High Multiplicity Scheduling with Switching Costs for Few Products

We study several variants of the single machine capacitated lot sizing problem with sequence-dependent setup costs and product-dependent inventory costs. Here we are given one machine and \(n \ge 1\) types of products that need to be scheduled. Each product is associated with a constant demand rate \(d_i\), production rate \(p_i\) and inventory costs per unit \(h_i\). When the machine switches from producing product i to product j, setup costs \(s_{i,j}\) are incurred. The goal is to minimize the total costs subject to the condition that all demands are satisfied and no backlogs are allowed. 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.