The research team, led by experts from the Beijing Institute of Technology, developed a layered network model to depict the interplanetary supply chain (ISC). This model consists of two primary networks: the Propellant Network (PN) and the Supply Network (SN). PN focuses on delivering cargo from Earth to Mars, while SN handles the propellant supply necessary for these missions. Despite sharing common nodes, each network has distinct arcs tailored to its specific function.
Nodes within this model are classified into four categories: Surface Nodes, which are locations on celestial bodies where supplies and demands originate; Orbital Nodes, which are stable orbits accessible from surface nodes; Lagrange Points, which are potential sites for on-orbit infrastructure; and Auxiliary Nodes, which serve as gateways for inter-cluster travel, such as LTO and DTO. The consumption of propellant is calculated based on a propellant mass fraction derived from the rocket equation, ensuring accurate assessments of fuel requirements.
Central to this study is the MSP model, designed to handle the unpredictable nature of demands at a Martian base. By employing random variables and specific probability distributions, the model effectively captures and reflects uncertainty over multiple time points. This approach differentiates between strategic, scenario-independent variables (decisions made before uncertainties unfold) and tactical, scenario-dependent variables (adjustments made as uncertainties become known). The primary goal of the MSP model is to minimize the Total Launch Mass (TLM), as articulated in the study's objective function.
The research includes extensive numerical studies covering a 6-year planning horizon, divided into 24 periods of 3 months each. Martian demands, influenced by the planet's harsh seasonal conditions, begin from period 9. Seasonal demand patterns for each period and scenario are computed using a method by Hahn and Kuhn, incorporating a harmonic oscillation with an amplitude of 0.1. To handle uncertainties, discrete scenarios are generated using a moment-matching heuristic by Hoyland et al. The comprehensive stochastic MILP model comprises over half a million constraints and thousands of variables, implemented via IBM ILOG CPLEX Optimization Studio.
Several critical insights emerged from this study. Space infrastructure installation accounts for more than 37% of the total launch mass, with ISRU facilities and on-orbit depots equally contributing. Supporting a Martian base requires approximately 170 times more propellant than dry mass, emphasizing the need for efficient propellant logistics. Specific spacecraft are designated for either transporting cargo or fetching propellant from depots, optimizing operational efficiency.
ISRU facilities are strategically located on the Moon, Phobos, and Deimos, while depots are positioned at L2, LDO, and LMO. Propellant storage capabilities at depots significantly reduce the need for large ISRU plants. Sensitivity analyses highlight that increases in payload capacity have minimal impact, whereas increases in propellant capacity and specific impulse substantially reduce TLM.
The study underscores the pivotal role of propulsion technology advancements in making ISCs feasible. Improved propulsion systems could dramatically enhance the efficiency of interplanetary supply chains, while the availability of ISRU locations is critical for optimal performance.
This pioneering study provides a robust framework for interplanetary supply chain planning, integrating production-distribution and in-space infrastructure decisions under demand uncertainty. Validated through case studies based on real data from NASA's trajectory browser, the model offers valuable insights into the logistics of space exploration. The proposed stochastic multi-stage MILP model not only enhances our understanding of space logistics but also paves the way for more efficient and reliable supply chain strategies for future missions to Mars and beyond.
Research Report:A Stochastic Modeling Approach for Interplanetary Supply Chain Planning
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Beijing Institute of Technology
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