Hierarchical Decomposition in Linear Economic Models

In decomposed linear programming models it is generally not possible to decentralize by prices alone. The Dantzig-Wolfe procedure, for instance, delegates weights on basic solutions in addition to the equilibrium prices. In this paper we present a decomposition procedure for linear models where we in addition to prices delegate a hierarchical ordering. In many problems this ordering makes the assignment of weights unnecessary, and gives the divisions more autonomy in their decision making. An operational condition is found for determining if, for any given problem, the new decomposition procedure will achieve coherent decentralization.