a b s t r a c tThe aim of this paper is to classify the literature related to the integration between the lot-sizing and cutting stock problem. A deterministic mathematical model, that considers multiple dimensions of integration and comprises several aspects found in practice, is proposed. This model is used as a framework 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 proposed model also considers the production of different types of items at three 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 analyze an integrated lot-sizing 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. Finally, we point out some possible interesting areas for future research. (R. Jans). that might correspond to customer requests, and a decision related to the cutting stock problem is needed. Part of the smaller reels can be cut again into paper sheets, according to some decision related to the lot size for the papers sheets. In the furniture industry, wooden plates are produced or purchased from different suppliers, and a decision about the size of the lots to be produced or purchased from each supplier must be taken. Then, these wooden plates are cut into several wooden parts (in a two-dimensional cutting stock process) to be assembled into the final products. A decision about the size of the lots of final products is also needed, and consequently there are three levels of decisions. Other examples can be found in the fiberglass industry, where fiberglass plates are cut to manufacture printed circuit boards and in the aluminium industry, where aluminium profiles are cut to make several window types. The basic idea of the integrated lot-sizing and cutting stock problem is to consider, simultaneously, the decisions related to both problems so as to capture the interdependency between these decisions in order to obtain a better global solution. Several papers from the literature present computational results showing the benefits of considering an integrated approach instead of taking decisions separately
The integrated lot sizing and cutting stock problem is studied in the context of furniture production. The goal is to capture the interdependencies between the determination of the lot size and of the cutting process in order to reduce raw material waste and production and inventory costs. An integrated mathematical model is proposed that includes lot sizing decisions with safety stock level constraints and saw capacity constraints taking into account saw cycles. The model solution is compared to a simulation of the common practice of taking the lot size and the cutting stock decisions separately and sequentially. Given the large number of variables in the model, a column-generation solution method is proposed to solve the problem. An extensive computational study is conducted using instances generated based on data collected at a typical small scale Brazilian factory. It includes an analysis of the performance of the integrated approach against sequential approaches, when varying the costs in the objective function. The integrated approach performs well, both in terms of reducing the total cost of raw materials as well as the inventory costs of pieces. They also indicate that the model can support the main decisions taken and can bring improvements to the factory's production planning.
ABSTRACT. Production processes comprising both the lot-sizing problem and the cutting stock problem are frequent in various industrial sectors. However these problems are usually treated separately, which can generates suboptimal overall solution and consequently causes production losses. In this paper, we propose different mathematical models for the integrated problem combining alternative models for the lot-sizing and the cutting stock problem, in order to evaluate and indicate the impact of these changes on the models' performance. An extensive computational study is done using randomly generated data and as a solution strategy we used a commercial optimization package and the application of a column generation technique.
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