How (not) to solve problem

By defining it properly?!

People most often solve problem like this:

h = 3 + 14t − 5t²

So h is equal to... hmmm... h.... h...

Then they look h from all sides but can't find a solution. Because they do not look at equation but only at h. If you define the problem in the way that explains your expectations about solution and with all parameters that your solution depends on, you can in most cases find a solution relatively easy.

This is by far best observed in modern management, where managers cut problems in small portions, departments, and expect problem to be solved without them managing communication and without including all parameters that problem is dependent on. They get nowhere by doing it. 

Also, in most cases everything is thrown on single solution. Management make decision and then all resources are used toward that solution... In many simple cases this is good enough, but in some cases this is devastating. 

And I do not understand why modern management ignore improvisations as part of solution? I do not mean patching problems, but real improvisations, meaning out of blue, not planned solution that actually work. Is that only in my company???