Hi: Can anyone recommend an introductory book on stochastic programming ? There are obviously so many books on Amazon but I can't tell easily which ones could be useful. It would be good if it had some balance between theory and application. Thanks.
I think you will want a few books since the best book for stochastic programming (but not dynamic, i.e. across time) is different than the best book(s) for stochastic dynamic programming.
For stochastic programming, Birge and Louveaux's Introduction to Stochastic Programming 2nd Ed. is the book I found most helpful. It covers many iterative and approximation techniques. It hurts me to say this (since Birge is a very good human), but I would not get the first edition: it has serious flaws with formatting in a few places. So make sure to get the 2nd edition.
For stochastic dynamic programming, Puterman's Markov Decision Processes is outstanding and even has enough theory to cover some continuous-time results. The jumping off point is stochastic processes, which I found very helpful and intuitive. I'm not sure, though, if it has as much on applications as the other two books I mention here.
You should also read up on approximate dynamic programing since that often lets you relax or reframe a stochastic problem enough to solve it more efficiently. We just read papers on the topic, but since then Powell has written Approximate Dynamic Programming which appears to be very good.