Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used. In this paper a set of approximation algorithms is presented for cases in which the ability to preview at most k(>=2) arriving bins is given. With the essential assumption that all bin sizes are not less than the largest item size, analytical results show the asymptotic worst case ratios of all k-bounded space and offline algorithms are 2. Based on experiments by applying algorithms to instances in which item sizes and bin sizes are drawn independently from the continuous uniform distribution respectively in the interval [0,u] and [u,1], average-case experimental results show that, with fixed k, algorithms with the Best Fit packing(closing) rule are statistically better than those with the First Fit packing(closing) rule.