Sensitivity analysis for multi-attribute project selection problems

The selection of projects from a large list of possibilities is a common problem in Civil and Environmental Engineering. Optimization models based on utility assessments and expert opinions tend to be neglected by decision-makers because of uncertainty in the inputs. Here we develop a multi-attribute optimization model for project selection problems that is based on a combination of multi-attribute utility theory, mixed-integer optimization, and statistical analysis. A series of procedures for conducting sensitivity analyses for both discrete and continuous parameter variations is provided. To demonstrate the model we use the example of selecting a portfolio of projects to fund within the New Zealand Department of Conservation. The results highlight the sensitivity of project selection to attribute weights, and the difficulty in removing non-critical parameters from an analysis when wide ranges in parameters are considered. The methods developed here will help decision-makers examine the robustness of the optimal solution to parameters, and help them focus improvements to their decision support on the most critical parameters.