
The sequential method starts with
an aisle layout and all subsequent solutions are also
aisle layouts. We repeat the example with the initial solution
determined with the sequence {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
For this method all pairs of departments are considered
for switching positions in the sequence. The layout is evaluated
for every pair assuming that the positions in the sequence are
switched. If a switch is discovered that results in a savings,
the aisle layout based on the new sequence is constructed and
used to continue the algorithm. For the example, the best switch
is D9 and D10, resulting in the sequence {1, 2, 3, 4, 5, 6,
7, 8, 10, 9}. The resulting layout is shown below.
Since the construction of the layout given a sequence
is well defined, this layout involves no arbitrary placement
of departmental cells. When the initial layout has rectangular
departments, the shapes of the departments remain rectangular
except when a departments is placed in more than one aisle.
The next best switch is
D1 and D3 resulting in the sequence {3, 2, 1, 4, 5, 6, 7, 8,
10, 9}. Notice that the change in sequence affects the relative
locations of the departments switched. When the departments
are of different size, the locations of all departments between
are also adjusted. For the example, in addition to D1 and D3,
the centroid of D2 is changed.
The process continues by
switching D6 and D7 resulting in the sequence {3, 2, 1, 4, 5,
7, 6, 8, 10, 9}. The result is shown below.
No improving switches are
available after this step.
As for the CRAFT method,
the final solution depends on the initial solution. There is
no guarantee of optimality. The final solution is a local optimum
when the neighborhood of adjacent solutions is the set of solutions
reached by switching two departments in the sequence. The addin
can generate random initial solutions, so several local optimum
may be generated, with the best selected as the layout to use. 

When the layout problem is stated
as a problem of finding the optimum sequence, it can be addressed
as a combinatorial optimization problem. We provide this capability
through the Optimize command of the Layout addin.
This command requires that the Optimize addin be installed.
This addin provides extensive search procedures for combinatorial
permutation problems such as represented by the sequential layout
problem. The addin allows the user to specify the number of
random starting solutions and the procedures used to improve
the solutions. The solution below was determined by generating
10 random solutions and improving each with a twochange procedure.
The solution method allows kchange variations
of the sequence, where k can be any integer less than
n  1. Of course the larger values of k
require many more computations than the 2change solution illustrated.
The Optimize addin provides a list of the best solutions
found during the search. The list for the example is below.
A row shows the positions of the departments in the sequence.
The figure above is the top entry in the list. D3 is the first
in the sequence, D1 is the second and so on. The sequence represented
by the top row is {3, 1, 4, 9, 2, 7, 6, 8, 10, 5} 