Optimal machine settings of imperfect component production processes for assembly operations

The present work is motivated by a problem occurring in a fabrication and assembly operation of fuel injectors for automobile engines. The production processes of the individual components to be assembled are imperfect. For a specific machine setting, which can be preset by an operator, the dimensions of the outputs of a component production process are variable. Components can be assembled only if their dimensions are within some given specification limits of each other. The problem of determining the optimal machine settings of two component production processes to maximize the expected outputs of the assembly operations is considered. The properties of the optimal solution are studied, and some numerical examples are presented