Haven't you heard "time is money!" by your boss or the executive board meeting, when there had been a proposal to improve operations or certain business processes?
Often from the manager's perspective this is meant in the sense, of not "wasting" money through conversations or dialogue dealing with the problem at hand.
How have you learned best in the past to deal with obstacles or constraints in your life? Certainly mostly without time pressure. We took the paths of learning that fitted our personal experience and accumulated knowledge. To do that we needed TIME.
Where and in which context could a manager allow himself to let the use of a bit of extra time (within the set time frame available) to find better solutions for pressing problems today?
Best area will be a process within the organization that is most troubling but rather not having relevant direct impact on the organization's outcome. Do the small experiment with an outreaching impact on the wealth of the organization.
Let an outsider, or by-stander have a deeper look at your business (at best a customer will be also involved) to advice you. Done in a lean thinking way, doing an insightful deep 2-hours conversation could already be really helpful to open up opportunity alleys of the future.
What do you think, would that be worth for your organization?