Dynamic Interval Scheduling with Random Start and End Times

TL;DR

This paper investigates the problem of maximizing expected weight in sequential interval scheduling with tasks having random start and end times, proposing models, LP relaxations, and computational analysis.

Contribution

It introduces two models for conflict enforcement, develops LP relaxations, and provides a computational study for scheduling with random task times.

Findings

LP relaxations provide bounds for the models

Models effectively handle random start and end times

Computational results demonstrate the approach's viability

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.