Autonomy in the workplace or in other settings means having some freedom to do things in your own way, with your own methods of achieving the stated goal. Or it might mean being able to at least think about better ways to complete the work goal and have a reliable method for suggesting the improvement to management.
Suggestion boxes may exist but do the suggestions ever go anywhere else? Is there any system in place for testing the suggestion to see if it is an improvement and would the employee get recognition or a bonus of some sort if the suggestion was implemented?
The book "Leadersights: Creating Great Leaders Who Create Great Workplaces" by David Veech includes ideas for creating workplace efficiency that incorporates autonomy for the workers. Examples and templates for an easy start for streamlining work methods and developing a system for submitting suggestions for change are included. (Amazon)
A similar substitute for the old fashioned suggestion box is described by The Chief Happiness Officer Blog, "Kill the Suggestion Box - Here's a Much Easier Way."
If keeping the suggestion box in a more modern form is preferred, there is a free online service provided by Centreli, a company who developed the software for use by their own employees and customers. It was so well received they are offering the confidential web-based site for any business or group interested in signing up for an account: FreeSuggestionBox.
For an overview about the value & limitations of autonomy, see: "Trust, but Verify: The Key Management Tool to Build Team Satisfaction," by Jimmy Daly, blog.IDoneThis.
Disclaimer: This information is provided for educational purposes