The capacitated lot sizing problem with setup carry-over

Although there is a significant amount of literature on the capacitated lot sizing problem, there has been insufficient consideration of planning problems in which it is possible for a lot size, or production run, to continue over consecutive time periods without incurring multiple setups. While there are papers that consider this feature, they typically restrict production to at most one product in each period. We present a set of mixed integer linear programs for the capacitated lot sizing problem that incorporate setup carry-over without restricting the number of products produced in each time period. Efficient reformulations are developed for finding optimal solutions, and a Lagrangian decomposition heuristic is provided that quickly generates near-optimal solutions. The computational results demonstrate that incorporating setup carry-over has a significant effect on both cost and lot sizes.