Two alterative bridge structures are proposed for X-10(B); (1) a suspesio bridge, or (2) a cable-stay bridge. The prelimiary cost estimates of the bridges alog with associated ifrastructures are $1809 millio ad $1814 millio respectively. I the case study, it is assumed that a suspesio bridge will be built. The cost compoets, are show i Table 1. The plaig for the bridge was started i A part of the plaig/desig/costructio egieerig cost is already icurred. The costructio is expected to be complete i 2014, ad the bridge will be ope to traffic i The cost elemets show i Table 1 are oly for the US part of the bridge. By the same toke, all the toll reveue compiled to assess the beefits reflects the fare collected at the Detroit ed of the bridge. 5.1 Travel Demad Ucertaity Travel demad data for the study area i the form of OD matrices for the study area are obtaied from MDOT for the yea 2015, 2025, ad There are a total of 960 Traffic Aalysis Zoes (TAZ) i the Detroit (US) side of the border ad 527 TAZs i the Widsor (Caada) side of the border. Icludig 23 exteral TAZs, the study area cosists of a total of 1510 TAZs. The aalysis period for the case study is cosidered as 35 yea ( ). The OD matrices for 19

20 FIGURE 2 Network of Study Area (Mishra 2009) 20

21 the yea 2045, projected by cosiderig the growth treds from each TAZ. A coefficiet of variatio 3 of 0.15 is cosidered to icorporate variace i travel demad. The potetial 4 OD matrix was ot available. The base ad horizo year projected OD matrices were icreased by te percet to obtai the potetial OD. The stadard deviatio of the OD matrix is obtaied from the coefficiet of variatio ad the expected demad of the OD matrix. Solutio Approach for Demad Ucertaity A Mote Carlo Simulatio (MCS) procedure was used to simulate the OD matrix. The potetial OD matrix (expected demad matrix) ad the variace OD matrix served as the iput to the MCS. The OD matrices were subjected to 200 realizatios ad each realizatio was recorded (Equatio 20). From the distributio of OD matrix, the media matrix was chose for further aalysis. However, oe ca use ay percetile from the distributed OD matrix. This procedure was followed for all the horizo yea. The resultig OD matrix from MCS icorporates the variatio ad resultig ucertaities i travel demad, which is used i the elastic traffic assigmet procedure. The proposed traffic assigmet model is calibrated for the base year Actual toll values for ca ad trucks for the year 2004 are utilized to determie the assiged volume o the existig river crossigs i the etwork. The proposed elastic traffic assigmet model ad the potetial OD matrix for the year 2004 are utilized to 3 The coefficiet of variatio (COV) is the ratio of the stadard deviatio ad the mea. For this research a COV of 0.15 is assumed by observig the variatio i demad over time for te yea. 4 The potetial OD matrix cotais the maximum possible trips that ca be made if the travele are ot sesitive to the user cost. I elastic traffic assigmet the potetial OD matrix is used to test the sesitivity of demad with respect to the user cost (both travel time ad travel cost). 21

22 determie the assiged volume for ca ad trucks. The observed car ad truck volumes are obtaied from MDOT (MDOT 2003). The close correspodece betwee the assiged ad observed volumes at the respective crossigs demostrates the calibratio of the model. Results of the calibratio are ot preseted i the paper for the sake of brevity. The details of calibratio of the model are discussed i the project report(khasabis ad Mishra 2009). TABLE 1 Cost Compoets for DRIC (MDOT 2008) Ivestmet Type Cost (Millio $) Costructio Costs DetroitRiverBridge (U.S. Cost Oly) 399 Toll ad IspectioPlaza 57 Iterchage ad Local Roadways 190 Ehacemets 21 Utilities 157 Maagemet Reserve (5%) 40 Plaig/Desig/Costructio Egieerig Fial Desig ad Permits (10%) 80 Costructio Egieerig (10%) 80 Iitial plaig, desig ad other costs 173 Property Acquisitio/Remediatio Property Acquisitio 365 Remediatio 17 Iflatio ROW 35 GSAPlaza Costs 200 Grad Total Cost 1, Sigle Etity Pepective Decisio Makig Uder Ucertaity For a viable trasportatio ivestmet, the iterest of three decisio makig etities (public, private, ad user) should be satisfied. The objectives of the three etities from ivestmet viewpoit are differet, as discussed earlier. Three etity objectives are used at the upper level ad ridehip is determied at the lower level. The bi-level process is solved i TrasCAD (Caliper 2008). A GISDK script is writte to solve the bi-level 22

23 model i TrasCAD. The output of the upper level (toll value ad the etity-specific objective fuctio) served as the iput to the lower level (ridehip estimatio). The bilevel process ca be viewed as a o-liear problem reflectig the ature of the objective fuctios at the upper ad the lower level. The elastic traffic assigmet problem is solved by user equilibrium method usig Frak Wolfe Algorithm (Sheffi 1985). 5.3 Base Case The base case sceario refe to exclusive etity participatio. Results of the base case are preseted for the three etities for differet horizo yea i Table 2. For private etity, the objective is profit maximizatio with the assumptio that the total cost (capital, operatio ad maiteace cost) will be bore by the private etity. Reveue is cosidered as a surrogate for profit i this paper. As explaied earlier, the profit maximizatio is solved by the bi-level process. Toll values are set at the upper level ad ridehip is determied at the lower level. For example, i the profit maximizatio strategy, toll values of $2 per car ad $14 per truck resulted i a aual reveue 5 of $68.54 millio i the year The toll values are obtaied i a iterative maer with directioal search 6 to obtai the optimum value of the objective fuctio for profit maximizatio, cosumer surplus maximizatio ad iequality miimizatio. For the same toll values the cosumer surplus ad Theil s idex are estimated to be $ millio ad 0.86 respectively for the year Whe the objective of the public etity is cosidered, the optimal toll is $0.5 per car ad $4.33 per truck (year 2015, secod row, Table 2) that resulted i a optimal 5 Reveue is defied as the moetary beefit obtaied by the toll/fare collectio oly. 6 Directioal search is a techique for fidig the optimal value of a uimodal fuctio by successively arrowig from the possible rage of values. 23

24 cosumer surplus of $ millio, which is higher tha the estimated cosumer surplus for profit maximizatio. The cosumer surplus allows more travele 7 to use the facility i lowerig the differece betwee willigess to pay ad what the travele actually pay. The reveue ad Theil s idex for toll value of $0.5 for ca ad $4.33 for trucks are estimated to be $25.78 millio ad 0.79 respectively. Similarly, whe the objective of the use is cosidered (year 2015, third row, Table 2) the optimal toll values obtaied are $0.25 per car ad $ 1.04 per truck, resultig i a Theil s idex of 0.70 (miimum of the three Theil s idex values) for the year For the toll value of $0.25 per car ad $ 1.04 per truck the correspodig reveue ad cosumer surplus are estimated at $7.41 ad $ millio respectively. Three distict toll values are obtaied for three differet etities, each of which represets the optimum values for the three objective fuctios defied i equatios 3,9, ad 12. The highest toll value resulted for profit maximizatio ad the least toll value for Theil s Idex, thereby demostratig that the objectives of the private ivestor ad the use are satisfied. Additioally, the toll value for the public etity pepective is lower tha that for the private pepective for all the yea. Similar treds are observed for the other horizo yea durig the aalysis period preseted i Table 2.Icreased travel demad i future yea resulted i higher toll values, higher reveue ad higher cosumer surplus i succeedig yea. The same is geerally true i Theil s Idex, although there are some exceptios. The Theil s Idex is cosidered as a miimizatio fuctio ad based o the distributio of trips amog the TAZs i the study area. 7 It should be oted that more travele usig the facility does ot ecessarily icrease the reveue, because reveue is the product of toll value ad the correspodig ridehip. 24

25 TABLE 2 Base Case Etity Objective Results (25) Year Car Toll Truck Toll Aual Aual Theil s ($) ($) Reveue Cosumer Iequality (Millio $) Surplus Idex (Millio $) 2015 Private Pepective Public Pepective User Pepective Private Pepective Public Pepective User Pepective Private Pepective Public Pepective User Pepective Private Pepective Public Pepective User Pepective Private Pepective Public Pepective User Pepective Owehip, Teure ad Goverace Strategies The autho iitial work o the cocept of OTG scearios was preseted at the World Coferece o Trasport Research at the Uiveity of Califoria, Berkeley i Represets the Optimal value of car toll from the Private Pepective 9 Represets the Optimal value of truck toll from the Private Pepective 10 Represets the maximum value of Reveue from the Private Pepective 11 Represets the Optimal value of car toll from the Public Pepective 12 Represets the Optimal value of truck toll from the Public Pepective 13 Represets the maximum value of Cosumer Surplus from the Public Pepective 14 Represets the Optimal value of car toll from the User Pepective 15 Represets the Optimal value of truck toll from the User Pepective 16 Represets the miimum value of Theil s value from the User Pepective 25

26 (Khasabis et al. 2007). Though sigle etity participatio i large trasportatio projects is importat, their ivolvemet with other etities is likely to icrease the overall viability of the project. Owehip, Teure ad Goverace (OTG) are the three pricipal compoets of a joit owehip. A umber of OTG strategies are cosidered to represet varyig levels ad types of public-private participatio i the DRIC project. The strategies vary i the degree of participatio by the public ad the private etity. Five types of OTG strategies are cosidered: 1. OTG-1: Exclusive Private Participatio 2. OTG-2: Major Private Participatio 3. OTG-3: Moderate Private Participatio 4. OTG-4: Major Public Participatio 5. OTG-5: Exclusive Public Participatio The trasitio from OTG-1 to OTG-5 is marked by decreasig levels of private ad icreasig levels of public participatio. A umber of relaxatio policies are also cosidered to ecourage joit owehip i DRIC. The sigificace of each OTG strategy is explaied i the project report (Khasabis ad Mishra 2009). The feasibility of OTG strategies are determied by cosiderig the aalysis period till

27 OTG-1 For OTG-1, the total capital cost is bore by the private etity. The objective of the strategy is profit maximizatio. After costructio of the facility, the private etity is authorized to collect toll, operates ad maitais the facility throughout the cocessio period. The evetual ower of the facility is the public etity, eve though the private etity is resposible for all the expeditures ad toll collectio durig cocessio period. The cumulative cash flow ad IRR are the two MOEs plotted i Figure 3. The egative cost elemets for represet the plaig ad costructio of the facility. Whe the facility is opeed to traffic, the cumulative egative value of cash flow decreases, as the toll charges are collected ad the break eve period occu i the year The Iteral Rate of Retur (IRR) 17 for OTG-1 strategy is 4.61% over the 35 yea of cocessio period. The Miimum Attractive Rate of Retur (MARR) 18 was assumed to be 6%. The IRR beig lower tha the MARR leds the project ecoomically ifeasible for the strategy (OTG-1) tested. 17 IRR provides a estimate of the retur or yield of the ivestmet, give a set of expediture ad reveue data alog with their expected dates over the life of the project. IRR is defied as the iterest rate at which the Net Preset Worth (or Net Aual Worth or Net Future Worth) of the ivestmet is equal to zero. 18 MARR is the rate of retur below which the ivestmet proposal is to be deemed uacceptable. 27

28 FIGURE 3 Cumulative Cash Flow ad IRR: Exclusive Private Participatio (OTG-1) (Note: There is o IRR value till the ed of 2025 as the cost is much higher beefit received. The IRR at the ed of 2030 is -1.82) tha the Other OTG s A complete descriptio of the four other OTG s is provided i the project report (Khasabis ad Mishra 2009). Essetially, the trasitio from OTG-1 to OTG-4 is marked by higher levels of subsidy to the private etity either by reduced cost, or by extesio of the cocessio period. Thesee relaxatio private participatio will obviously reflect o higher public sector. OTG-5, represets a completely public policies adopted to ecourage fiacial resposibility for the udertakig, ecompassig all fiacial, maagemet, operatioal ad maiteace resposibilities. 28

29 TABLE 3 OTG Strategies, Relaxatio Policies ad IRR s OTG Strategy Explaatio Relaxatio Policy Etity Objective OTG-1 Exclusive Private No Relaxatio Profit Participatio Maximizatio OTG-2 Major Private 1. Toll Plaza Cost Subsidy Profit Participatio 2. Toll Plaza, Iterchage, ad Ispectio Plaza Maximizatio Cost Subsidy OTG-3 Moderate Private Participatio 3. Costructio Cost Subsidy 1. Costructio Cost Subsidy 2. Cocessio Period Extesio 3. Costructio Cost Subsidy ad Cocessio Period Extesio Profit Maximizatio IRR (percet) OTG-4 Major Public Participatio 1. Partly Costructio Cost by Private Etity 2. Operatio ad Maiteace Cost Public Etity 3. Costructio Cost Subsidy-Public Etity Cosumer Surplus Maximizatio 22.97* 3.69** 3.95** OTG-5 Exclusive Public No Relaxatio Cosumer 3.51** Participatio Surplus Max. Note: *: Private etity is oly resposible for a part of the costructio cost ad receives all the beefits throughout the cocessio period. Lesser ivestmet ad higher retur for the private etity has resulted i relatively larger IRR. This OTG strategy is cosidered as a attractive optio for the private etity.**: IRR for the public etity (the remaider of the IRR are for the private etity). 29

30 Sythesis of Results for OTG Strategies The objective of OTG strategy aalysis is to formulate a series of joit owehip scearios for the public ad private etities for large scale ivestmets. Results of this aalysis are preseted i Table 3, ad ca be summarized as follows: For exclusive private participatio (OTG-1), the project is sot fiacially viable. Further, varyig degree of relaxatio are proposed i (OTG-2 ad OTG-3) to ecourage private participatio. All relaxatio policies i OTG-3 resulted i fiacially viable solutios for the project. For major ad exclusive public participatio (OTG-4ad OTG-5), the project is ot fiacially viable, with the assumed levels of charges eeded for the maximizatio of cosumer surplus. I summary, OTG strategies represetig joit owehip scearios provided fiacial viability for the project aalyzed. Table 3 also shows that for OTG strategies 2, 3, ad 4, there are a umber of sub-strategies cosidered i the aalysis. 5.5 Risk Aalysis The OTG strategies are further cosidered i the risk aalysis. Feasible optios from the relaxatio polices are subjected to risk aalysis. Toll values for the horizo yea were determied from the ucertaity aalysis. The upper ad lower limit of the toll values are set usig a assumed coefficiet of variatio of te percet. MCS techique was used to 30

31 obtai the simulated cumulative cash flow for desig yea. The radom values are istrumetal i developig ridehip estimates resultig from elastic traffic assigmet, ad the correspodig operatio ad maiteace cost. For each radom toll value, ad the appropriate ridehip, operatio ad maiteace cost chages, the IRR value is estimated. 10, 000 such iteratios are performed, ad the correspodig IRR s are recorded. The distributio of all realizatios of IRR is plotted i Figure 4. Procedure for Obtaiig VaR VaR is measured i absolue ad relative terms. Absolute VaR is defied as the maximum expected loss at a give level of cofidece. Relative VaR is defied as the differece betwee mea ad the absolute VaR. Figure 4 shows the mea value of IRR o the X- axis, the frequecy o primary Y-axis, ad the probabilities o secodary Y-axis for the OTG-3, cocessio period extesio. The 5 th ad the 50 th percetile IRR of the distributio are 5.99 percet 6.04 percet respectively. The VaR for OTG-3 cocessio period extesio is 5.99 percet at 95 percet level of cofidece. I other words, the maximum expected loss for five percet of the times i IRR ca ot be lower tha 5.99 percet. The 95th percetile relative VaR is the differece betwee the 50 th percetile (mea) IRR ad 5 th percetile IRR (or VaR at 95 th percetile), i.e = 0.05 percet.the 95 th percetile relative VaR suggests that the maximum loss i IRR at 95 th percetile level of cofidece ca ot exceed 0.05 percet for the OTG-3 cocessio period extesio strategy. Similarly,the 90 th percetile VaR ca be determied. The 95 th ad 90 th percetile absolute ad relative VaR for all the strategie are preseted i Table 4. 31

32 % 1400 Mea IRR 90% Frequecy % VaR (5% Loss) 80% 70% 60% 50% 40% 30% 20% Cumulative Probability % 0 0% IRR FIGURE 4 Value at Risk for OTG-3 Cocessio Period Extesio 6. Itegratio of Ucertaity ad Risk Ucertaity ad risk are addressed idividually i the earlier sectios of this chapter. The implicatios of both ucertaity ad risk are importat from ivestmet viewpoit. A approach is to itegrate ucertaity ad risk for explorig differet optios for the DRIC project is preseted i this sectio, with IRR servig as the MOE for ucertaity aalysis, VaR for the risk aalysis. 32

33 TABLE 4 Risk Aalysis Summary OTG Strategy Relaxatio Policy Mea IRR (%) 95% VaR (%) 90% VaR (%) 95% Relative VaR (%) 90% Relative VaR (%) OTG-1 No Relaxatio OTG-2 1. Toll Plaza Cost Subsidy Toll Plaza, Iterchage, ad Ispectio Plaza Cost Subsidy Costructio Cost Subsidy OTG3 1. Costructio Cost Subsidy Cocessio Period Extesio Costructio Cost Subsidy ad Cocessio Period Extesio OTG-4 1. Partly Costructio Cost by Private Etity Operatio ad Maiteace Cost Public Etity OTG-5 No Relaxatio

34 95% Relative VaR 0.50% 0.45% 0.40% 0.35% 0.30% 0.25% 0.20% 0.15% 0.10% 0.05% 0.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% IRR FIGURE 5(a) Itegratio of Ucertaity ad Risk (Note: The outlier i the graph represets higher IRR ad VaR) 0.12% 0.10% 95% Relative VaR 0.08% 0.06% 0.04% 0.02% 0.00% 0.00% 2.00% 4.00% 6.00% 8.00% IRR FIGURE 5(b) Itegratio of Ucertaity ad Risk (without the outlier) The MOE s are preseted i Figure 5(a) ad 5(b) to demostrate both ucertaity ad risk o the OTG strategies. o the X-axis ad Y-axis respectively. A favorable OTG strategy is the oe with higher IRR (higher tha the MARR of six percet i this case) ad lower relative VaR. Table 3 shows that four OTG strategies 34

35 resulted i IRR s of greater tha six percet. The highest IRR (22.97%) resulted for the OTG-4 strategy for the private etity with costructio cost subsidy. For the same OTG strategy, the relative VaR is also the highest (0.46%, at 95 percet level of cofidece), which makes the OTG strategy vulerable to future risks (also show i Figure 5(a)). From the remaiig feasible strategies, the combiatio of costructio cost subsidy ad cocessio period extesio (OTG-3) resulted i a IRR of 7.24% ad a relative VaR is 0.06% at 95 percet level of cofidece. However, all the OTG-3 strategies appear to be feasible with higher IRRs ad lower relative VaR (Figure 5(b)). 7. Coclusios The primary objective of this study is to develop a framework for large scale trasportatio ifrastructure ivestmet decisios that icorporates the cocept of ucertaities ad risks; ad apply the framework o a real world case-study to augmet the decisio makig process. The etities ofte ivolved i, or affected by, large-scale ifrastructure ivestmet decisio are elisted as: private, public, ad use each with differet set of objectives ad expectatios; profit maximizatio, cosumer surplus maximizatio ad iequality miimizatio, respectively. A procedure for sigle etity ucertaity aalysis is preseted as a bi-level process. The upper level costitutes the preferece of the policy maker, ad the lower level determies the user s respose to the policy. The output of ucertaity aalysis is desiged to serve as iput to risk aalysis. IRR ad VaR are cosidered as the MOE s for ucertaity ad risk aalysis respectively ad determied usig MCS techique. The objective of each etity, whe subjected to ucertaity, is cosidered i assessig the optimal demad ad toll estimates. 35

36 Typically, ecoomic aalysis of ifrastructure projects are based upo the assumptio of determiistic cash flows usig the premise that all future costs ad reveues are fully kow. I reality, there are sigificat ucertaities stemmig from the lack of kowledge about the future cash flow streams. The picture is further complicated by the fact that trasportatio projects are typically log-term i ature, ad that the loger the project, the higher the ucertaity. The proposed framework is a attempt by the autho to address the effect of ucertaity ad risk o trasportatio ivestmet decisios. Ucertaity aalysis ca be used to determie the optimal value of the etityspecific objective fuctio (profit maximizatio or welfare maximizatio or iequality miimizatio) i a joit owehip project, i the face of variable travel demad, toll, operatio ad maiteace costs. With o prior iformatio o demad, toll, ad cost, a determiistic aalysis ca result ito misleadig coclusios, whereas ucertaity aalysis determies the optimal results from each etity pepective. Further, risk aalysis coside iputs from ucertaity aalysis to further determie the maximum expected loss at a give level of cofidece. If the sigle etity ucertaity aalysis does ot result i feasible solutios, relaxatio policies are proposed. Relaxatio policies may iclude extesio of the cocessio period ad fiacial support from the other etities ivolved i the decisio makig process, leadig to the formulatio of a set of OTG strategies. A set of joit OTG scearios are created cosiderig the multi etity operatio of the trasportatio facilities. For some OTG strategies, relaxatio policies are proposed to esure feasibility of the 36

37 project. The IRR is cosidered as the measure of feasibility for ucertaity aalysis. Similarly, the VaR is recommeded as a measure of risk. A methodology for itegratig ucertaity ad risk is proposed. It is observed that projects producig higher IRR may also be associated with higher VaR. The itegratio of ucertaity ad risk allows the decisio maker to choose from a set of alterative ivestmet strategies of a project to miimize ucertaity ad risk subject to the IRR meetig the MARR criterio. The cocept of itegratig ucertaities ad risks demostrated the eed to cosider ot oly the retur o the ivestmet (IRR) i the decisio makig process, but also the risk factor (VaR). The fial decisio should be based upo the joit cosideratio of both facto. The framework is applied to study the ivestmet decisio makig of DRIC coectig two coutries US, ad Caada; a project i the plaig stage for over te yea. Results of the case study idicate that the framework preseted is viable; however additioal research is eeded to itegrate the pepectives of all the etities ito a multiobjective framework. The case study preseted clearly demostrates that a strategy cosidered ecoomically viable uder determiistic sceario, may ot be so whe risk facto are icorporated i the aalysis. As aother future task, the effect of chages i the toll structure of the competig bridges o DRIC ca be icorporated ito the ucertaity ad risk aalysis framework. The proposed procedure may be used by trasportatio ad fiacig professioals ivolved i ifrastructure ivestmet decisios. Such professioals iclude: egiee/plae/ecoomists, ivestmet ad cost aalysts ivolved both i private ad public fiacig of ifrastructure projects. 37

38 Ackowledgemet This research was supported by the U.S. Departmet of Trasportatio (USDOT) through its Uiveity Trasportatio Ceter (UTC) program. The autho would like to thak the USDOT ad the Uiveity of Toledo for supportig this research through the UTC program, ad Waye State Uiveity (WSU) for providig crucial matchig support. The autho would like to ackowledge the assistace of Michiga Departmet of Trasportatio (MDOT) ad Southeast Michiga Coucil of Govermets (SEMCOG) for their assistace durig the coue of the study. Lastly, the autho are immesely grateful to the WSU Ceter for Legal Studies for supportig the prelimiary research o this topic i The commets ad opiios expressed i this report are etirely those of the autho, ad do ot ecessarily reflect the programs ad policies of ay of the agecies metioed above. 38