A COMPUTER FLT PLAN ANOMALY ALLOWED A B737-400 TO OPERATE WITH LESS FUEL THAN REQUIRED AND SO HAD INSUFFICIENT ALTERNATE FUEL.

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I FLT PLANNED FLT ZZZ-ZZZ2-ZZZ3-ZZZ WITH OUR FLT PLANNING SYS WHICH IS WHAT WE USE FOR ALL FLT PLANS. I REQUESTED A FLT PLAN FOR THE FINAL LEG ZZZ3 TO ZZZ WITH A 25000 LB PAYLOAD AND ALTERNATE. THE ZZZ3-ZZZ FLT CAME BACK WITH A FUEL BURN OF 2757 LBS; FLT TIME OF 49 MINS AND DISTANCE OF 305 MI. THE ACTUAL DISTANCE FOR THIS FLT IS 481 MI AND TAKES ABOUT 1 HR 17 MINS AND WILL BURN ABOUT 7600 LBS OF FUEL. WITH THE ALTERNATE AND 45 MIN RESERVE FUEL ON THIS FLT AND 300 LBS OF TAXI FUEL; THE REQUIRED FUEL CAME UP TO 10335 LBS. NEITHER THE FLT CREW NOR MYSELF NOTICED THAT THIS WAS A LIGHT FUEL LOAD FOR THIS FLT THUS OPERATED WITH 10400 LBS OF FUEL AND LANDED IN ZZZ WITH 4200 LBS OF FUEL; FAR SHORT OF WHAT HE WOULD HAVE NEEDED TO DIVERT TO AN ALTERNATE. THIS SEEMED TO BE A SINGLE ANOMALY IN THE FLT PLANNING SYS THAT COULD NOT BE EXPLAINED BY OUR FLT PLANNING VECTOR. DURING MY SHIFT ON AUG/XA/06; I REQUESTED AT LEAST 54 FLT PLANS WITH THIS COMPUTER SYS. I AM RESPONSIBLE FOR THE WX; REGULATORY COMPLIANCE AND SAFETY OF ALL THESE FLTS. I DO NOT HAVE TIME IN AN 8 HR SHIFT TO CHK THAT THE COMPUTER GENERATED FLT PLANS ARE USING THE CORRECT DISTANCES ON OUR STORED RTES. SUPPLEMENTAL INFO FROM ACN 706148: FO CALLED ME AFTER LNDG IN ZZZ; SAYING FLT PLAN HAD AN UNUSUALLY SHORT FLT TIME. I COMPARED THE TOTAL DISTANCE BTWN THIS FLT PLAN AND A FLT PLAN ON ANOTHER ACFT FLYING ZZZ3-ZZZ -- THE DISTANCE ON THE BAD FLT PLAN WAS SHORT BY 176 MI. NEITHER THE DISPATCHERS NOR THE FLT CREW CAUGHT THIS ERROR. AS A RESULT; THE FLT LANDED ZZZ WITH ONLY 4200 LBS OF FUEL.