An asymptotic approximation scheme for the concave cost bin packing problem

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant ϵ, there exists a polynomial-time approximation algorithm with an asymptotic worst-case performance ratio of no more than 1 + ϵ.