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.

Abstract
Sugarcane cultivation is important for the economy of many countries, particularly for Brazil. This plant has been used to produce sugar, ethanol, second generation ethanol, fertilizers, as well as bioelectricity. Due to production growth and the establishment of mechanized sugarcane harvesting, this process needs to be optimized. High costs are linked to mechanized harvesting, which affect the total cost of production. One of the costs of harvesting is related to the long time the sugarcane harvesting machine takes to change the crop row to be cut. To help reduce costs, this work proposes a mathematical model to the Route Planning Problem for Mechanized Harvesting. This mathematical model minimizes the time of maneuvering the harvesting machine and, consequently, reduces fuel and labor costs, among others. Computer tests were performed using data supplied by a company from the sugarcane energy sector located in the state of São Paulo, Brazil. The results were compared to the traditional routes used by the company and proved the efficiency of the mathematical model in supplying solutions that minimize the time of harvesting machine maneuvers. Not only are there economic benefits, but also environmental ones that can be obtained.

Abstract
Inventory management can be considered as one of the main components of planning and production control. In the literature numerous mathematical models are presented for inventory management, which approach different aspects related to this management. The development of efficient inventory models and the adoption of appropriate optimization methods for solving these models are needed to support in making decisions to inventory management. In this paper, we propose an inventory model that works with multiple products and multiple resource constraints, deciding between the continuous review and periodic review systems. This model is formulated as a nonlinear mixed integer optimization problem. It explores for the resolution of this model, an approach based on Branch-And-Bound method and interior point method. In order to propose this model and choose the method for its resolution, initially an investigation in the literature review on the topic is done. Then, the concept of continuous review and periodic review systems is explored. Finally, two computational tests are proposed, one to compare the results of proposed nonlinear model with the linear model and the other to verify its efficiency and applicability. The results show the potential of the model and solution method used to work with inventory system.