This　paper　studies　a　new　dial-a-ride　problem　(DARP)　called　multiple　depots　heterogeneous　dial-a-ride　problem　with　flexible　depots　(MHDARP-FD),　which　considered　multiple　depots,　heterogeneous　vehicles　and　users,　and　flexible　depots.　The　assumption　of　flexible　depots　allows　the　vehicle　to　end　its　route　at　any　depot.　As　a　result,　the　total　travel　cost　may　be　reduced.　A　mixed　integer　nonlinear　programming　model　was　firstly　formulated　for　the　considered　problem.　To　make　the　MHDARP-FD　tractable,　the　original　model　was　reformulated　by　linearizing　constraints,　aggregating　variables,　and　strengthening　model.　The　new　model　is　solved　by　the　state-of-the-art　IP　solver　CPLEX.　Computational　results　of　numerical　experiments　show　the　validity　of　the　proposed　model　and　its　effectiveness　for　addressing　realistic　problem.　©　2017　IEEE.