Classification and Literature Review of Integrated Lot-Sizing and Cutting Stock Problems

In this paper, a mathematical model for a general integrated lot-sizing and cutting stock (GILSCS) problem is proposed. This model considers multiple dimensions of integration and comprises several aspects found in practice, and as such enables us to classify the current literature in this field. The main classification of the literature is organized around two types of integration. In a planning horizon which consists of multiple periods, the inventory provides a link between the periods. This integration across time periods constitutes the first type of integration. The general problem also considers the production of different types of items at different levels: objects are fabricated or purchased and next cut into pieces which are then assembled into final products. The integration between these three production levels constitutes the second type of integration. The classification indicates that, even though many papers in the current literature analyse an integrated lotsizing and cutting stock problem, they vary widely with respect to the level of integration on the time and production level dimensions. Furthermore, our analysis indicates that the current models also consider varying assumptions with respect to the inventory, the production capacities and the setups. This highlights the value of a comprehensive model, as formulated in this paper. Finally, we give some possible extensions to the general integrated model and point out interesting areas for future research. The focus of the classification is on mathematical models and their applications. Consequently, solution methods and computational results are not discussed in this paper.