I am trying to model the following rather general optimization problem.
Let $p_{t}$ be a given non time series of product prices. These are fixed points $p_{t}$ is not described as a random variable. If you produce or have the product stored at time $t$, you may chosse to sell an arbitrary quantity of your stock and gain the current price $p_{t}$ as profit.
We have a machine, producing that product, that can run at most $h$ hours a day. Also we have a warehouse, that allows to store us up to $c$ hours of the machines output. For simplicity we assume that warehouse and machine costs are negligible.
We want to find the schedule for the machine that maximizes our profit.
In the case of $c=0$ the answer is clearly to produce on the $h$ hours of the day with maximal price.
How do i model the influence of the warehouse correctly? What changes if $c$ increases? How do i adapt my scheme?
The question whetever something should be stored depends on all future prizes and seems therefore very hard to express. I suspect it might be a NP-hard problem of sorts, but i could not find any formulation of the problem, even though it seems very common.