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Is processing airline payment really “complex”, like something that cannot be computed or automated, or is it only “complicated”, like something that takes time and knowledge but can be automated?

This article by Duffel is actually an excellent summary of why airline payments are “complicated”:
? the multiple layers of intermediaries (payment gateway, PSP, seller, GDS, BSP) between the customer and the airline, with one or many vendors for each layer, and each time a specific agreement is required
? the issues to manage in the payment flow (rising card fees, virtual cards, refunds, chargebacks, credit risk, fraud…)

It is “complicated”, i.e. it takes knowledge and time, but it is not complex, in the sense that airlines collect annually 100s of billions of dollars (pre-Covid) using multiple payment methods.

It is “complicated” means that if airline payments were invented today, we would make them simpler. This was the point of the IATA’s Simplifying the Business program since 2004, for example:
? It is simpler to store an e-ticket than to carry a paper ticket
? It is simpler to show a barcode on a phone than to print a paper boarding pass

In a “complicated” problem, you know what you don’t know. You can plan and program for it. In a “complex” problem, you don’t know what you don’t know. You cannot program for it. The Clay Institute explains that for a complex problem, it is easy to verify a solution, once you know it, but it is almost impossible to find a solution. See links in comments.

The difference between “complicated” and “complex” has a major implication in business – see link to article in comments. For example, running a multi-year multi-stakeholder global change program is complex, with many unknowns (nobody knows) – but implementing an airline payment solution is complicated, with some unknowns (but someone knows). The approach to planning, risks, resources, etc. will vary depending on the nature of the program.

Back to airline payments, I see two opportunities to make them less complicated:
? Remove some layers of intermediaries, aiming for solutions that connect seamlessly customers to airlines, e.g. a digital wallet
? For the remaining layers, focus on solutions that facilitate the transition from (virtual) cards to more efficient payment methods, e.g. a payment gateway that supports crypto payments