An experimental approach for examining solution errors of engineering problems with uncertain parameters

- An “optimal” solution contains errors when the parameters of the model are uncertain.
- An experimental approach is proposed to examine solution errors with uncertain parameters.
- The proposed approach is an alternative to the commonly used sensitivity analysis approach.
- Regression models are estimated to evaluate potential errors of a solution.
- Regression models can also be used to determine optimality tolerance in solution algorithms.

One potential overlook for applying optimization models to solve engineering problems is that their parameters are rarely error-free, implying that their solutions usually contain errors even when the models are solved to optimality. If the deviation between the solution based on parameters containing errors and the true optimal (but unavailable) solution based on error-free parameters is significant, the following decision-making could be meaningless. In this study, an experimental method is developed to evaluate solution errors of optimization models in which uncertain parameters are included in objective functions. A project scheduling problem is used as the case study. The effect of parameter errors and optimality tolerances in solution algorithms on solution errors are studied. The case study shows that the model solution errors increase as the scale of problem increases for the same range of parameter errors. It also shows that the model solution errors are similar for an optimality tolerance of within 4%. Regression models are estimated, which are useful for estimating potential errors between a solution based on parameters containing errors and the true optimal solution before a model is actually solved. They can also be used to determine values of optimality tolerance in solution algorithms that achieve the balance between solution quality and time.