A Consistent Markov Chain-Based Framework for Life-Cycle Optimization and Cost–Benefit Evaluation of Infrastructure Maintenance Policies

A consistent computational framework is presented that integrates Markov chain modeling, decision optimization, and cost–benefit analysis for the life-cycle management of engineering assets. The approach combines deterioration modeling with a complete economic evaluation and optimization of maintenance decisions. Each condition state of the system is associated with possible actions such as do-nothing, preventive maintenance, major repair, and replacement, each defined by its own transition matrix or generator describing state changes. The expected one-step reward is formulated as the difference between benefits and all relevant costs including operating, action, and failure costs. The optimization problem is expressed as a discounted Markov decision process and solved by linear programming. The resulting stationary policy specifies the optimal decision rule for every state. Both discrete-time and continuous-time variants are implemented. Transition matrices and generator matrices are linked using a matrix exponential mapping for the selected step length. Under state-dependent policies, the discrete step model and the continuous-time feedback model may lead to different long-run state shares. This is caused by different decision timing. The continuous-time variant also provides reliability indicators such as survival and hazard. It can also provide mean time to absorption under an absorbing failure interpretation. Simulation under the optimal policy yields state trajectories, present values of benefits and costs, and key economic indicators such as net present value, benefit–cost ratio, equivalent annual cost, and equivalent annual net benefit. The framework forms a unified and practical tool that connects reliability analysis, Markov optimization, and life-cycle cost–benefit evaluation for long-term infrastructure management.