Research background: Project portfolio optimization isa demanding process in the case of considering a large number of project intentions and has so far been the subject of research by many authors, especially foreign authors. However, the issue of project portfolio optimization is an area that is not sufficiently addressed by Slovak authors. This was the main impulse to create a specific mathematical model of integer programming with bivalent variables to optimize the company's project portfolio with the intention to reflect the specific requirements of Slovak companies. Purpose of the article: The aim of the article is to propose a mathematical model of integer programming with bivalent variables to optimize the project portfolio with a focus on Slovak companies. Methods: In accordance with the aim of the article, a questionnaire survey was carried out with the intention of identifying the criteria that are perceived by the managers of Slovak companies as important in the optimization of the project portfolio. These criteria were subsequently reflected in the mathematical model design using the mathematical programming method. Findings & Value added: Based on a literature review aimed at the project portfolio optimization, we have found a gap in considering the compliance of project intentions and strategic objectives of the company within the optimization of the project portfolio. Based on the results of the questionnaire survey, the significance of the mutual compliance of project intentions with the strategic objectives of the company was confirmed from the point of view of Slovak companies. Given the fact that our aim was to create an innovative integer programming model with bivalent variables orientated to the conditions of Slovak companies, we included in the resulting model the criteria that were not considered within the scope of existing research in this area, and which are perceived as important by the Slovak companies.
In order to maintain or increase market share, every company tries to use the most optimal combination of marketing communication tools or marketing mix tools. There are a large number of products placed on the market from a large number of companies that need to distinguish one another from competing companies. The most important tool to differentiate from competitors is the brand of products. The aim of each company is to ensure that their product brand is brought to the attention of customers and that customers associate especially positive associations with its brand(s). We are of the opinion that if the first and then repeated purchase of customers of the same product of a given brand confirms that the product meets the required characteristics and quality they expect from the product, customers will not doubt the quality of the products sold under the brand and will regard it as quality. For this reason, the aim of the paper was to confirm the importance of the brand in consumer buying decisions and to find out whether consumers really perceive the brand as a guarantee of product quality. To meet the aim of the paper, we conducted a questionnaire survey, which confirmed the importance of the brand in consumer purchasing decisions and the perception of the brand as a guarantee of product quality. We also confirmed a statistically significant dependence between brand perception as a guarantee of product quality and the age of respondents, confirming the importance of demographic characteristics in the implementation of company marketing activities. JEL Classification Numbers: M37,
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