Browsing by Subject "Shortest Path Problem"

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    The robust shortest path problem with interval data uncertainties
    (2001) Karaman, Abdullah Sıddık
    In 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.
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    Shortest path problem with re-routing en-route
    (2008) Karakaya, Banu
    In this study, we examine the shortest path problem under the possibility of “re-routing” when an arc that is being traversed is blocked due to reasons such as road and weather conditions, congestion, accidents etc. If an incident occurs along the arc being traversed, the vehicle either waits until all effects of the incident are cleared and then follows the same path thereafter, or returns to the starting node of that arc and follows an escape route to the destination node, the latter course of action is called as “re-routing”. Also, we consider that this arc is not visited again throughout the travel along the network when an incident occurs and the alternative of not following this arc after the event is chosen. We propose a labeling algorithm to solve this specific problem. Then, a real case problem is analyzed by the proposed algorithm and several numerical studies are conducted in order to assess the sensitivity of the probability and travel time parameters.