  Facility Location problems ask to place facilities in a way that optimizes a
given objective function so as to provide a service to all clients. These are
one of the most well-studied optimization problems spanning many research areas
such as operations research, computer science, and management science.
Traditionally, these problems are solved with the assumption that clients need
to be served by one facility each. In many real-world scenarios, it is very
likely that clients need a robust service that requires more than one facility
for each client. In this paper, we capture this robustness by exploring a
generalization of Facility Location problems, called Multi-Facility Location
problems, in the online setting. An additional parameter k, which represents
the number of facilities required to serve a client, is given. We propose the
first online algorithms for the metric and non-metric variants of
Multi-Facility Location and measure their performance with competitive
analysis, the standard to measure online algorithms, in the worst case, in
which the cost of the online algorithm is compared to that of the optimal
offline algorithm that knows the entire input sequence in advance.
