| Summary: | This paper introduces <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>-MILP, a powerful variant of the mixed-integer linear programming (MILP) optimization framework to solve NASA’s Deep Space Network (DSN) scheduling problem. This work is an extension of our original MILP framework (DOI:10.1109/ACCESS.2021.3064928), and inherits many of its constructions and strengths, including the base MILP formulation for DSN scheduling. To provide more feasible schedules with respect to the DSN requirements, <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>-MILP incorporates new sets of constraints including 1) splitting larger tracks into shorter segments and 2) preventing overlapping between tracks on different antennas. Additionally, <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>-MILP leverages a heuristic to balance mission satisfaction and allows to prioritize certain missions in special scenarios including emergencies and landings. Numerical validations demonstrate that <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>-MILP now satisfies 100% of the requested constraints and provides fair schedules amongst missions with respect to the state-of-the-art for the most oversubscribed weeks of the years 2016 and 2018.
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