We investigate the relationship between the Lagrangian Floer superpotentials
for a toric orbifold and its toric crepant resolutions. More specifically, we study an open
string version of the crepant resolution conjecture (CRC) which states that the Lagrangian
Floer superpotential of a Gorenstein toric orbifold X and that of its toric crepant resolution
Y coincide after analytic continuation of quantum parameters and a change of variables.
Relating this conjecture with the closed CRC, we discover a geometric explanation (in terms
of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots
of unity which appeared in Y. Ruan’s original CRC [39]. We prove the open CRC for the
weighted projective spaces X = P(1, . . . , 1, n) using an equality between open and closed
orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem
for these toric orbifolds.