HDG TRACK DEV DURING CRUISE WHEN FLC IS IN A NON ADHERENCE TO ATC CLRNC INSTRUCTION. ALSO A POSSIBLE ARTCC ARTCC INTERFAC COORD PROBLEM.

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ON AUG/MON/92 WE HAD AN ACTUAL DAY OF 8+17 INCLUDING OUR FIRST LEG A DEADHEAD LEG OF 2+15. A PM32 PDT ARR IN LAX WITH A 25 HR LAYOVER FOLLOWED BY A 'RED EYE' TO MKE. MEETING IN THE HOTEL LOBBY WE ALL REMARKED ON HOW LITTLE SLEEP WE HAD ALL RECEIVED DURING THE DAY; FROM 2 HRS OR LESS; PRIOR TO OUR FLT. DEP AND CRUISE TO MKE WERE NORMAL; ON ARR AT MKE APCH CTL GAVE US 3 DIFFERENT ARR RWYS PRIOR TO A FINAL SELECTION OF 19; HAVING TO PROGRAM THE FMCG 3 DIFFERENT TIMES PRIOR TO LNDG. APCH AND LNDG WERE UNEVENTFUL. WE MAKE AN ACFT CHANGE FOR A FLT TO MSP. ACFT WAS FULL WITH 2 PEOPLE REQUESTING THE JUMPSEAT AND AN AGENT LOOKING FOR AN ON TIME DEP. A HURRIED DEP BUT WE WERE READY. TKOF WAS UNEVENTFUL. ON CLB SEVERAL HDG CHANGES WERE GIVEN UNTIL A DIRECT MSN WAS RECEIVED. WE WERE FILED FOR FL330 RECEIVED FL280 AS A FINAL. RTE OF FLT WAS MSN DIRECT RST; V411 FGT. FROM MSN TO RST WE RECEIVED SEVERAL INSTRUCTIONS FROM ATC IN REGARDS TO ALT AND HDGS AND AIRSPDS. ORD ARTCC GAVE US A PRESENT HDG UNTIL FURTHER ADVISED. I ASSUMED THE FO; WHO WAS FLYING; PULLED THE HDG KNOB AS OUR HDG WOULD FOLLOW OUR GREEN FLT PATH LINE FOR THE NEXT 200 MI TO THE RST VOR. I DID NOT CONFIRM WITH THE FMA AS TO THE PROPER SELECTION OF THE HDG KNOB. I DID READ BACK THE PROPER INSTRUCTION OF ATC BUT THEN MY DUTIES WERE TO THEN LISTEN AND COPY THE MSP ATIS AND THEN GIVE AN IN-RANGE RPT WITH MSP OPS. AFTER THE IN-RANGE RPT WAS MADE; OPS INFORMED US THAT A RANDOM DRUG TEST WAS TO BE CONDUCTED OF THE PLTS; AFTER INFORMING THE FO OF THE DRUG TEST OUR CONVERSATION THEN CONCENTRATED ON THE FACT OF A DRUG TEST AT THE END OF A RED EYE WITH 2 LEGS AND HOW TIRED WE WERE. AND THE CONSTITUTIONALITY OF THE DRUG TESTING. AT THAT POINT THE ACFT WAS OVER THE RST VOR AND MADE A TURN TO INTERCEPT V411; SHORTLY AFTER MSP ARTCC ASKED OUR HDG AND INFORMED US TO TURN BACK TO A 270 HDG TO FOLLOWING TFC ON THE ARR. THE CTLR THEN SAID THAT THE PREVIOUS CTLR SHOULD HAVE GIVEN US THAT HDG WHICH I RESPONDED WITH 'UNDERSTAND.' WE WERE NEVER IN A POS TO CONFLICT WITH THE ARR TFC AND THE REMAINDER OF THE FLT TO MSP WAS UNEVENTFUL. RED EYES WITH A FOLLOWING LEG HAVE BEEN MORE COMMON THAN THE NORM OF LATE AT MY AIRLINE. THE FIRST LEG WENT UNEVENTFUL CONSIDERING THE AMOUNT OF ACTUAL SLEEP WE RECEIVED DURING THE DUTY PERIOD AND PREVIOUS REST PERIOD. HAVING TO PROGRAM THE FMCG SEVERAL TIMES ON THE APCH ADDS TO THE FATIGUE LEVEL; THEN TO FLY A LEG TO A HUB ARPT AT A PEAK TFC TIME FOR ARRS; WHERE MULTIPLE TASKS SUCH AS STEP CLBS; AND HDG CHANGES; INCREASED WORKLOADS OF A 2-PLT ACFT WHERE ACARS IS INOP BURDENS ONESELF TO AN INTENSE LEVEL OF FATIGUE. OTHER PLTS HAVE CALLED IN TIRED AT THE END OF A RED EYE FLT WHERE A CONTINUATION EXISTS; THEY HAVE GONE TO A HOTEL FOR A REST PERIOD; THAT DOESN'T HELP IN THE RELIABILITY OF THE AIRLINE SCHEDULES; HOWEVER; FOR SAFETY AIRLINES SHOULD NOT SCHEDULE A SECOND SEGMENT AFTER A RED EYE FLT. A REST PERIOD SHOULD FOLLOW A RED EYE SEGMENT.