The Concept of Contiguity in Models Based on Time-Indexed Formulations

This paper describes an extension which can be added to any production planning model based on time-indexed formulations with at most one setupor mode-change per period. It allows to add constraints involving accumulated quantities over several time-slices implementing the concept of contiguity into the model. This feature is relevant to any kind of process industry. It allows to model batch and campaign production, or to require that the minimum time between mode-changes must be larger than a specified lower bound. The key idea used in the technical approach is to identify which time-indexed quantities belong to certain contiguous components, e.g., campagains, over several time slices and to replace products of continuous variables and binaries, or absolute value terms by linear relations involving additional binary variables. In this contribution we apply this approach to a special case and extend a production planning problem in chemical industry.