QAP - different space requirements 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 OE-boundaries Rectilinear distance between centre points, e.g. centroid locations (centre of gravity, balance point) -> we use this for the CRAFT algorithm 1 4 2 5 3 (c) Prof. Richard F. Hartl Layout and Design

CRAFT 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

CRAFT The selection of departments for exchange is based on the following considerations. It is always possible to exchange OE without affecting the remaining OE 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

CRAFT 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

CRAFT Example: 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