Matrix Methods for Optimal Manifesting of Multinode Space Exploration Systems

This paper presents matrix-based methods to determine optimal cargo manifests for supplying resources in a space exploration system. An exploration system consists of transports (both in-space and on-surface) and resource demands occurring during both transportation between nodes and exploration at nodes. Each transport is defined by origin and destination nodes, departure and arrival times, and a cargo capacity. Matrices represent cargo carried by transports, cargo used to satisfy demands, and cargo transferred to other transports. The resulting matrix formulation is equivalent to a network flow problem representing the transportation of resources through a time-expanded network. The formulation allows for evaluating general exploration system feasibility by determining if a solution exists to a linear program (LP). In addition to modeling the manifesting problem, a few metrics, such as the transport criticality index, are formulated to allow for analysis and comparisons. The proposed matrix manifest modeling methods are demonstrated with a notional lunar exploration exploration system comprised of 32 transports including 8 cargo and 9 crewed landings at a base at the Lunar South Pole and several surface excursions to Malapert Crater and Schrodinger Basin. It is found that carry-along and pre-positioning logistics strategies can yield different manifesting solutions in which transport criticality varies. For the specific scenario considered in this study, it is found that transport criticality is larger for a pre-positioning strategy (mean value of 3.02) as compared to a carry-along case (mean-value of 1.99).