Chapter 3
Layout on Several Rows
In this chapter we consider the problem of optimally placing a set of departments
on two or more rows, given the lengths of the departments, the number of rows, and
a pairwise non-negative connectivity for each pair of departments. We refer to such
problems as row layout problems, and we divide this class of problems into two
types, namely double-row facility layout and multi-row facility layout, where the
latter involves three or more rows. It is worth treating double-row facility layout
separately because it is amenable to specialized models that are typically more
efficient than those for multi-row layout.
Facility layout problems on rows arise in manufacturing systems, and the type
of layout depends on the choice of material handling system. While single-row and
double-row layouts use the same type of system, an AGV, layouts on three or more
rows are of interest when using a gantry robot.
Another application is in the design of some integrated circuits for which the
layout of the components is organized in rows (called base layers). The objective
is to minimize the total wirelength required to connect the components, where the
space between the rows is used for the wires connecting the components.
A separation between the rows is often specified to account for factors such as
the movements of the material handling system and/or the workers. This is usually
straightforward to accommodate in an optimization model. A more challenging
aspect is that within each row, a minimum clearance between departments is
normally required to meet safety and operational requirements. For simplicity, we
assume that this clearance is included in the lengths of the departments, but it can
also be handled by adjusting the nonoverlap constraints to enforce the clearance.
In this chapter we assume that the rows and departments all have the same height,
that every department can be assigned to every row, and that the distances between
© 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_3
33
Layout on Several Rows
In this chapter we consider the problem of optimally placing a set of departments
on two or more rows, given the lengths of the departments, the number of rows, and
a pairwise non-negative connectivity for each pair of departments. We refer to such
problems as row layout problems, and we divide this class of problems into two
types, namely double-row facility layout and multi-row facility layout, where the
latter involves three or more rows. It is worth treating double-row facility layout
separately because it is amenable to specialized models that are typically more
efficient than those for multi-row layout.
Facility layout problems on rows arise in manufacturing systems, and the type
of layout depends on the choice of material handling system. While single-row and
double-row layouts use the same type of system, an AGV, layouts on three or more
rows are of interest when using a gantry robot.
Another application is in the design of some integrated circuits for which the
layout of the components is organized in rows (called base layers). The objective
is to minimize the total wirelength required to connect the components, where the
space between the rows is used for the wires connecting the components.
A separation between the rows is often specified to account for factors such as
the movements of the material handling system and/or the workers. This is usually
straightforward to accommodate in an optimization model. A more challenging
aspect is that within each row, a minimum clearance between departments is
normally required to meet safety and operational requirements. For simplicity, we
assume that this clearance is included in the lengths of the departments, but it can
also be handled by adjusting the nonoverlap constraints to enforce the clearance.
In this chapter we assume that the rows and departments all have the same height,
that every department can be assigned to every row, and that the distances between
© 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_3
33