5.3 Layout on Several Floors
77
corridors and elevators) cannot be moved. We assume that the available locations
and their dimensions (and hence their areas) are known. We also assume that the area
requirements of the departments to be relocated are known (these may be different
from the original requirements). Given the information that relocated department
i needs area A i and location p has area B p , we can add constraints of the form
A i x ip ≤ B p to any of the approaches in Chap. 4.
A further possible simplification is to assume that any of the departments to
be relocated can be assigned to any of the available locations. In other words, we
neglect all considerations about the area or shape of either departments or locations.
It is straightforward to formulate this simplified version of re-layout as a QAP
using the formulation (5.2)–(5.5) in Sect. 5.1, but re-layout (or facility layout itself)
remains a difficult problem.
We have assumed that there is an equal number of departments and locations. If
we have an instance with more locations than departments, then some locations will
be left unassigned. This can be accommodated in the formulations in Chap. 4 and
in the QAP model by changing constraint (5.4) to an inequality, so that at most one
department is assigned to each location:
n
i=1
x ip ≤ 1, 1 ≤ p ≤ n.
5.3 Layout on Several Floors
The multi-floor FLP (MF-FLP) involves finding the optimal arrangement of departments in a facility with multiple floors. Practical applications include production
facilities, hotels, office buildings, and hospitals. This problem is more complex
than the UA-FLP because we must consider the interactions between departments
on different floors. Furthermore, elevators and/or stairwells are required to transfer
people and/or materials between the floors, and these need to be placed at coherent
locations across floors.
5.3.1 MISOCO Formulation of the MF-FLP
We assume that the following parameters are given:
• the number of departments and their areas,
• the interconnection costs between pairs of departments,
• the number of floors,
• the dimensions and height of the floors, and
• the number and size of the elevators.
77
corridors and elevators) cannot be moved. We assume that the available locations
and their dimensions (and hence their areas) are known. We also assume that the area
requirements of the departments to be relocated are known (these may be different
from the original requirements). Given the information that relocated department
i needs area A i and location p has area B p , we can add constraints of the form
A i x ip ≤ B p to any of the approaches in Chap. 4.
A further possible simplification is to assume that any of the departments to
be relocated can be assigned to any of the available locations. In other words, we
neglect all considerations about the area or shape of either departments or locations.
It is straightforward to formulate this simplified version of re-layout as a QAP
using the formulation (5.2)–(5.5) in Sect. 5.1, but re-layout (or facility layout itself)
remains a difficult problem.
We have assumed that there is an equal number of departments and locations. If
we have an instance with more locations than departments, then some locations will
be left unassigned. This can be accommodated in the formulations in Chap. 4 and
in the QAP model by changing constraint (5.4) to an inequality, so that at most one
department is assigned to each location:
n
i=1
x ip ≤ 1, 1 ≤ p ≤ n.
5.3 Layout on Several Floors
The multi-floor FLP (MF-FLP) involves finding the optimal arrangement of departments in a facility with multiple floors. Practical applications include production
facilities, hotels, office buildings, and hospitals. This problem is more complex
than the UA-FLP because we must consider the interactions between departments
on different floors. Furthermore, elevators and/or stairwells are required to transfer
people and/or materials between the floors, and these need to be placed at coherent
locations across floors.
5.3.1 MISOCO Formulation of the MF-FLP
We assume that the following parameters are given:
• the number of departments and their areas,
• the interconnection costs between pairs of departments,
• the number of floors,
• the dimensions and height of the floors, and
• the number and size of the elevators.