However you do, you might want to do it one-on-one. If A gets upset easily, it's important to let them do that in private instead of in front of the person that is the cause (not assigning blame here). Maybe also give your postdoc some space and time to move past this before assigning them something new. Working two years on something that another student gets in a month is going to be a significant blow to their ego, and they will need some time to get over it.

Well, If A is going to get upset at B for knowing something they didn't, that is A's problem to figure out how to deal with their own disappointment and not take it out on B. Becoming upset with B is just not an acceptable professional action, period. Now, the fact that B came to you first (rather than bringing up the potential idea with A a month ago) I take as a warning sign that B knows it may not go well also, and they already don't have a good working relationship. As their boss, you need to make it clear to A that their behavior needs to be acceptable.

@JonCuster I don't know that I would go so far as saying it's a 'warning sign': it should be very understandable to everyone involved that even if "A" is an absolute saint they're going to be upset by this: they've been working on something for two years, and they're about to hear news that will make them feel very disappointed.

The combined answers of Moishe and Buffy cover all the bases of my thoughts for an answer. Co-authorship on a paper detailing both approaches, and why one is superior (and by how much). B learns about the problem itself from A, A learns about the new approach from B. A provides literature expertise and one method, B provides a solution and another method. In my mind this is a near-equal scientific exchange and a beautiful opportunity for everyone involved.

I hope that it goes that way, and marketing it that way to A may help smooth the situation if there is any perceived risk of friction.

It's understandable that you'd want to avoid sharing too much information about this just yet on a public website. That said.. this might be a scenario where there might be a good play you could make depending on the details. For example, if a professor and a postdoc worked on a problem for 2-years not realizing that there was a simple method for a better solution, then that might reflect a weakness in the field itself that might be constructive to address. Point being, this situation might present a new opportunity.

BTW, this seems like a common issue in computational fields that require a lot of Science/Engineering knowledge to understand. The thing's that folks who go into such fields spend so much of their education working to just understand the background context that they might be under-informed about useful computational methods.

I think OP is trying to get us to solve a problem he stupidly created himself. You have to keep researchers in the same group from making uninvited contributions to each other's projects. OP must have somehow communicated his desire for a better solution than A's to B. This shows a clear management limitation on OP's part. Research groups can't work that way.

@Trunk: sorry, but this is not aplliciable in fields I am familiar with..people jn a group talk about their porblems, give talks..secrecy should never be the way to go!

@user111388 But that didn't happen in this case. B was working for one month on a new approach to A's problem without A's know it. All because the common supervisor wouldn't keep his sentiments on A's work from B. Had A and B discussed the matter of their own accord - and had B then looked into his alternative approach - it would be so different. A would still feel scooped but could not say it was all done behind his back.

@Tru k: where do ,ou get thw one month from?

@user111388 A new postdoc (“B”) joined my lab a month ago. Recently, B told me that they had given some thought to A’s problem . . .

@Trunnk: Yea, they joined a month ago. But you said "B was working for one month on a new approach to A's problem". Where did you get this month from?

@Trunk: See message above. (Sorry, chat on phone is rubbish)