Flexible system design: A perspective from service levels

We consider the capacity portfolio investment problem with flexible machines facing multiple products and demand uncertainty. For the problem of maximizing the service level, we approximate the objective with the largest inscribing sphere and provide a linear program formulation. We show, under certain conditions, that the optimal flexibility configuration consists only of dedicated machines and machines capable of producing only two types of products. Our work not only strengthens the sufficiency of limited flexibility in capacity investment but also suggests a novel way for approximating flexible system design problems in a computationally tractable form.