Challenging one..!!!(help please) - combinations

T

the_storm

New Member
Joined
Mar 12, 2011
Messages
4
Good day experts,

This is my first question in this forum and I am optimistic to find the perfect solution here in MrExcel J ….. My question is about formulating combinations.

Imagine that I have 3 different production lines (1, 2 & 3) and I want to find all the possible combination between those production lines to evaluate what is more economical combination. These combinations will vary from no combination to all together.

The solution of the three production lines (1,2 & 3) will be as follows:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.65pt; WIDTH: 207.75pt; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=277 border=0><TBODY><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" noWrap width=64>
#<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
Combinations<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
Mix<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
1<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
1,2,3<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #c2d69a; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" noWrap width=106>
No combinations<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
2<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
1,23<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #ffc000; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: black 1pt solid; HEIGHT: 15pt" width=106 rowSpan=3>
1-2 or 2-1<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
3<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
2,13<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
4<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
3,12<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
5<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
123<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #00b0f0; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" width=106>
All together<o:p></o:p>​


</TD></TR></TBODY></TABLE>​
<o:p></o:p>
If there is a 4 production lines (1,2,3 & 4) the solution will be as follows:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.75pt; WIDTH: 207.65pt; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=277 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" noWrap width=64>
#<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
Combinations<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
Mix<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
1<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
1,2,3,4<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #c2d69a; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=106>
No combinations<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
2<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
1,234<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; BACKGROUND: #ffc000; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" width=106 rowSpan=4>
1-3 or 3-1<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
3<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
2,134<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
4<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
3,124<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
5<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" noWrap width=107>
4,123<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
6<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
12,3,4<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #00b0f0; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt" width=106 rowSpan=6>
2-1-1 only<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
7<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
13,2,4<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
8<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
14,2,3<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
9<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
23,1,4<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
10<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
24,1,3<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
11<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
34,1,2<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
12<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
12,34<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #a5a5a5; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15pt" width=106 rowSpan=3>
2-2 only<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
13<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt" noWrap width=107>
13,24<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 14"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" noWrap width=64>
14<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #f0f0f0; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" noWrap width=107>
14,23<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 15; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=64>
15<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 79.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt" vAlign=bottom noWrap width=107>
1234<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #00b050; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 79.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt" vAlign=bottom noWrap width=106>
All together<o:p></o:p>​


</TD></TR></TBODY></TABLE>​
<o:p></o:p>
The above was done manually since the numbers are small, what about if I have 9 production lines or 20 production lines!!! ,,,,, How can I formulate this in Excel?

I want to enter any arbitrary number (i.e.4,7, 9, 10, 20 ….. etc.) and the program will give me all possible combinations.

Thanks in advance and I am really looking forward to hearing from you experts J …
 
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Hi gentlemen,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
<o:p></o:p>
It seems I confused you. I gave the production line example to make it easier to be understood but it didn't work. Therefore, I will give the real case which needs a little illustration. <o:p></o:p>
<o:p></o:p>
I am working in a refinery and we have 20 plants and I need to perform heat integration between those plants with the best combination that will result in minimizing the total cost. The best combination might vary from no integration at all to integrate all the 20 plants together. In between solution might be:<o:p></o:p>
- 10 plants together and the other 10 together, or<o:p></o:p>
- Each two plants together, or<o:p></o:p>
- Each five plants together, or<o:p></o:p>
- Five plants together, 10 plants together and the remaining five plants will not be integrated.<o:p></o:p>
<o:p> </o:p>
And so on,,, there are thousands of possible combinations<o:p></o:p>
<o:p> </o:p>
To make it easier, consider that we have 3 plants (A, B & C), the possible combination of these plants will be 5 and they are:<o:p></o:p>
<o:p> </o:p>
1) No combination between A, B & C. <o:p></o:p>
Symbol: A, B, C<o:p></o:p>
2) Plant A is alone and B is integrated with C.<o:p></o:p>
Symbol: A, BC<o:p></o:p>
3) Plant B is alone and A is integrated with C.<o:p></o:p>
Symbol: B, AC<o:p></o:p>
4) Plant C is alone and A is integrated with B.<o:p></o:p>
Symbol: C, AB<o:p></o:p>
5) A,B and C are all integrated together.<o:p></o:p>
Symbol: ABC<o:p></o:p>
<o:p> </o:p>
Now, consider that we have 4 plants (A, B, C & D), the possible combination of these plants will be 15 and they are: <o:p></o:p>
<o:p> </o:p>
<TABLE class=MsoNormalTable style="BORDER-RIGHT: medium none; BORDER-TOP: medium none; MARGIN: auto auto auto 4.65pt; BORDER-LEFT: medium none; WIDTH: 266.25pt; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-yfti-tbllook: 1184; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext" cellSpacing=0 cellPadding=0 width=355 border=1><TBODY><TR style="HEIGHT: 15pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
A,B,C,D<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270>No combination between the 4 plants<o:p></o:p>
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
A, BCD<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270>Plant A is alone while plants B, C & D are integrated together<o:p></o:p>
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
B, ACD<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
C, ABD<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
D, ABC<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
AB, C, D<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270>Plant A and B are integrated together while C is alone and plant D is alone as well <o:p></o:p>
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
AC, B, D<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
AD, B, C<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
BC, A, D<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
BD, A, C<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
CD, A, D<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
AB, CD<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270>Plant A is integrated with plant B. while Plant C is integrated with plant D<o:p></o:p>
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
AC, BD<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
AD, BC<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270></TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 14; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.75pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
ABCD<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #f0f0f0; WIDTH: 202.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=270>all 4 plants are integrated together<o:p></o:p>
</TD></TR></TBODY></TABLE>
<o:p> </o:p>
<o:p> </o:p>
I hope it is clear now J. I desperately need a program that I can enter any arbitrary number of plants (i.e. 4,7, 9, 10, 20 ) and the program will give me the number of possible combinations and will list all of these combinations as well.<o:p></o:p>
<o:p> </o:p>
Thanks and looking forward to hearing from you <o:p></o:p>
 
Upvote 0

Excel Facts

How to find 2nd largest value in a column?
MAX finds the largest value. =LARGE(A:A,2) will find the second largest. =SMALL(A:A,3) will find the third smallest
I'm not really investing a lot of time in your problem but a quick look at these posts suggests to me the pgc01's response is indeed what you seek - namely, to know the total number of ways a set can be divided into subsets. Since these possible combinations increase so rapidly, it's hard to see how it could be helpful to list them (e.g., when there are millions of them).

ξ
 
Upvote 0
Following pgc's lead with Bell numbers, and using the algorithm at http://delphiforfun.org/programs/Math_Topics/set_partitions.htm,

Code: 
Sub Demo()
    Main 8
End Sub
 
Function Main(n As Long) As String
    Dim aiInx()     As Long
    Dim iRow        As Long
 
    ReDim aiInx(0 To n - 1)
    aiInx(n - 1) = -1
 
    Columns(1).ClearContents
 
    Do While aiRG(aiInx)
        iRow = iRow + 1
        Cells(iRow, "A").Value = Sets(aiInx)
    Loop
End Function
 
Function aiRG(aiInx() As Long) As Boolean
    Dim iPos        As Long
    Dim iVal        As Long
    Dim iMax        As Long
    Dim i           As Long
 
    iPos = UBound(aiInx)
    If iPos = 0 Then
        If aiInx(0) < 0 Then
            aiRG = True
            aiInx(0) = 0
        End If
 
    Else
        Do While iPos > 0 And Not aiRG
            iVal = aiInx(iPos) + 1
            iMax = 0
 
            For i = 0 To iPos - 1
                If aiInx(i) > iMax Then iMax = aiInx(i)
            Next i
 
            If iVal <= iMax + 1 Then
                aiInx(iPos) = iVal
                For i = iPos + 1 To UBound(aiInx)
                    aiInx(i) = 0
                Next i
                aiRG = True
            Else
                iPos = iPos - 1
            End If
        Loop
    End If
End Function
 
Function Sets(aiInx() As Long) As String
    Dim i           As Long
    Dim j           As Long
 
    For i = 0 To WorksheetFunction.Max(aiInx)
        Sets = Sets & "{"
        For j = i To UBound(aiInx)
            If aiInx(j) = i Then Sets = Sets & j + 1 & ","
        Next j
        Sets = Sets & "}"
    Next i
 
    Sets = Replace(Sets, ",}", "}")
End Function
 
Upvote 0
Example output for n=4:

Code: 
       -----A------
   1   {1,2,3,4}   
   2   {1,2,3}{4}  
   3   {1,2,4}{3}  
   4   {1,2}{3,4}  
   5   {1,2}{3}{4} 
   6   {1,3,4}{2}  
   7   {1,3}{2,4}  
   8   {1,3}{2}{4} 
   9   {1,4}{2,3}  
  10   {1}{2,3,4}  
  11   {1}{2,3}{4} 
  12   {1,4}{2}{3} 
  13   {1}{2,4}{3} 
  14   {1}{2}{3,4} 
  15   {1}{2}{3}{4}
 
Last edited:
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