Travel time resilience of roadway networks under disaster

A bi-level, three-stage Stochastic Mathematical Program with Equilibrium Constraints (SMPEC) is proposed for quantifying and optimizing travel time resilience in roadway networks under non-recurring natural or human-induced disaster events. At the upper-level, a sequence of optimal preparedness and response decisions is taken over pre-event mitigation and preparedness and post-event response stages of the disaster management life cycle. Assuming semi-adaptive user behavior exists shortly after the disaster and after the implementation of immediate response actions, the lower-level problem is formulated as a Partial User Equilibrium, where only affected users are likely to rethink their routing decisions. An exact Progressive Hedging Algorithm is presented for solution of a single-level equivalent, linear approximation of the SMPEC. A recently proposed technique from the literature that uses Schur’s decomposition with SOS1 variables in creating a linear equivalent to complementarity constraints is employed. Similarly, recent advances in piecewise linearization are exploited in addressing nonseparable link travel time functions. The formulation and solution methodology are demonstrated on an illustrative example.