A Three-Stage Approach to a Multirow Parallel Machine Layout Problem

Xingquan Zuo, Shubing Gao, Meng Chu Zhou, Xin Yang, Xinchao Zhao

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Facility layout is vital to save operational cost and enhance production efficiency. Multirow layout is a common pattern in practical manufacturing environment. Although parallel machines are frequently implemented in practice to enhance productivity, there lacks any in-depth study on multirow layout problem with parallel machines. In this paper, its mathematical programming formulation is established to minimize material flow cost. A three-stage approach is proposed to solve it. First, a Monte Carlo heuristic is devised to optimize the sequence of machines on multiple rows. Second, a linear program is used to determine the optimal exact location of each machine. Finally, an exchange heuristic is adopted to reassign material flows among parallel machines in different machine groups. An iterative optimization strategy is suggested to execute the three stages repeatedly to improve the solution quality. This approach is applied to a number of problem instances and compared against others. The experimental results show that it is able to effectively solve this new problem and significantly decrease material flow cost. Note to Practitioners-Multirow layout is common in practical manufacturing systems in which parallel machines are often used to improve productivity, shorten production time, and guarantee some flexibility. This paper studies a multirow parallel machine layout problem that involves machine groups, each of which contains parallel machines. Solving it is to locate all machines at multiple parallel rows to minimize material flow cost. It is challenging because one needs to decompose material flows and determine exact locations of machines simultaneously. A three-stage approach is proposed to do so. It is applied to many problem instances. The results demonstrate that it works well for such layout problems with parallel machines.

Original languageEnglish (US)
Article number8489959
Pages (from-to)433-447
Number of pages15
JournalIEEE Transactions on Automation Science and Engineering
Issue number1
StatePublished - Jan 2019

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


  • Facility layout problem (FLP)
  • linear program (LP)
  • metaheuristic algorithm
  • parallel machine


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