Modular reconfigurable machines offer the possibility to efficiently produce a family of different parts. This paper formalizes a cost optimization problem for flow lines equipped with reconfigurable machines which carry turrets, machining modules and single spindles. The proposed models take into account constraints related to: i) design of machining modules, turrets, and machines, ii) part locations, and iii) precedence relations among operations. The goal is to minimize equipment cost while reaching a given output and satisfying all the constraints. A Mixed Integer Program (MIP) is developed for the considered optimization problem. The approach is validated through an industrial case study and extensive numerical experiments.