MD88 ACFT IN CRUISE WAS GIVEN CLRNC TO CLB AND FLC DIDN'T START CLB UNTIL QUESTIONED BY CTLR.

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AFTER DEP FROM CVG; DURING CLB TO CRUISE ALT; ATC (ZID) ASSIGNED A HEADING. WHILE STILL ON THAT HEADING; WITH ACFT LEVEL AT FL230; ATC ASSIGNED 'MAINTAIN PRESENT HEADING; CLB MAINTAIN FL310.' THE FO (PNF) RESPONDED AND PUT THE ALT IN THE ALT WINDOW. WITH THE AUTOPLT ENGAGED; I (PF) SHOULD HAVE PUT THE ASSIGNED ALT IN THE WINDOW. NO ACTION WAS TAKEN TO INITIATE THE CLB. SHORTLY THEREAFTER ATC AGAIN ASSIGNED; 'CLB MAINTAIN FL310.' I NOTICED FL310 WAS ALREADY IN THE WINDOW AND I INITIATED THE CLB. ATC DID NOT MENTION ANY TFC CONFLICT AND SOUNDED NORMAL (DID NOT SOUND CONCERNED). I AM NOT CERTAIN HOW MUCH TIME PASSED BTWN CLRNCS. FACTORS: 1) INEXPERIENCE. I AM RELATIVELY NEW CAPT (LESS THAN 200 HRS); SECOND MONTH. THE FO WAS ONLY 3 MONTHS IN HIS FIRST R SEAT WITH THE COMPANY; AND NEW TO FMS ACFT. 2) FATIGUE. I HAD ARRIVED HOME PAST MIDNIGHT THE PREVIOUS EVENING AFTER COMPLETING A 4 DAY TRIP WITHOUT MUCH SLEEP OPPORTUNITY; THEN GOT CALLED OUT ON RESERVE FOR THIS TRIP. 3) FIRST FLT WITH THE OTHER CREW MEMBER. 4) FMS ON MD88 DOES NOT INITIATE AUTOMATIC CLB WITH NEW ALT IN THE WINDOW. MY PREVIOUS ACFT (B767) DID. INTERRUPTION OF NORMAL HABIT PATTERNS PROBABLY CAUSED THE EVENT (PF PUTS ALTS IN WINDOW WITH THE AUTOPLT ENGAGED); COMBINED WITH FATIGUE. MORE CLOSELY MONITOR SIT WITH LESS EXPERIENCED CREW MEMBERS.