A Framework for Analyzing Public-Private Partnerships for Road Transportation under Demand Uncertainty


Dissertation by Ke Wang 
Adviser: Professor Jean-Daniel Saphores 


The 2013 ASCE infrastructure report card gave roads nationwide a “D”. While capital
investments reached $91 billion annually for all levels of government, this falls way short of the
$170 billion that FHWA estimates are needed annually to substantially improve road conditions.
Given politicians’ reluctance to increase revenues for transportation, it is urgent to revisit Public-
Private Partnerships (PPP) to attract capital and engineering expertise from the private sector. It
is well known that applying a standard cost-benefit analysis (which is static and deterministic) to
uncertain projects could be highly misleading (Dixit and Pindyck, 1994) so this paper presents a
real-options framework for analyzing public-private partnerships that could be used to fund roads.
We derive analytical results for the optimal timing and capacity of a new Build-Operate-Transfer
(BOT) highway project between two cities already linked by a congested road when the demand
between these cities follows a reflecting geometric Brownian motion (RGBM). Our framework
includes demand uncertainty, congestion modeled via a Bureau of Public Roads (BPR) function,
endogenous tolls, endogenous road capacity, and it accounts for the lag between the beginning of
a project and its completion. A numerical illustration with realistic parameter values inspired
from the California State Route-125 toll road project shows that ignoring demand uncertainty
could lead to invest prematurely. It was found that (i) ignoring demand uncertainty can lead to
premature investment; (ii) assuming that travel demand can increase infinitely without setting
upper barrier cause severe overestimation of project value with considerable demand uncertainty;
(iii) the demand threshold is always smaller than but not equal to the upper barrier of travel
demand; (iv) capacity choice problem has three possible outcomes depends on project-specific
parameters. In one case, there are multiple demand thresholds and it is optimal to delay the
3 investment even if demand is higher than one of demand thresholds, while the other two cases
can be simplified to problem with predetermined capacity.


Financing, Timing, and Capacity of a New Intercity Highway under Demand Uncertainty: The BOT Case