Chapter 2
Layout on a Single Row
Single-row layout has a simple structure. Given a set of departments to place
alongside each other in a single row, the problem typically boils down to finding
a permutation of the departments that minimizes the total distance travelled.
2.1 Introductory Example
We start with an example from a manufacturing context. Consider a factory that
needs to place 12 machines, described in Table 2.1, in a line. This could be because
they are to be placed along a single wall of a large factory, for example. There
is traffic (of people and/or parts) between the machines, and Table 2.2 gives the
amount of traffic between each pair of machines when the factory is in operation.
Given this information, we seek to arrange the machines in a single row so that the
total distance travelled when they are operating is minimized. This is an example of
the single-row facility layout problem (SRFLP).
Figure 2.1 illustrates the SRFLP in the context of placing the machines along the
path of an automated guided vehicle (AGV) transporting material between them;
here, the objective is to minimize the distance travelled by the AGV.
To build a mathematical optimization model, we represent each machine as a
rectangle of the same length as the machine. The heights of the rectangles can be
all equal, say one, because they are not relevant to the optimization. We measure
the distances in one dimension, say along the x-axis, and we introduce variables
x 1 , x 2 , . . . , x 12 to denote the location along the x-axis of the centre of each machine.
Using these variables, we can express the distance between each pair of machines i,
j as the absolute value of the difference of the locations of their centres: |x i − x j |.
© 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_2
3
Layout on a Single Row
Single-row layout has a simple structure. Given a set of departments to place
alongside each other in a single row, the problem typically boils down to finding
a permutation of the departments that minimizes the total distance travelled.
2.1 Introductory Example
We start with an example from a manufacturing context. Consider a factory that
needs to place 12 machines, described in Table 2.1, in a line. This could be because
they are to be placed along a single wall of a large factory, for example. There
is traffic (of people and/or parts) between the machines, and Table 2.2 gives the
amount of traffic between each pair of machines when the factory is in operation.
Given this information, we seek to arrange the machines in a single row so that the
total distance travelled when they are operating is minimized. This is an example of
the single-row facility layout problem (SRFLP).
Figure 2.1 illustrates the SRFLP in the context of placing the machines along the
path of an automated guided vehicle (AGV) transporting material between them;
here, the objective is to minimize the distance travelled by the AGV.
To build a mathematical optimization model, we represent each machine as a
rectangle of the same length as the machine. The heights of the rectangles can be
all equal, say one, because they are not relevant to the optimization. We measure
the distances in one dimension, say along the x-axis, and we introduce variables
x 1 , x 2 , . . . , x 12 to denote the location along the x-axis of the centre of each machine.
Using these variables, we can express the distance between each pair of machines i,
j as the absolute value of the difference of the locations of their centres: |x i − x j |.
© 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_2
3