There was no end button for the missions, though. They would be assigned to take the quest and deduce the game time, happiness and compliance which is shown in their stats at the mission's tab. They will return also with the materials they have collected from the mission instantly too (or if you have low prob chances that they will fail frequently too.)
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Also if their happiness and compliance are negative it means you abused them much and since the game isn't finish they will stay that way until the story progress, even though they like you. You should also consider your story progression (some are probably stuck due to the player not progressing, the crew respect on you (which contributes why they don't want to work).