Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost

In this paper, we study the one-dimensional multi-period cutting stock problem with setup costs on cutting patterns. We present pattern-based and pseudo-polynomial formulations for the problem. Reformulations are also proposed to improve the lower bounds. We then present a thorough theoretical analysis to establish the strength of the various proposed formulations in comparison to each other. Finally, a computational analysis is conducted to complement the theoretical analysis and provide further insights with respect to the complexity and strength of the formulations.