Dual-head placement machines, which operate according to a highly complex logic, are commonly used in circuit-card assembly lines to place large components with a high degree of accuracy. The purpose of this paper is to present a unique approach for optimizing the picking operations of a dual-head placement machine with the ultimate goal of improving the efficiency of assembly operations. Research objectives are a model that reflects relevant, practical considerations; a solution method that can optimize problems effectively (i.e., within acceptable run times); and tests to establish computational benchmarks. We formulate a general integer, set covering model, and optimize it using column generation, generating columns by solving a specially designed, constrained shortest-path subproblems. Test results demonstrate the efficacy of our optimizing approach on problems of realistic size and scope. Note to Practitioners-The dual-head placement machine (DHPM) motivated this research because it is widely used in the circuit-card assembly industry and is an extremely intricate machine that operates according to a highly complex logic. No earlier study provided a method to optimize DHPM picking operations. This paper presents a novel solution methodology that formulates a unique model of picking operations and adapts ways to solve it progressively to optimize picking operations. The solution improves the efficiency and productivity of a DHPM by prescribing a process plan that minimizes the total time required to pick all components that are then placed on a circuit card. This paper relates key insights that allow the problem to be structured for solution, including certain rules that govern DHPM picking operations and ways in which components can be picked. Key contributions include methods to construct graphical representations of the complex logic of picking operations (e.g., representing nozzle changes and five types of picks, including gang picking), specialized solution algorithms, and computational benchmarks that illustrate the capabilities of the solution approach. The approach does not appear to be limited in representing picking operations but must be combined with other methods to prescribe a complete process plan, including assigning compon- ent types to feeder slots, placing operations, and sequencing pick/place operations. This work can be extended by adapting the column generation approach to prescribe optimal DHPM placing operations and to prescribe process plans for other types of placement machines.