Excel Solver with Multiple Input Variables - excel

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).