Abstract
This paper surveys the facility location problems in dynamic flow networks that have been actively studied in recent years. These problems have been motivated by evacuation planning which has become increasingly important in Japan. The evacuation planning problem is formulated using a dynamic flow network consisting of a graph in which a capacity as well as a transit time is associated with each edge. The goal of the problem is to find a way to send evacuees originally existing at vertices to facilities (evacuation centers) as quickly as possible. The problem can be viewed as a generalization of the classical k-center and k-median problems. In this paper we show recent results about the difficulty and approximability of a single facility location for general networks and polynomial time algorithms for k-facility location problems in path and tree networks. We also mention the minimax regret version of these problems.
Highlights
It has become increasingly important to establish effective evacuation planning systems against large-scale disasters, e.g., earthquakes, tsunamis, and hurricanes, for example
The minimax regret facility location problems in dynamic flow networks have been studied in recent years
The minimax regret k-facility location problem in a dynamic flow path network has first been studied by Arumugam et al [3]
Summary
It has become increasingly important to establish effective evacuation planning systems against large-scale disasters, e.g., earthquakes, tsunamis, and hurricanes, for example. To decrease the loss of human lives, many cities along the coast of the Pacific Ocean are planning to increase tsunami evacuation buildings This motivates us to study the facility location problems in dynamic flow networks. For the optimality of location, the following two criteria can be naturally considered: the minimization of maximum cost and total cost (in a facility location in static flow networks, these criteria correspond to the center problem and the median problem, respectively). We explain these criteria in the integral flow model. The objective of the first player is to choose x that minimizes the maximum regret (Tables 3, 4)
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