In this paper we study the computational complexity of the capacitated lot size problem with a particular cost structure that is likely to be used in practical settings. For the single item case new properties are introduced, classes of problems solvable by polynomial time algorithms are i.dentified, and efficient solution procedures are given. We show that special classes are N-hard, and that the problem with two items and independent setups is NP-hard under conditions similar to those where the single item problem is easy. Topics for further research are discussed in the last section, On leave from INPE, Brazil. Research partially supported by the Conselho National de Pesquisas, Brazil.

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