Service　operation　problems　arising　from　electric　carsharing　services　have　been　the　research　subject　of　many　scholars　in　the　past　few　years.　Previous　studies　did　not　consider　customers’　psychological　waiting　stress　in　the　decision-making　of　electric　carsharing　services.　This　study　addresses　a　fleet　size　problem　for　one-way　electric　carsharing　services　while　considering　vehicle　relocation,　vehicle　charging,　and　customers’　waiting　tolerance　as　well　as　psychological　waiting　stress.　A　mixed-integer　nonlinear　programming　(MINLP)　model　is　first　developed　for　the　problem.　By　exploring　the　model　convexity,　we　put　forward　an　effective　outer-approximation　algorithm　such　that　the　Ε-optimal　solution　can　be　obtained.　Numerical　experiments　are　conducted　to　demonstrate　the　efficacy　of　the　proposed　model　and　solution　method.　We　also　analyze　how　the　consideration　of　customers’　waiting　tolerance　and　waiting　stress　influences　the　fleet　size,　system　profitability,　and　service　level.　©　2024　Elsevier　Ltd