\contentsline {section}{\numberline {1}Introduction}{4}{section.1}%
\contentsline {subsection}{\numberline {1.1}Background}{4}{subsection.1.1}%
\contentsline {subsection}{\numberline {1.2}Restatement of the Problem}{4}{subsection.1.2}%
\contentsline {subsection}{\numberline {1.3}Our Work}{5}{subsection.1.3}%
\contentsline {section}{\numberline {2}Assumptions and Justifications}{5}{section.2}%
\contentsline {section}{\numberline {3}Notations}{6}{section.3}%
\contentsline {section}{\numberline {4}Model I: Universal Energy-Equivalent and Temporal Coordination Model}{6}{section.4}%
\contentsline {subsection}{\numberline {4.1}Model Overview}{6}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}Energy-Equivalent as a Cost Proxy}{7}{subsection.4.2}%
\contentsline {subsubsection}{\numberline {4.2.1}Cost Convergence Analysis}{7}{subsubsection.4.2.1}%
\contentsline {subsubsection}{\numberline {4.2.2}Empirical Industry Validation}{7}{subsubsection.4.2.2}%
\contentsline {subsection}{\numberline {4.3}Ideal Energy Cost Modeling}{8}{subsection.4.3}%
\contentsline {subsubsection}{\numberline {4.3.1}Rocket Momentum Dynamics}{8}{subsubsection.4.3.1}%
\contentsline {subsubsection}{\numberline {4.3.2}Space Elevator Mechanics}{8}{subsubsection.4.3.2}%
\contentsline {subsection}{\numberline {4.4}Ideal Timeline and Logistic Efficiency Modeling}{9}{subsection.4.4}%
\contentsline {subsubsection}{\numberline {4.4.1}Transport Progress Formulas}{9}{subsubsection.4.4.1}%
\contentsline {subsubsection}{\numberline {4.4.2}Spatial and Geographical Optimization}{10}{subsubsection.4.4.2}%
\contentsline {subsection}{\numberline {4.5}Unified Cost Optimization via Time Opportunity Scaling}{11}{subsection.4.5}%
\contentsline {subsubsection}{\numberline {4.5.1}Reformulation via Opportunity Cost}{11}{subsubsection.4.5.1}%
\contentsline {subsubsection}{\numberline {4.5.2}Calibration of Cost Parameter $\lambda $}{11}{subsubsection.4.5.2}%
\contentsline {subsection}{\numberline {4.6}Results of Task 1}{11}{subsection.4.6}%
\contentsline {subsubsection}{\numberline {4.6.1}Comparison of Baseline Scenarios}{12}{subsubsection.4.6.1}%
\contentsline {subsubsection}{\numberline {4.6.2}Optimal Strategy Selection and Allocation}{12}{subsubsection.4.6.2}%
\contentsline {subsubsection}{\numberline {4.6.3}Sensitivity and Parameter Stability}{13}{subsubsection.4.6.3}%
\contentsline {subsection}{\numberline {4.7}Stochastic Risk and Robustness Analysis}{14}{subsection.4.7}%
\contentsline {subsubsection}{\numberline {4.7.1}Stochastic Perturbation Modeling}{14}{subsubsection.4.7.1}%
\contentsline {subsubsection}{\numberline {4.7.2}Risk-Adjusted Optimization}{14}{subsubsection.4.7.2}%
\contentsline {subsubsection}{\numberline {4.7.3}Monte Carlo Lifecycle Assessment}{14}{subsubsection.4.7.3}%
\contentsline {subsection}{\numberline {4.8}Results of Task 2}{15}{subsection.4.8}%
\contentsline {subsubsection}{\numberline {4.8.1}Assessment of Performance Degradation}{15}{subsubsection.4.8.1}%
\contentsline {subsubsection}{\numberline {4.8.2}Resilient Strategic Adjustments}{15}{subsubsection.4.8.2}%
\contentsline {subsubsection}{\numberline {4.8.3}Evolution of Key Indicators}{16}{subsubsection.4.8.3}%
\contentsline {section}{\numberline {5}Model II: Life-Support Logistics and Stochastic Water Balance Model}{17}{section.5}%
\contentsline {subsection}{\numberline {5.1}Model Overview}{17}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Water Demand Architecture}{17}{subsection.5.2}%
\contentsline {subsubsection}{\numberline {5.2.1}Domestic Water Evolution}{17}{subsubsection.5.2.1}%
\contentsline {subsubsection}{\numberline {5.2.2}Medical Emergency Demand Modeling}{18}{subsubsection.5.2.2}%
\contentsline {subsection}{\numberline {5.3}Replenishment and Buffer Strategies}{18}{subsection.5.3}%
\contentsline {subsubsection}{\numberline {5.3.1}Initial Month Filling}{18}{subsubsection.5.3.1}%
\contentsline {subsubsection}{\numberline {5.3.2}Monthly Routine Compensation}{18}{subsubsection.5.3.2}%
\contentsline {subsection}{\numberline {5.4}Results of Task 3}{19}{subsection.5.4}%
\contentsline {subsubsection}{\numberline {5.4.1}Demand Scaling Across Comfort Tiers}{19}{subsubsection.5.4.1}%
\contentsline {subsubsection}{\numberline {5.4.2}Integrated Trade-off Analysis of Transport Schemes}{19}{subsubsection.5.4.2}%
\contentsline {subsection}{\numberline {5.5}Sensitivity Analysis for Water Supply Model}{20}{subsection.5.5}%
\contentsline {subsubsection}{\numberline {5.5.1}Parameter Sensitivity Ranking via Tornado Analysis}{20}{subsubsection.5.5.1}%
\contentsline {subsubsection}{\numberline {5.5.2}Quantitative Sensitivity Coefficients}{21}{subsubsection.5.5.2}%
\contentsline {subsubsection}{\numberline {5.5.3}Worst-Case Stress Testing}{21}{subsubsection.5.5.3}%
\contentsline {subsection}{\numberline {5.6}Conclusion and Strategic Insights}{22}{subsection.5.6}%
\contentsline {section}{\numberline {6}Model Extension}{22}{section.6}%
\contentsline {subsection}{\numberline {6.1}Quantification of Baseline Environmental Impacts}{22}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Earth Port Assessment}{23}{subsection.6.2}%
\contentsline {subsection}{\numberline {6.3}Tri-objective Decision Framework}{23}{subsection.6.3}%
\contentsline {subsection}{\numberline {6.4}Result of Task 4}{24}{subsection.6.4}%
\contentsline {section}{\numberline {7}Strengths and Weaknesses}{25}{section.7}%
\contentsline {subsection}{\numberline {7.1}Strengths}{25}{subsection.7.1}%
\contentsline {subsection}{\numberline {7.2}Weaknesses and Possible Improvement}{25}{subsection.7.2}%
\contentsline {section}{References}{26}{section*.31}%