Simultaneous sensitivity analysis of mixed-integer location-allocation models using machine learning tools: cancer hospitals’ network design

Uncertainty analysis is an inevitable attribute of location-allocation problems due to unforecastable parameter changes. Although the simultaneous variation of parameters is more realistic than their instinct variation, the simultaneous sensitivity analysis (SSA) of mixed-integer mathematical models’ outputs upon simultaneous changes of parameters’ value has taken no attention. In the metamodeling process using machine learning tools like regression models and artificial neural networks, several combinations of input values are used for metamodel creation. This paper employs this feature of metamodeling to propose an approach for global sensitivity analysis of mixed-integer mathematical models. The proposed approach is applied in analyzing a newly developed multi-period mixed integer mathematical model for cancer hospitals’ location-allocation problem in a case study. The comparison of results using SSA based on using Regression metamodel (RMM) and traditional one-factor-at-a-time (OFAT) methods showed different ranks of parameters. In addition to more adaptation of SSA to simultaneous changes of parameters in the real world, the created machine learning tools aim to forecast the corresponding outputs approximately when the mixed-integer mathematical model is infeasible or long-run upon some combinations of input parameters’ value. Finally, some applicable managerial insights and recommendations for future works are provided.