Capacitated lot-sizing and scheduling with sequence-dependent, period-overlapping and non-triangular setups

In production planning, sequence dependent setup times and costs are often incurred for switchovers from one product to another. When setup times and costs do not respect the triangular inequality, a situation may occur where the optimal solution includes more than one batch of the same product in a single period — in other words, at least one sub tour exists in the production sequence of that period. By allowing setup crossovers, flexibility is increased and better solutions can be found. In tight capacity conditions, or whenever setup times are significant, setup crossovers are needed to assure feasibility. We present the first linear mixed integer programming extension for the capacitated lotsizing and scheduling problem incorporating all the necessary features of sequence sub tours and setup crossovers. This formulation is more efficient than other well known lotsizing and scheduling models.