| Summary: | 碩士 === 元智大學 === 工業工程研究所 === 83 === This Research focuses on solving the large scale linear
programming problems with variable upper bound. Such
linear programming problems have special block structures
in their coefficient matrices so that the famous
Dantzig-Wolfe decomposition method can be applied to solve.
In our research, we shall propose an efficient way-rank
pivot rules, which, we believe, is new, for Dantzig-Wolfe
decomposition method to solve subproblems efficiently. We
also demonstrate how to obtain the optimal shadow prices from
the Karush-Kuhn-Tucker Conditions. On the other hand,
together with Dantzig-Wolfe decomposition method, we
propose a three-phase algorithm to avoid the
accumulation of round-off errors during the iterative
processes. Examples will be employed to show the complete
process of solving such problems.
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