Robust Alpha-Reliable Network Design Problem under Distribution-free Demand

A general assumption in the reliable network design problem is that probability distributions of the sources of uncertainty are known. However, in reality, this distribution may be unavailable as we may have no (insufficient) data to calibrate the distribution. In this paper, we relax this assumption and present two robust alpha reliable network design models under distribution-free demand by adopting worst-case Value-at-Risk (WVaR) and worst-case conditional Value-at-risk (WCVR) risk measures, where only requires that the first m moments (m is a positive integer and associated with the form of link cost function) of demand to be known. We prove that the two models are equivalent to the same model under general distribution. The equivalent NDP model is formulated as mathematical programs with complementarity constraint (MPCC). A manifold sub optimization algorithm is developed to solve this alpha robust reliable network design problem (NDP). Numerical example is presented to illustrate the features of the proposed NDP model.