I am interested in researching how to best get rid of large size of inventory, given you want to maximize or minimize some objective function. Does this problem have a name in the literature?
Here is an example:
- A clothing store has 1000s of shirts to sell, how much should they keep at their main store, and how much should be sent to store A, store B, etc. If you want to maximize profit or minimize how long you hold the inventory.
Ultimately I want to frame this as a reinforcement learning problem so if characteristics / variables of the environment change, the allocation changes as well.
This problem reminds me of Lagrange multipliers from Calculus $1$ or Calculus $3$.
You can think of the problem as maximizing or minimizing some function $f(x_1,\ldots, x_n)$ subject to the constraints $g_1(x_1,\ldots, x_n)=a_1, \ldots, g_M(x_1,\ldots, x_n)=a_M$, which can be solved by taking the gradient of the Lagrangian: $$ \nabla f(x_1,\ldots, x_n) = \sum_{i=1}^{M} \lambda_i\nabla g_i(x_1,\ldots, x_n), $$ where $\lambda_1,\ldots, \lambda_M$ are scalars called Lagrange multipliers.
The above equality will give you $n$ equations. These $n$ equations together with the $M$ constraints amount to solving for $n+M$ equations in $n+M$ variables.
As an aside, this problem may also go by the name profit maximization or simplex method in operations research.