Facility Location Problem for Space-Based Assets
Published:
This work proposes an adaptation of the Facility Location Problem for the optimal placement of on-orbit servicing depots for satellite constellations in high-altitude orbit. The high-altitude regime, such as Medium Earth Orbit (MEO), is a unique dynamical environment where lowthrust propulsion systems can provide the necessary thrust to conduct plane-change maneuvers between the various orbital planes of the constellation. As such, on-orbit servicing architectures involving servicer spacecraft that conduct round-trips between servicing depots and the client satellites of the constellation may be conceived. To this end, a new orbital facility location problem formulation is proposed based on binary linear programming, in which the costs of operating and allocating the facility(ies) to satellites are optimized in terms of the sum of the Equivalent Mass to Low Earth Orbit (EMLEO).
1. Review of Facility Location Problem
The facility location problem
The placement of facilities is a fundamental problem in terrestrial logistics. The facility location problem (FLP) is a classical problem in operations research, for which various formulations and extensions have been proposed. The FLP has seen a wide range of applications, including emergency services, telecommunications, healthcare, waste disposal management, and disaster response.
2. Applications to space problem: on-orbit servicing depot
The problem of designing and deploying large-scale space-based architectures may be posed as an FLP. In doing so, considerations specific to space must be taken into account to successfully adapt to the application in question. One such application is the placement of on-orbit servicing depots.
We consider the problem
\[\begin{aligned} \min_{X,Y} \quad& \sum_{j=1} f_j Y_j + \sum_{i=1}^m \sum_{j=1}^n c_{ij} X_{ij} \\ \text{such that} \quad & \sum_{j = 1}^n X_{ij} = 1 \quad \quad\, \forall i \in \mathcal{M} \\ & X_{ij} \leq Y_j \quad \quad \quad \,\,\,\, \forall i \in \mathcal{M}, j \in \mathcal{N} \\ & X_{ij}, Y_j \in \{0, 1\} \quad \forall i \in \mathcal{M}, j \in \mathcal{N} \end{aligned}\]Related publication:
Y. Shimane, N. Gollins, and K. Ho, “Orbital Facility Location Problem for Satellite Constellation Servicing Depots,” J. Spacecr. Rockets, pp. 1–18, Mar. 2024, doi: 10.2514/1.A35691. https://arc.aiaa.org/doi/full/10.2514/1.A35691
Y. Shimane, A. Shirane, and K. Ho, “Lunar Communication Relay Architecture Design via Multiperiod Facility Location Problem,” 2023.
Y. Shimane, K. Tomita, and K. Ho, “Strategic Regions for Monitoring Incoming Low-Energy Transfers to Low-Lunar Orbits Yuri Shimane , Kento Tomita , and Koki Ho Georgia Institute of Technology,” 2023.