Theoretical Lower Bounds for the Oven Scheduling Problem

TL;DR

This paper introduces fast, problem-specific lower bounds for the NP-hard Oven Scheduling Problem, aiding in evaluating solution quality and enhancing exact and heuristic scheduling methods in semiconductor manufacturing.

Contribution

It develops and analyzes new theoretical lower bounds for the Oven Scheduling Problem, facilitating better solution assessment and integration into optimization algorithms.

Findings

Lower bounds can be computed quickly.

Lower bounds improve solution quality assessment.

Integration enhances exact and heuristic methods.

Abstract

The Oven Scheduling Problem (OSP) is an NP-hard real-world parallel batch scheduling problem arising in the semiconductor industry. The objective of the problem is to schedule a set of jobs on ovens while minimizing several factors, namely total oven runtime, job tardiness, and setup costs. At the same time, it must adhere to various constraints such as oven eligibility and availability, job release dates, setup times between batches, and oven capacity limitations. The key to obtaining efficient schedules is to process compatible jobs simultaneously in batches. In this paper, we develop theoretical, problem-specific lower bounds for the OSP that can be computed very quickly. We thoroughly examine these lower bounds, evaluating their quality and exploring their integration into existing solution methods. Specifically, we investigate their contribution to exact methods and a metaheuristic local search approach using simulated annealing. Moreover, these problem-specific lower bounds enable us to assess the solution quality for large instances for which exact methods often fail to provide tight lower bounds.