The production scheduling problem aims to determine a feasible sequence operation processes and resources over a period of time to optimize one or more measures of performance, usually associated with the time factor or balancing the use of resources. In this problem, precedence constraints between operations and availability of resources per operation may exist. Such operations are part of the tasks or customer orders for products or services. Scheduling problems can be difficult, particularly because time is a limiting factor to get the best sequence among possible feasible sequences. However, finding good solutions for complex optimization problems in an acceptable amount time is crucial in competitive production systems, where the scheduling problems are usually found. The dissertation is focused on the development of a new computational method for solving scheduling problems in the operations environments: flow shop, flexible job shop, integrated resource selection and operation sequences and advanced planning and scheduling. Inspired by Newton s method for continuous multiobjective optimization problems of Fliege et al. (2008), the proposed method is adapted to each operating environment. Examples and numerical experiments with the proposed method are presented for each operating environment, showing some comparisons with existing algorithms, as well.