I'm trying to address the question of how many times should I order a product from my supplier, assuming highly stochastic demand.
In my mind there would something like the Newsvendor model, but would not only provide me with an optimal buy quantity, but also the optimal number of times I should reorder (i.e. should I buy again tomorrow and the next day? Should I buy once a day for the next week? etc...)
There are several models available to make the sort of decisions you are asking about. Most tend to make ordering decisions based on inventory level rather than on time: That is, they say things like "when the IL = 12, order 25" rather than "order 25 every 3 days".
The newsvendor problem is usually interpreted as a periodic-review model, so if you're looking for a multi-periodic model that is analogous, consider either the base-stock model or the $(s,S)$ model. Both assume that the period length is already fixed (e.g., 1 day). The base-stock model assumes we order every period, while the $(s,S)$ model assumes there is a fixed ordering costs, which means the orders are spaced out more.
The main model that uses order interval as a decision variable (i.e., focusing on time, not IL) is the $(r,T)$ model.
In continuous review, the relevant model is the $(r,Q)$ model, but I wouldn't exactly think of that as multi-period newsvendor, since it's continuous review.
