ZFW CTLR CONCERNED WITH SECTOR CONFIGN DURING THE MID-SHIFT DUE TO CTLR SICK LEAVE.

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JEN SPECIALTY AT ZFW IS APPROX 360 MI LONG; 2 SECTORS IS NORMAL MIDNIGHT CONFIGN. ON MAR/THU/02; MID-SHIFT CTLR CALLED IN SICK AND OVERTIME WAS NOT AUTH. ALL 6 NAS SECTORS WERE COMBINED AT EDNAS. VSCS FREQS AND LAND LINES WERE DIVIDED BTWN EDNAS AND AQN SECTORS. THIS CREATED A CONGESTED DANGEROUS SECTOR AS TFC BUILT UP. THE CTLR THAT RELIEVED ME ALSO LOST FREQS AS MGMNT ATTEMPTED TO RECONFIGURE VSCS FOR MORNING OP. SUPPLEMENTAL INFO FROM ACN 540425: AT XA30 I RELIEVED THE POS; AND THE DAY SHIFT SUPVR INSTRUCTED ANOTHER CTLR TO OPEN THE OTHER 'NORMAL' MID-SHIFT SECTOR. SINCE THE CONFIGN WE WERE IN HAD NEVER BEEN USED; NO ONE WAS SURE HOW TO DECOMBINE/REOPEN THE OTHER 'NORMAL' SECTOR. IT TOOK 2 SUPVRS APPROX 20-25 MINS TO ACCOMPLISH THIS TASK. IN THE MEANTIME; I WAS WORKING APPROX 15 ACFT USING 2 HANDSETS ON 2 DIFFERENT POS. ALSO THE RANGE NECESSARY TO SEE ALL OF THE INVOLVED AIRSPACE (FROM GLEN ROSE; TX TO W OF WINK; TX; SURFACE AND ABOVE) WAS SO LARGE THAT THE EASTERN HALF OF THE SECTOR HAD TO BE QUICK-LOADED ON AN ADJACENT SCOPE TO MONITOR IN-TRAIL SPACING INTO DFW APCH CTL. THE OSIC ENTERED A MESSAGE TO TRY AND RECONFIGURE VSCS AT THE ORIGINAL POS. THIS RESULTED IN THE LOSS OF FREQS FOR 3 OF MY 6 SECTORS. EVENTUALLY WE RETURNED TO OUR NORMAL MID-SHIFT CONFIGN; BUT THE TRANSITION WAS TOTAL CHAOS. THIS SIT COULD VERY EASILY HAVE LED TO AN OPERROR/OPDEV. THIS ENTIRE SIT WAS CAUSED BECAUSE FACILITY MGMNT WOULD NOT AUTH OVERTIME TO ADEQUATELY STAFF OUR SPECIALTY ON A MID-SHIFT; WHICH LED TO AN UNSAFE SECTOR CONFIGN.