This work deals with a facility location problem in which location and allocation (transportation) policy is defined in two stages such that a first-stage solution should be robust against the possible realizations (scenarios) of the input data that can only be revealed in a second stage. This solution should be robust enough so that it can be recovered promptly and at low cost in the second stage. In contrast to some related modeling approaches from the literature, this new recoverable robust model is more general in terms of the considered data uncertainty; it can address situations in which uncertainty may be present in any of the following four categories: provider-side uncertainty, receiver-side uncertainty, uncertainty in-between, and uncertainty with respect to the cost parameters.
For this novel problem, a sophisticated branch-and-cut framework based on Benders decomposition is designed and complemented by several non-trivial enhancements, including scenario sorting, dual lifting, branching priorities, matheuristics and zero-half cuts. Two large sets of instances that incorporate spatial and demographic information of countries such as Germany and US (transportation) and Bangladesh and the Philippines (disaster management) are introduced. They are used to analyze in detail the characteristics of the proposed model and the obtained solutions as well as the effectiveness, behavior and limitations of the designed algorithm.
ÁLVAREZ-MIRANDA, E., FERNÁNDEZ, E. et LJUBIC, I. (2015). The Recoverable Robust Facility Location Problem. Transportation Research Part B: Methodological, 79(1), pp. 93-120.