Background. Many types of toothpastes contain substances that can remineralize initial enamel caries. This study aimed to assess the effect of nano-hydroxyapatite (NHA) on microhardness of artificially created carious lesions.Methods. In this in vitro study, NHA was prepared using sol-gel technique and added to the toothpaste with 7% concentration. A total of 80 extracted sound teeth were collected. The crowns were polished using 500-grit abrasive paper. The specimens were randomly coded from 1 to 80. Number 1 to 40 were assigned to group A and numbers 41 to 80 to group B. The microhardness was measured using HVS-1000 Vickers microhardness tester. The specimens were demineralized using 37% phosphoric acid for 3 minutes in order to create artificial carious lesions and then were rinsed with water, air-sprayed for 3 minutes and dried. Microhardness was measured again. Next, the specimens were brushed for 15 days, twice daily, for 15 seconds. After 15 days, microhardness was measured again. Toothpaste A contained NHA and fluoride and toothpaste B contained fluoride alone. Data were analyzed using SPSS 16, with one-sample Kolmogorov-Smirnov test and ANOVA at a significance level of P<0.05.Results. The microhardness of specimens significantly decreased following acid exposure (P<0.01) but increased again in both groups after exposure to toothpastes. The increase in microhardness was significantly greater in group A (P<0.01).Conclusion. The toothpaste containing NHA was more effective than the toothpaste without NHA for the purpose of remineralization.

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Purpose Supplier selection problem is the key process in decision making of supply chain management. An effective selection of vendors is heavily responsible for the success of any organization. Vendor selection problem (VSP) reflects a more practical view when the decision makers involved in the problem are present on different levels. Moreover, vendor selection consists of various random parameters to be dealt with in real life. The purpose of this paper is to present a decentralized bi-level VSP where demand and supply are normal random variables and objectives are fuzzy in nature. Decision makers are present at two levels and are called as leader and follower. As the next purpose, this paper extends and presents a solution approach for fuzzy bi-level multi-objective decision-making model with stochastic constraints. Different scenarios have been developed within a real-life case study based on different sets of controlling factors under the control of leader. Design/methodology/approach This study uses chance-constrained programming and fuzzy set theory to generate the results. Stochastic constraints are converted into deterministic constraints using chance-constrained programming. Decision variables in the bi-level VSP are partitioned between the two levels and considered as controlling factors. Membership functions based on fuzzy set theory are created for the goals and controlling factors and are used to obtain the overall satisfactory solutions. The model is tested on a real-life case study of a textile industry and different scenarios are constructed based on the choice of leader’s controlling factors. Findings Results showed that the approach is quite helpful as it generates efficient results producing a good level of satisfaction for the decision makers of both the levels. Results showed that on choosing the vendors that are associated with worst values in terms of associated costs, vendor ratings and quota flexibilities as controlling factors by the leaders, the level of satisfaction achieved is highest. The level of satisfaction of solution is lowest for the scenario when the leader chooses to control the decision variables associated with vendors that are profiled with minimum vendor ratings. Results also showed that higher availability of materials and budget with vendors proved helpful in obtaining quota allocations. Different scenarios generate different results along with different values of satisfaction degrees and objective values which shows the flexible feature of the approach based on leader’s choice of controlling factors. Numerical results showed that the leader’s control can be effectively incorporated maintaining satisfaction levels of the followers under various scenarios or conditions. Research limitations/implications The paper makes a certain contribution toward the study of vendor selection existing in a hierarchical manner under uncertain environment. A wide set of data of different factors is needed which can be seen as a limitation when the available time is short for the supplier selection process. Practical implications VSP which is generally adopted by most of the large organizations is characterized with hierarchical decision making. Moreover, dealing with the real-life concern, the data available for some of the parameters are not complete, representing an uncertainty of parameters. This study is quite helpful for decentralized VSP under uncertain environment to reduce the costs, improve profit margins and to create long-term relationships with selected vendors. The proposed model also provides an avenue to explore the decision making when the leader has control over some of the decision variables. Originality/value Reviewing the literature available, this is the first attempt to present a multi-objective VSP where the decision makers are at hierarchical levels considering uncertain parameters such as demand and supply as per the best knowledge of authors. This research further provides an approach to construct scenarios or different cases based on the choice of leader’s choice of controlling factors.

Multicriteria mathematical modeling is an analytical framework for formally describing real‐life problems involving multiple and conflicting objectives. In the past decade, multicriteria decision‐making techniques have been applied in almost every area of the decision‐making including energy‐economic planning and sustainable development. Various mathematical and analytical models have been presented for the sustainable development planning and their assessment. In this paper, we discuss an approach related to multicriteria decision‐making and apply it for the assessment of the sustainable development goals of India by the year 2030. In the INDC report submitted to United Nations Framework Convention on Climate Change (2015, http://www4.unfccc.int/submissions/INDC/Published%20Documents/India/1/INDIA%20INDC%20TO%20UNFCCC.pdf), India has identified many goals related to the sustainable development like energy consumption, greenhouse gas emissions, GVA growth, and an increase in the employment by the year 2030. This paper overcomes the energy resource allocation problem in related literature due to the lack of sectorial data for the same year by calculating the estimates for each sector for the year 2030. We presented a multicriteria decision‐making model which allocates public labor force in the key economic sectors of India. The presented model is validated with the data of the key economic sectors and their contribution in the identified goals. The paper provides a decision support for the better management of future sustainable policies by assessing the efficiencies of the current policies toward future sustainable goals. We evaluated the identified goals using the multicriteria decision‐making approaches so that the strategic planning can be implemented by the policy makers and to present a quantitative justification of planning strategies.