In transition to a new era of human space exploration, the question is what the next-generation space logistics paradigm should be. The past studies on space logistics have been mainly focused on a "vehicle" perspective such as propulsive feasibility, cargo capacity constraints, and manifesting strategies, with the arbitrarily predetermined logistics network. But how do we select an optimal logistics network? Especially if we can utilize in-situ resources on the Moon and Mars, it will add complexity to network selection problem. The objective of this paper is to develop a comprehensive graph-theoretic modeling framework to quantitatively evaluate and optimize space exploration logistics from a "network" perspective. In an attempt to create such a modeling framework, we develop a novel network flow model referred to as the generalized multi-commodity network flow (GMCNF) model. On top of the classical network flow problems, the GMCNF model proposed in this paper introduces three types of matrix multiplications (requirement, transformation, and concurrency), and also allows loop edges associated with nodes (graph loops) and multiple edges between the same end nodes (multigraph). With this modification, the model can handle multiple commodities that interact with each other in the form of requirement at nodes, transformation on edges, and concurrency within edges. A linear programming (LP) formulation of the GMCNF model is applied to human exploration of Mars. First we solve the baseline problem with a demand that is equivalent to that of the NASA's Mars Design Reference Architecture (DRA) 5.0 scenario. It is found that the solution saves 67.5% from the Mars DRA 5.0 reference scenario in terms of the initial mass in low-Earth orbit (IMLEO) primarily because chemical (LOX/LH2) propulsion is used along with oxygen-rich ISRU. We also present one possible scenario with two "gateway" resource depots at GTO and DTO with orbital transfer vehicles (OTVs) running in the cislunar and Martian systems. Then we solve variant problems that have different settings to see the effect of each factor. Findings include: taking advantage of oxygen-rich ISRU, LOX/LH_2 is preferred to nuclear thermal rocket (NTR), the aerobraking option as well as ISRU availability on the Moon make great contributions in reducing the total mass to be launched from Earth, and as the ISRU production rate decreases, ISRU in each location becomes worthless at a certain threshold and the network topology changes toward direct paths using NTR.
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