Stochastic Optimization: Casual Notes [to be continued]

Currently learning stochastic optimization (SO) theory, I will note important content here.

Multi-stage vs Multi-period

• Stage: is defined according to decisions made
• Period: is defined according to the occurence of random events
  For example, consider a facility location problem considering random daily demands in the future. Fixing the location of facilities is one-stage decision, while the random demands occur every day, so it is about multi-period.

Define Stages

As i understood, the basic form of a two-stage problem:
optimize $f(x) + E_{\xi}(\min y(w,x) + q(w))$
where $x$ is the first-stage decision, while $w\in \xi$ is a random event. The objective is to find the optimal FIRST-STAGE decision resulting the best expected profit/cost.

Time Line

1st stage decision (here and now) -> some uncertainty disclosed -> 2nd stage decision (wait and see)-> some uncertainty disclosed…