$1\mathrm{.}1$ The below table shows a machine$-$part matrix.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$cline $\{2-5\}\backslash$multicolumn$\{1\}\{$c$|\}\{\}$ & $\backslash$multicolumn$\{4\}\{$c$|\}\{$ Machine $\}\backslash \backslash$

$\backslash$hline Part No$.$ & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $\backslash (\backslash$mathbf$\{4\}\backslash )\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $1$ & & $1\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{2\}\backslash )$ & $1$ & & $1$ & $\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{3\}\backslash )$ & $\backslash (\backslash$mathbf$\{1\}\backslash )$ & $1$ & & $1\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{4\}\backslash )$ & & & $1$ & $\backslash \backslash$

$\backslash$hline $\backslash (\backslash$mathbf$\{5\}\backslash )$ & $1$ & $1$ & $1$ & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$1\mathrm{.}1\mathrm{.}1$ Use direct clustering algorithm to form cells for the machine$-$part matrix.

$1\mathrm{.}1\mathrm{.}2$ Propose alternatives for resolving any conflicts.

$(8)$

$[18]$