Joint chance-constrained survivable capacitated multi-commodity network design problem with demand uncertainty

In this paper, we present a cost-capacity efficient model for the survivable capacitated network design problem with demand uncertainty. To deal with uncertainty, various methods were presented in the optimization theory. We focus on the method of joint chance-constrained programming and formulate the corresponding deterministic model taking into account the dependence between the random variables. In this case, we use the copula theory, and the dependency is driven by an appropriate Archimedean copula. We propose a customized approximation optimization approach and use piecewise tangent approximation (PTA) and piecewise linear approximation (PLA) methods to obtain its lower and upper bounds, respectively. Finally, computational results show the efficiency of the proposed model and approximation methods for relatively large-scale networks.