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Resource-dependent process times in hybrid flexible flowshops

Ioannis Avgerinos, Ioannis Mourtos, Dimitrios Papathanasiou, Georgios Zois

TL;DR

This work tackles resource-dependent processing times in Hybrid Flexible Flowshops by formulating a CP-based LBBD approach that decomposes the problem into a CP master and CP subproblem, augmented with eight dual bounds and a malleable scheduling relaxation to tighten lower bounds. The CP model handles buffers, transportation times, and renewable workforce constraints, while the LBBD framework iterates between master and subproblem cuts to converge toward optimality. Computational results show that CP alone scales to moderate sizes (up to ~100–200 jobs) but struggles on 400-job instances, whereas CP-oriented LBBD solves all tested instances (up to 400 jobs) with consistently strong upper bounds and competitive real-gap performance. The methodology demonstrates scalable, exact solution capabilities for complex HFFS variants and offers a transferable approach via its malleable-scheduling reduction to other resource-constrained scheduling problems.

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.

Resource-dependent process times in hybrid flexible flowshops

TL;DR

This work tackles resource-dependent processing times in Hybrid Flexible Flowshops by formulating a CP-based LBBD approach that decomposes the problem into a CP master and CP subproblem, augmented with eight dual bounds and a malleable scheduling relaxation to tighten lower bounds. The CP model handles buffers, transportation times, and renewable workforce constraints, while the LBBD framework iterates between master and subproblem cuts to converge toward optimality. Computational results show that CP alone scales to moderate sizes (up to ~100–200 jobs) but struggles on 400-job instances, whereas CP-oriented LBBD solves all tested instances (up to 400 jobs) with consistently strong upper bounds and competitive real-gap performance. The methodology demonstrates scalable, exact solution capabilities for complex HFFS variants and offers a transferable approach via its malleable-scheduling reduction to other resource-constrained scheduling problems.

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.
Paper Structure (14 sections, 3 theorems, 22 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 14 sections, 3 theorems, 22 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem description
  4. Logic-Based Benders Decomposition
  5. Mathematical Modelling
  6. The CP model
  7. Relaxation of the problem
  8. Subproblem
  9. Lower bound via a malleable scheduling relaxation
  10. CP-oriented LBBD
  11. Computational experience
  12. Applied testbeds
  13. Comparison between the CP and the LBBD
  14. Further work

Key Result

Lemma 1

The optimal solution of (LP) provides a lower bound on the makespan of any feasible solution to the malleable job scheduling problem.

Figures (3)

  • Figure 1: An indicative example of three jobs on three stages
  • Figure 2: Parallelisability of operations to workers
  • Figure 3: Gap (%) values of all 125 instances

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof