Dynamic Interval Scheduling with Random Start and End Times
Rui Gong, Alejandro Toriello
TL;DR
Dynamic interval scheduling with random start and end times studies sequential decision-making where the task set and weights are known but each task's realization $[s_i,e_i]$ is drawn from known distributions and revealed upon commitment. The authors introduce two conflict-enforcement models, DSRSE and Conservative DSRSE (CDSRSE), and develop LP relaxations and dual bounds built around probabilistic start/end information and pessimistic interval graphs $G_{ ext{pes}}$, enabling tractable performance guarantees. They establish NP-hardness in general, show that deterministic times reduce to maximum independent set on interval graphs with classic LP relaxations, and analyze the uniform-weight case to derive explicit bounds. Through computational experiments, they compare LP-based bounds to Monte Carlo realizations and demonstrate that simple, weight-based heuristics perform competitively under uncertainty, offering practical guidance for stochastic scheduling in dynamic environments.
Abstract
We study sequential interval scheduling when task start and end times are random. The set of tasks and their weights are known in advance, while each task's start and end times are drawn from known discrete distributions and revealed only upon commitment; this also eliminates tasks that conflict with the committed task, and remaining tasks are those that do not conflict. The objective is to maximize the expected weight of a conflict-free schedule. We propose two models that differ in how conflicts are enforced, develop LP relaxations and bounds for each, and present a computational study.