Hearts' home match with Inverness will be one of the opening fixtures in the Betfred Cup first-round group stage.
The match will be one of 12 on the evening of Tuesday 6 October, with four more games the following night.
Dunfermline will meet Falkirk on 9 October and St Johnstone host Premiership and Tayside rivals Dundee United on 10 November.
And, on 11 November, there will be a Renfrewshire derby between St Mirren and Greenock Morton in Paisley.
Eight of the 12 Scottish Premiership clubs and all clubs from the Championship and Leagues One and Two feature in the group stage along with Highland and Lowland League winners Kelty Hearts and Brora Rangers.
Aberdeen, holders Celtic, Motherwell and Rangers, who all have upcoming European matches, enter at the second-round knockout stage.