The lot sizing problem consists in determining lot sizes and their scheduling to meet the required demands. This chapter focuses on a multiplant lot sizing problem with a planning with multiple items, each plant with their own demands and multiple periods. In spite of not been widely investigated, their theoretical and practical importance are supported by applications from private and public sectors. The first part of this chapter pays special attention to the multiplant uncapacitated lot sizing problem (MPULSP). In particular, a novel network flow formulation is introduced, and some computational experiments were carried out to assess the performance of commercial solvers in solving a number of large instance problems. Moreover, a comparative analysis is performed by considering two other formulations for the MPULSP found in the literature. The second part of this chapter turns its attention to the multiplant capacitated lot sizing problem (MPCLSP) and some extensions that add flexibility to the production process. Mathematical formulations are presented and evaluated through computational results.