Computing an optimal single machine schedule with sequence dependent setup times using shortest path computations

TL;DR

This paper introduces a novel polynomial-time method for solving single-machine scheduling problems with sequence-dependent setup times by transforming them into shortest path problems on layered graphs, applicable especially in manufacturing contexts.

Contribution

The paper presents a new graph-based framework that encodes sequence-dependent effects, enabling efficient computation of optimal schedules for specific cases.

Findings

Polynomial-time solution for two-color case

Structural properties of optimal schedules revealed

Practical applicability in manufacturing processes

Abstract

We study a single-machine scheduling problem with sequence dependent setup times, motivated by applications in manufacturing and service industries - in particular, the calendering stage in rubber flooring production. In this phase, setup times are primarily driven by temperature and color transitions between consecutive jobs, with significant impact on throughput and energy efficiency. We present a novel solution framework that transforms the scheduling problem into a path-finding problem on a specially constructed layered graph. By encoding sequence-dependent effects directly into the graph's structure, we enable the use of classical shortest-path algorithms to compute optimal job sequences. The resulting method is polynomial-time solvable for the two-color case and reveals key structural properties of optimal schedules. Our approach thus provides both a theoretically grounded and practically applicable optimization technique.