Rade Tešić

One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly such a problem is solved in this paper, which integrates linear programming and a Multi-Criteria Decision-Making (MCDM) model. First, linear programming was applied to optimize production and several potential solutions lying on the line segment AB were obtained. A list of criteria was created and evaluated using the Improved Fuzzy Stepwise Weight Assessment Ratio Analysis (IMF SWARA). To obtain the final solution, a novel Rough compromise ranking of alternatives from distance to ideal solution (R-CRADIS) method was developed and verified through comparative analysis. The results show that the integration of linear programming and a Fuzzy-Rough MCDM model can be an exceptional solution for solving specific optimization problems.

The quality of output or decision-making depends on high-quality input data, their adequate evaluation, the application of adequate approaches, and accurate calculation. In this paper, an objective criticism of applying the fuzzy SWARA (step-wise weight assessment ratio analysis) method based on the Chang TFN (triangular fuzzy number) scale is performed. Through research, it has been noticed that a large number of studies use this approach and, as an epilogue, there are wrong decisions based on inconsistent values in relation to the initial assessment of decision-makers (DMs). Seven representative studies (logistics, construction industry, financial performance management, and supply chain) with different parameter structures and decision matrix sizes have been singled out. The main hypothesis has been set, which implies that the application of this approach leads to wrong decisions because the weight values of the criteria are incorrect. A comparative analysis with the improved fuzzy SWARA (IMF SWARA) method has been created and a number of negative conclusions has been reached on using the fuzzy SWARA method and the Chang scale: Primarily, that using such an approach is impossible for two or more criteria to have equal value, that allocating TFN (1,1,1) leads to criteria values that are inconsistent with expert evaluation, that the last-ranked criteria in the fuzzy SWARA method have no influential value on the ranking of alternatives, that there is a great gap between the most significant and last-ranked criteria, and that the most significant criterion has a huge impact on the evaluation of alternative solutions and decision making. As a general conclusion, it is given that this approach is not adequate for application in problems of multi-criteria decision making because it produces inadequate management of processes and activities in various spheres.