WinQSB FUNCTIONAL LAYOUT
A functional layout problem usually considers to position functional departments in
relative locations. This program solves the functional layout problems using a
Computerized Relative Allocation of Facilities Technique (CRAFT)-type algorithm,
which is a heuristic to improve the layout by exchanging departments. The inputs
include interdepartmental flows, unit flow contributions, and an initial layout with
reduced departmental dimensions. The exchange methods are:
Two-way exchange: switch two departments at a time.
Three-way exchange: switch three departments at a time.
Two-way then three-way exchange
Three-way then two-way exchange
The flows between two departments can be material flows, traffic flows, customer
flows, cash flows, information flows, and the like. The unit contribution represents
the cost or revenue to move one unit of flow per one unit of distance from one
department to another. The default unit contribution is unity. Distance measures
include rectilinear, squared Euclidean, or Euclidean distance.
Let Dij, Wij, and Cij represent the distance, interdepartmental flow, and unit flow
contribution, respectively, between departments i and j. Then the objective
function of the problem can be specified as
Maximize or Minimize: F = ∑ij Cij Wij Dij
Let n represent the number of departments. For each iteration, the number of twoway exchanges is n(n-1)/2 and the number of three-way exchange is n(n-1)(n-2)/6.
These numbers tend to be huge when n is large. That is, when the number of
departments is large, say 15 or 20, the run time may be very long. To simplify the
improvement process, the program only considers to exchange departments with
common borders or of equal space.
When defining the layout area, use as large a unit as possible to define a row or a
column. This will reduce the total numbers of rows and columns and therefore
reduce the computation time for exchanges. Generally, the greatest common
denominator (GCD) of the horizontal and vertical dimensions for each department
is the appropriate unit to define a row and a column. The row and column must
have the same scale; otherwise, the distance measures may not be correct. For
nonrectangular-shaped initial layouts, you may add dummy departments with zerovalued flows to make it rectangular. These dummy departments should be
specified as being fixed.
Since it is difficult to imagine the shape of a department, two departments with
irregular shapes, that is, non-rectangular, may end up with odd shapes after the
exchange. It is recommended to define each department as rectangular wherever
possible in the initial layout.