Exploring and treating the effect of outliers in unconstrained linear decision-making models and linear regression models (with practical application)

Abstract

The presence of outliers within a set of data greatly affects the results of the statistical analysis of the data and therefore the appropriate decision-making process. Therefore, these values and methods of detection and estimation must be studied. This problem has been studied in some issues of linear regression and linear programming models, but it has not received the same attention. In unconstrained linear programming models (their models contain free variables), which is considered one of the most important topics in operations research for its multiple uses and its ability to deal with decision variables that are not constrained by a sign (the variable is allowed to be negative, positive or zero). In this research, the outlier values in these models were explored and how these values could affect the optimal solution and thus the appropriate decision-making. The estimated matrix method was used to identify the abnormal constraints and treat them to make the adopted model more appropriate to achieve the objectives. Where this method was characterized by simplicity and ease of calculation as well as clarity in identifying anomalous observations.