This has the flavour of a problem that might be best tackled through discrete event simulation. See, for example (alternatives are available).
Do you have an understanding of the goal of the system? Without one, it's premature to discuss optimal production lot size. Dr. Deming encouraged us all to first think about the 'aim of the system' before designing the system. There are many aspects to this question/problem that are more in the Lean/MRP realm than a pure statistics problem. Discrete event simulation can help as my colleague Ian suggests, but I'd also recommend a reading of Lean production control systems and schemes. An interesting 'fun to watch' simulation is The Beer Game. There are many videos on YouTube that demonstrate this simulation. Optimal production lot size (in the factory) in this very constrained but very similar to real life simulation brings all the critical issues to those that participate in the simulation.