Facility-level and system-level stochastic optimization of bridge maintenance and replacement decisions using history-dependent models
This dissertation addresses the determination of optimal decisions for bridge maintenance and repair both for one facility and for a system of heterogeneous facilities. Deterioration models are used to predict the future condition of facilities, which is required in the optimization. More specifically, deterioration models decrease or capture the uncertainty regarding future condition. This dissertation concentrates on the use of deterioration models that take into account aspects of the history of deterioration and maintenance.
The first part of the dissertation presents the optimization of bridge inspection, maintenance, and repair decisions for a system of heterogeneous facilities, using a deterioration model from the literature; this model is non-Markovian, and its formulation makes the optimization problem computationally complex. The determination of exact optimal solutions is unlikely to be achieved in polynomial time, and we derive bounds on the optimal cost. We show in a case study that these bounds are close to the optimal cost, which indicates that the corresponding policies are near optimal.
The second part of the dissertation presents the optimization of maintenance and repair decision for a system of heterogeneous bridge decks, using a Markovian deterioration model. The dependence of this model on history is achieved by including aspects of the history of deterioration and maintenance as part of the state space of the model. We present an approach to estimate the transition probabilities of the model, using Monte Carlo simulation. This model is then used to formulate the problem of optimizing maintenance and repair decisions for one bridge deck as a finite-state, finite-horizon Markov decision process. Numerical simulations show that the benefits provided by this augmented-state model, compared to a simpler Markovian model, are substantial.
Based on the facility-level results, optimal maintenance and repair decisions are determined for a system of heterogeneous facilities. Recommendations are provided for each facility, and we provide formal proofs of optimality in the continuous case. A numerical study shows that the results obtained in the discrete-case implementation seem to be valid approximations of the continuous-case results. The computational efficiency of the system-level solution makes this approach applicable to systems of realistic sizes.