Essays on some combinatorial optimization problems with interval data

In this study, we investigate three well-known problems, the longest path problem on directed acyclic graphs, the minimum spanning tree problem and the single machine scheduling problem with total flow time criterion, where the input data for all problems are given as interval numbers. Since optimal solutions depend on the realization of the data, we define new optimality concepts to aid decision making. VVe present characterizations for these “optimal” solutions and suggest polynomial time algorithms to find them in some special cases.