I am currently working on a size-pack optimization problem and and need guidance in modeling the equations to achieve the best prepack configuration with the goal of maximizing the fill rate.
Here's an example of the historical demands:
| Size 1 | Size 2 | Size 3 | Size 4 | Size 5 | Size 6 |
|---|---|---|---|---|---|
| 6 | 6 | 18 | 12 | 24 | 18 |
| 6 | 6 | 18 | 12 | 18 | 18 |
| 6 | 6 | 12 | 6 | 18 | 12 |
| ... | ... | ... | ... | ... | ... |
| 60 | 12 | 72 | 12 | 48 | 18 |
| 24 | 6 | 30 | 6 | 18 | 6 |
| 12 | 0 | 12 | 0 | 6 | 0 |
The objective is to find the ideal combination of different sizes that maximizes the fill rate. Identifying multiple such combinations would be even more beneficial.
One crucial constraint is that the total quantity in a prepack should be exactly equal to "$n$" units. While we can order multiple units of the same prepack to satisfy demand, the total quantity of a single combination should be precisely equal to "$n$" (e.g., $6$ units).
An example of prepack could be
| Size 1 | Size 2 | Size 3 | Size 4 | Size 5 | Size 6 |
|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 2 | 2 |
However, I'm uncertain about how to model these equations technically. I'd greatly appreciate any guidance, general direction, or advice on how to approach this problem.
Apologies if my question lacks proper formatting or requires additional information; I am more than willing to provide any necessary details.
Thanks in advance.