A stochastic optimization model to support decisions in infrastructure operation projects (2020)
Public Private Partnerships (PPPs) are associations between a private party and a government agency for providing a public asset or service, most commonly infrastructure. Financing comes from an upfront investment from the private sector but requires funding from financial institutions, and payments from the public sector and/or users over the project's lifetime. The private partner's role in the partnership is the design, completion, implementation and funding of the project, while the public partner focuses on defining and monitoring compliance with the objectives. This research is focused on PPPs associated to maintenance of a road throughout a given horizon. We propose a stochastic optimization model that describes the life-cycle performance of the system (as a result of deterioration and maintenance processes), and the private partner's earnings and costs associated to maintenance decisions. A Mixed Integer Program (MIP) is formulated to model the situation, and the resulting problem is solved by the Sample Average Approximation (SAA) method using Monte Carlo simulation. We generate realizations of the deterioration process considering the system degradation as a general increasing Non-Homogeneous (NH) Lévy process. We model progressive and shock-based degradation using a Gamma Process and a compound Poisson process, respectively, and we consider multiple sources of degradation by the superposition of any of these models. We provide a decision-support tool for private entities involved in infrastructure projects operated via PPPs that can be used for the analysis of diverse scenarios by running the model under different conditions. We test our methodology with a synthetic case study based on available information for infrastructure projects executed under PPPs in Colombia