A bi-level multi objective programming approach to solve grey problems: an application to closed loop supply chain network

Abstract

Purpose This paper aims to develop a grey decentralized bi-level multi-objective programming (MOP) model. A solution approach is also proposed for the given model. A production and transportation plan for a closed loop supply chain network under an uncertain environment and different scenarios is also developed. Design/methodology/approach In this paper, we combined grey linear programming (GLP) and fuzzy set theory to present a solution approach for the problem. The proposed model first solves the given problem using GLP. Membership functions for the decision variables under the control of the leader and for the goals are created. These membership functions are then used to generate the final solutions. Findings This paper provides insight for fomenting the decision-making process while providing a more flexible approach in uncertain logistics problems. The deviations of the final solution from the individual best solutions of the two levels are very little. These deviations can further be reduced by adjusting the tolerances associated with the decision variables under the control of the leader. Practical implications The proposed approach uses the concept of membership functions of linear form, and thus, requires less computational efforts while providing effective results. Most of the organizations exhibit decentralized decision-making under the presence of uncertainties. Therefore, the present study is helpful in dealing with such scenarios. Originality/value This is the first time, formulation of a decentralized bi-level multi-objective model under a grey environment is carried out as per the best knowledge of the authors. A solution approach is developed for bi-level MOP under grey uncertainty.

Determinants of Remanufacturing Adoption for Circular Economy: A Causal Relationship Evaluation Framework

“…The second phase identifies the relationships between the finalized determinants. Numerous methods for developing the causal relationship are available in the literature, including Interpretative Structural Modelling (ISM), Total Interpretative Structural Modelling (TISM), WING, and DEMATEL [41][42][43][44]. These approaches have some drawbacks-for example, ISM and TISM only provide qualitative assessment; quantitative components are absent from these methods [45].…”

“…Numerous methods for developing the causal relationship are available in the literature, including Interpretative Structural Modelling (ISM), Total Interpretative Structural Modelling (TISM), WING, and DEMATEL [39][40][41][42]. These approaches have some drawbacksfor example, ISM and TISM only provide qualitative assessment; quantitative components are absent from these methods [43]. Additionally, Gupta et al [30] claim that DEMATEL has the ability to assess the degree of interaction between the barriers.…”

A fuzzy multiobjective linear programming approach for green multiechelon distribution network design

“…Several mathematical programming modeling approaches consist of single-objective mixed-integer linear programming or MILP (Sadjady and Davoudpour, 2012; Askin et al , 2013; Cortinhal et al , 2015; Santosa and Kresna, 2015; Le et al , 2019), multi-objective mixed-integer linear programming (MOMILP) (Paksoy et al , 2010; Boronoos et al , 2021), normalized normal constraint (Wang et al , 2011), evolutionary multiobjective algorithm (Bhattacharya and Bandyopadhyay, 2010; Harris et al , 2014), weighted sum method (Amin and Zhang, 2013), goal programming (Yaghin et al , 2012; Mohammed and Wang, 2017; Yaghin and Sarlak, 2020), LP-metric (Mohammed and Wang, 2017; Khalilzadeh and Derikvand, 2018), min–max approach (Kannan et al , 2013; Mohammed and Wang, 2017; Olapiriyakul et al , 2019; Jinawat and Buddhakulsomsiri, 2021), ε -constraint (Amin and Zhang, 2013; Jindal and Sangwan, 2017; Mohammed and Wang, 2017; Mohammed et al , 2019) and augmented ε -constraint (Mohebalizadehgashti et al , 2020). In addition, several studies, including that of Liang (2006), Paksoy et al (2012), Pishvaee and Razmi (2012), Amin and Zhang (2013), Dey et al (2015), Gholamian et al (2015), Jindal and Sangwan (2017), Mohammed and Wang (2017), Mohammed et al (2019), Yaghin and Sarlak (2020) and Asim et al (2021), consider uncertainty in their model parameters. For heuristics, widely used methods are simulated annealing (Santosa and Kresna, 2015), Lagrangian relaxation (Sadjady and Davoudpour, 2012; Harris et al , 2014), genetic (Askin et al , 2013), particle swarm (Shankar et al , 2013) and memetic algorithms (Jamshidi et al , 2012).…”

Risk assessment model for halal supply chain using an integrated approach of IFN and D number

“…These experts' input is subjective and many times imprecise in nature which lowers the accuracy of the assessment (Shankar, Choudhary, & Jharkharia, 2018;Li & Yazdi, 2022a, b;Agarwal et al, 2022). The three major complications involved with the expert's input as the vagueness of the linguistic scale (Yazdi, 2022), inconsistent information (Gholamizadeh, Zarei, Omidvar & Yazdi, 2022) and uncertainty in the expert's opinion (Zhou, Shi, Deng, & Deng, 2017;Asim, Jalil, Javaid, & Muneeb, 2021;Hashmi, AqibJalil, & Javaid, 2022). These three issues are not handled simultaneously by the conventional risk assessment technique.…”