  We study a variant of the single machine capacitated lot-sizing problem with
sequence-dependent setup costs and product-dependent inventory costs. We are
given a single machine and a set of products associated with a constant demand
rate, maximum loading rate and holding costs per time unit. Switching
production from one product to another incurs sequencing costs based on the two
products. In this work, we show that by considering the high multiplicity
setting and switching costs, even trivial cases of the corresponding "normal"
counterparts become non-trivial in terms of size and complexity. We present
solutions for one and two products.
