Project Management work is tough enough and it comes with an added bonus - the fact that you're directly accountable if the project fails. What adds to this difficulty is if you have a teammate that is not cooperating.
An example is a teammate who's allocation to your project is confirmed but they are resisting when work is assigned to them in the correct context. Of course, you cannot ask a developer to do work that a business analyst should be doing. However, if a teammate is normally accountable to produce a deliverable and they resist, this becomes a problem.
The first thing that needs to be done is that you need to speak to this resource directly without an escalation. For this, you need to plan for this discussion and what follows are some ideas to help you get prepared.
Firstly, talk with your direct manager about what is going on and that you have a plan to speak to this resource directly. Ask about alternative actions if the resource doesn't cooperate during this meeting. Normally, if the resource doesn't cooperate, this situation will be escalated to the resource's management. You want to make sure your management is involved early so they are not surprised later on.
In preparation for the meeting, write down what this person is doing to negatively impact the project. Be prepared to back this up with proof as this person will likely push back when you confront them. Describe the situation and the specific impact it is having on the project. From here, write down an improvement plan for this resource to get them back on track to being a top performer. Be very specific because you will use these notes during your meeting with this resource.
Then, make sure you understand the full benefits of the project you're working on. You want to do this because you want to leverage this information for when you want to provide motivation for the difficult person to perform. An example would be: If we complete this project this year, our organization is set to realize $25 million in extra revenue over the next 4 years.
When you arrange to meet with this resource, make sure that you make clear what the meeting is about with a good agenda. Allow that person to prepare also so that you can understand their position.
As the meeting gets underway, describe the concerns you have. Be very clear as to how these concerns are impacting the project and emphasize how your project teammates are affected by this person's performance. Let this person also know about the criticality of the project and what benefits it brings. If it's a high-visibility project, emphasize how senior management will know about your team's accomplishments.
At this point, allow the resource to respond to your concerns and gain an understanding as to what's going on so that you can help. For example, if the resource is mentioning they are having difficulty making time to complete tasks, maybe you can help them establish a prioritization system or tell them which tasks are normally high-priority. After this, establish an overall improvement plan with this person so that they can increase their performance. Leverage the information you gathered from your notes when you prepared for this meeting.
If the resource is non-cooperative during the meeting or ignores your call to an improvement plan then this is where you escalate to their management. Begin by debriefing your management on the meeting and establish an escalation plan. Normally, your management will work with you to escalate to the difficult resource's management.
The end result would normally be either the resource being removed from the project or they will continue on in the project under the conditions of their improvement plan.