Browsing by Subject "Interval Data"
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Item Open Access Essays on some combinatorial optimization problems with interval data(Bilkent University, 1999) Yaman, HandeIn 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.Item Open Access The robust shortest path problem with interval data uncertainties(Bilkent University, 2001) Karaman, Abdullah SıddıkIn this study, we investigate the well-known shortest path problem on directed acyclic graphs under arc length uncertainties. We structure data uncertainty by taking the arc lengths as interval ranges. In order to handle uncertainty in the decision making process, we believe that a robustness approach is appropriate to use. The robustness criteria we used are the minimax (absolute robustness) criterion and the minimax regret (relative robustness) criterion. Under these criteria, we de ne and identify paths which perform satisfactorily under any likely input data and give mixed integer programming formulation to nd them. In order to simplify decision making, we classify arcs based on the realization of the input data. We show that knowing which arcs are always on shortest paths and which arcs are never on shortest paths we can preprocess a graph for robust path problems. Computational results support our claim that the preprocessing of graphs helps us signi cantly in solving the robust path problems.