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

The single-item capacitated economic lot-sizing (CELS) problem is a fundamental problem of production and inventory management. The first fully polynomial approximation scheme (FPTAS) for this problem with concave cost functions was developed by Van Hoesel and Wagelmans [C.P.M. Van Hoesel, A.P.M. Wagelmans, Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems, Mathematics of Operations Research 26 (2001) 339–357]. Chubanov et al. [S. Chubanov, M.Y. Kovalyov, E. Pesch, An FPTAS for a single-item capacitated economic lot-sizing problem, Mathematical Programming Series A 106 (2006) 453–466] later presented a sophisticated FPTAS for the general case of the CELS problem with a monotone cost structure. In this paper, we present a better FPTAS for this case. The ideas and presentation of our FPTAS are simple and straightforward. Its running time is about n4ε2 times faster than that of Chubanov et al. [5], where n   is the number of production periods and εε is the anticipated relative error of the approximate solution.