Chapter 4
Layout of a Single Floor
This chapter is concerned with the problem of physically arranging a set of twodimensional departments inside a two-dimensional facility. Mathematically, the
problem is to find the optimal placement of a given number of nonoverlapping
indivisible departments, with a given area requirement for each department, so as
to minimize the total cost of flows inside the floor. This single floor facility layout
problem is often called the unequal-areas facility layout problem (UA-FLP), and
it differs substantially from row layouts. The departments are now genuinely twodimensional, and determining the optimal dimensions for each department such that
the area requirements are met is part of the problem.
4.1 Nonconvex Continuous Optimization Formulation
We begin with an exact formulation of the UA-FLP using only continuous variables.
This formulation is of limited use in practice, but it is straightforward, it allows us
to establish the notation for this chapter, and it highlights the challenging aspects of
the UA-FLP, thus motivating the solution approaches presented in the remainder of
the chapter.
The constraints for the UA-FLP can be grouped into two sets:
• Department shape constraints ensure the required area of each department and
enforce restrictions on its dimensions (height and width). These requirements
generally lead to linear or convex constraints but still pose some challenges.
• Department location constraints place every department within the facility
and ensure that there is no overlap between pairs of departments. The main
challenge here is the nonoverlap constraints that are inherently nonconvex and
combinatorial.
© Springer Nature Switzerland AG 2021
M. F. Anjos, M. V. C. Vieira, Facility Layout, EURO Advanced Tutorials
on Operational Research, https://doi.org/10.1007/978-3-030-70990-7_4
57
Layout of a Single Floor
This chapter is concerned with the problem of physically arranging a set of twodimensional departments inside a two-dimensional facility. Mathematically, the
problem is to find the optimal placement of a given number of nonoverlapping
indivisible departments, with a given area requirement for each department, so as
to minimize the total cost of flows inside the floor. This single floor facility layout
problem is often called the unequal-areas facility layout problem (UA-FLP), and
it differs substantially from row layouts. The departments are now genuinely twodimensional, and determining the optimal dimensions for each department such that
the area requirements are met is part of the problem.
4.1 Nonconvex Continuous Optimization Formulation
We begin with an exact formulation of the UA-FLP using only continuous variables.
This formulation is of limited use in practice, but it is straightforward, it allows us
to establish the notation for this chapter, and it highlights the challenging aspects of
the UA-FLP, thus motivating the solution approaches presented in the remainder of
the chapter.
The constraints for the UA-FLP can be grouped into two sets:
• Department shape constraints ensure the required area of each department and
enforce restrictions on its dimensions (height and width). These requirements
generally lead to linear or convex constraints but still pose some challenges.
• Department location constraints place every department within the facility
and ensure that there is no overlap between pairs of departments. The main
challenge here is the nonoverlap constraints that are inherently nonconvex and
combinatorial.
© Springer Nature Switzerland AG 2021
M. F. Anjos, M. V. C. Vieira, Facility Layout, EURO Advanced Tutorials
on Operational Research, https://doi.org/10.1007/978-3-030-70990-7_4
57