Resource-dependent process times in hybrid flexible flowshops

TL;DR

This paper investigates resource-dependent processing times in hybrid flexible flowshops, proposing a novel constraint programming approach with decomposition and bounds, demonstrating scalability and effectiveness on large instances.

Contribution

It introduces a new CP formulation with LBBD for resource-dependent times in HFFS and enhances it with makespan bounds, addressing a gap in practical scheduling research.

Findings

Effective decomposition approach for large instances

Strong makespan lower bounds improve solution quality

Scalable results on instances with up to 400 jobs

Abstract

The effect of resource allocation on manufacturing motivates us to examine a scheduling variant that is of practical significance yet remains overlooked. We examine a Hybrid Flexible Flowshop (HFFS), i.e., an environment where a set of jobs is scheduled across multiple stages (each stage having multiple identical machines) yet some jobs may skip some stages. In addition, we consider processing times that depend on the resources assigned to a job at each stage, transportation times between machines and limited-capacity buffers before and after each stage. We introduce a Constraint Programming (CP) formulation, which we then decompose through Logic-Based Benders Decomposition (LBBD). We tighten formulations by a set of makespan lower bounds, the strongest of which arises from a reduction to malleable scheduling. By modifying recent instance generators, we experiment with up to 400 jobs, 8 stages, and 10 parallel machines per stage. The results demonstrate competitive integrality gaps, highlighting the efficiency of our approach at scale and on an HFFS variant quite beyond the current literature.