An approach to the distributionally robust shortest path problem

In this study we consider the shortest path problem, where arc costs are subject to distributional uncertainty. Basically, decision-maker attempts minimize her worst-case expected loss over an ambiguity set (or a family) of candidate distributions that consistent with decision-maker’s initial information. The is formed by all satisfy prescribed linear first-order moment constraints respect subsets arcs and individual probability particular arcs. Under some additional assumptions resulting distributionally robust problem (DRSPP) admits equivalent mixed-integer programming (MIP) reformulations. reformulation shown be NP-hard, whereas without proved polynomially solvable. We perform numerical experiments illustrate advantages considered approach; also demonstrate MIP DRSPP can solved effectively using off-the-shelf solvers.