D antzig– W olfe Decomposition

Abstract In this section, the development of the Danztig–Wolfe (DW) decomposition method is presented. The topics include not only the details of the DW decomposition algorithm, but also the discussions of computational efficiency, long‐tail effect, column dropping, parallel implementation, the concept of price‐directive coordination, optimal degree of decentralization, and organizational studies. Moreover, other non‐LP developments of the DW method are briefly introduced. They are the DW method of staircase LP, NLP, MIP, and variational inequality problems. It should be noted that the DW method may be significantly less efficient than the simplex approach. Hence, the DW method should be the only algorithmic choice when the problem is too large to be solved in one piece. Another motivation of the use of the DW decomposition is to ease model development and maintenance by its solution method that links separately developed submodels only when a joint model solution is desired. On the other hand, the recent applications of the DW method concern (i) how to generalize the DW method to integer programming's branch‐and‐price procedures and (ii) how to apply the DW method to equilibrium models.