This　work　investigates　the　problem　of　optimally　locating　an　automotive　service　firm　(ASF)　subject　to　stochastic　customer　demands,　varying　setup　cost　and　regional　constraints.　The　goal　is　to　minimize　the　transportation　cost　while　maintaining　the　specified　profit　of　the　ASF.　This　work　studies　two　variants　of　the　problem:　ASF　location　with　known　demand　probability　distributions　and　with　partial　demand　information,　i.e.,　only　the　support　and　mean　of　the　customer　demands　are　known.　For　the　former,　a　chance-constrained　program　is　formulated　that　improves　an　existing　model,　and　then　an　equivalent　deterministic　nonlinear　program　is　constructed　based　on　our　property　analysis　results.　For　the　latter,　a　novel　distribution-free　model　is　developed.　The　proposed　models　are　solved　by　solver　LINGO.　Computational　results　on　the　benchmark　examples　show　that:　i)　for　the　first　variant,　the　proposed　approach　outperforms　the　existing　one;　ii)　for　the　second　one,　the　proposed　distribution-free　model　can　effectively　handle　stochastic　customer　demands　without　complete　probability　distributions;　and　iii)　the　results　of　the　distribution-free　model　are　slightly　worse　than　those　of　the　deterministic　nonlinear　one,　but　the　former　is　more　cost-efficient　for　the　practical　ASF　location　as　it　is　less　expensive　in　obtaining　demand　information.　Moreover,　the　proposed　models　and　approaches　are　extended　to　address　a　multi-ASF　location　allocation　under　demand　uncertainty.