Generalized multi-commodity network flows : case studies in space logistics and complex infrastructure systems
2013
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
thesis 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 thesis 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 and a mixed integer linear programming
(MILP) formulation of the GMCNF model are described in preparation
for the two case studies. For the MILP formulation, in addition to
the flow, we introduce two more variables, capacity expansion and
decision binary, and additional constraints including the big-M
method. The first case study applies the GMCNF LP model 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/LH2 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. The
other case study applies the GMCNF MILP model to the complex
infrastructure systems in Saudi Arabia, focusing on the couplings
between water and energy. Considering the capacity of the online…
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