# An Algorithmic Approach to Online Multi-Facility Location Problems

### Christine Markarian, Abdul-Nasser Kassar, Manal Yunis

#### Abstract

Facility Location problems ask to optimally place facilities with respect to some objective so that all clients requesting a facility service are served. These are one of the most well-studied optimization problems spanning many research areas, such as operations research, computer science, and management science. Classical algorithmic study of Facility Location problems is based on the assumption that clients need to be served with one facility each. Nevertheless, in many real-world applications, facilities experience disruptions and to overcome their failures, a robust service is desired. To obtain this, clients are served with more than one facility, and this is commonly represented by an additional input parameter. The aim of the algorithm is then to provide a robust service to all clients while minimizing costs. This is known as the Multi-Facility Location problem (MFL), a well-known optimization problem, studied in the offline setting in which the entire input sequence is known to the algorithm in advance. In this paper, we address MFL in the online setting, in which client requests are not known in advance but revealed over time. We refer to it as the Online Multi-Facility Location problem (OMFL) and study its metric and non-metric variants. We propose the first online algorithms for these variants and measure their performance using the standard notion of competitive analysis. The latter is a worst-case analysis that compares the cost of the online algorithm to that of the optimal offline algorithm that is assumed to know all demands in advance.

Download#### Paper Citation

#### in Harvard Style

Markarian C., Kassar A. and Yunis M. (2021). **An Algorithmic Approach to Online Multi-Facility Location Problems**.In *Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-485-5, pages 29-35. DOI: 10.5220/0010212200290035

#### in Bibtex Style

@conference{icores21,

author={Christine Markarian and Abdul-Nasser Kassar and Manal Yunis},

title={An Algorithmic Approach to Online Multi-Facility Location Problems},

booktitle={Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2021},

pages={29-35},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010212200290035},

isbn={978-989-758-485-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - An Algorithmic Approach to Online Multi-Facility Location Problems

SN - 978-989-758-485-5

AU - Markarian C.

AU - Kassar A.

AU - Yunis M.

PY - 2021

SP - 29

EP - 35

DO - 10.5220/0010212200290035