ABSTRACT
This chapter focuses on two variants of the one-dimensional bin packing problem: the variable sized bin packing problem, and the bin covering problem. It discusses the algorithms for packing into bins of different sizes, a problem first studied by D. K. Friesen and M. A. Langston in 1986. The chapter explores the bin covering problem that asks for a partition of a given set of items into a maximum number of subsets such that, in every subset, the total item size is always at least some lower bound. As covering problems can be viewed as a kind of inverse or dual version of the packing problem, they are sometimes called “dual bin packing” problems in the literature. In the classical bin packing problem the measure of a packing is the number of bins used. The wasted space in the packing is an equivalent measure; a packing that minimizes one of these measures minimizes the other.
