Take a scenario where the project deadline is predetermined by senior management and the project team is asked to execute.
Is there any methodology which can be used?
How can a project plan be created in such a case?
Planning values are always fixed. No one in their right mind will commission a project with an open checkbook and timeline. Planning values are typically aggressive and optimistic, as they should be, because who wants to commit to pay for a product or an outcome more than other pays for the same product or outcome?
So you create your plan and schedule targeting those aggressive planning values and then expose the risk you are facing in execution. And then during execution, you forecast and expose your variances to management as you move along, with any mitigation strategies you can develop and use. And, if your forecasting a late delivery or over cost budget with no chance of recovery, communicate it out and request use of your contingency/reserve dollars and finish your project.
Work is and will always be probabilistic. Targets will likely always be optimistic. And you will always have variances, sometimes favorable, sometimes unfavorable. Great PM is not about meeting targets all the time but is about knowing where you are, predicting where you're going, communicating effectively, planning for risks, and having plans b and c to cover those risks when they're realized.
Sure; the example you give, while not ideal (particularly the part where the timeline is decided by management, rather than the team), is not impossible to work in. Nor is it that uncommon, unfortunately.
Most methodologies should still work, you just have to frame your thinking differently. For instance, instead of determining whether or not you need to extend your deadline (which in this case is possible), you can determine whether or not you need to strip out some of the features.
If that's not possible (ie. if both time and scope are fixed), then the most significant benefit from forecasting is determining how likely you are to succeed/fail at the project - there's not much way to actually prevent it from failing.
If the schedule is fixed, you will need some wiggle room on the other corners of your project management triangle (cost, schedule, scope). If you are free to reduce your scope, you are fine. If you are not, you might need more resources, which increases cost. If your fixed on all three of them, you're in trouble.
As for as a methodology is concerned, it's hard to tell what works for you. If you are strictly time boxed, your requirements are yet unclear or changing quickly and your scope is flexible, you might want to go ahead agile (e.g. SCRUM). In a different environment another approach might work. But for that we'd need to know more detail, e.g. type of project, requirements, team etc.