Robust tactical qualification decisions in flexible manufacturing systems

In some flexible manufacturing systems, such as semiconductor manufacturing systems, machines must be qualified, i.e. certified and eligible, to process a product. This paper investigates a tactical capacity planning problem that consists in minimizing the number of (product, machine) qualifications to ensure that the manufacturing system is robust against the uncertainty on the product mix. First, we propose a deterministic modeling of the problem, followed by a robust modeling based on the robust optimization paradigm when demand uncertainty is characterized by product cannibalization. Then, a mathematical model, also based on the robust optimization paradigm, to characterize the robustness of a set of qualifications is introduced. Finally, in the computational study on industrial data, we show that the price of uncertainty is small, often less than a few additional qualifications by machine whereas the robustness of the qualifications determined for the nominal product mix often lead to capacity constraint violations. We also show that a restricted number of new relevant qualifications out of all possible new qualifications is required to achieve the same robustness as the case where all new qualifications are performed. Considering demand uncertainty in qualification management is therefore critical since robustness is relatively cheap.