Just to clarify the terminology that I am using the following: the EOQ (economic order quantity) is a quantity decided by the client, the MOQ (minimal order quantity) is a quantity imposed by the supplier. Here, my understanding is that the question is oriented toward EOQs (my answer below); but I am wondering if it's not about picking the right MOQs to impose to clients (which is another problem entirely).

The "mainstream" methods approach EOQs, especially all of those that promise any kind of optimality suffer from a series of problems:

• ignore variations of the demand, which is expected to be stationary (no seasonality for example)
• ignore variations of the lead time, which expected to be constant
• apply only to "simple EOQ" that apply to a single P/N at a time (but not to a EOQ for the whole shipment)
• ignore macro-budgeting constraints, aka this PO competing against other POs (from other suppliers for example)
• ignore the ramification of the EOQs across dependent BOMs (client don't care about anything but the finished products)

Do not expect a formula for EOQs. There isn't one. A satisfying answer requires a way "to factor in" all those elements. What we have found at Lokad for better EOQs in manufacturing (not "optimal" ones, I am not even sure we can reason about optimality), is that a certain list of ingredients are needed:

• probabilistic forecasts that provide probability distributions at least for the future demand and the future lead times. Indeed, classic forecasts deal very poorly with irregular flows (both demand and supply), and MOQs, by design, magnifies the erraticity of the flow.
• stochastic optimization, that is the capacity to optimize in presence of randomness. Indeed, the EOQ is a cost-minimization of some kind (hence an optimization problem), but this optimization happens under uncertain demand and uncertain lead time (hence the stochastic flavor).
• financial perspective, aka we don't optimize percentages of errors, but dollars of error. Indeed, EOQs is typically a tradeoff between more stock and more overhead (shipment, paperwork, manhandling, etc)

In my series of supply chain lectures, I will be treating (probably somewhere next year) the fine print of MOQs and EOQs in my chapter 6. For now, the lecture 6.1 provides a first intro into the main ingredients needed for economic order optimization, but without delving (yet) into the non-linearities:
https://tv.lokad.com/journal/2022/5/12/retail-stock-allocation-with-probabilistic-forecasts/

It will come. Stay tuned!