Demand-responsive　transit　(DRT)　with　smartphone-based　applications　is　emerging　as　a　flexible　and　sustainable　mobility　service,　transforming　urban　transportation.　Nevertheless,　to　satisfy　the　real-time　and　inconsistent　demand,　it　is　becoming　increasingly　important　to　capture　the　decision-making　psychology　of　order　cancellations.　In　this　study,　a　two-phase　optimization　framework　is　presented　in　response　to　real-time　disruptions,　including　order　cancellations　and　the　insertion　of　new　real-time　passengers.　In　contrast　to　random　real-time　demand,　this　paper　is　more　concerned　about　the　impacts　of　the　feedback　information　on　order　cancellations.　Bounded　rationality　is　incorporated　into　the　model　to　discuss　the　decision-making　process　of　cancellation　behaviors.　With　regard　to　the　soft　window,　a　compensation　strategy　is　proposed　to　promote　the　profit　while　encouraging　passengers　for　a　long-term　use.　Additionally,　solution　algorithm　based　on　variable　neighborhood　search　(VNS)　and　rolling　horizon　is　constructed　to　approach　the　Pareto　solutions　set.　To　testify　the　validity　of　the　proposed　algorithm,　small-scale　experiments　in　simplified　Sioux　Falls　network　are　investigated　for　multiple　runs.　Meanwhile,　a　real-world　case　study　in　Beijing　is　explored　to　evaluate　the　system　performance　considering　real-time　disruptions.　The　results　indicate　that　the　dynamic　DRT　service　can　substantially　improve　the　system　profit　but　increase　the　penalty　cost.　The　profit　presents　a　significant　improvement　to　940　(renminbi)　RMB　as　a　result　of　the　insert　of　real-time　passengers.　This　study,　therefore,　not　only　provides　a　deeper　insight　into　the　analysis　of　passenger　cancellation　behavior　but　also　contributes　to　construct　a　more　flexible　DRT　service.