---
title: "Maximizing Flexibility: A Retraction Heuristic for Oversubscribed Scheduling Problems"
authors:
  - "Laurence A. Kramer"
  - "Stephen F. Smith"
doi: ""
url: "https://ijcai.org/proceedings/2003/173"
pdf: "https://ijcai.org/proceedings/2003/0173.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "1218-1222"
track: ""
keywords:
---

# Maximizing Flexibility: A Retraction Heuristic for Oversubscribed Scheduling Problems

Laurence A. Kramer, Stephen F. Smith

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 1218-1222.

## Abstract

In this paper we consider the solution of scheduling problems that are inherently over-subscribed. In such problems, there are always more tasks to execute within a given time frame than available resource capacity will allow, and hence decisions must be made about which tasks should be included in the schedule and which should be excluded. We adopt a controlled, iterative repair search approach, and focus on improving the results of an initial priority-driven solution generation procedure. Central to our approach is a new retraction heuristic, termed max-flexibility, which is responsible for identifying which tasks to (temporarily) retract from the schedule for reassignment in an effort to incorporate additional tasks into the schedule. The max-flexibility heuristic chooses those tasks that have maximum flexibility for assignment within their feasible windows. We empirically ev a luate the performance of max-flexibility using problem data and the basic scheduling procedure from a fielded airlift mission scheduling application. We show that it produces better improvement results than two contention-based retraction heuristics, including a variant of min-conflicts[Minton et a/., 1992], with significantly less search and computational cost.