Investigating model solution correctness for parameter uncertainty in both objective function and constraints

Parameter uncertainty, which may arise due to changes in the environment or human error, may be incorporated into the objective function and the constraints in an optimization model. However, to simplify the modeling, the values of these parameters are usually set or projected as deterministic values. It is no wonder that the modelling results based on these inaccurate parameters are neither correct nor reliable. Thus, it is important to examine the correctness of the model results in relation to parameter uncertainty. This study aims to analyze solution correctness in relation to different degrees of parameter uncertainty for the parameters in the objective function and the constraints, specifically for a project scheduling model. To examine the relationship between the solution correctness, the parameter uncertainty and the solution tolerance error, we conduct a numerical experiment including a number of different scenarios, each associated with a degree of uncertainty for all parameters in both the objective function and the constraints. Finally, the regression technique is adopted to more efficiently analyze the relationship between model input error, solution tolerance error and model output error, by estimating equations representative of their relationship. The obtained results and findings could be useful for the planners to apply any optimization models, including maritime transport optimization models, and to design solution algorithms in practice.