### Abstract

In this paper, a new mixed-integer programming (MIP) formulation based on the flexible bay structure (FBS) is presented to optimally solve the facility layout problem (FLP) with unequal departmental areas in a continuous plane. The FBS is a continuous layout representation where departments are allowed to be located only in parallel bays bounded by straight aisles on both sides. Bays are completely filled by departments and departments are not allowed to span over multiple bays. Although the FBS restricts possible layout configurations in theory, many manufacturing facility designs follow an implicit bay structure. In addition, the bay structure forms the basis of an aisle structure that facilitates the designers transferring the block design into an actual facility design in a short time. However, no exact methods exist to find optimal solution for this layout representation. An important difficulty in the MIP approach to FLP is to model nonlinear department area equations. These equations define the relationship between the length of departments in the x-axis and y-axis. Some of the existing formulations implement surrogate constraints or approximation techniques to linearize these nonlinear equations, and some others make assumptions, such as equal-sized departments and departments with fixed shapes and orientations. In the FBS, the departments in the same bay have the same length in the x-axis. which is equal to the width of the bay. Therefore, the departments located in the same bay must have lengths in the y-axis proportional to their areas, i.e., equality h _{i}a _{j} = h _{j}a _{i}, where h _{i} and a _{i} are the length in the y-axis and the area of department i, respectively, must hold for each department pair _{i} and _{j} assigned to the same bay. In the new MIP formulation, this relationship is used to model department area equations in the continuous plane without using any surrogate constraints, linearization, or specifying the department shape and orientation a priori. Computational analyses have demonstrated that the proposed formulation is capable of solving problems bigger than those that could be previously solved to optimality with a more general MIP formulation. Problems as big as 14 departments have been optimally solved and new best integer solutions have found for some of the problems from the literature.

Original language | English |
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Pages | 63 |

Number of pages | 1 |

State | Published - 2004 |

Event | IIE Annual Conference and Exhibition 2004 - Houston, TX, United States Duration: May 15 2004 → May 19 2004 |

### Conference

Conference | IIE Annual Conference and Exhibition 2004 |
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Country | United States |

City | Houston, TX |

Period | 05/15/04 → 05/19/04 |

### Keywords

- Facility design
- Facility unequal area layout
- Mixed integer programming

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## Cite this

*A new mixed-integer programming formulation for unequal area facility layout problem in a continuous plane*. 63. Paper presented at IIE Annual Conference and Exhibition 2004, Houston, TX, United States.