The influence of constraint uncertainty on model solution correctness

Mathematical optimization models have often been used to solve engineering optimization problems. However, in practical engineering problems, some of the parameters of the optimization model may be uncertain. These then have to be estimated using suitable methods determined by the practitioners. However, such input data as model input may result in errors in the solutions. This study develops an approach to evaluate solution correctness for a project scheduling model in which uncertain parameter values are included in the constraint set, under various controllable and random error scenarios, coupled with various solution tolerance error settings. To simulate possible controllable and random errors contained in the constraint set, we designed a number of scenarios to examine the effect of different tolerance errors on the correctness of the model solution. To better understand the influence of model input errors and solution tolerance errors, a regression analysis is additionally performed for each error scenario. Finally, some useful information and managerial implications for real-world practices are extrapolated from the test results.