Integration of an Improved Grey-Based Method and Fuzzy Multi-Objective Model for Supplier Selection and Order Allocation

For multi-attribute decision making (MADM) problems, a grey based approach (LI) had been developed to evaluate, rank and select the best suppliers. The method calculates a grey possibility degree between compared suppliers alternatives set and positive ideal referential alternative. The drawback of the method is that the negative ideal referential alternative is not considered in evaluating and ranking of the alternatives. Moreover, the method can only consider interval fuzzy number as input data and real number is neglected. Based on this model and other MADM methods, all demand was sold by the best supplier. In other cases, if the best supplier cannot satisfy all demand, multi-objective programming is used to formulate the problem and assign optimum order quantities to the best suppliers (multi-sourcing). Some techniques, such as goal programming (GP) approach, ε-Constraint method, Reservation level (RL) driven Tchebycheff procedure (RLTP) method had been proposed to solve the multi-objective models. It may be a problem that these techniques traced back to more than 10 years ago. Therefore, there may be still the need to produce a new technique in order to solve the multi-objective models. In this study, to overcome the first drawback, the LI method was improved based on the concepts of technique for order preference by similarity to ideal solution (TOPSIS) to consider both the positive and the negative ideal referential alternative for evaluation of the suppliers. The improved version of the LI method is called the I.LI method. Based on the concepts of TOPSIS, the chosen alternative should have the shortest distance from the positive ideal solution and the farthest from the negative ideal solution. Moreover, in order to solve the problems, a new grey based method (NG) based on the TOPSIS concepts was proposed that can easily consider both interval fuzzy number and real number simultaneously. Afterwards, an innovative comparative approach was proposed to compare the three MADM methods, the LI, the I.LI and the NG methods, and to show that which method is more optimal than the other methods. Subsequently, in this thesis, an integration of the NG method and fuzzy multi-objective model was suggested for multi-sourcing and multi-product supplier selection problem. The score of suppliers calculated by the NG method was served as coefficients in one objective function of the multi-objective model. In this fuzzy multi-objective model, the products are divided into two independent and dependent products so that (1) the price breaks (discounts) depend on the size of the order quantities, (2) independent products’ sales volume affect the prices and discounts of the dependent products and (3) all products must be sold as a bundle. Finally, to overcome the third problem, a new weighted additive function, which is able to consider relative importance of each objective as well as condition of fuzzy situation, is proposed to solve the fuzzy multi-objective model and assign optimum order quantities to the suppliers evaluated and ranked by the NG method. The results of the innovative comparative approach showed that the result of the NG method is more optimal than the I.LI method and the latter is more optimal than the LI method. Therefore, the NG method was selected to be integrated with the fuzzy multi-objective model. Also, the fuzzy multi-objective model was solved by the new weighted additive function, and the results demonstrated that besides considering the relative importance of the objectives, the new technique is also able to consider the condition of fuzzy situation

TOPSIS extension for multi-objective supplier selection problem under price breaks

For supplier selection problem (SSP), if suppliers offer quantity discounts as well as buyer wants to buy multi-product, SSP becomes more complicated. In order to solve the complicated problem, an integration of TOPSIS approach and multi-objective mixed integer linear programming (MOMILP) is used to define the optimum quantities among the selected suppliers. In this article, we also apply TOPSIS approach to solve the MOMILP problem. In this solution, TOPSIS minimizes the measure of distance, providing that the closest solution should have the shortest distance from the positive ideal solution (PIS) and the longest distance from the negative ideal solution (NIS) as well. Therefore, a q-dimensional objective space is reduced to a twodimensional space (PIS and NIS). Finally, a single objective function is then proposed as a suitable one to resolve the conflict between the new criteria (the shortest distance from the PIS and the longest distance from the NIS)

An optimal grey based approach based on TOPSIS concepts for supplier selection problem

Supplier selection is a multi-attribute decision making (MADM) problem that is affected by quantitative and qualitative factors, some of which may conflict with each other. Since most of the input information is not known accurately, selecting the right suppliers becomes more difficult. Grey theory is one of the new mathematical methods used to analyze systems with uncertain and incomplete information. In this article, we firstly described two previous grey based methods and then, we proposed a new method based on TOPSIS concepts in grey theory to deal with the problem of selecting suppliers. The new method calculates the weighted connection between each of the alternatives sequence and the positive and negative referential sequence to compare the ranking of grey numbers and select the most desirable supplier. Through this article, it is demonstrated that the new method is a good means of evaluation, and it is also more optimal than the two methods

Overview of Identified Genomic Regions Associated with Various Agronomic and Physiological Traits in Barley under Abiotic Stresses

Climate change has caused breeders to focus on varieties that are able to grow under unfavorable conditions, such as drought, high and low temperatures, salinity, and other stressors. In recent decades, progress in biotechnology and its related tools has provided opportunities to dissect and decipher the genetic basis of tolerance to various stress conditions. One such approach is the identification of genomic regions that are linked with specific or multiple characteristics. Cereal crops have a key role in supplying the energy required for human and animal populations. However, crop products are dramatically affected by various environmental stresses. Barley (Hordeum vulgare L.) is one of the oldest domesticated crops that is cultivated globally. Research has shown that, compared with other cereals, barley is well adapted to various harsh environmental conditions. There is ample literature regarding these responses to abiotic stressors, as well as the genomic regions associated with the various morpho-physiological and biochemical traits of stress tolerance. This review focuses on (i) identifying the tolerance mechanisms that are important for stable growth and development, and (ii) the applicability of QTL mapping and association analysis in identifying genomic regions linked with stress-tolerance traits, in order to help breeders in marker-assisted selection (MAS) to quickly screen tolerant germplasms in their breeding cycles. Overall, the information presented here will inform and assist future barley breeding programs

Overview of Identified Genomic Regions Associated with Various Agronomic and Physiological Traits in Barley under Abiotic Stresses

Climate change has caused breeders to focus on varieties that are able to grow under unfavorable conditions, such as drought, high and low temperatures, salinity, and other stressors. In recent decades, progress in biotechnology and its related tools has provided opportunities to dissect and decipher the genetic basis of tolerance to various stress conditions. One such approach is the identification of genomic regions that are linked with specific or multiple characteristics. Cereal crops have a key role in supplying the energy required for human and animal populations. However, crop products are dramatically affected by various environmental stresses. Barley (Hordeum vulgare L.) is one of the oldest domesticated crops that is cultivated globally. Research has shown that, compared with other cereals, barley is well adapted to various harsh environmental conditions. There is ample literature regarding these responses to abiotic stressors, as well as the genomic regions associated with the various morpho-physiological and biochemical traits of stress tolerance. This review focuses on (i) identifying the tolerance mechanisms that are important for stable growth and development, and (ii) the applicability of QTL mapping and association analysis in identifying genomic regions linked with stress-tolerance traits, in order to help breeders in marker-assisted selection (MAS) to quickly screen tolerant germplasms in their breeding cycles. Overall, the information presented here will inform and assist future barley breeding programs

Association Analysis for Some Biochemical Traits in Wild Relatives of Wheat under Drought Stress Conditions

In the present study, we estimated genetic diversity and population structure in 186 accessions of Triticum and Aegilops species using 24 simple sequence repeat markers (SSR). Furthermore, an association analysis was performed for antioxidant activities, including guaiacol peroxidase (GPX), ascorbate peroxidase (APX), peroxidase (POX), catalase (CAT), and dry matter (DM) under two control and drought stress conditions. Our findings showed that drought treatment significantly decreased DM, whereas activities of all antioxidant enzymes were increased compared to the control conditions. The results of correlation analysis indicated that, under drought stress conditions, all biochemical traits had a positive and significant association with each other and with dry matter. In the molecular section, the results of the analysis of molecular variance (AMOVA) indicated that the molecular variation within species is more than within them. The dendrogram obtained by cluster analysis showed that grouping the investigated accessions was in accordance with their genomic constitutions. The results of association analysis revealed 8 and 9 significant marker–trait associations (MTA) under control and drought stress conditions, respectively. Among identified MTAs, two associations were simultaneously found in both growing conditions. Moreover, several SSR markers were associated with multiple traits across both conditions. In conclusion, our results could provide worthwhile information regarding marker-assisted selection for the activity of antioxidant enzymes in future breeding programs

Association Analysis for Some Biochemical Traits in Wild Relatives of Wheat under Drought Stress Conditions

In the present study, we estimated genetic diversity and population structure in 186 accessions of Triticum and Aegilops species using 24 simple sequence repeat markers (SSR). Furthermore, an association analysis was performed for antioxidant activities, including guaiacol peroxidase (GPX), ascorbate peroxidase (APX), peroxidase (POX), catalase (CAT), and dry matter (DM) under two control and drought stress conditions. Our findings showed that drought treatment significantly decreased DM, whereas activities of all antioxidant enzymes were increased compared to the control conditions. The results of correlation analysis indicated that, under drought stress conditions, all biochemical traits had a positive and significant association with each other and with dry matter. In the molecular section, the results of the analysis of molecular variance (AMOVA) indicated that the molecular variation within species is more than within them. The dendrogram obtained by cluster analysis showed that grouping the investigated accessions was in accordance with their genomic constitutions. The results of association analysis revealed 8 and 9 significant marker–trait associations (MTA) under control and drought stress conditions, respectively. Among identified MTAs, two associations were simultaneously found in both growing conditions. Moreover, several SSR markers were associated with multiple traits across both conditions. In conclusion, our results could provide worthwhile information regarding marker-assisted selection for the activity of antioxidant enzymes in future breeding programs

An Analysis of Genetic Variability and Population Structure in Wheat Germplasm Using Microsatellite and Gene-Based Markers

Knowledge of the natural patterns of genetic variation and their evolutionary basis is required for sustainable management and conservation of wheat germplasm. In the current study, the genetic diversity and population structure of 100 individuals from four Triticum and Aegilops species (including T. aestivum, Ae. tauschii, Ae. cylindrica, and Ae. crassa) were investigated using two gene-based markers (start codon targeted (SCoT) polymorphism and CAAT-box derived polymorphism (CBDP)) and simple-sequence repeats (SSRs). The SCoT, CBDP, and SSR markers yielded 76, 116, and 48 polymorphism fragments, respectively. The CBDP marker had greater efficiency than the SCoT and SSR markers due to its higher polymorphism content information (PIC), resolving power (Rp), and marker index (MI). Based on an analysis of molecular variance (AMOVA) performed using all marker systems and combined data, there was a higher distribution of genetic variation within species than among them. Ae. cylindrica and Ae. tauschii had the highest values for all genetic variation parameters. A cluster analysis using each marker system and combined data showed that the SSR marker had greater efficiency in grouping of tested accessions, such that the results of principal coordinate analysis (PCoA) and population structure confirmed the obtained clustering patterns. Hence, combining the SCoT and CBDP markers with polymorphic SSR markers may be useful in genetic fingerprinting and fine mapping and for association analysis in wheat and its germplasm for various agronomic traits or tolerance mechanisms to environmental stresses

An Analysis of Genetic Variability and Population Structure in Wheat Germplasm Using Microsatellite and Gene-Based Markers

Knowledge of the natural patterns of genetic variation and their evolutionary basis is required for sustainable management and conservation of wheat germplasm. In the current study, the genetic diversity and population structure of 100 individuals from four Triticum and Aegilops species (including T. aestivum, Ae. tauschii, Ae. cylindrica, and Ae. crassa) were investigated using two gene-based markers (start codon targeted (SCoT) polymorphism and CAAT-box derived polymorphism (CBDP)) and simple-sequence repeats (SSRs). The SCoT, CBDP, and SSR markers yielded 76, 116, and 48 polymorphism fragments, respectively. The CBDP marker had greater efficiency than the SCoT and SSR markers due to its higher polymorphism content information (PIC), resolving power (Rp), and marker index (MI). Based on an analysis of molecular variance (AMOVA) performed using all marker systems and combined data, there was a higher distribution of genetic variation within species than among them. Ae. cylindrica and Ae. tauschii had the highest values for all genetic variation parameters. A cluster analysis using each marker system and combined data showed that the SSR marker had greater efficiency in grouping of tested accessions, such that the results of principal coordinate analysis (PCoA) and population structure confirmed the obtained clustering patterns. Hence, combining the SCoT and CBDP markers with polymorphic SSR markers may be useful in genetic fingerprinting and fine mapping and for association analysis in wheat and its germplasm for various agronomic traits or tolerance mechanisms to environmental stresses

TOPSIS for solving multi-objective multi-product supplier selection problem under price breaks

Supplier selection is a multi-criteria decision-making problem (MCDM) that is affected by quantitative and qualitative (conflicting) factors. For supplier selection problem, if suppliers offer quantity discounts and buyer wants to buy multiple products as well, this problem becomes more complicated. To solve the problem, an integration of technique for order preference by similarity to ideal solution (TOPSIS) and multi-product multi-objective mixed integer linear programming (MOMILP) is used to consider both tangible and intangible factors in choosing the best suppliers and define the optimum quantities among the selected suppliers. The problem includes the three objective functions: to maximize the total value of purchasing (TVP), and to minimize the total defect rate and total cost, while satisfying demand requirement and capacity constraints. In this paper, to solve the multi-objective model, TOPSIS and later a single objective function are proposed which can consider the relative importance of the three goals