Determining and Estimating the Weights of Best-Worst Method Criteria through Solving Linear Programming or Mixed Integer Linear Programming Models

Subject Areas : Statistics

Mehdi Abbasi ¹ , Mohammad Reza Dehghani ²

1 - Department of Industrial Engineering, Shiraz Branch,, Islamic Azad University, Shiraz, Iran
2 - Expert in Quality Management and Improvement of Methods of Fars Power Generation Management Company, Shiraz, Iran

Received: 2021-10-10 Accepted : 2022-02-19 Published : 2024-11-30

Keywords: محدوده وزن شاخص‌ها, روش بهترین-بدترین (BWM), مدل برنامه‌ریزی خطی مختلط (MILPM), مدل برنامه‌ریزی خطی (LPM), تقریب تکه‌ای خطی (PLA),

Abstract :

The Best-Worst Method (BWM) is one of the latest methods for determining the weight of criteria in multiple attribute decision making problems. The optimal weights of criteria are determined through forming and solving of a Non-Linear Programming Model (NLPM). Being completely consistent, consistent, or inconsistent of the problem can be determined by calculating consistency ratio and comparing with its threshold. Considering the difficulties of solving NLPM through BWM, some attempts have been done to determine and estimate the criteria weights through forming and solving LPMs or Mixed-Integer LPMs (MILPMs). The presentation of the LPM and the SOS2 Piecewise Linear Approximation (PLA) were the main results of these attempts. The LPM is suitable for determining the weight criteria of completely consistent problems. In the PLA, the weights of criteria were estimated by solving some MILPMs. The necessity of many MILPMs solving and PLAs using to solve all problems is the main deficiencies of this method. In the suggested method of this paper, LPM is solved for weight determining of completely consistent problems criteria. Also, MILMs are solved for weight estimating of consistent problems criteria. For weight estimating of criteria, being criteria weights in the defined bounds are considered as another stop conditions, too. Also, the method doesn’t solve inconsistent problems. The results of applying the method to determine and estimate the criteria weights of the 384 sample tests show that results of proposed methods in 79% samples were improved and quality of results were as good as PLA in remained samples.

References:


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