Transcript 1 Einleitung - univie.ac.at

QAP - different space requirements
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We assume departments, i.e. OE,
being either rectangular shaped or
consisting of rectangular pieces.
Exchange of 2 departments may also
have a direct influence on shape
and/or location of other departments.
We have to determine a method for
measuring distances, since the
distance may depend on the shape of
a department.
 Orthogonal distance between OEboundaries
 Rectilinear distance between
centre points, e.g. centroid
locations (centre of gravity,
balance point) -> we use this for
the CRAFT algorithm
(c) Prof. Richard F. Hartl
Layout and Design
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Kapitel 4 / 1
CRAFT
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Computerized relative allocation of facilities techniques
One of the first computer-aided layout routines
Improvement method -> an initial layout (starting solution) is
required
Actually, CRAFT means to evaluate all possible exchanges
(pairwise; triples is also possible), and performs the among them.
For the general QAP (similar space requirements for all OE) it
equals a combination of rule C1 + D1 (see course material on QAP).
Some extensions concerning the evaulation of possible exchanges
enables the application to the QAP for different space requirements.
(c) Prof. Richard F. Hartl
Layout and Design
Kapitel 4 / 2
CRAFT
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The selection of departments for exchange is based on the following
considerations. It is always possible to exchange OE without affecting the
remaining OE
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that have the same space requirement,
that share a common boundary (having a common boundary means that the OE
share at least 1 side boundary of their rectangles). E.g. OE 2 and OE 5 in
Figure 2-2 share 1 side boundary.
For the evaluation of exchanges we assume that, if we, e.g., exchange OE
A and OE B, the old centroid of OE B becomes the new centroid of A, and
vice versa (-> exact if we have similar space requirements, but not in case
of different requirements).
Thus, whenever we have performed an exchange (which has been
identified as the best one in the current iteration) we have to revise the
estimated costs (predicted costs) taking the „real“ new centroid into
account.
(c) Prof. Richard F. Hartl
Layout and Design
Kapitel 4 / 3
CRAFT
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Estimate total transportation costs considering all
pairwise exchanges of OE that share at least 1 border
or that are of same size (i.e. equal number of
rectangles).
Perform that exchange that leads to the minimum
estimated total transportation costs (based on an
estimation of distances as described above). If all
possible exchanges lead to an increase of predicted
total costs, stop here.
Revise the estimated distance chart and calculate the
new total costs. Go back to step 1.
(c) Prof. Richard F. Hartl
Layout and Design
Kapitel 4 / 4
CRAFT
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Example:
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A manufacturing firm has built a new facility in order to house 4
departments (A, B, C, D). The facility is 100m2 by 50m2.
The plant manager has chosen an initial layout and determined
the material flow between all departments.
The distance between departments is assumed to be the
rectilinear distance between centroid locations.
Try to improve the initial layout by applying the CRAFT algorithm
(pairwise exchanges).
-> EXCEL FILE…
Nahmias, S.: Production and Operations Analysis, 4th ed., McGraw-Hill, 2000, Chapter 10
(c) Prof. Richard F. Hartl
Layout and Design
Kapitel 4 / 5