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Trolley Optimisation for Loading Printed Circuit Board Components

Vinod Kumar Chauhan, Mark Bass, Ajith Kumar Parlikad, Alexandra Brintrup

TL;DR

The paper tackles the challenge of loading PCB components onto trolleys and stackers under assembly-line capacity constraints by introducing the Trolley Optimisation Problem (TOP), a novel $NP$-complete extension of the bin packing problem. It decomposes TOP into two identical subproblems and develops a MILP formulation, with constraint programming offering practical performance advantages in their case study. Using aerospace-manufacturing datasets, the approach achieves substantial reductions in setup time (from weeks to hours) and lowers the number of required trolleys, while increasing build flexibility to respond to changing demands. The work demonstrates both theoretical and practical significance, providing a concrete pathway to automate complex, low-volume, high-mix PCB production and suggesting future integration with broader scheduling across assembly lines.

Abstract

A trolley is a container for loading printed circuit board (PCB) components, and a trolley optimisation problem (TOP) is an assignment of PCB components to trolleys for use in the production of a set of PCBs in an assembly line. In this paper, we introduce the TOP, a novel operation research application. To formulate the TOP, we derive a novel extension of the bin packing problem. We exploit the problem structure to decompose the TOP into two smaller, identical, and independent problems. Further, we develop a mixed integer linear programming model to solve the TOP and prove that the TOP is an NP-complete problem. A case study of an aerospace manufacturing company is used to illustrate the TOP which successfully automated the manual process in the company and resulted in significant cost reductions and flexibility in the building process.

Trolley Optimisation for Loading Printed Circuit Board Components

TL;DR

The paper tackles the challenge of loading PCB components onto trolleys and stackers under assembly-line capacity constraints by introducing the Trolley Optimisation Problem (TOP), a novel -complete extension of the bin packing problem. It decomposes TOP into two identical subproblems and develops a MILP formulation, with constraint programming offering practical performance advantages in their case study. Using aerospace-manufacturing datasets, the approach achieves substantial reductions in setup time (from weeks to hours) and lowers the number of required trolleys, while increasing build flexibility to respond to changing demands. The work demonstrates both theoretical and practical significance, providing a concrete pathway to automate complex, low-volume, high-mix PCB production and suggesting future integration with broader scheduling across assembly lines.

Abstract

A trolley is a container for loading printed circuit board (PCB) components, and a trolley optimisation problem (TOP) is an assignment of PCB components to trolleys for use in the production of a set of PCBs in an assembly line. In this paper, we introduce the TOP, a novel operation research application. To formulate the TOP, we derive a novel extension of the bin packing problem. We exploit the problem structure to decompose the TOP into two smaller, identical, and independent problems. Further, we develop a mixed integer linear programming model to solve the TOP and prove that the TOP is an NP-complete problem. A case study of an aerospace manufacturing company is used to illustrate the TOP which successfully automated the manual process in the company and resulted in significant cost reductions and flexibility in the building process.
Paper Structure (13 sections, 1 theorem, 5 equations, 4 figures, 3 tables)

This paper contains 13 sections, 1 theorem, 5 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. The bin packing problems
  4. PCB related problems
  5. Trolley optimisation: a case study
  6. Problem definition
  7. Problem formulation
  8. Solution approach
  9. Dataset and experimental settings
  10. Comparative study
  11. Sensitivity analysis
  12. Trolley optimisation is an NP-complete problem
  13. Conclusion and discussions

Key Result

Theorem 4.2

The trolley optimisation is an NP-complete problem.

Figures (4)

  • Figure 1: An example of trolleys, slots on the trolley, and a CAP machine (pictures are shared by our industrial partner).
  • Figure 2: Distribution of component sizes in terms of number of slots required on a trolley/stacker.
  • Figure 3: Comparative study of the existing manual method versus the proposed automated TOP method
  • Figure 4: Utilisation status of selected trolleys on (a) Dataset A and (b) Dataset B

Theorems & Definitions (3)

  • Definition 4.1: Trolley optimisation
  • Theorem 4.2
  • proof