Multiperiod production planning carrying over set-up time

Set-ups eat production capacity time and continue troubling production planning, especially on bottlenecks. The shortening of production planning periods to days, shifts or even less has increased the relative length of set-up times against the periods. Yet, many production planning models either ignore set-up times or, paradoxically, split longer multiperiod batches by adding set-ups at breaks between planning periods. The MILP-based capacitated lot-sizing models that include set-up carry-overs, i.e. allow a carry-over of a set-up of a product to the next period in case a product can be produced in subsequent periods, have incorporated fixed set-up fees without consideration of capacity consumed by set-up time. Inspired by production planning in process industries where set-up times still remain substantial, we incorporated set-up time with associated cost in two modifications of carry-over models. Comparison with an earlier benchmark model without set-up carry-over shows that substantial savings can be derived from the fundamentally different production plans enforced by carry-overs. Moreover, we show that heuristic inclusion of carry-overs by removal of set-ups from non-carry-over solutions is inefficient.