This paper introduces $\Delta$-MILP, a powerful variant of the mixed-integer linear programming (MILP) optimization framework to solve NASA's Deep Space Network (DSN) scheduling problem. work is an extension our original MILP (DOI:10.1109/ACCESS.2021.3064928) and inherits many its constructions strengths, including base formulation for DSN scheduling. To provide more feasible schedules with res...

Abstract We study linear bilevel programming problems, where (some of) the leader and follower variables are restricted to be integer. A discussion on relationships between optimistic pessimistic setting is presented, providing necessary sufficient conditions for them equivalent. new class of inequalities, optimality cuts, introduced. They used derive a single-level non-compact reformulation pr...

A variety of combinatorial problems (e.g., in capital budgeting, scheduling, allocation) can be expressed as a linear integer programming problem. However, the standard devices for doing this often produce an inordinate number of variables and constraints, putting the problem beyond the practical reach of available integer programming methods. This paper presents new formulation techniques for ...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...