Example $3\mathrm{.}3$

Clustering $26$ machines

Consider the machine$-$part matrix for a situation involving $13$ parts and $26$ machines given

in Figure $3\mathrm{.}31.$ Applying the DCA algorithm yields the results depicted in Figures $3\mathrm{.}32$

through $3\mathrm{.}34.$ As with the previous example, step $3$ was not required, since shifting rows

would not improve the formation of cells. From Figure $3\mathrm{.}34,$ it is evident that only two

$$pure$$ cells can be formed, due to machines $1$ and $3.$ However, if multiple machines are

needed, such that Figure $3\mathrm{.}34$c is feasible, then three $$pure$$ cells can be formed for this

example. As noted in the previous example, an alternative approach is to form the cells as

shown in Figure $3\mathrm{.}34$b and locate machines $1$ and $3$ at the boundary between cells A and

B to minimize material handling between cells.

Using cellular manufacturing terminology, machines $1$ and $3$ are called $$bottleneck$$

machines since they bind two cells together. When bottleneck conditions exist, as discussed

previously, one can attempt to minimize the disruptive effects of having parts from other cells

intrude on neighboring cells by locating bottleneck machines at the boundary between cells.

Alternatively, the parts that require processing by the bottleneck machines could be reexamined to determine if alternative processing approaches can be used. Perhaps parts can be

$105$

$3$ FLOW SYSTEMS, ACTIVITY RELATIONSHIPS, AND SPACE REQUIREMENTS

Figure $3\mathrm{.}30$ Formation of cells with duplicate of $($a$)$ machine $2$ and $($b$)$ machine $3.$

$3$

$6$

$5$

$4$

$2$

$1$

$542$a $2$b $31$

Machine #

$111$

$11$

$1$

$11$

$1$

$1$

Part #

$1$

$($a$)$

$1$

$3$

$6$

$5$

$4$

$2$

$1$

$542$a $3$a $3$b $1$

Machine #

$111$

$11$

$11$

$11$

$1$

$1$

Part #

$1$

$($b$)$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$13$

$9$

$9$

$9$

$9$

$9$

$9$

$9$

$8$

$8$

$10$

$10$

$10$

$10$

$1$

Machine #

# of $1$s

# of $1$s

$11$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$2$

$2$

$1$

$1$

$3$

$11$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$4$

$2$

$1$

$1$

$5$

$4$

$1$

$1$

$1$

$1$

$6$

$3$

$1$

$1$

$1$

$7$

$2$

$1$

$1$

$8$

$7$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$9$

$7$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$10$

$2$

$1$

$1$

$11$

$7$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$12$

$2$

$1$

$1$

$13$

$4$

$1$

$1$

$1$

$1$

$14$

$4$

$1$

$1$

$1$

$1$

$15$

$4$

$1$

$1$

$1$

$1$

$16$

$4$

$1$

$1$

$1$

$1$

$17$

$7$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$18$

$7$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$19$

$2$

$1$

$1$

$20$

$2$

$1$

$1$

$21$

$4$

$1$

$1$

$1$

$1$

$22$

$7$

$1$

$1$

$1$

$1$

$1$

$1$

$1$

$23$

$2$

$1$

$1$

$24$

$4$

$1$

$1$

$1$

$1$

$25$

$4$

$1$

$1$

$1$

$1$

$26$

$4$

$1$

$1$

$1$

$1$

Part #

Figure $3\mathrm{.}31$ Machine$-$part matrix