A new formulation of the two-dimensional cutting-stock problem with consideration of demand planning

This paper focuses on the two dimensional rectangular non-oriented guillotine cutting stock problem (TDRCSP) in which many pieces with different dimensions need to be cut with different quantities in order to satisfy customers' orders. In order to maximise the use of raw materials, make-to-order 'MTO' and make-to-stock 'MTS' production strategies are combined; in addition to the (firm) orders that need to be fulfilled, other quantities of pieces are considered when designing cutting patterns in order to satisfy the forecast plan over a fixed time horizon. A new formulation of the optimisation problem is proposed in this paper considering multi-period demand planning as well as inventory management constraints. To solve this new problem, a hybrid heuristic, based on the combination of the Bottom Left and Shelf algorithms, is considered. It is shown that formulating the problem combining the original non-oriented guillotine TDRCSP with demand and inventory planning optimises the raw material use and yields good solutions in very short computational times. Results show that integrating forecast and inventory constraints are much more of an additional way to improve the raw material use than a real constraint. Finally, a discussion on the hybrid heuristic sensitivity and robustness is reported.