Hierarchical optimization framework for network resource allocation under uncertainty

This paper introduces hierarchical optimization algorithms to solve, in a data-driven manner, an uncertain resource allocation problem over a two-layered tree network. In this optimization problem, the root of the tree aims to minimize the cost of procuring a certain resource, the demand for which is uncertain and originates at the leaves of the network. The demand is to be met with a certain probability which is represented as chance-constraints. We assume that data regarding the uncertain demand is available at each leaf of the network and we design a general framework of hierarchical optimization procedures where the chance-constrained allocation problem is solved using the available data with the constraint that the data is not transferred to the root. Our hierarchical procedure, termed the abstraction-allocation framework, is adapted to three data-driven algorithms for solving the chance-constrained problem: the scenario method, sample average approximation, and distributionally robust optimization. In our framework, the middle layer of the network facilitates the abstraction and allocation when information flows from leaves to the root and the other way around, respectively.