An AFPTAS for variable sized bin packing with general bin costs

In variable sized bin packing problems, bins of different sizes
are to be used for the packing of an input set of items. We
consider variable sized bin packing with general costs. Each bin
type has a cost associated with it, where the cost of a bin may be
smaller or larger than its size, and the costs of different bin
sizes are unrelated. This cost is to be paid for each instance of
this bin type which is used for the packing of input items. This
generalized setting of the problem has numerous applications in
storage and scheduling. We introduce new reduction methods and
separation techniques, which allow us to design an AFPTAS for the
problem. Joint work with Leah Epstein