kobayashi maru of interviewing

Do I have any obligations to complete a scheduled in-person interview with one company if in the meantime I obtain and accept an offer from another company?
 

I started initial contact with two companies on the same day. I committed to appearing at company A for an in-person interview 4 weeks later due to my travel schedule. But company B doesn't require in-person interviews. Using phone and video interviews I complete the interview process with company B and they deliver an offer before I have a chance to meet with company A. I like the offer from B and want to take it. But it doesn't seem fair to A . 

 
Is it better to cancel the interview or proceed with the interview knowing I can't accept an offer? 
 
Either option doesn't seem fair to A because my own travel restrictions delayed their timeline to make an offer. I wouldn't be able to accept an offer with A because doing so would mean I'd have to cancel the offer I already accepted with B. My reputation will be mud. And it's not fair to B, too. Delaying the response to company B's offer could erode goodwill or jeopardize the (only) offer I have in front of me; and I can't delay it until I may or may not get an offer from A.

 
Is there another option?