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형생우,朴慶洙 全北大學校 1989 論文集 Vol.31 No.-
Large linear programming problems usually have some special structural form that can be exploited to develop efficient computational procedures. One common structure is where there are a number of separate activity areas that are linked through common resource constraints. Each activity must meet internal requirements that do not interact with the constraints of others; But in addition there are common resources that must be shared among activities and theredy represent linking constraints. A problem of this form can be solved by Decomposition Principle, which can be derived as a special version of the revised simplex method. The method is an iterative process where at each step a number of seperate subproblems are solved. The subproblems are themselves linear programs within the separate areas. The objective functions of these subproblems are varied from iteration to iteration and are determined by a seperate calculation based on the results of the previous iteration. This action coordinates the individual subproblems so that, ultimately, the solution to the overall problem is solved. In this method, the subproblems correspond to evaluation of reduced cost coefficients for the main problem. Discussed here are the mathematical background and the Algorithm of Decomposition Principle and implemented its calculational procedures by an illustrative solution.
오목과 볼록조건을 갖는 동적로트결정모형의 알고리즘 개선
형생우 全北大學校 1993 論文集 Vol.35 No.-
This paper is concerned with the single-product dynamic lot size model. Let n be the number of periods in the planning horizon. In 1958 Wagner and Whitin proposed an O(n^2) time algorithm for the model. We consider the case of the model in which the cost function satisfies the quadrangle inequality, and present a single forward algorithm which solves the case in O(n log n) time.