  In this paper, we study the stochastic unbounded min-knapsack problem
($\textbf{Min-SUKP}$). The ordinary unbounded min-knapsack problem states that:
There are $n$ types of items, and there is an infinite number of items of each
type. The items of the same type have the same cost and weight. We want to
choose a set of items such that the total weight is at least $W$ and the total
cost is minimized. The \prob~generalizes the ordinary unbounded min-knapsack
problem to the stochastic setting, where the weight of each item is a random
variable following a known distribution and the items of the same type follow
the same weight distribution. In \prob, different types of items may have
different cost and weight distributions. In this paper, we provide an FPTAS for
$\textbf{Min-SUKP}$, i.e., the approximate value our algorithm computes is at
most $(1+\epsilon)$ times the optimum, and our algorithm runs in
$poly(1/\epsilon,n,\log W)$ time.
