The first step would be to find out and truly understand why things are the way they are today. They didn't get there on accident - so before cooking up a plan to "improve" the industry you must first understand what the industry would consider an improvement.
Also, it will be difficult to break out into an industry like Airlines. They will be conservative in nature and risk averse. It's unlikely they will take a gamble on an unknown startup's service/platform.
Lastly - the issue they've experienced over the past few days is not something a startup or SaaS platform would have prevented.