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AbstractWhen implicit enumeration algorithms are used for solving integer programs, a form of primal decomposition can be used to reduce the number of solutions which must be implicitly examined. If the problem has the proper structure, then under the proper decomposition a different enumeration tree can be defined for which the number of solutions which must be implicitly examined increases with a power of the number of variables rather then exponentially. The proper structure for this kind of decomposition is that the southwest and northeast corners of the constraint matrix be zero or equivalently that the matrix be decomposable except for linking columns. Many real traveling salesmen, plant location, production scheduling, and covering problems have this structure.

ABSTRACTWhile Dantzig and Wolfe have formulated the decomposition algorithm as a computational device, it was subsequently recognized that the principle underlying the algorithm may also be utilized by a planning system to achieve a centralized planning within the framework of a decentralized organizational structure. This paper illustrates the workings of such a planning system and, at the same time, explores some of the problems connected with its actual implementation. The planning system under the study is called the decomposed planning system in order to distinguish it from either the centralized planning or the decentralized planning.

Sociology, writes Irving Louis Horowitz, has changed from a central discipline of the social sciences to an ideological outpost of political extremism. As a result, the field is in crisis. Some departments have been shut down, others cut back, research programs have dried up, and the growth ofprofessional organizations and student enrollments have been either curbed or atrophied. In The Decomposition of Sociology, Professor Horowitz, for four decades a leading social scientist, offers a frank and full account of the maelstrom engulfing this field. Horowitz pulls no punches in this provocative

This paper argues that the typical practice of performing growth decompositions based on log-transformed productivity values induces fallacious conclusions: using logs may lead to an inaccurate aggregate growth rate, an inaccurate description of the microsources of aggregate growth, or both. We identify the mathematical sources of this log-induced fallacy in decomposition and analytically demonstrate the questionable reliability of log results. Using firm-level data from the French manufacturing sector during the 2009-2018 period, we empirically show that the magnitude of the log-induced distortions is substantial. Depending on the definition of accurate log measures, we find that around 60-80% of four-digit industry results are prone to mismeasurement. We further find significant correlations of this mismeasurement with commonly deployed industry characteristics, indicating, among other things, that less competitive industries are more prone to log distortions. Evidently, these correlations also a affect the validity of studies that investigate the role of industry characteristics in productivity growth.