Minmax Regret 1-Sink Location Problems on Dynamic Flow Path Networks with Parametric Weights

This paper addresses the minmax regret 1-sink location problem on dynamic flow path networks with parametric weights. We are given a network consisting of an undirected positive edge lengths, capacities, and nonnegative vertex A can be considered as road, length distance along road weight number people at site. An capacity limits that enter per unit time. consider locating sink in network, to which all evacuate from vertices quickly possible. In our model, each is represented by linear function common parameter t, decision maker who determines does not know value t. formulate under such uncertainty problem. Given t x, cost x sum arrival times for determined The gap between optimal task formulated one find minimizes maximum over For problem, we propose \(O(n^4 2^{\alpha (n)} \alpha (n) \log n)\) time algorithm where n \(\alpha (\cdot )\) inverse Ackermann function. Also special case every has same capacity, show complexity reduced \(O(n^3 n)\).