A review of methods for estimating coefficients of objective functions and constraints in mathematical programming models

Considering the high importance of the optimization problem, this study evaluated mathematical programming models by considering various methods of estimating model coefficients. Correct and accurate data must be entered into the model to get accurate and robust result from the model. Most input data to the presented model are technical and objective function coefficients. Therefore, it is necessary to determine the information related to these coefficients with the utmost precision and, as much as possible, to develop a suitable scientific method to estimate the value of these coefficients [۵]. Finding the best method for estimating the coefficients of mathematical programming models can significantly optimize the final values of the variables extracted from the mathematical programming model. For this reason, it is essential to study the methods used so far in this field and examine their advantages and disadvantages. This review study investigated various methods of estimating technical coefficients of mathematical planning models in the conditions of possible decision-making and uncertainty after reviewing ۱۱۷ articles published between ۱۹۵۵ and ۲۰۲۲. These methods include fuzzy methods, statistical methods, and data analysis methods. Statistical methods such as regression methods, time series methods, exponential smoothing, and linear non-linear and non-parametric, machine learning and data mining methods were investigated in this article. The methods of data-driven analysis explained in this article can be referred to as decision trees, random forests and the Lasso methods. After evaluating and comparing these methods, suggestions for choosing the best method were provided.

Keywords:

mathematical programming model , data-driven analysis methods , data mining methods , Objective function , technical coefficients , time factor , machine learning