What steps in the control process will be important as Starbucks tries to reduce the number of paper cups it uses? How can Starbucks maintain its commitment to reducing waste as it keeps sending paper cups to landfills? What benefits does Starbucks gain by controlling this outcome?

There are any number of actions Starbucks could take, but out of the control process, the customer validation and testing step will likely be the most important. In any situation, verifying the voice of the customer is necessary.
When Starbucks attempts to reduce its carbon footprint by removing paper cups from stores, it would do best to phase them out. So as not to alienate customers who aren’t ready for the switch, it could consider increasing its discount for using reusable cups or perhaps offering a more recyclable alternative. This would give it more time to transition away from paper cups while also making a concerted effort to reduce the number it currently uses, all the while maintaining its current customer base.
In the end, there may be a financial benefit for the company, especially if it transitions to primarily reusable cups. By doing this, it would not only help the environment but also no longer need to purchase millions of paper cups annually. Additionally, there would also be a morality benefit for the company itself, which would give it credit and appreciation in the eyes of environmentally conscious customers.

While Starbucks attempts to reduce the number of paper cups it sends to the landfill, there are some vital intermediate steps to ensure they don't crash their own system in the process. First, it needs to implement options other than paper cups, and promote their use—for instance, offering a discount for customers who bring their own reusable mug or tumbler, as many small coffee shops do. Or, it could offer biodegradable or recyclable plastic cups at a small discount as well. This would encourage customers to use better materials while also offering an option that they can integrate into their supply chain.
While it does this, the company must maintain its commitment to reducing waste by showing a preference toward reusable materials and by guiding customers towards better decisions. The benefit to Starbucks is the publicity and public image of being a forward-thinking, "green" company.

The control process has four parts (some experts combine the statement of steps two and three):
Establish standard performance measurements.
Measure performance.
Compare performance to standards.
Take corrective action.
Assume the Starbucks vision and mission statements, strategic plan, and organizational objectives—the bedrock of performance control and corrective action—are up-to-date and reflect current sustainability, non-toxic materials, and green practices standards. The steps in the control process that will be important as Starbucks reduces paper cup use are to establish standards for what is an eco-friendly and sustainable number of paper cups to use; measure actual performance in paper cup use; compare that measured quantity to the established standards; and develop and take corrective action.
Since steps one, two, and three are in part or wholly matters of research and leadership discussion, step four will prove the most challenging. In exploring corrective action plans, Starbucks will have to investigate what potential solutions already exist in the marketplace for reducing plastic-lined paper cup use. For instance, if it is determined that reusable glass containers should replace paper cups, in part or wholly, that corrective action employs an already existing solution: glass bottles and cups. Barring a readily implemented, currently available marketplace solution, Starbucks may determine corrective action requires innovating a presently unknown solution. Consequently, the fourth step of taking corrective action may be the most important—and challenging—of the four needed steps.
https://sloanreview.mit.edu/article/the-control-function-of-management/