Evaluating the Effectiveness of Integrated Benders Decomposition Algorithm and Epsilon Constraint Method for Multi-Objective Facility Location Problem under Demand Uncertainty مقالة

مؤلف: Rahimi، Iman ؛ Hong Tang، Sai ؛ Ahmadi، Abdollah ؛ Azfanizam Binti Ahmad، Siti ؛ Soon Lee، Lai ؛ M. Sharaf، Adel ؛

Iranian Journal Of Management Studies Summer 2017, Volume 10 - Number 3 التصنيف: الف/ISC (‎26 صفحة - من 551 إلی 576 )

الکلمات المفتاحية: Demand Uncertainty Multi|objective optimisation Benders decomposition algorithm

خلاصة:

One of the most challenging issues in multi-objective problems is finding Pareto optimal points. This paper describes an algorithm based on Benders Decomposition Algorithm (BDA) which tries to find Pareto solutions. For this aim, a multi-objective facility location allocation model is proposed. In this case, an integrated BDA and epsilon constraint method are proposed and it is shown that how Pareto points in multi-objective facility location model can be found. Results are compared with the classic form of BDA and the weighted sum method for demand uncertainty and deterministic demands. To do this, Monte Carlo method with uniform function is used, then the stability of the proposed method towards demand uncertainty is shown. In order to evaluate the proposed algorithm, some performance metrics including the number of Pareto points, mean ideal points, and maximum spread are used, then the t-test analysis is done which points out that there is a significant difference between aforementioned algorithms

ملخص الجهاز:

"672575 Evaluating the Effectiveness of Integrated Benders Decomposition Algorithm and Epsilon Constraint Method for Multi-Objective Facility Location Problem under Demand Uncertainty Iman Rahimi1, Sai Hong Tang1, Abdollah Ahmadi2, Siti Azfanizam Binti Ahmad1, Lai Soon Lee3, Adel M. In this case, an integrated BDA and epsilon constraint method are proposed and it is shown that how Pareto points in multi-objective facility location model can be found. (2014) used Normal Boundary Intersection (NBI) and BDA for their multi-objective framework; however, one drawback of the combined NBI algorithm is that Pareto optimality solution is not guaranteed (Das &amp; Dennis, 1998; Ghane-Kanafi &amp; Khorram, 2015). This model is an extension of Klimberg and Ratick’s (2008); they have considered capacitated facility location combined with data envelopment analysis as a bi-objective and indeterministic model, then a new framework solution procedure has been proposed for solving the proposed multi-objective facility location problem under deterministic and uncertainty cases. In other words, the proposed algorithm benefits from epsilon constraint solution that could cover non-convex points while the classic form of BDA and the weighted sum method possesses the weakness of not being able to find Pareto points of the non-convex optimisation problem. Number of Pareto Solution To check the reflect of change and variation under different conditions, design of experiment (DOE) is proposed, thus, Taguchi method is suggested (Taguchi, 1986; Behmanesh &amp; Rahimi, 2012). Conclusion In this paper, integrated BDA and epsilon constraint have been applied for multi-objective facility location model; the primary goal of this model is to find the optimal number of potential customers, the minimum cost and high efficiency to serve."

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