# Optimal service level and order quantity

In the inventory optimization literature, one of the most recurring concepts is the **service level**, i.e. the desired probability of not hitting a stock-out situation. The service level expresses the tradeoff between *too much inventory* and _too many stock-outs**. **_However, **experts remain typically vague when it comes to choose service level values**; a pattern also followed by most inventory software products…

That’s why we have spent a bit of time to craft a formula that gives optimal service levels. Naturally, the optimality is not obtained without assumptions. However, we believe those are reasonable enough to preserve the efficiency of the formula for most businesses.

Then, another subject, that receives too little attention, is the **optimal order quantity**: the quantity to be ordered in order to minimize the combination of purchase costs, carrying costs, shipping costs, etc. As of January 2012, it’s fascinating to notice that **most of the industry still relies on the Wilson formula** devised back in 1913. Yet, this formula comes with strong assumptions that do not make much sense any more for the supply chain of the 21st century.

Thus, we have designed another economic order quantity formula that emphasizes **volume discounts** (instead of a flat ordering cost) for larger purchases. The formula (or rather the approach) is fairly general, and could be applied to any pricing structure, including non-linear situations where specific quantities are _favored_ because they matche the size of a crate or a pallet.

*Both situations are illustrated with Excel sheets (so you don’t even need Lokad to get started).*