Markov Decision Process Theory with State Aggregation for Large-Scale Infrastructure Maintenance Planning in Federal Nigeria

Infrastructure maintenance planning across Nigeria's extensive road, bridge, and public building portfolio presents a large-scale Markov decision process (MDP) problem in which the curse of dimensionality renders exact dynamic programming solutions computationally infeasible, necessitating theoretical advances in state space approximation and value function representation. This dissertation develops original Markov decision process theory with state aggregation methods for large-scale infrastructure maintenance planning, with theoretical innovations motivated by the empirical characteristics of federal infrastructure deterioration and maintenance processes in Nigeria. A comprehensive review of infrastructure maintenance optimization, MDP theory, and approximate dynamic programming literature establishes the state of knowledge and identifies critical gaps in state aggregation methods for infrastructure applications with spatially correlated deterioration and maintenance budget constraints. Original theoretical contributions include: a novel state aggregation scheme based on infrastructure condition clustering with formal bounds on value function approximation error; a Lagrangian relaxation approach to decoupling geographically distributed infrastructure assets with budget constraint handling; and convergence results for a temporal difference learning algorithm adapted for infrastructure deterioration MDPs with non-stationary transition dynamics. The theoretical framework is applied to a dataset of 4,200 federal road segments across Nigeria's six geopolitical zones, with deterioration model parameters estimated from Federal Roads Maintenance Agency inspection records. Optimal maintenance policies generated by the framework reduce expected total life-cycle cost by 23 percent relative to current maintenance practice over a 20-year planning horizon. Keywords: Markov decision process, state aggregation, infrastructure maintenance, dynamic programming, Nigeria