This paper presents an efficient criterion for solving the redundancy of the muscle recruitment problem in inverse dynamics of musculo-skeletal systems. It is a minimum fatigue criterion that is formulated as a min/max optimization problem. The criterion is briefly reviewed in comparison to other criteria and its implementation for large and complex system, such as the human body, is explained in detail. The optimization problem is solved numerically by means of linear programming, providing a very efficient, final algorithm. It is shown that special care must be taken of systems with groups of sub-maximally loaded muscles and methods to deal with this automatically are presented. The algorithms are implemented into a software system called AnyBody, and examples involving up to 100 muscles are demonstrated. Even models of this size are solved in fractions of a second for a single time step on a standard PC.