Define a mathematical statistical model of a production process.

We are looking for an advanced mathematical model to optimize the production parameters. The market demand is statistical. Production capacity is partly fixed, partly flexible. We want to be able to answer questions like: How much will we spend on flexible capacity if we need a customer service level of s%, occupy our fixed capacity on average at x% and keep stocks at level y?

We need some smart brains to work on this project to define a model that can be put into software in a later phase.