Inventory control problem
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The inventory control problem is a type of problem encountered within the field of optimal control. It exists in several variations, and is typically formulated as follows:
A store has, at time k, xk items in stock. It then orders (and receives) uk items, and sells wk items, where w follows a given probability distribution. Thus
- xk + 1 = xk + uk − wk.
The store has costs that are related to the number of items in store and the number of items ordered:
- ck = c(xk,uk).
The store wants to select uk in an optimal way, i.e. to minimize
.
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