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

Authors:
Sergei Chubanov;Mikhail Y. Kovalyov;Erwin Pesch
Affiliations:
Faculty of Economics, Belarus State University and the Institute of Information Systems at the University of Siegen, Germany;Faculty of Economics, Belarus State University, and United Institute of Informatics Problems, National Academy of Sciences of Belarus, Skorini 4, 220050, Minsk, Belarus;Institute of Information Systems at the University of Siegen, , Skorini 4, 220050, Minsk, Germany
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

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.