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Bridges are an important type of transportation infrastructures. Once more than one bridge in a transportation network is extensively or completely damaged in a severe earthquake, the traffic capacity of the network may degrade significantly, resulting in considerable social and economic consequences to the community served. The principles of build back better (BBB) require that the performance level of a critical infrastructure facility should be properly determined in the post-hazard recovery process to reduce the future risk. This paper proposes a continuous-time Markov decision process framework based on life-cycle cost (LCC) for determining the optimum earthquake-resistant levels of the rebuilt bridges. Compared to other optimisation methodologies, the proposed one owns two distinctive features: (1) network-level LCC analyses are performed in the context of BBB principles; (2) optimum decisions are made sequentially at random time points of earthquake occurrence, and the optimum earthquake-resistant level of a rebuilt bridge depends on the performance levels of other bridges in the network. A hypothetical transportation network is investigated to demonstrate the application of the proposed methodology. In particular, the sensitivity of the optimum policy on network topology is studied. [ABSTRACT FROM AUTHOR]