A short-cut potential reduction algorithn for linear programming

Article Abstract:

Decomposition techniques which can reduce the amount of work involved in linear programming interior point methods such as dual affine scaling and dual potential reduction algorithms. The value of these decomposiitoning methods are assessed through a comparative analysis of the dual potential reduction algorithm and a set of decompositioning randomly-generated transportation problems, without subjecting the first set of variables to decompositioning techniques. These techniques are validated by testing implementation details and computational results of one such technique. The study shows that decomposition of variables prove to be a useful method for resolving a given problem when the number of variables exceed the number of constraints. The decomposition method allow matrix calculations to be performed on a smaller set of variables.

Linear programming, Usage, Decomposition method, Potential theory (Mathematics)

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A theory of cutoff formation under imperfect information

Article Abstract:

A study is conducted to examine the use of a cutoff to limit subsequent evaluations and the ways in which this heuristic can be applied optimally. In this heuristic, the number of alternatives is limited using a screening strategy that involves two general methods: Quota cutoffs and Level cutoffs. The Quota method determines the optimal number of options to evaluate, while the Level method determines the lowest acceptable level of the imperfect screening indicator. Aside from defining the two methods, the study introduces the concomitants of order statistics as a strategy for examining decision problems involving imperfect information. It also explores the role of fallback options in a large class of search problems.

Decision-making, Decision making, Optimal stopping (Mathematical statistics), Order statistics

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