AN APPROACH TO INCORPORATE UNCERTAINTY AND RISK IN TRANSPORTATION INVESTMENT DECISION MAKING: DETROIT RIVER INTERNATIONAL CROSSING CASE STUDY

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1 AN APPROACH TO INCORPORATE UNCERTAINTY AND RISK IN TRANSPORTATION INVESTMENT DECISION MAKING: DETROIT RIVER INTERNATIONAL CROSSING CASE STUDY By Sabyasachee Mishra, Ph.D. Faculty Research Associate Natioal Ceter for Smart Growth Research ad Educatio Uiveity of Marylad College Park, MD Phoe: (301) Sehamay Khasabis, Ph.D. Professor of Civil ad Evirometal Egieerig Waye State Uiveity Detroit, MI Phoe: (313) Subrat Swai Graduate Research Assistat Waye State Uiveity Detroit, MI Phoe: (313) Word Cout: Number of Tables: 4 Number of Figures: 5 Total Cout: = 5, 463+ (9 x 250) = 7,713 Date Submitted: July 31, 2010 Submitted for Peer Review ad for Compedium of Pape CD-ROM at the Aual Meetig of the Trasportatio Research Board (TRB) i Jauary 2011, ad for Publicatio i the Joural of TRB

2 ABSTRACT Large scale trasportatio projects represet major ivestmets devoted to the 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 fiacial feasibility of such projects are based upo the assumptio of determiistic future cash flows that are ot subject to ay ucertaity ad risk. I reality, may of these projects are associated with sigificat ucertaities ad risks stemmig from lack of kowledge about future cost ad beefit streams. There is a lack of comprehesive literature i addressig 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, 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 trasportatio 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 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. 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 city of Detroit i the US ad the city of Widsor i Caada. The combiatio of both ucertaity ad risk reveals isights to the probable outcomes for a 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. INTRODUCTION Trasportatio ifrastructures are itegral parts of a atio s etwork coectivity. Large-scale trasportatio projects represet major ivestmets devoted to the 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. Examples are masstrasit 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 (1). Similarly expeditures i operatig, maitaiig ad admiisterig the atio s trasportatio 1

3 facilities are over $200 billio aually. Projected federal, state ad local highway reveues are isufficiet to meet estimates of future highway requiremets (2). Lack of capital fuds to meet the ifrastructure eeds of the coutry may result i icreased private participatio i such projects (3). The potetial of trasportatio ifrastructure projects to produce ecoomic beefits has become a icreasigly importat factor i the ivestmet decisio makig process. Some of these large ivestmets may also ivolve the private eterprise i the costructio, operatio ad maiteace process alog with the federal, state ad local govermets. 2. PROBLEM STATEMENT 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 ivolved i the assessmet of 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 (4). Curret trasportatio literature does ot idicate the availability of a methodology to icorporate risks ad ucertaities i trasportatio ivestmet, though sigificat research is reported i the fields of ecoomics ad fiacial maagemet. This research presets a aalytic framework that ca explore the merits ad demerits associated with public ad/or private owehip of a trasportatio ifrastructure, where potetials for cost recovery through future reveues appear to be high at oe ed, but the project may be fraught with risks at the other. 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. The cocept of joit owehip has become icreasigly popular i Europe, Australia ad more recetly i Asia, as it allows part or the whole of the capital fuds from private resources i exchage of future reveues (5,6). 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 PPP project, its owehip of the property/facility may belog to the public etity, private 2

4 etity, or both (joit owehip), durig the cocessio period. Owehip is also likely to chage at the ed of the cocessio period. 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, exceptio 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. The objective of the research is to propose a theoretical framework to icorporate ucertaity ad risk from sigle ad multiple etity pepective, ad to evaluate the framework with a real world case study. 3. A COMBINED FRAMEWORK FOR UNCERTAINTY AND RISK ANALYSIS A framework to icorporate the cocept of ivestmet decisios uder ucertaity ad risk is preseted i this sectio. The proposed framework is illustrated i Figure 1 ad is categorized ito two steps; Step 1: Ucertaity Aalysis Step2: Risk Aalysis 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 federal ad state levels relatig to ew trasportatio projects (7). These policy optios may represet various combiatios of resposibilities of public ad private agecies that may vary a wide rage. A evaluatio of the proposed policy optios ca be viewed as a bi-level process (Step 1.2). 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 policy maker s decisio to determie the toll value, while road use are assiged to the proposed facility at the lower level. I the bilevel 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, the lower level is a user equilibrium assigmet problem with elastic demad which is desiged to cosider the ucertaity i travel patter. 3

5 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 Step-1.3 Measures of Effectiveess for Policy Optios Cosider Ivestmet Optios Impose (or Relax) Policy Regulatios Feasibility of Ecoomic ad Fiacial Regulatios No Yes Simulatio Cycle Risk Aalysis (Step-2) Risk Aalysis Process Idetify Project Risk Variables Set up Risk Model Assig Probabilities to Risk Variables Perform Mote Carlo Simulatio No Start Simulatio Geerate Radom Numbe for Risk Variables Recalculate MOE Record Simulatio Result Desired # of Iteratios Performed Estimate VaR Provide Set of Feasible Solutios Yes Ed Simulatio FIGURE 1 Proposed Methodology for Sigle Etity Ucertaity ad Risk Aalysis 4

6 Various ivestmet optios ca be cosidered i step 1.1. Policy regulatios such as costructio cost subsidy, cocessio period extesio, (or similar relaxatio policies) ca be cosidered if ecessary. After relaxatio of policy regulatios, viability of the project ca be tested ad a set of ivestmet strategies ca be examied (Step 1.3). The fit three steps take ito accout the ucertaity i demad (umber of road use usig the facility) subjected to various toll values. Step - 2: Risk Aalysis I step 2, risks associated with differet ivestmet optios are determied. The term Value at Risk (VaR) for a policy optio is used to deote the maximum expected loss over a give horizo at a give cofidece level. This step will eable the decisio maker avoid risky policy optios, ad focus more o these optios with modest risk exposure. 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 future 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. The public ad private etities are iterested i explorig optimal tollig strategies that may yield differet solutios (8-11). While the public etity always would like to maximize the cosumer surplus 1 (social welfare); the private etity is iterested i maximizig profit. Sice the public sector will be evetually the ower ad operator of the facility; it must esure that the facility attracts use ad serves the eeds of the commuity (12). 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. Descriptio of objective/pepective of each etity is preseted below. 1 The additioal value or beefit received over ad above the expeses actually made is kow as cosumer surplus. 5

7 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 (13). ( ( )) P τ,x τ, ε = B C (1) Where, P is the profit geerated i year, which is a fuctio of the demad (x) ad toll (τ). 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: P,x, x C O x N a A ( τ ( τ ε )) = γ a ( τ ) τ a a,c a ( a ) 6 (2) where, γ is a parameter which coverts hourly lik flows to aual lik flow, 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(, ) τ τ ε (3) subject to: τ,x( τ, ε ) 0 (4) where, x ( τ, ε ) is determied from the lower level program ad suggests that the toll value ad the volume caot be egative. Public Ivestor s Pepective The objective of the public etity is to maximize social surplus / cosumer surplus. The additioal moetary value over ad above the price paid is termed as cosumer surplus (14). Oe ca determie whether the extra cost required to improve a facility from two levels. Mathematically, q 1 = q ( ) d q 0 φ ω ω π (5) where, φ is the cosumes surplus for the O-D pair r-s for the year, 1 betwee O-D pair r-s for year, q ( ω) x a, τ a q is the demad is the ivee demad fuctio for O-D pair r-s, ad π is the miimum travel cost betwee 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

8 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 (12, 13, 15-18). Cosumer surplus for a O-D pair r-s for a improved case is give by (15): The cosumer surplus for the total etwork ca be represeted as: q 1 φ = q ( ω) dω q π 0 (6) The aual cosumer surplus i moetary terms ca be represeted as: γ 1 φ ω ω π θ q q d q (7) = ( ) 0 where, θ is a parameter which coverts time value to moetary terms, γ 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 (12,13). This ca be represeted as; ( ( )) ψ τ,x τ, ε = ϕ C (8) where, ψ 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(, ) ψ τ τ ε (9) subject to: τ,x( τ, ε ) 0 (10) where, x ( τ, ε ) 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 (19). Theil s idex, i its simplest form, ca be estimated as (19): 7

9 q φ φ s s s T b =..l (11) r q φ φ where, q ) for the whole etwork, r s q is the travel demad of OD pair r-s i the th year, q is the total demad (i.e. φ is the cosumer surplus improvemet for OD pair r- s i the th year, φ is the total cosumer surplus improvemet (i.e. φ ). 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. Lower the Theil s idex more equitable is the project. The objective fuctio for user iequality (betwee groups) miimizatio ca be formulated as: ( ) mi. T,x(, ) b τ τ ε (12) subject to: τ,x( τ, ε ) 0 where, x ( τ, ε ) 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 (20). xa xa q ( ) ( ) (13) ( ) + ( ) + θτ 1 mi ta w dw ta w dw q w dw ( τ ε ) a ( A A) 0 a A 0 0 x, subject to: fk = q (14) k fk 0 (15) q 0 (16) x = f δ (17) a k a,k r s k r s δ a,k 1 if lik ais o path k betwee O-D r - s = 0 Otherwise (18) 8

10 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 ad 16 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 (τ ) which is a fuctio of a set of lik flows (x a ( τ, ε ) ) ad a set of OD demads (q ( τ, ε ) ). 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. The improvemet ca result i icreasig demad betwee the correspodig OD. A expoetial demad fuctio ca be used to estimate the aual demad (20). % ( ) q = q exp λπ (19) Where, % q is the radom potetial demad betwee r-s, π is the miimum travel cost betwee r-s which icludes the desiged toll value, λ is a positive costat, ad q is the realized travel demad for year betwee the OD pair r-s. Ucertaity i travel demad radom samplig approach is used with 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 (13). % % q = q + zσ (20) Where, q %, σ 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 (20): 4 0 x a ta ( xa ) = t a G a (21) where, t 0 a ad Ga is the free flow travel time ad capacity for lik a. 9

11 3.2 Decisio Tool for Risk Aalysis Risk is ofte defied as the probability of occurrece of a udesirable outcome. Risk aalysis cosists of simulatig the various iputs for 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 as well as costs. The MOE thus obtaied reflects the effect of risk. I the proposed risk aalysis, a MCS model is used, which employs pre-defied probability distributios 2 to aalyze the effect of idecisive iputs o outputs of the modeled system. The volatility of iputs is expressed through defiig their bouds accordig to the data poits required by the iput distributios. Essetially, a MCS risk aalysis describes the effect of the volatility of iput variables o the simulatio output. Risk ca be quatified ad measured i differet ways (21). Value at Risk (VaR) is oe of such methods ad used i Decisio Tool for Risk Aalysis. VaR ca be defied as the maximum expected loss over a target horizo, with a give level of cofidece (22). 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 area. Surface trade betwee Southwester Otario ad Southeaster Michiga exceeded 200 billio i 2004 ad is expected to icrease by twofold by the year 2030 (23). 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 (24). 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 Widsor i Caada. This large trade volume has a sigificat positive effect o the local, regioal ad atioal ecoomies, through crossborder 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 across the Detroit River, both built durig the late 1920s. AB is a privately owed four-lae 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 2 The pre-defied probability distributio fuctios are obtaied from the ucertaity aalysis. 10

12 arch structure built i The bridge was 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 of people ad goods betwee Michiga ad Otario (24). 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 do ru 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, MDOT, i collaboratio with the Otario Miistry of Trasportatio have idetified a bridge kow as X-10(B) as the most preferred alterative to built i the viciity of the Ambassador Bridge (25). The alterative has bee referred to as the Detroit River Iteratioal Crossig (DRIC) i the case study. Proposed DRIC ad other river crossigs are preseted i Figure RESULTS Two types of bridges are proposed for X-10(B); (1) suspesio bridge, ad (2) cable-stay bridge. The costs 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 reflect the fare collected at the Detroit ed of the bridge. 5.1 Travel Demad Ucertaity The Origi-Destiatio (O-D) matrices (1510*1510) 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 the yea 2045, ad 2050 were 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. 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. 11

13 Blue Water Bridge U.S. Detroit Widsor Tuel Caada Etire Network FIGURE 2 Network of Study Area 12

14 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. TABLE 1 Cost Compoets for DRIC (25) Ivestmet Type Cost (Millio $) Costructio Costs Detroit River Bridge (U.S. Cost Oly) $399 Toll ad Ispectio Plaza $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 GSA Plaza Costs $200 Grad Total Cost $1,814 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 cotais the variatio i travel patter ad icorporates the ucertaity 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 is utilized to 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). 13

15 determie the assiged volume for ca ad trucks. The observed car ad truck volumes are obtaied from MDOT (22). The relative closeess of assiged ad observed volume 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 (26). 5.2 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 i the upper level ad the ridehip determiatio is used i the lower level. The bi-level process is solved i TrasCAD (27). A GISDK script is writte to solve the bi-level 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 procedure is solved by user equilibrium method usig Frak Wolfe Algorithm (20). 5.3 Base Case The base case sceario refe to exclusive etity participatio. Table 2 represets the results for the base case sceario. The results of the base case are preseted for the three etities for differet horizo yea durig the aalysis period. For private etity, the objective is profit maximizatio. For profit maximizatio strategy, it is assumed that the total cost (capital, operatio ad maiteace cost) will be bore by the private etity. As explaied earlier, the profit maximizatio is solved by the bi-level process. I the upper level toll values are set ad i the lower level ridehip is determied. 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 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 cosumer surplus of $ millio, which is higher tha the estimated cosumer 5 Reveue is cosidered as the surrogate of profit ad the i the remaider of the chapter reveue is used i the cases of profit maximizatio. Reveue is defied as the moetary beefit obtaied by the toll/fare collectio oly. 14

16 surplus for profit maximizatio. The cosumer surplus allows more travele 6 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 car ad $4.33 for truck is estimated to be $25.78 millio ad 0.79 respectively. TABLE 2 Base Case Etity Objective Results (25) Year Car Toll ($) Truck Toll ($) Aual Reveue (Millio $) Aual Cosumer Surplus (Millio $) Theil s Iequality Idex 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 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. 7 Represets the Optimal value of car toll from the Private Pepective 8 Represets the Optimal value of truck toll from the Private Pepective 9 Represets the maximum value of Reveue from the Private Pepective 10 Represets the Optimal value of car toll from the Public Pepective 11 Represets the Optimal value of truck toll from the Public Pepective 12 Represets the maximum value of Cosumer Surplus from the Public Pepective 13 Represets the Optimal value of car toll from the User Pepective 14 Represets the Optimal value of truck toll from the User Pepective 15 Represets the miimum value of Theil s value from the User Pepective 15

17 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 results i optimum value for the three objective fuctios defied i equatio 3, 9, ad 12. The highest toll value resulted for the profit maximizatio ad the least toll value for the 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. 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. 5.4 Owehip, Teure ad Goverace Strategies The ecoomic feasibility from etity pepectives is imperative from a ivestmet view poit. The autho iitial work o the cocept of OTG scearios was preseted at the World Coferece o Trasport Research at the Uiv. of Califoria, Berkeley i 2007 (28). 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 ecourage joit etity participatio i the DRIC project. The strategies vary i the degree of participatio by the public ad the private etity. The five types of OTG strategies cosidered are 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 degree of private to public participatio is varied from OTG-1 through OTG-5. 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 (26). The feasibility of OTG strategies are determied by cosiderig the aalysis period till

18 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 collects toll, operates ad maitais the facility. The private etity is permitted to collect toll 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) 16 for OTG-1 strategy is 4.61% over the 35 yea of cocessio period. The Miimum Attractive Rate of Retur (MARR) 17 was assumed to be 6%. The IRR beig less tha the MARR leds the project ecoomically ifeasible for the strategy (OTG-1) tested. FIGURE 5 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 tha the beefit received. The IRR at the ed of 2030 is -1.82) 16 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. 17 MARR is the rate of retur below which the ivestmet proposal is to be deemed uacceptable. 17

19 Other OTG s A complete descriptio of the four other OTG s is provided i the project report (26). 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 cocessio period. These relaxatio policies adopted to ecourage private participatio will obviously reflect o higher fiacial resposibility for the public sector. OTG-5, by cotrast, represets a completely public udertakig, ecompassig all fiacial, maagemet, operatioal ad maiteace resposibilities. 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. Five OTG strategies (with differet optios withi certai strategies) were proposed ragig from exclusive private participatio to exclusive public participatio. The aalysis was coducted with a assumed MARR of 6 percet. Results of this aalysis are preseted i Table 3, ad ca be summarized as follows: For exclusive private participatio (OTG-1), the project is ot 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-4 ad 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. 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 value are set usig a assumed coefficiet of variatio of te percet. MCS techique was used to obtai the simulated cumulative cash flow for desig yea. Radom values are geerated with upper ad lower limits. The radom toll values automaticaly choose the ridehip 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 al realizatio of IRR is plotted i Figure 4. 18

20 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). 19

21 Procedure for Obtaiig 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 OTG-3 cocessio period extesio. The mea IRR of the distributio is 6.04%. Mea of IRR is determied by drawig a imagiary horizotal lie from the 50 th percetile o the secodary Y-axis to the cumulative distributio profile. A imagiary vertical lie ca be draw from the iteectio of 50 th percetile lie from secodary Y-axis ad the cumulative distributio profile to the X-axis. The mea IRR resulted is 6.04%. To determie the 95 th percetile IRR, a imagiary horizotal lie ca be draw from the 5% of the secodary Y-axis to the cumulative probability distributio profile. Further, a vertical lie ca be draw to the X-axis, to determie the 95 th percetile IRR to be 5.99%. The VaR for OTG-3 cocessio period extesio is 5.99%. I other words, the maximum expected loss (or the lower level) i IRR ca be 5.99%. The 95th percetile relative VaR is the differece betwee the mea IRR ad 95th percetile IRR, i.e. 6.04%-5.99% = 0.05%.The 95th percetile relative VaR suggests that the maximum loss i IRR at 95 percetile level of cofidece ca ot exceed 0.05% for the OTG-3 cocessio period extesio strategy. Similarly 90th percetile VaR ca be determied. The 95th ad 90th percetile absolute ad relative VaR is determied for all the strategies, ad preseted i Table % 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 20

22 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 4.66% 4.58% 4.59% 0.08% 0.07% OTG-2 1. Toll Plaza Cost Subsidy 5.19% 5.10% 5.11% 0.09% 0.08% 2. Toll Plaza, Iterchage, ad Ispectio Plaza Cost Subsidy 5.95% 5.86% 5.88% 0.08% 0.07% 3. Costructio Cost Subsidy 5.90% 5.81% 5.83% 0.08% 0.07% OTG3 1. Costructio Cost Subsidy 6.19% 6.10% 6.12% 0.09% 0.07% 2. Cocessio Period Extesio 6.04% 5.99% 6.00% 0.05% 0.04% 3. Costructio Cost Subsidy ad Cocessio Period Extesio 7.24% 7.18% 7.19% 0.06% 0.05% OTG-4 1. Partly Costructio Cost by Private Etity 23.66% 23.19% 23.27% 0.46% 0.39% 2. Operatio ad Maiteace Cost 3.83% 3.74% 3.76% 0.09% 0.07% 3. Public Etity 4.10% 4.01% 4.02% 0.08% 0.08% OTG-5 No Relaxatio 3.65% 3.55% 3.59% 0.10% 0.07% 21

23 6. INTEGRATION OF UNCERTAINTY AND 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. The purpose of this sectio is to itegrate ucertaity ad risk for explorig favorable optios for the DRIC project. For the ucertaity aalysis, IRR is the MOE for all the OTG strategies cosidered ad aalyzed. Likewise, for risk aalysis, the VaR is the MOE for all the OTG strategies. MOE s of both ucertaity ad risk aalysis are preseted i Figure 5 to ivestigate the combied effect of both features o the OTG strategies aalyzed. I Figure 5, the MOE of ucertaity (IRR) is cosidered i the X-axis, ad MOE of risk (VaR) is cosidered i the Y-axis. 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 Itegratio of Ucertaity ad Risk (Note: The outlier i the graph represets higher IRR ad VaR) The favorable OTG strategy is the oe with higher IRR ad lesser relative VaR. Oe the other had the favorable OTG strategy should have IRR greater tha the six percet of MARR. Four OTG strategies resulted i IRR 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, relative VaR is also the highest (0.46%, at 95 percet level of cofidece), which makes the OTG strategy vulerable to future risks. From the remaiig feasible strategies, the combiatio of costructio cost subsidy ad cocessio period extesio strategy (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. 22

24 7. CONCLUSION 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 i a real world case study to augmet the decisio makig process. The etities ofte ivolved i large-scale ifrastructure ivestmet decisio are elisted as: private, public, ad user 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 cosists of the etity uder cosideratio, while the lower level represets a elastic traffic assigmet problem. 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. 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 project. The IRR is cosidered as the measure of feasibility of ucertaity aalysis for OTG strategies. VaR is determied for each OTG strategy. A methodology for itegratig ucertaity ad risk is proposed. It is observed that projects producig higher IRR are also 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. The framework is applied to study the ivestmet decisio makig of DRIC coectig 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 multi-objective framework. 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. ACKNOWLEDGEMENT 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 23

25 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. REFERENCES 1. BTS. Trasportatio statistics aual Report. U.S Departmet of Trasportatio, Bureau of Trasportatio Statistics, Washigto D.C, USDOT. Maual for Usig Public Private Partehips o Highway Projects. Federal Highway Admiistratio, Roth, G. Roads i a market ecoomy. Avebury Techical, Kight, F. H. Risk, Ucertaity ad Profit. New York: AM Kelley, Garber, N., ad Hoel, L. Traffic ad Highway Egieerig. Brooks/Cole. Thompso Publishig Compay, Khasabis, S., Dhigra, S.L., Mishra, S., ad Safi, C. Emergig Roles of the Private Sector i Trasportatio Asset Maagemet i Idia, Compedium of Pape preseted at the 87 th Aual Meetig of the Trasportatio Research Board, Washigto, D.C., Jauary FHWA. P3 Defied. Federal Highway Admiistratio Office of Iovative Program Delivery: Public Private Partehip, Accessed, July 25, Hyma, G., ad Mayhew, L. Toll optimizatio o river crossigs servig large cities. Trasportatio Research Part A, 42(1), 2008, pp Palma, A., Lidsey, R., ad Proost, S. Research challeges i modelig urba road pricig: A overview. Trasport Policy, 13(2), 2006, pp Rouwedal, J., ad Verhoef, E. T. Basic ecoomic priciples of road pricig: From theory to applicatios. Trasport Policy, 13(2), 2006, pp Wog, W. K. I., Nolad, R. B., ad Bell, M. G. H. The theory ad practice of cogestio chargig. Trasportatio Research Part A, 39(7-9), 2005, pp Yag, H., ad Meg, Q. Highway pricig ad capacity choice i a road etwork uder a build operate trasfer scheme. Trasportatio Research Part A, 34(3), 2000, pp

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