I have a demand forecast that gives me a distribution for future demand, for each time period in percentiles (e.g. demand for period 1 will be between 6 and 25 (zero and 100th percentiles, and i know all other percentiles in between, and this is given for each time period). I don't know which distribution each product follows.
The inventory optimization I feed this to currently only uses a point from the forecast, thus I am missing a lot of information I could use to create a better optimization.
I'm currently considering (1) determining a critical factor for each product as the ration of underage and overage cost, or (2) running the optimization across e.g. the 10th, 20th, 30th etc percentile of the forecast of each product, weighing these "scenarios" with their likelihood and choosing the optimal outcome.
I'm missing the vocabulary to be able to research these options. Can you help me with what terms should I search for to find relevant research for this? any other ideas I should look at to solve this?