Safety stocks account for uncertainty both on demand and provider lead times, but never mention how to include the effect of incomplete orders. For example, what would happen if a provider always delivers on time but on average orders have 50% of the promised quantity?
I couldn't find any papers that include this effect.
What you’re describing is known as inventory optimization under yield uncertainty. There is quite a bit of literature on it. Two relevant literature reviews are Yano and Lee (OR 1995) and Grosfeld-Nir and Gerchak (AOR 2004).
Yield uncertainty is only one type of supply uncertainty. A closely related form is disruptions; my students and I wrote a review paper on this topic a few years ago (Snyder, et al., IIET 2016).
We discuss inventory models with both yield uncertainty and disruptions in our textbook, if that helps.
