50
3 Layout on Several Rows
3.5 Additional Special Cases of Multi-Row Facility Layout
In this section we present other special cases for layout on several rows with specific
additional structure.
3.5.1 Corridor Allocation Problem
The corridor allocation problem (CAP), like the DRFLP, is concerned with assigning departments to two rows. However, the CAP has the following additional
conditions:
• no empty space is allowed between two adjacent departments;
• the leftmost points of each row must be aligned, typically at the origin.
Note that because the CAP is a version of the DRFLP with additional restrictions, it
follows that for the same set of departments and connectivities, the optimal cost of
the CAP will always be at least as high as that of the DRFLP. This is illustrated in
Example 3.2 where the optimal solutions of the DRFLP and CAP are different for
the same set of departments with the same connectivities.
Example 3.2 We consider an instance with 5 departments. The length of departments 1, 2, and 3 is 8, and the length of departments 4 and 5 is 2. The nonzero
connectivities are c 12 = c 45 = 1 and c 13 = c 24 = 10. The optimal solutions for the
DRFLP and CAP are illustrated below (Figs. 3.3 and 3.4).
Row 1
2
3
Row 2
1
4
5
Fig. 3.3 Optimal layout for the DRFLP with a total cost equal to 10
Row 1
2
3
Row 2
4
5
1
Fig. 3.4 Optimal layout for the CAP with a total cost equal to 20
3 Layout on Several Rows
3.5 Additional Special Cases of Multi-Row Facility Layout
In this section we present other special cases for layout on several rows with specific
additional structure.
3.5.1 Corridor Allocation Problem
The corridor allocation problem (CAP), like the DRFLP, is concerned with assigning departments to two rows. However, the CAP has the following additional
conditions:
• no empty space is allowed between two adjacent departments;
• the leftmost points of each row must be aligned, typically at the origin.
Note that because the CAP is a version of the DRFLP with additional restrictions, it
follows that for the same set of departments and connectivities, the optimal cost of
the CAP will always be at least as high as that of the DRFLP. This is illustrated in
Example 3.2 where the optimal solutions of the DRFLP and CAP are different for
the same set of departments with the same connectivities.
Example 3.2 We consider an instance with 5 departments. The length of departments 1, 2, and 3 is 8, and the length of departments 4 and 5 is 2. The nonzero
connectivities are c 12 = c 45 = 1 and c 13 = c 24 = 10. The optimal solutions for the
DRFLP and CAP are illustrated below (Figs. 3.3 and 3.4).
Row 1
2
3
Row 2
1
4
5
Fig. 3.3 Optimal layout for the DRFLP with a total cost equal to 10
Row 1
2
3
Row 2
4
5
1
Fig. 3.4 Optimal layout for the CAP with a total cost equal to 20