An FPTAS for a single-item capacitated economic lot-sizing problem with monotone cost structure

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ɛ in time polynomial in the problem size and in 1/ɛ. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) production and backlogging cost functions. We omit concavity and convexity restrictions. Furthermore, we take advantage of a straightforward dynamic programming algorithm applied to a rounded problem.