This　study　addresses　the　problem　of　optimally　locating　vehicle　inspection　facilities　under　uncertain　customer　demand　and　varying　velocity　considering　regional　constraints.　The　objective　is　to　simultaneously　minimize　the　transportation　time　of　all　customers　and　their　transportation　cost,　while　ensuring　consumers　to　reach　their　desired　destinations　within　their　expected　time　and　cost.　We　study　two　variants　of　the　problem:　vehicle　inspection　location　with　complete　probability　distributions　of　customer　demand　and　vehicle　velocity,　and　that　with　partial　information　of　customer　demand　and　vehicle　velocity,　i.e.,　only　the　supports　and　means　of　the　stochastic　variables　are　known.　For　the　former　problem,　an　expected　value　model　and　a　chance-constrained　program　are　first　formulated.　Then　based　on　explored　problem　properties,　the　expected　value　program　is　equivalently　reformulated　as　a　deterministic　non-linear　program.　To　efficiently　deal　with　the　chance-constrained　program,　a　sample　average　approximation　(SAA)-based　approach　is　proposed.　For　the　latter　one,　we　develop　a　new　distribution-free　model.　Computational　results　for　benchmark　examples　demonstrate　that:　i)　for　the　former,　the　proposed　deterministic　program　reformulation-based　approach　and　SAA　algorithm　outperform　the　state-of-the-art　approaches;　ii)　for　the　latter,　the　proposed　distribution-free　model　can　effectively　deal　with　the　problem　with　partial　demand　and　velocity　information.