Modified metaheuristic algorithms to design a closed-loop supply chain network considering quantity discount and fixed-charge transportation

• Published in: Expert systems with applications Vol. 202; p. 117364
• Main Authors: Chaharmahali, Golara, Ghandalipour, Davoud, Jasemi, Milad, Molla-Alizadeh-Zavardehi, Saber
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 15.09.2022; Elsevier BV
• Subjects: Algorithms; Closed-loop supply chain; Design modifications; Evolutionary computation; Fixed-charge transportation; Heuristic methods; Modified metaheuristic algorithm; Operating costs; Quantity discount; Supply chains; Taguchi method; Taguchi methods; Transportation; Quantity discount; Fixed-charge transportation; Closed-loop supply chain; Modified metaheuristic algorithm; Taguchi method
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2022.117364

•Applying quantity discount and transportation fixed cost together for the first time in a closed-loop supply chain.•Application of eight basic and modified algorithms for the new NP-hard model.•Application of Taguchi method to calibrate the proposed algorithms' parameters and operators.•Development of a modified backtracking search algorithm and a modified differential evolution algorithm.•Suggesting some meta-heuristic algorithms with considerably good performances. Discount is an efficient way to reduce the closed-loop supply chain costs, and applying it would make the model closer to real ones. In this paper, the quantity discount is firstly applied along with fixed and variable transportation costs. The application of well-known, efficient algorithms, alongside developing modified versions to address the developed model is another contribution of this study. To calibrate the proposed algorithms’ parameters and operators, the Taguchi method is used. In this regard, several test problems in different sizes are generated considering the concerns of real-world cases, and the algorithms’ efficiencies are investigated by the relative percentage deviation method. The results show the superior performance of the hybrid algorithm of modified differential evolution and restart mechanism (MDE_Restart) and the algorithm of modified differential evolution (MDE) compared to the other employed algorithms.