multi-stage stochastic programming interpretation In multi-stage stochastic programming a two-stage approach is sequentially repeated. In general a two-stage model contains first-stage decisions  (e.g. production quantity) and second-stage decisions also known as recourse variables (e.g. external production supply). In between the two stages a random event takes place (e.g. customer demand).
Graphically a multi-stage optimization problem can be represented as a tree consisting of different states/nodes which are linked to probablities. So in reality at each stage only one of the nodes will "happen" (e.g. demand is 1000 OR demand is 500). 
However the results of such an optimization problem provide the optimal decisions for all possible states. What is the interpretation of this result knowing in advance that not all events linked to a node are going to happen?
Thanks in advance.
 A: The result of a stochastic dynamic programming exercise (basically what you're describing) is a policy.  The policy maps states to optimal actions.  You can think of this as a contingency plan, similar to how I plan my morning commute; if, when I reach the freeway, the traffic looks really bad, I take the frontage road two entrances down and get on there; otherwise I get on the freeway.  Once I'm on the freeway, however I got there, if the morning traffic report indicates an accident on the Bay Bridge, I get off the freeway at a particular exit and go to a nice coffee shop and work from there for an hour before continuing into work, otherwise I continue on over the bridge.  On any given day, only one of these possibilities {(light traffic, no accident), (light traffic, accident), (heavy traffic, no accident), (heavy traffic, accident)} will come to pass, but I have a (pre-determined) contingency plan for dealing with whichever one actually does come to pass.  The stochastic dynamic programming algorithm (or in your case the multi-stage stochastic programming algorithm) calculates that contingency plan for me.
