arXiv:2411.15361v4 Announce Type: replace
Abstract: In the design of cellular manufacturing systems (CMS), numerous technological and managerial decisions must be made at both the design and operational stages. The first step in designing a CMS involves grouping parts and machines. In this paper, four integer programming formulations are presented for grouping parts and machines in a CMS at both the design and operational levels for a generalised grouping problem, where each part has more than one process plan and each operation of a process plan can be performed on more than one machine. These four integer programming formulations have the ability to simultaneously optimise cell formation and operational routing decisions within a unified framework, whereas prior models often treat these as sequential or independent stages. By integrating machine flexibility and alternative process plans directly into the mathematical objective, this approach ensures a more globally optimal configuration for generalised grouping problems. Minimising inter-cell and intra-cell movements is achieved by assigning as many consecutive operations of a part type as possible to the same cell and machine. This objective is evaluated against alternatives like reducing machine investment and operating costs. Numerical examples demonstrate how the proposed formulations work and highlight their effectiveness in practice.
Abstract: In the design of cellular manufacturing systems (CMS), numerous technological and managerial decisions must be made at both the design and operational stages. The first step in designing a CMS involves grouping parts and machines. In this paper, four integer programming formulations are presented for grouping parts and machines in a CMS at both the design and operational levels for a generalised grouping problem, where each part has more than one process plan and each operation of a process plan can be performed on more than one machine. These four integer programming formulations have the ability to simultaneously optimise cell formation and operational routing decisions within a unified framework, whereas prior models often treat these as sequential or independent stages. By integrating machine flexibility and alternative process plans directly into the mathematical objective, this approach ensures a more globally optimal configuration for generalised grouping problems. Minimising inter-cell and intra-cell movements is achieved by assigning as many consecutive operations of a part type as possible to the same cell and machine. This objective is evaluated against alternatives like reducing machine investment and operating costs. Numerical examples demonstrate how the proposed formulations work and highlight their effectiveness in practice.
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