Research on Value of Information to Combinatorial Optimization

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This research is to investigate value of information to combinatorial optimization. The aim of this research is to clarify the effects of random and fuzzy factors in the combinatorial optimization models. Especially the solutions are changed according to the existence of uncertainty and/or ambiguity. First we considered linear programming problems under both random and fuzzy factors. Based on the results on so called these fuzzy random linear programming problems, we considered scheduling problems with fuzzy data and fuzzy constraint, spanning tree problems with fuzzy random edge costs, knapsack problem with fuzzy and random coefficients and facility location problem with fuzzy distance and fuzzy goal. In order to find the difference between the solution of ordinary problem and that of fuzzy random version, we introduced fuzzy random variables to above problems of combinatorial optimization and proposed efficient algorithms for solving their deterministic equivalent problems. We obtained some results on solutions of these problems. Further we investigated also basic mathematical analysis of value of information by considering functional analysis, especially variational inequality and introduced a new concept of fuzzy derivatives to apply optimization under ambiguity.