Introduction to Stochastic Programming

Introduction to Stochastic Programming

This textbook is J.R. Birge and Francois Louveaux, Introduction to Stochastic Programming, Springer Verlag, New York, 1997. It is aimed at beginning graduate students and advanced undergraduates with a background in optimization and probability (although some younger students apparently qualify, viz. Jacob Linderoth, son of Jeff Linderoth.)

For ordering information, you can check the Springer page at this location or at this address.

Misprints and Corrections

This list will include misprints and text corrections that we have received. Please send any that you encounter in looking at the book (john.birge at (These are in TeX form.)

Front matter

  • page xvi, the symbol "-" should give $a^-=\max(-a,0)$. ( Thanks to Stuart Corrigall (SC).)

Chapter 1

  • p. 7, Table 4, sales for sugar beets should also be $6000$. (Thanks to Scott Grasman.)
  • p. 8, line 5, "to" should be inserted before "seek". (SC)
  • p. 16, line 11, no transpose superscript $T$ is necessary. (SC)
  • p. 24, line -4, $EV$ should be $-3.79$; line -1, also replace $3.84$ by $3.79$ and $2.32$ by $2.27$. (SC)
  • p. 41, the expected value for using the deterministic solution is in fact $-26.79$. The result is that the VSS is $8.94 - (-26.79)=35.73$. In this case, the stochastic formulation causes profits to increase from a large loss to actual profits. (Thanks to Stuart Corrigall from University of the Witwatersrand for pointing out that the book calculation was missing the second constraint violation penalty.)
  • p. 46, line 15, the car should start ``braking" not ``breaking." (SC)

Chapter 2

  • p. 54, $T(\omega)$ is $m_2\times n_1$. (SC)
  • p. 75, The dual in (9.2) should have $\pi$ unrestricted.
  • p. 78, line 6, the inequality in the definition of $Lipschitzian$ should be $|f(x)-f(w)|\le M \|x-w\|$. (Thanks to Robert Finn.)

Chapter 3

  • p. 85, display (1.6), $x$ should multiply $T(\omega)$ not $y$. (Thanks to Wichai Narongwanich (WN).)
  • p. 90, line 7, $b$ should be $b_\lambda$. (SC)
  • p. 106, Theorem 18, $x$ should multiply $\bar A_{1\cdot} $ in the definition of $K_1(\alpha)$. (WN)
  • p. 112, Proof of Proposition 22, $K_2(\xi)$ should be $=\{x | Q(x,\xi) < \infty \}$. (SC)

Chapter 5

  • p. 158, (1.7) and (1.8), the subscript $s$ should be $r$; (1.10) and (1.11) and line after (1.11), the subscript $t$ should be $s$. (SC)
  • p. 169, line -3, ``Step 5" should be ``Step 3." (SC)

Chapter 6

  • p. 227, definition of $\Psi_2$, the second line should have $-20\chi_2$ instead of $-20\chi_1$. (WN)

Chapter 9

  • p. 287, line above (1.3), $c_{B_i}$ should be $q_{B_i}$; line after (1.4) missing end parentheses after $T(\omega) x$; (1.5), last parenthesis should be after x, $\bar T_i x)$. (WN)

Chapter 10

  • p. 333, last two lines of the statement of Theorem 1: $g^*$ should be $\nabla {\overline g^*}$.
  • p. 333, line 17: In Example 1, the expectation should be $x^2+1$ instead of $x^2$.
  • p. 337, two lines after (2.8): the density $g(\xi)$ should be $Q(x,\xi)*f(\xi)/{\cal Q}(x)$ (i.e., $f(\xi)$ is missing). (Thanks to Golbon Zakeri for pointing out these omissions.)


  • p. 394, line -3, title should be ``Stochastic quasigradient methods." (SC)