To　achieve　effective　care,　it　is　critical　to　match　patients　with　capable　physicians　in　specialty　care.　Motivated　by　the　rising　popularity　of　patient-and-physician　matching　applications　in　specialty　care,　this　study　optimizes　the　matching　and　appointment　scheduling　problems　simultaneously　in　a　stochastic　environment,　in　which　a　decision-maker　determines　the　patient-and-physician　pair　assignment　and　the　starting　times　of　services.　We　develop　a　stochastic　optimization　model　to　minimize　the　matching　and　operational　costs　(i.e.,　patients’　waiting　time　costs,　service　providers’　idle　time　and　overtime　costs).　This　paper　is　the　first　study　that　incorporates　matching　and　appointment　scheduling　problems　together.　The　benefits　of　combining　these　two　problems　are　enormous.　The　experimental　results　show　that　the　operational　costs　gap　is　as　large　as　51%　between　the　ill-matched　and　the　well-matched　patient-and-physician　scenarios.　We　first　reformulate　this　problem　as　a　two-stage　optimization　problem.　With　the　analysis　for　the　optimal　solution　of　the　second　stage　problem,　a　Benders　decomposition　algorithm　is　developed.　To　improve　the　efficiency　of　the　proposed　algorithm,　we　also　prove　a　low　bound　of　our　problem　and　use　it　to　construct　a　set　of　feasibility　cuts.　Then,　we　extend　our　method　to　incorporate　no-shows.　Our　algorithm　can　solve　problems　efficiently,　and　it　can　obtain　optimal　solutions　for　medium-size　problems　within　2　or　3　min.　In　contrast,　traditional　optimal　methods　require　nearly　2　h.　For　large-size　problems,　our　algorithm　can　obtain　optimal　solutions　within　5　or　6　min,　whereas　traditional　optimal　methods　cannot　generate　a　result　within　5　h.　Finally,　numerical　experiments　are　conducted　to　evaluate　the　performance　of　our　proposed　algorithm　and　to　investigate　the　variation　of　the　optimal　solutions　in　different　scenarios.　To　provide　quality　care　as　well　as　minimize　the　total　cost　of　appointment　scheduling　in　specialty　care,　we　suggest　that　physicians　should　develop　or　train　their　specialties　based　on　the　local　patients’　disease　pattern.　We　also　disclose　that　the　no-show　has　less　influence　on　the　service　system　when　the　weight　of　the　matching　cost　is　substantial.　©　2020　Elsevier　Ltd