A Fully Polynomial Time Approximation Scheme for the Replenishment Storage Problem

TL;DR

This paper introduces the first Fully Polynomial Time Approximation Scheme (FPTAS) for the Replenishment Storage Problem with different item cycle lengths, enabling efficient near-optimal solutions for complex inventory systems.

Contribution

The paper develops the first FPTAS for RSP with varying individual cycle lengths and constant joint cycle length, extending previous work limited to identical cycle lengths.

Findings

FPTAS achieves near-optimal solutions efficiently.

Addresses previously unresolved case with different cycle lengths.

Extends theoretical understanding of RSP complexity.

Abstract

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.