In　this　paper,　we　propose　a　novel　dynamic　decision　method　by　applying　the　sensitivity-based　optimization　theory　to　find　the　optimal　energy-efficient　policy　of　a　data　center　with　two　groups　of　heterogeneous　servers.　Servers　in　Group　1　always　work　at　high　energy　consumption,　while　servers　in　Group　2　may　either　work　at　high　energy　consumption　or　sleep　at　low　energy　consumption.　An　energy-efficient　control　policy　determines　the　switch　between　work　and　sleep　states　of　servers　in　Group　2　in　a　dynamic　way.　Since　servers　in　Group　1　are　always　working　with　high　priority　to　jobs,　a　transfer　rule　is　proposed　to　migrate　the　jobs　in　Group　2　to　idle　servers　in　Group　1.　To　find　the　optimal　energy-efficient　policy,　we　set　up　a　policy-based　Poisson　equation,　and　provide　explicit　expressions　for　its　unique　solution　of　performance　potentials　by　means　of　the　RG-factorization.　Based　on　this,　we　characterize　monotonicity　and　optimality　of　the　long-run　average　profit　with　respect　to　the　policies　under　different　service　prices.　We　prove　that　the　bang-bang　control　is　always　optimal　for　this　optimization　problem,　i.e.,　we　should　either　keep　all　servers　sleep　or　turn　on　the　servers　such　that　the　number　of　working　servers　equals　that　of　waiting　jobs　in　Group　2.　As　an　easy　adoption　of　policy　forms,　we　further　study　the　threshold-type　policy　and　obtain　a　necessary　condition　of　the　optimal　threshold　policy.　We　hope　the　methodology　and　results　derived　in　this　paper　can　shed　light　to　the　study　of　more　general　energy-efficient　data　centers.