A holonic manufacturing system (HMS) is a manufacturing system where key elements, such as machines, cells, factories, parts, products, persons, teams, etc., are modeled as 'holons' having autonomous and cooperative properties. The distributed decision authority, the cooperative nature, and the integration of physical and informational aspects of system elements or holons make the HMS a new manufacturing paradigm, with great potential for meeting today's agile manufacturing challenges. Critical issues to be investigated include how to define holons for a given problem context, what should be the appropriate system architecture, and how to design effective cooperation mechanisms among holons for overall system performance. In this paper, holonic scheduling is developed for a factory consisting of multiple cells. Holons are identified, and their relationships are delineated through a novel modeling of the interactions among cells. The cooperation mechanisms among holons are established based on the 'Lagrangian relaxation technique' of mathematical optimization, and cooperation across cells is performed without accessing individual cells' local information nor intruding on their decision authority. The holonic system developed also possesses structural recursivity, and this property, combined with the integrability of individual holons, enables high system extendibility. Numerical testing shows that the method can generate high quality schedules in a timely fashion, and has comparable computational requirements as compared to a single-level Lagrangian relaxation method. The method thus provides a theoretical foundation for guiding the cooperation among holons, leading to globally near-optimal performance.