Easy distributions for combinatorial optimization problems with probabilistic constraints

Bernard Fortz (bfortzulb.ac.be)
Michael Poss (mpossulb.ac.be)

Abstract: We show how we can linearize probabilistic linear constraints with binary variables when all coefficients are distributed according to either $\mathcal{N}(\mu_i,\lambda \mu_i)$, for some $\lambda >0$ and $\mu_i>0$, or $\Gamma(k_i,\theta)$ for some $\theta >0$ and $k_i>0$. The constraint can also be linearized when the coefficients are independent and identically distributed if they are, besides, either positive or strictly stable random variables.

Keywords: probabilistic constraint, combinatorial optimization, continuous distributions

Category 1: Stochastic Programming

Category 2: Combinatorial Optimization

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Entry Submitted: 10/22/2009
Entry Accepted: 10/22/2009
Entry Last Modified: 02/22/2010

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