Two-stage facility location problems with restricted recourse

We introduce a new class of two-stage stochastic uncapacitated facility location problems under system nervousness considerations. The location and allocation decisions are made under uncertainty, while the allocation decisions may be altered in response to the realizations of the uncertain parameters. A practical concern is that the uncertainty-adaptive second-stage allocation decisions might substantially deviate from the corresponding pre-determined first-stage allocation decisions, resulting in a high level of nervousness in the system. To this end, we develop two-stage stochastic programming models with restricted recourse that hedge against undesirable values of a dispersion measure quantifying such deviations. In particular, we control the robustness between the corresponding first-stage and scenario-dependent recourse decisions by enforcing an upper bound on the Conditional Value-at-Risk (CVaR) measure of the random CVaR-norm associated with the scenario-dependent deviations of the recourse decisions. We devise exact Benders-type decomposition algorithms to solve the problems of interest. To enhance the computational performance, we also develop efficient combinatorial algorithms to construct optimal solutions of the Benders cut generation subproblems, as an alternative to using an off-the-shelf solver. The results of our computational study demonstrate the value of the proposed modeling approaches and the effectiveness of our solution methods.