A stochastic programming approach for budget allocation to structural strengthening and post-earthquake buildings repair in seismic areas

In this work we study the optimal budget allocation for proactive strengthening actions on buildings located in seismic areas and reactive repair after an earthquake. The problem is modeled as a two-stage stochastic model with recourse, in which the goal is to minimize the number of evacuated people. A maximum cumulative budget is allowed for proactive and/or reactive actions. For each building is known the vulnerability level, the cost of three levels of seismic strengthening, (seismic retrofitting, seismic improvement, or local strengthening) as well as the reduction of vulnerability achievable with each type of action. We also know the repair cost corresponding to 5 different post-earthquake damage levels. A set of earthquake outcome scenarios is generated, for each one of which is known the level of damage which would occur on each building if no reinforcement action were undertaken. The strongest is the reinforcement action, the lower is the probability that a specific level of damage occurs. We provide a mathematical formulation in which first stage variables address the decisions related to which type of strengthening action undertake on which building, while the second-stage ones deal with the repair decisions. The solution of the stochastic model is compared with several different deterministic approaches. Results show the strong benefit achievable by exploiting a stochastic programming approach, and determine, under which conditions, a deterministic approximation could be considered a viable option. Detailed results on a real case analysis based on a small town in Sicily (Patti) are discussed and analyzed.