The theory of two-level planning (alternatively, Kornai–Liptak decomposition) is a method that decomposes large problems of linear optimization into sub-problems.
There are some constraints on overall resources (D) for which a central planning agency is assumed to be responsible, and n blocks of coefficients (F1 through Fn) that are the concern of individual firms.
The central agency starts the process by providing each firm with tentative resource allocations which satisfy the overall constraints D. Each firm optimizes its local decision variables assuming the global resource allocations are as indicated.
It has been shown that this process will converge (though not necessarily in a finite number of steps) towards the global solution for the overall problem.
(In contrast the Dantzig Wolfe method converges in a finite number of steps).