LEAN

Just to make sure you understand what lean manufacturing is all about, I wish to explain the following. "Lean" is eliminating waste from your value stream, pure and simple.  The result is many things, lower operating expenses, shorter lead times, increased value added ratio, reduced quality issues, etc.  Waste comes in many different forms.  Overproduction, producing product before the next process or operation is ready to consumeit, is only one form of waste.  It is waste because the products value added ratio (the time value is being added versus total time in the valuestream)is low, also you need more space to store the overproduction, also you increase your exposure for potential rework (more waste).  I am only covering this because of your comment "minimize inventory level and shorten lead time". The goal of any business is first to satisfy the customer demand/need, and to do that in such a way as to make a profit, so you can continue to stay in business to do that. What I am trying to tell you is that you need a clearly defined purpose, one that everyone in the organization can clearly understand for "going Lean", and look to your customer - your competition - your market for this purpose.
 I'll give you an example: In my industry (connector manufacturing) my customers want quality products, when they want them, at a competitive price.  Sounds easy enough.  But they also do not want to carry inventory - They want them when they are ready to consume them.  They are also responding to their customers on short lead times and without a clear forcast as to quantity or product mix.  They in turn expect to call with a product demand and have delivery within a week, in some cases within a day. In order to accomplish this I need to strategically locate some inventory in time expectation of my customer.  I do this through a Kanban system. Finally now to get to your main question of how to communicate and win acceptance of the workers.  
The transition is difficult because it is a culture change, but it will actually make the workers job easier.  Most people would naturally like that.  You have to make them part of the solution by empowering them to make decisions consistent with lean thinking (eliminating waste).  They are the "owners" of the process, they understand the issues which prevent them from doing their job.  They have to become part of the team.  You want to move to "continuous flow lines" and away from isolated islands of work with high inventory.  Communicate to them the "goal of satisfying" the requirements of your specific customer.  Mentally rearrange you organization chart with the direct workers at the top and everyone else there to support them.  Communicate this to the operators, that you want to make their jobs better by helping them get organized, helping them make setups insignificant, helping them make the processes error proof, and helping them continually add value to the product.

If you need additional thoughts from me let me know.  PS: my background has been Industrial engineering - and includes Mgr. of IE, consultant with HB MAYNARD, corporate staff IE with Bausch and Lomb, and 18 years operations management - I have been implementing lean concepts since the early 1980's. You will also find an article I wrote for the fifth edition of Maynard's Industrial Engineering Handbook "Supporting Lean Flow Production Strategies".

1.THE LEAN COMPANY: Making the Right Choices
                James A. Jordan , Jr.Frederick J.Michel

2.Lean Manufacturing for the Small Shop
                Gray B.Conner