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In this article, we review published studies that consider the solution of the one-dimensional cutting stock problem (1DCSP) with the possibility of using leftovers to meet future demands, if long enough. The one-dimensional cutting stock problem with usable leftovers (1DCSPUL) is a problem frequently encountered in practical settings but often, it is not dealt with in an explicit manner. For each work reviewed, we present the application, the mathematical model if one is proposed and comments on the computational results obtained. The approaches are organized into three classes: heuristics, item-oriented, or cutting pattern-oriented. © 2014 Elsevier B.V. All rights reserved.

Abstract
This paper addresses the cutting stock/leftover problem (CSLP), which differs from the ordinary cutting stock problem (CSP) by retaining stock leftovers that can be cut in the future to meet new demands. Therefore, leftovers are not considered waste in the current period. A new mathematical model for the CSLP is presented to capture a well-used strategy in the practice of cutting, which consists of partially cutting the objects in stock, and keeping the leftovers to be cut in the next periods. Computational experiments were made for the one-dimensional case, although other dimensions can be considered straightforward.

Abstract
This paper proposes a mathematical model and two heuristic procedures to solve the cutting stock problem with usable leftovers, relating the implications of the model with aspects considering sustainability in terms of environmental, economic and social issues. The possibility of generating leftovers that can be used or sold, reduces raw material waste during the cutting process and, consequently, increases companies’ profits. By reducing waste and increasing profits, companies can become more competitive in the market. They can also integrate environmental aspects into their operational strategies and, therefore, create a better self-image and profitability, generating more jobs and contributing to a stronger local economy. We believe that the model is more likely to be adopted by smaller companies, which generally face numerous barriers but at the same time have a significant social impact, generating income and jobs. Based on the knowledge of the authors, this is the first study that relates a cutting problem with its implications for sustainability. Computational tests were performed, and the obtained results are discussed considering the win-win approach to sustainability.