  The Replenishment Storage problem (RSP) is to minimize the storage capacity
requirement for a deterministic demand, multi-item inventory system where each
item has a given reorder size and cycle length. The reorders can only take
place at integer time units within the cycle. This problem was shown to be
weakly NP-hard for constant joint cycle length (the least common multiple of
the lengths of all individual cycles). When all items have the same constant
cycle length, there exists a Fully Polynomial Time Approximation Scheme
(FPTAS), but no FPTAS has been known for the case when the individual cycles
are different. Here we devise the first known FPTAS for the RSP with different
individual cycles and constant joint cycle length.
