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• W2405962973 abstract "In large and complicated management systems, solutions with the same indices, but with different degrees of aggregation, are used and coordinated. For example, in hierarchical systems, those in higher management levels make decisions with more aggregated indices than those in lower management levels. Managers of an individual subsystem within a large and complicated system use detailed information about their own subsystem and aggregated information (in some degree or other) about other subsystems. The principal idea of the iterative aggregation method is to consecutively recompute the aggregated indices characterizing the activities of the whole system, followed by a recomputation of the detailed indices characterizing each of its subsystems. From a theoretical point of view these methods are generalizations of some classes of iterative and decomposition methods. 1. CLASSICAL APPROACHES TO THE SOLUTION OF LARGE-SCALE PROBLEMS THE DIFFICULTIES ENCOUNTERED in solving large-scale problems have usually been tackled in one of two ways. The first involves replacing the initial large-scale problem by a number of subproblems each of which is solved separately, the procedures for combining the solutions of adjacent subproblems being obtained heuristically. However, such combinations are as a rule inadequate for obtaining a rigorous solution of the whole problem, and this has led to the development of decompositional methods. These methods make possible a rigorous formulation of multidimensional problems; the initial problem is decomposed into subproblems and at the same time a corresponding procedure for coordinating the solutions is derived, thus ensuring convergence to the solution of the original problem. The first decompositional algorithm, for the solution of linear programming problems with a block structure, was that of Dantzig and Wolfe [12, 13] and Dantzig [11]. Its main idea is to use the block structure of the initial problem by substituting for it a number of subproblems, corresponding to the number of blocks in the initial matrix. The local problems are formed from the local constraints of the corresponding blocks and the linear optimality criteria. The coefficients of the local criterion function take into account the common resource prices that have emerged at that iteration. The local solutions make it possible to optimize the input and output of common resources at these prices. The coordinating problem (master program) is then formulated. Its variables are the common-resource requirements resulting from the subproblems; their number is fairly small and remains constant, although the different input-output 1 At the end of 1977, when the last version of this paper was in the process of editing already, L. M. Dudkin and L. N. Rabinovich constructed some new iterative aggregation algorithms for which global convergence was proved at once. The main distinction of these algorithms is in a new approach to the construction of aggregate models. Now numerical investigations are being conducted to compare the practical rate of convergence of the new algorithms with those reported in this paper." @default.
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• W2405962973 title "SOLUTION OF LARGE-SCALE PROBLEMS'" @default.
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