Real options models for better investment decisions in road infrastructure under demand uncertainty

An efficient transportation system requires adequate and well-maintained infrastructure to relieve congestion, reduce accidents, and promote economic competitiveness. However, there is a growing gap between public financial commitments and the cost of maintaining, let alone expanding the U.S. road transportation infrastructure. Moreover, the tools used to evaluate transportation infrastructure investments are typically deterministic and rely on present value calculations, even though it is well-known that this approach is likely to result in sub-optimal decisions in the presence of uncertainty, which is pervasive in transportation infrastructure decisions. In this context, the purpose of this dissertation is to propose a framework based on real options and advanced numerical methods to make better road infrastructure decisions in the presence of demand uncertainty. I first develop a real options framework to find the optimal investment timing, endogenous toll rate, and road capacity of a private inter-city highway under demand uncertainty. Traffic congestion is represented by a BPR function, competition with an existing road is captured by user equilibrium, and travel demand between the two cities follows a geometric Brownian motion with a reflecting upper barrier. I derive semi-analytical solutions for the investment threshold, the dynamic toll rates and the optimum capacity. The result shows the importance of modeling congestion and an upper demand barrier – features that are missing from previous studies. I then extend this real options framework to study two additional ways of funding an inter-city highway project: with public funds or via a Public-Private Partnership (PPP). Using Monte Carlo simulation, I investigate the value of a non-compete clause for both a local government and for private firms involved in the PPP. Since road infrastructure investments are rarely made in isolation, I also extend my real options framework to the multi-period Continuous Network Design Problem (CNDP), to analyze the investment timing and capacity of multiple links under demand uncertainty. No algorithm is currently available to solve the multi-period CNDP under uncertainty in a reasonable time. I propose and test a new algorithm called “Approximate Least Square Monte Carlo simulation” that dramatically reduces the computing time to solve the CNDP while generating accurate solutions.