A hierarchical approach for the capacitated lot-sizing and scheduling problem with a special structure of sequence-dependent setups

This research deals with the single machine multi-product capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup times and setup costs. The CLSP determines the production quantities and the sequence to satisfy deterministic and dynamic demand during multiple periods. The objective is to minimise the total sum of the inventory holding costs and the sequence-dependent setup costs. We consider a special form of sequence-dependent setup times where the larger product we produce next, the more setup time we need. As a solution approach, we propose a two-level hierarchical method consisting of upper-level planning and the lower-level planning. In the upper-level planning, we solve the lot-sizing problem with estimated sequence-independent setup times utilising the characteristic of the special structure of setup times. Then we solve the scheduling problem in the lower-level planning. The proposed method is compared with the single-level optimal CLSP solution and an existing heuristic developed for the uniform structure of setup times.