A framework for modelling setup carryover in the capacitated lot sizing problem

This paper addresses the single-level capacitated lot sizing problem (CLSP) with setup carryover. Specifically, we consider a class of production planning problems in which multiple products can be produced within a time period and significant setup times are incurred when changing from one product to another. Hence, there might be instances where developing a feasible schedule becomes possible only if setups are carried over from one period to another. We develop a modelling framework to formulate the CLSP with setup times and setup carryovers. We then extend the modelling framework to include multiple machines and tool requirements planning. The need for such a model that integrates both planning and lot sizing decisions is motivated by the existence of a similar problem in a paper mill. We apply the modelling framework to solve optimally, an instance of the paper mill's problem.