# Combining first come first served with random selection from a waiting list.

##### New Member
I'm part of an organisation that is altering the way it manages a waiting list, and we have decided we want a way of picking n people per year to join. However, we don't want this done on a first-come-first-served basis, nor do we want an entirely randomised selection, rather a combination of the two where the probability of being picked at random increases linearly with increasing time on the waiting list i.e. someone that has been on the waiting list for longer will be more likely to be picked than someone who has recently joined, though some chance remains for someone new to the waiting list to be picked. Any suggestions on how to model this in Excel?

Fairly proficient user, so nothing off limits!

Rory

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##### New Member
One extra bit of information (just to make it even more complicated!), we would like the chances of the person that has been on the waiting list the longest to be 5x as likely (or ideally p​ times, i.e. take the value from a cell) to be picked vs. the newest member.

##### New Member
Hi @pvr928

It is more of a theoretical problem than a real-life one, and is actually for use in a similar report that going to look into modelling the effects of how different 'selection processes' affect will diversity etc. in the organisation, when there is a distinct correlation for various reasons between the time people join the waiting list and their characteristics.

I do appreciate the link though!

Rory

#### StephenCrump

##### MrExcel MVP
Perhaps:

C3: =C2+IFERROR(((B2-MIN(B\$2:B\$5))*N+MAX(B\$2:B\$5)-B2)/(MAX(B\$2:B\$5)-MIN(B\$2:B\$5)),1)
B8: =INDEX(A2:A5,MATCH(RAND(),C2:C5/C6)) Array entered

<b></b><table cellpadding="2.5px" rules="all" style=";background-color: #FFFFFF;border: 1px solid;border-collapse: collapse; border-color: #BBB"><colgroup><col width="25px" style="background-color: #DAE7F5" /><col /><col /><col /><col /><col /></colgroup><thead><tr style=" background-color: #DAE7F5;text-align: center;color: #161120"><th></th><th>A</th><th>B</th><th>C</th><th>D</th><th>E</th></tr></thead><tbody><tr ><td style="color: #161120;text-align: center;">1</td><td style="text-align: right;;"></td><td style="font-weight: bold;;">Days waiting</td><td style="font-weight: bold;;">Cumulative weight</td><td style="font-weight: bold;text-align: center;;">N</td><td style="font-weight: bold;text-align: center;;">5</td></tr><tr ><td style="color: #161120;text-align: center;">2</td><td style=";">Mary</td><td style="text-align: right;;">5</td><td style="text-align: right;;">0</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">3</td><td style=";">Martha</td><td style="text-align: right;;">10</td><td style="text-align: right;;">1.00</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">4</td><td style=";">Bill</td><td style="text-align: right;;">15</td><td style="text-align: right;;">2.21</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">5</td><td style=";">Bob</td><td style="text-align: right;;">100</td><td style="text-align: right;;">3.63</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">6</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">8.63</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">7</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr><tr ><td style="color: #161120;text-align: center;">8</td><td style="font-weight: bold;;">Pick</td><td style=";">Bob</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td></tr></tbody></table><p style="width:3.6em;font-weight:bold;margin:0;padding:0.2em 0.6em 0.2em 0.5em;border: 1px solid #BBB;border-top:none;text-align: center;background-color: #DAE7F5;color: #161120"></p><br /><br />

Last edited:

#### StephenCrump

##### MrExcel MVP
Left field, but there is research suggesting serving the last person in the queue first speeds up the process:

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