This work presents a study on the resolution method of the single product lot sizing problem formulated by Trigeiro et al. This problem consists of determining the quantities to be produced in different periods of time, minimizing the sum of costs of production, setup and inventory. The quantity to be produced in each period should be sufficient to attend the demands of items, without exceeding the capacity of the machine. The aspects of consumption of resources, setup and production times are included in the model. The resolution method developed by Trigeiro et al. consists of a heuristic method based on Lagrangean relaxation, subgradient optimization and a heuristic smoothing procedure. In this work that method is implemented considering variable costs. Furthermore, a modification is proposed, based on the optimality conditions of the problem, during the phase of the improvement of the feasible solution. Some computational experiments are presented comparing both versions.
