An integrated scheduling problem of PCB components on sequential pick-and-place machines: Mathematical models and heuristic solutions

William Ho, Ping Ji

Research output: Journal article publicationJournal articleAcademic researchpeer-review

26 Citations (Scopus)


This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-and-place (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.
Original languageEnglish
Pages (from-to)7002-7010
Number of pages9
JournalExpert Systems with Applications
Issue number3 PART 2
Publication statusPublished - 1 Apr 2009


  • Component sequencing
  • Feeder arrangement
  • Genetic algorithm
  • Mathematical modeling
  • Printed circuit board manufacturing
  • Surface mount technology

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Engineering(all)

Cite this