Combination of numbers to return minimum value

[Amd]

Hi
I need a help for a problem of number combinations:
I have data in the following format

Category	Number
AAA	32
BBB	52
CCC	55
DDD	113
EEE	70
FFF	80
GGG	125
HHH	100
III	111
JJJ	32
KKK	117
LLL	27
MMM	53

I need to combine/add the categories in maximum 9 sets so as to give minimum addition but must include all the categories.
To do this, there are following constraints:

• A Category cannot be split up.
• In the above example, the combinations of various categories should be close to 125 (since 125 is the max of all the numbers)
• A set can have 1 or more categories.
• Number of sets can be 1 to 9.

Example:
Set 1
Category GGG: 125= 125

Set 2
Category HHH & LLL: 100+27= 127

Set 3
Category FFF & BBB: 80+52= 132

Set 4
Category AAA, CCC & JJJ: 32+55+32= 119

Set5……

These are just examples and not actual solution.
I hope I have made my problem clear.

Regards,
Amd

 

[navic]

See if this suits you with this suggestion in my attachment.
Option: If you enter a manual combination of categories.
I used helper columns.

 

[Peter Bartholomew]

I believe the problem can be solved with the objective reaching 125.



The solution was obtained by minimising the maximum value, calculated in the right-hand table, using Solver's Evolutionary method. The optimisation variables were the set membership numbers in the left table which were required to be integers between 1 and 9.

 

[Peter Bartholomew]

Just to make the problem more interesting, here is the best solution found with 8 sets