This paper shows how to generalize the Dantzig-Wolfe decomposition principle to integer programming. It does this in a unified way, regardless of the choice between the two main solution methods: 'Branch and bound' or 'cutting plane'. In both instances the authority at the central level issues price dirkctives in the form of a polyhedral, concave price function, where the purpose is to charge the sublevels for the use of central resources including a penalty for any attempts to violate the

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... rality of the result. The sublevels then respond with their optimal activities given this price function. Finite convergence of the procedure is established.