I have a question about some stochastic linear programming formulas, namely (4.3),(4.4),(4.5) and (4,6) in the snippet below. I do not follow how was created the argument of $c$ in (4.3), the formula (4.4) and from (4.4) the formula (4.5), and finally (4.6). I'm looking on it almost a week without any success.

The snippet is taken from the book Introduction to stochastic programming by John Birge,the second edition. enter image description here


My reputation it too low to add a comment, so don't take this as an answer rather than comment.

What exactly is your problem?

Those (4.3-4.5) are just assumptions/pre-conditions to give a real sounding problem/illstration. And those assumptions are summarized into the optimization problem (4.6). c is a new variable introduced which is (later) used for optimization purposes.

  • $\begingroup$ Thank you for your interest. My problem is how $\frac{w\cdot \pi \cdot x^2}{4}$ was created. And also both sides of the inequality $\frac{w}{\xi^3}\leq 39.27$ was created. And finally $\frac{w^3}{\xi^4}\leq 63,169$ and $Q(w,x,\xi)$. Just as I've said in my OQ, all the (,)'s. Are they all just ilustration examples with no rule ? Is $c$ a variable or rather a function in (4.3) ? $\endgroup$ – user3357120 Sep 25 '19 at 18:32

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