Exact modeling of sequence- and time-dependent transition times

Develop an exact optimization formulation for sequence- and time-dependent transition times in Earth observation satellite scheduling at the resolution of the underlying orbital data, while exploiting structural properties such as the first-in-first-out rule and the triangle inequality and avoiding the size limitations or unquantified approximation errors of existing approaches.

Background

Sequence- and time-dependent transition times depend on the precise observation times and the resulting satellite look angles. The reviewed formulations either discretize visibility windows, which limits solvable instance sizes, or approximate angle profiles and transition times to preserve tractability. The paper notes that the effects of these approximations on solution quality have not been quantified.

The authors identify the first-in-first-out property and triangle inequality of the transition-time function as structural properties that have so far been used only in heuristic search. An unresolved problem is to use these properties in an exact formulation.

References

The most immediate one concerns the exact treatment of sequence and time-dependent transition times, which no reviewed formulation achieves at the resolution at which the underlying orbital data are available. Existing approaches either discretize the visibility windows, which limits the size of the instances that can be solved, or approximate the angle profiles and the resulting transition times, which makes the model tractable at the cost of an approximation whose effect on solution quality is not quantified.

— Earth Observation Satellite Scheduling Models: Taxonomy, Classification and Open Challenges  (2610.23520 - Caleiras et al., 16 Oct 2026) in Section Conclusion and future directions

This paper establishes how the alternative representations differ structurally, but their relative computational performance remains unknown, since studies proposing a formulation compare it against the algorithms of the works they extend rather than against alternative formulations of the same problem, and the instances used differ in size, geographic distribution and modeling assumptions.

— Earth Observation Satellite Scheduling Models: Taxonomy, Classification and Open Challenges  (2610.23520 - Caleiras et al., 16 Oct 2026) in Section Conclusion and future directions