Decomposition, Pricing for Decentralization and External Economies

The decomposition procedure for the solution of large scale linear programs is described in an elementary manner with illustrative calculations. Its economic interpretation as a procedure for decentralized decision by the multi-division firm or the multi-sector economy is explained in detail. Decomposition is shown to provide internal prices for decentralized decision making in the presence of external economies or diseconomies. However, it is demonstrated that in many cases there exist no prices which will lead divisions to make independent decisions that are optimal from the point of view of the company (or the economy) as a whole.