An APTAS for Generalized Cost Variable-Sized Bin Packing

Bin packing is a well known problem which has a large number of applications. Classical bin packing is a simple model where all bins are identical. In the bin packing problem with variable sized bins, we are given a supply of a variety of sizes. This latter model assumes, however, that the cost of a bin is always defined to be its exact size. In this paper we study the more general problem where an available bin size is associated with a fixed cost, which may be smaller or larger than its size. The costs of different bin sizes are unrelated. This generalized problem has various applications in storage and scheduling. In order to generalize previous work, we design new rounding and allocation methods. Our main result is an APTAS for the generalized problem.