Online Facility Location
52 Pages Posted: 28 Sep 2021 Last revised: 8 Jun 2022
Date Written: September 18, 2021
We formulate and solve an online facility location problem. The scope of facility location problems continues to expand. However, models addressing the facility location problem thus far have largely been restricted to static, offline models that prescribe one-shot facility placement, based on the past and current data on hand. Motivated by the prospect of a vibrant urban future, in which mobile facilities (e.g., pop-up stores, mobile chargers, and micro-depots) prevail, we consider an online setting where decision makers are subject to an unknown environment. However, they are able to adjust facility locations over time while updating their parameter estimation from historical observations. More specifically, the objective in this "learning-and-earning" setting is to choose facility locations in every period so as to maximize profit expectations, conditioned on the contextual information. To solve this problem, we leverage analytical convenience that is inherent in facility location models and use continuous approximation (CA) to overcome the computational hurdle. Then, we combine the CA technique with an optimistic optimization problem to balance between exploration and exploitation in online learning. Under this "continuous-approximation optimistic" (CA-O) framework, we develop two algorithms to account for different location model structures and then theoretically characterize their regret performance. Numerical studies show that the proposed CA-O framework is effective in terms of both regret sublinearity and computational efficiency; its versatility makes it applicable in solving both traditional uncapacitated facility location problems and emerging micro-depot location problems for last-mile deliveries.
Keywords: facility location, continuous approximation, contextual bandits, joint learning and optimization
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