Properties of the multiple lot-sizing problem with rigid demand, general cost structures, and interrupted geometric yield

In the study of multiple lot-sizing problem with rigid demand, the cost structure and yield distribution are two main factors to determine the behavior of such problems. Various yield distributions, such as the binomial, discrete uniform, and interrupted geometric yields, all with the linear cost structure, are studied in the literature. In this paper, we shall study the effects of general cost structures with the interrupted geometric yield. We present results characterizing the behavior of the optimal total cost function and optimal lot sizes. In particular, we present results of the lot sizes which hold for the linear cost structure but may fail in the framework of a general cost structure.