Online bin packing with (1,1) and (2, $$R$$ R ) bins

Abstract

We study a variant of online bin packing problem, in which there are two types of bins: $$(1,1)$$(1,1) and $$(2,R)$$(2,R), i.e., unit size bin with cost 1 and size 2 bin with cost $$R > 1$$R>1, the objective is to minimize the total cost occurred when all the items are packed into the two types of bins. When $$R > 3$$R>3, the offline version of this problem is equivalent to the classical bin packing problem. In this paper, we focus on the case $$ R \le 3$$R≤3, and propose online algorithms and obtain lower bounds for the problem.