When spatially deploying centers in a facility or locating facilities around the world, there exist rela-tionships between them that result in wanting them near each other or conversely far from each other.
Such relationships can be between pairs of facilities or between a center and a fixed location. Each rela tionship exists for a set of reasons which may involve factors such as shared infrastructures, resources
and personnel, organizational interactions and processes, incompatibility and interference, security and safety, as well as material and resource flow. Each case may generate specific relationships and reasons for each one.
These relations can be expressed as proximity relationships, which can be used for assessing the quality of a proposed design and for guiding the development of alternative designs. A proximity relationship is generically composed of two parts: a desired proximity and an importance level. Figure 5.5 shows a variety of proximity relationships between the 12 centers of a facility. For example, it states that it is important for centers MP and A to be near each other for flow reasons. It also states that it is very important that centers D and G be very far from each other for safety reasons. Such relationships can also be expressed with fixed entities. For example, in Figure 5.5, there are relationships expressed between a center and the outside of the facility. This is the case for center G: it is critical that it be adjacent to the periphery of the facility.
The desired proximity and the importance level can both be expressed as linguistic variables according to fuzzy set theory (Evans et al. 1987). In Figure 5.5, the importance levels used are vital, critical, very important, important, and desirable. The desired proximity alternatives are adjacent, very near, near, not far, far, and very far. Other sets of linguistic variables may be used depending on the case.
On the upper left side of Figure 5.5, the proximity relationships are graphically displayed, overlaid on the proposed net layout of the facility. Each relationship is drawn as a line between the involved entities.
Importance levels are expressed through the thickness of the line. A critical relationship here is drawn as a 12-thick link while an important relationship is 3-thick. A vital relationship is 18-thick and is further highlighted by a large X embedded in the line. Gray or color tones can be used to differentiate the desired proximity, as well as dotted line patterns. Here a dotted line is used to identify a not distance variable such as not far or not near. In the color version of Figure 5.5, desired proximity is expressed through distinctive colors. For example, adjacent is black while very far is red. Such a graphical representation helps engineers to rapidly assess visually how the proposed design satisfies the proximity relationships. For example, in Figure 5.5, it is clearly revealed that centers E and PF do not respect the very near desired proximity even though it is deemed to be critical. Using graphical software it is easy to show first only the more important relationships, then gradually depict those of lesser importance.
Even though just stating that two centers are desired to be near each other may be sufficient in some cases, in general it is not precise enough. In fact, it does not state the points between which the distance is mea-sured, and using which metrics. In Figure 5.5 are depicted the most familiar options within a facility. For example, inter-center distances can be measured between their nearest boundaries, their centroid, or their pertinent I/O stations. Distances can be measured using the rectilinear or Euclidean metrics, or by comput-ing the shortest path along a travel network such as the aisle network. The choice has to be made by the engineer based on the logic sustaining the relationship. In the wide area location context, distances are simi-larly most often either measured as the direct flight distance between the entities or through the shortest path along the transport network. This network can offer multiple air-, sea-, and land-based modes of transportation.
When evaluating a design it is possible to come up with a proximity relationship-based design score.
Figure 5.5 illustrates how this can be achieved. When starting to define the relationships, each importance level can be given a go/no-go status or a weight factor. In Figure 5.5, a vital importance results in an infea-sible layout if the relationship is not fully satisfied. A critical importance level is given a weight of 64 while a desirable importance level has a weight of one. For each desired proximity variable a graph can be drawn to show the relationship satisfaction given the distance between the entities in the design. For example, in the upper right side of Figure 5.5, it is shown that the engineers have stated that a not far relationship is entirely satisfied within a 9-m distance and entirely unsatisfied when the distance exceeds 16 m. At a dis-tance of 12 m it is satisfied at 50%. It is important to build consensus about the impordis-tance factors and prox-imity-vs.-distance satisfaction levels prior to specifying the relationships between the entities. Given a design, the distance associated with every specific relationship is computed. It results in a relationship sat-isfaction level. For example, it is important that centers A and C be near each other, as measured through the distance between their I/O stations assuming aisle travel. The computed distance is 12 m, which results
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Adjacent Very Near Near Not Far Far Very Far Desired proximity relationship satisfaction given an actual distance in a design
Proximity Identification Adjacent : Black Very near : Dark green Near : Light green Far : Orange Very far : Red Not : Dotted line Importance Line width Vital : 18, white X Critical : 12 6 3 2 Very important : Important : De sirable :
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MP C H I D PF F E J G Importance Center 1 Center 2 I mportanc eDesired Proximit yReaso nBet we en Distance metric Weight Distanc eS atisfactio nContribution MP A Important Near Flow I/ O A isle4 24 MP E Very important Near Flow I/ O A isle 1610 0, ,4 MP OUT Vital Adjacent Flow Boundaries Rectilinea r 0 1 Feasible A C Important Near /O Aisl e 4 12 0,0 0 4 6 1 0 ,4 B C Very important Not far entroid Rectilinea r 1616 B D Very important Not far entroid Rectilinea r 1629 B J Important Near /O Aisl e 4 28 C D Very important Not far entroi ec tilinea r 1613 0, ,4 C E Important Near /O Aisl e 4 22 0 0 D G Very important Very far entroid Euclidea n 1617 E F Very important Near Flow I/ isle 1610 0, ,4 E G Desirable Not farBoundaries Aisl e 1 66 E PF Critical Very near Flow+Org I/ isle 6424 F G Important Far Centroid Euclidea n 4 33 F H Very important Near Flow I/ isle1630 G H Important Not far Flow Infrastructure Infrastructure Flow Infrastructure Flow Safety Organization Noise Process Boundaries Aisl e 4 4 G I Very important Near Flow I/ isle 1646
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0 0 0 0 0 0 0 4 6 0 0 0 0 1 4 G OUT Critical Adjacent Flow Boundaries Rectilinear 6464 H I Vital Infra+Org+Flow Boundaries Rectilinea r 2 1 Feasibl e I PF Critical Adjacent Near Flow I/
d R O A O A O A O A O A isle 6464 PF OUT Vital Adjacent Flow Boundaries Rectilinear
4 1 0 0 0 0 0 1 6 1 6 1 Feasible Ma ximum possible value : 34 5 Design value: 155, 6 Desi gn score :45,1%
Measure Pair of centers Proximity relationship Design evaluation I C C I C I C FIGuRE 5�5Qualitative proximity relationships based on evaluation of a layout design.
in a satisfaction level of 10%. Since the weight associated with such an important relationship is four, the contribution of this relationship to the design score is 0.4, whereas the upper bound on its contribution is equal to its weight of four. When totaling all relationships, the score contributions add up to a total of 155.6. The ideal total is equal to the sum of all weights, which in this case is 345. Therefore, the design has a proximity relationship score of 45.1%. This leaves room for potential improvement.
Simplified versions of this qualitative proximity relationships representation and evaluation scheme exist. For decades, the most popular has been Muther’s AEIOUX representation (Muther 1961), where the only relationships allowed are: A for absolutely important nearness, E for especially important nearness, I for important nearness, O for ordinarily important nearness, U for unimportant proximity, and X for absolutely important farness. In most computerized implementations using this representation, a weight is associated to each type of relationship and proximity is directly proportional to the distance between the centroids of the related centers. Simpler to explain and compute, such a scheme loses in terms of flexibility and precision of representation.
In general, the reliance on qualitative relationships requires rigor in assessing and documenting the specific relationships. In an often highly subjective context, the relationship set must gain credibility from all stakeholders, otherwise it will be challenged and the evaluation based on the relationship set will be discounted. This implies that the perspectives of distinct stakeholders must be reconciled. For example, one person may believe a specific relationship to be very important while another may deem it merely desirable. Some may be prone to exaggerate the importance while others may do the inverse. It is also important to realize that some relationships may be satisfied with other means than proximity. For example, two centers may be desired to be far from each other since one generates noise while the other requires a quiet environment. If noise proofing isolation is installed around the former center, then the pertinence of the proximity relationship between the two centers may disappear.