A novel method for solving linear programming with grey parameters

Mahmoudi, Amin; Liu, Sifeng; Javed, Saad Ahmed; Abbasi, Mehdi

doi:10.3233/jifs-181071

Cited by 32 publications

(25 citation statements)

References 20 publications

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“…In another study, Li, Liu, and Wang (2014) improved covered solution, but this method suffers from some specific shortcomings including a high volume of calculations and a need to reduce the length of grey parameters. Mahmoudi, Liu, Javed, and Abbasi (2019) proposed a novel method to overcome the aforementioned shortcomings. Their model is convenient and can present high‐quality solutions for fully grey linear models.…”

Section: Grey System Theorymentioning

confidence: 99%

“…Their model is convenient and can present high‐quality solutions for fully grey linear models. The current study has employed the model proposed by Mahmoudi, Liu et al (2019). Therefore, for solving GLP, model 15 can be employed.…”

Section: Grey System Theorymentioning

confidence: 99%

“…Step 5: Solving the OPA‐G model, finding the weights of the criteria, and ranking the alternatives: Based on the collected data in Steps 1 to 4, the linear model 16 should be formed. This model can be solved based on the proposed GLP method by Mahmoudi, Liu et al (2019), which has been explained in the previous section.

Max \otimes normalZ normalS . normalt : \otimes Z \leq \otimes i (\otimes j (\otimes r (\otimes {W_{italicijk}}^{r} - \otimes {W_{italicijk}}^{r + 1}))) \forall i, j, k and r \otimes Z \leq \otimes i \otimes j \otimes m \otimes {W_{italicijk}}^{m} \forall i, j and k {falsefalse}_{\sum}^{i = 1} {falsefalse}_{\sum}^{j = 1} {falsefalse}_{\sum}^{k = 1} \otimes W_{ijk} = ([], 0.8,1.2) \otimes W_{ijk} \geq 0 \forall i, j and k

where ⊗ Z is unrestricted in sign…”

Section: Grey Ordinal Priority Approachmentioning

confidence: 99%

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Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach

et al. 2020

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Due to mounting environmental and social challenges, supplier selection has become one of the most critical tasks of project‐oriented organizations. Because supplier selection can affect the long‐term success and profitability of the organizations and their projects, directly, embracing sustainability can add value in the equation. Considering sustainability measures can positively guide project managers in making better decisions for the projects in the long term. Therefore, the current study attempts to provide a conceptual model for selecting the best supplier based on a sustainability framework in megaprojects. Meanwhile, decision‐making methods can be employed as a proper tool to find the best supplier. Ordinal priority approach (OPA) is a recent development in multiple criteria decision making (MCDM), while it has many benefits compared with other methods like analytic hierarchy process (AHP) and technique for order of preference by similarity to ideal solution (TOPSIS). However, this method cannot consider multiple ranks during the decision‐making process, and using an uncertainty approach feels strongly. Grey systems theory (GST) can consider uncertainties with no need for large sample or proposing membership function. Hence, the current study employed the GST to consider multiple ranks for criteria and alternatives in the OPA method. This is the first time that a sustainable supplier selection framework has been presented for megaprojects with the aid of the Grey OPA (OPA‐G) method. Finally, a case study has been examined to evaluate the performance of the proposed approach. The results show that the proposed approach can be used in real‐world situations and it has acceptable performance under uncertainty conditions.

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Section: Grey System Theorymentioning

confidence: 99%

Section: Grey System Theorymentioning

confidence: 99%

Max \otimes normalZ normalS . normalt : \otimes Z \leq \otimes i (\otimes j (\otimes r (\otimes {W_{italicijk}}^{r} - \otimes {W_{italicijk}}^{r + 1}))) \forall i, j, k and r \otimes Z \leq \otimes i \otimes j \otimes m \otimes {W_{italicijk}}^{m} \forall i, j and k {falsefalse}_{\sum}^{i = 1} {falsefalse}_{\sum}^{j = 1} {falsefalse}_{\sum}^{k = 1} \otimes W_{ijk} = ([], 0.8,1.2) \otimes W_{ijk} \geq 0 \forall i, j and k

where ⊗ Z is unrestricted in sign…”

Section: Grey Ordinal Priority Approachmentioning

confidence: 99%

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Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach

et al. 2020

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“…A black system implies a system for which no information is available and the white system is the system for which the entire information is available. Thus, a grey system becomes a system with partially known and partially unknown information [32]. The key strength of GST and its models is their predictions and decision making using small sample size, poor data and incomplete information [33][34][35][36].…”

Section: Grey Relational Analysismentioning

confidence: 99%

Systems Evaluation through New Grey Relational Analysis Approach: An Application on Thermal Conductivity—Petrophysical Parameters’ Relationships

et al. 2019

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The current study introduces a new technique for the analysis of uncertain systems and uncertain processes in geothermics/earth sciences. The method is the second synthetic grey relational analysis (SSGRA) model, which incorporated the advantages of both Deng’s GRA model and the bidirectional absolute GRA model. The SSGRA model has been earlier successfully applied in project management and healthcare systems. The current study is a pioneer in demonstrating the feasibility of the SSGRA model in a geothermal environment. In the current study, the model was used to determine the associations between thermal conductivity and petrophysical parameters in an Algerian reservoir. The results revealed that thermal conductivity is most strongly associated with porosity followed by density and permeability. Their relationships are also discussed. The study concludes with valuable insights about the model and its application in engineering and natural sciences especially when the system contains uncertainty, which may arise either due to insufficient data or uncertain relationships among the parameters associated with the system or its processes.

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“…Several methods for solving grey linear programming problems can be seen in Li (2007), Liu et al (2009), Li et al (2014), Nasseri et al (2016), Razavi et al (2012) and Mahmoudi et al (2019). One of the most convenient of these methods is based on the concept of the whitenization of grey numbers in positioned programming (Liu et al , 2009).…”

Section: Introductionmentioning

confidence: 99%

Grey linear programming: a survey on solving approaches and applications

Darvishi

Liu

Forrest

2020

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PurposeThe purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.Design/methodology/approachAfter presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.FindingsThe progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.Originality/valueDifferent methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

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A novel method for solving linear programming with grey parameters

Cited by 32 publications

References 20 publications

Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach

Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach

Systems Evaluation through New Grey Relational Analysis Approach: An Application on Thermal Conductivity—Petrophysical Parameters’ Relationships

Grey linear programming: a survey on solving approaches and applications

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