Campaign planning in time-indexed model formulations

This paper deals with a production planning problem typical for process industries. There the production amount of one continuous production run – referred to as a campaign – is often constrained by a lower and/or upper bound or such that it has to be in multiples of a predefined batch size. For this kind of problem, a new mixed-integer-programming model formulation is proposed that is based on a standard lot-sizing model with uniform time buckets. Thereby the concept of time continuity is integrated into a standard bucket-oriented lot-sizing model formulation. Furthermore, some algorithmic (valid inequalities) and modelling enhancements to the formulation are presented. Extensive computational tests show that this new model formulation clearly outperforms a benchmark model formulation. Moreover, they show the additional computational effort associated with different types of restrictions imposed on campaigns.