Excel Solver with Multiple Input Variables

Question

I have an Excel sheet that has a list of sports players, their positions, a salary assigned to those players, and a projected amount of points.

I'm currently using solver to create the best group of sports players possible with certain position restrictions and within a predefined salary cap.

In my specific example, the different player positions are: PG, SG, SF, PF, C, G, and F. Note that a G can be either a PG or a SG, and a F can be either a SF or PF.

This solver is working currently, but in some cases a player might have multiple positions. So, for example, Player A can be used as a SF OR a SG.

Is there any way to account for this within a Solver function so that the player in question can be used in either slot?

To help explain, I'll provide some examples of the data being used. Here is a small sample of the player list:

Position Player             Salary     Game                Points   Pos 1   Pos 2
PF/C    Kevin Love          $10,400     Pho@Min 09:30PM ET  53.17    PF      C
PG/SG   Stephen Curry       $10,000     GS@Bkn 07:30PM ET   47.50    PG      SG
SG/SF   James Harden        $9,500  LAL@Hou 08:00PM ET  41.13    SG      SF 
PF/C    LaMarcus Aldridge   $9,500  Orl@Por 10:00PM ET  45.22    PF      C
PF/C    Anthony Davis       $9,200  Was@NO 08:00PM ET   42.97    PF      C
PF/C    Blake Griffin       $9,000  Bos@LAC 10:30PM ET  42.66    PF      C
PG      John Wall           $8,900  Was@NO 08:00PM ET   42.09    PG
PF/C    Dwight Howard       $8,700  LAL@Hou 08:00PM ET  41.19    PF      C
SG/SF   Paul George         $8,600  Ind@Atl 07:30PM ET  40.06    SG      SF
PF      Paul Millsap        $8,400  Ind@Atl 07:30PM ET  37.96    PF
PF/C    Al Horford          $8,300  Ind@Atl 07:30PM ET  37.33    PF      C

To solve the G and F issue, I have a list that tallies the "selected" players, and that list has a min/max of each. So in this example I need 1 PG, 1 SG, and 1 G. So I have a PG column with a min of 1 and a max of 2, a SG column with a min of 1 and a max of 2, and a G column, which adds PG/SG together that has a min of 3 and a max of 3. Then part of the solver criteria is all the min/max must match.

I have split the first column into POS1 and POS2 to separate the two possible positions, but I can't figure out how to include both in the solver function. For a player like Kevin Love, I want the solver to take into account that he can be placed in either the PF, F, or C spots.

Here is that table:

    PG  SG  SF  PF  C   G   F   Ttl
Min 1   1   1   1   1   3   3   8
Max 3   3   3   3   2   4   4   8
Cur 1   3   1   2   1   4   3   8

So for example, the Solver criteria is:

Sum of Salary <= Salary Cap (50000)
PG Cur >= PG Min
Repeat for all Min
PG Cur <= PG Max
Repeat for all Max
Maximize Points

And finally, here's an example of a solution:

PG   Stephen Curry    $10,000     47.5
SG   James Harden     $9,500      41.13
SF   Paul George      $8,600      40.06
PF   Dwight Howard    $8,700      41.19
C    Blake Griffin    $9,000      42.66
G    John Wall        $8,900      42.09
F    Al Horford       $8,300      37.33
Total                 $63,000     292.5

Each player fits into their slot because one of their two positions (POS1 or POS2) fits the criteria. Obviously the total doesn't fit, so this wouldn't be a viable solution, but it's just an example.

Hopefully I've provided enough details, but if not please let me know and I'll be happy to explain further. Thanks in advance.

Answer 1

Your question is still a bit vague because your Salary Cap is $50,000 but you show $63,000 of players selected.

Assumptions:
1. You want 5 players since that is the number of players floor and the only way to get a team consisting of your player-list below $50,000. This is probably Fantasy hoops and you want 7 or 8, but the solution should still work for 8 players with either a broader list of options and lower salaries.
2. I'll also assume that there is little-no VBA in here since you didn't provide any - or at least none of that needs to be adjusted.

My solution (which is still in testing) is to throw/cast (or VBA equivalent) for Pos1 and Pos2 to a text of position number (i.e., 1 = PG, 2=SG, etc.).

Next, =concatenate(Pos1, Pos2) so that a PG is an 11, a PG/SG is a 12, etc. ("G" is also an 11 in this scenario which might put a glitch in my logic).

Change your Position Table with Min/Max/Cur values looks something like this:

Pos.    | PG | G  | PG/SG | SG | SG/SF | SF/PF | F  | PF | PF/C | C  
--------------------------------------------------------------------  
Pos1    | 1  | 1  | 1     | 2  | 2     | 3     | 3  | 4  | 4    | 5  
Pos2    | 1  | 2  | 2     | 2  | 3     | 4     | 4  | 4  | 5    | 5  
PosNbr  | 11 | 12 | 12    | 22 | 23    | 34    | 34 | 44 | 45   | 55  
--------------------------------------------------------------------  
Min     | 1  | 3  | 3     | 1  |       | 3     | 4  | 1  |      | 1  
Max     | 3  | 4  | 4     | 3  |       | 4     | 4  | 3  |      | 2  
Curr    | 1  | 1  | 1     | 0  | 0     | 0     | 0  | 0  | 3    | 0  

(values are my own).