Good message, Bob.
When it comes to getting corrective action to serious problems, I tend to treat suppliers something like the way I treat employees and my kids. That is, I follow a disciplinary progression of conversation/action intended to achieve the desired result, in fairness to all concerned.
Having problems is a natural part of business relationships and personal relationships alike. Surviving problems actually strengthens relationships. as we are "tested", our strengths and weaknesses come out, which enables us to understand one another better, and work together better. Problem-solving becomes a valuable learning experience.
First, I explain the problem and ask nicely for a specific response.
If that doesn't work, I re-state the problem and my expectation for the desired response.
If One and Two don't work with the key contact, then I move on up the ladder of authority until the problem is resolved. At each step, the ones who fail to get it done are aware of what's next. In a big company, it can be time-consuming to touch all the bases.
If One, Two, and Three fail to get results, I become more forceful and start talking about the consequences of not responding. Of course, sometimes the perpetrator doesn't care about consequences. If so, that's important to know, too.
If all of that fails, I might review the whole mess again. Or, if the vibes are really bad, I might just terminate the relationship. (Note: Don't try this with the kids; they keep moving back.)
This progression is for serious problems, and I keep notes of every step (names, dates, promises or comments made, etc.) I don't sweat the small stuff unless it gets big. Then we talk. After all, none of us is perfect and we all make mistakes. Plan on it.
Throughout this communication process I try to remain objective and not let my personal feelings get into the matter. It's business, not personal. And no matter what point of view one has, reason has universal appeal. Besides, few of us function well in emotion mode.
In any case where the relationship is terminated -- whether an employee or a supplier -- the termination is no surprise; they always see it coming l-o-n-g before it happens. Indeed, sometimes it's almost anti-climactic.
So, Pamela, If I were you I'd deal with the supplier privately and not publicly, unless it's a matter of supplier policy/procedure/situation that clearly affects all of us. In that case, it might be good for all of us to know about that. It's your call.