What is the quickest strategic managerial system to increase workers production?

As a supervisor, the best way to increase productivity is to gain the respect of your workers. You can try and motivate them everyday but if they do not respect you as a supervisor you will never get 100% out of them. One thing is to get out of the office and learn what each person does, do some hands on with them. Show them you are one of them, not just some white collar jerk with a BA degree and don't care about them. Of course some jobs it might be easier then others. I am speaking mainly from a Maintenance Supervisor's position.

Firstly, there is no such thing as a 'strategic managerial system'.   What you are really asking is, "How can management increase productivity quickly?"

The answer is simple, and cheap and easy to implement.  (It is NOTHING to do with motivating the workforce.) 

Figure out the management activity that inhibits productivity the most, and stop doing it.

If the management is good, then productivity will already be high.  If it is low, then the management must, by definition, be poor.  Fixing this is a medium term thing.  In the short term, the best thing to do is discover the worst thing that management does, and stop it. 

Out of the book answer is MOTIVATION. But, there's much more to your question that is unsaid, like which industry, which job or what kind of work, or ... And, it's often a question of doing more than one thing and it's never quick.

Motivation in sense of incentives, appraisal or 'employee of the week' program might be quick solutions. Long term solution needs more work - you should understand why the production is not on the level you wish it is. Then you should set up monitoring and measurements of the work - usually KPI's help. And then it's additional education, practice and inf necessary, change in the workforce. And some work can't / should not be hurried as it brings the results of work down!

Feel free to share more details, so that help/advice would be more specific.

Increasing productivity is one of the most critical goals in business. Unfortunately, it’s an activity seldom accepted by HR professionals as a legitimate mandate. While most HR professionals acknowledge that their job entails establishing policy, procedures, and programs governing people management, few attempt to connect such elements to increasing employee output (volume, speed, and quality) per each dollar spent on labor costs (or as an easier to measure alternative, revenue per employee).

Bonus programs are typically enacted that keep total compensation in line with market trends, regardless of the value of work warranting incentive comp. Training tools are often secured via the lowest-cost provider method with minimal consideration given to which provider would be most effective. Recruiting practices too are more often managed with the primary goal of minimizing cost, not enabling business capability/capacity. Regardless of the function you look at, in the typical organization, HR is more concerned with executing transactions instead of delivering productivity solutions.

If you believe as most should that the combined efforts of the human resource function should positively influence the performance capability of the workforce instead of hindering it, you should understand the factors that influence performance.

I'm totally agree with you Mr Pigac, Motivation is the best way to increase "production" in any production company, but it depends, you can motivate workers today, but tomorrow you will need to motivate them much more, so I m making a resurch to find the best way to motivate continually and progressively the operational workers.