Operational statistics: Do things togather rather than separately

This friday Max Shen came to give talk on the 'operational statistics'. The idea is that when you seperate forecast and decision, you lose the potential saving. For example, if we don't know the demand distribution exactly under newsboy setting, we will forecast the parameters and make the order decision. It gives us lower profit. But if you directly design order quantity function instead of predict demand parameters and transform it to order quantity, we can gain a lot. It's managerial insight behind this paper to do things togather than separately.

But I just wonder what makes it work mathematically.

At seminar, I ask the question about unbaised and baised paramters. After I think it a little, I believe, by transform their order function into sample estimation space. It is likely that we get the baised estimation but with smaller variance. Then there is map between sample estimation space to the revenue space. Now we have two kinds of distribution of estimation. One is unbaised with large variance and the other one is baised with smaller variance. Suppose the map is concave, you can image the latter one will have bigger revenue if that estimation is well designed. So from statistical perspective, we need to balance how bais and how big variance of your estimation from the point of map between estimation and your objective function.

It is still hard for me to express these subtle things real time. Usually I have a very rough thought and need a discussion to clarify what I really think finally. Messy minds.