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This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

The purpose of this work is to present the modelling of the conditions of provision of growth of public–private partnership using digital technologies based on the game approach.

The methods of a systemic approach, linear programming and linear correlation, as well as statistical method, are used.

We performed the modelling of the conditions of provision of growth of public–private partnership using digital technologies based on the game approach. We also determined the level of development of public–private partnerships at the level of developed (United States, United Kingdom, Sweden and Denmark) and developing countries (Bulgaria, Venezuela and South Africa) and analysed the level of implementing digital technologies within the studied countries. We note a high level of public–private partnership in developed countries and a low level of this indicator in developing countries (except for Bulgaria, which has the positive dynamics of improvement). We also determine the main competitive advantages of implementing digital technologies, which have an impact on the improvement of the state of public–private partnerships at the level of the studied countries. Using the linear method of programming (game approach), we formulate the models of development of this type of interaction, within which the positive experience of developed countries is taken into account.

The originality and value of this research consist in the study of the specifics of the use of the game approach in the modelling of public–private partnership, which is based on the use of digital technologies.

Purpose – Agribusiness is crucial for the Brazilian trade balance surplus. Innovation, not only that focused on technology or productivity, is a basic condition for its development. The context of the agribusiness activities in a developing country is dynamic and requires a multilevel and multifaceted view. This suggests that these features need to be incorporated both in the theories and methods. Therefore, we propose a method, from within the perspective of Configurations Theory, of capturing this dynamic multidimensionality. The method was applied in the context of the rice-farming business in Southern Brazil.

Methodology/approach – The proposed method, which we refer to as a Case Study Method with Multiple Units of Analysis and Mixed Methods, was applied in a research organization in an attempt to identify the evolution of innovation while considering a theoretical perspective based on multilevel rules.

Findings – Six different configurations in the temporal organization of research were identified. These six configurations describe the evolution of four emphases given to innovation, the drivers associated with the evolution of these emphases, and the changes that have occurred over time.

Social implications – The results may provide support for new public policies for rice farming and lead to improvements in the organization's strategies for innovation.

Originality/value of chapter – The combination of methods used (Case Study, Qualitative Comparative Analysis, Social Network Analysis, Path Dependence, and Patterns of Decision Making) to study configurations, together with the dynamic approach to innovation based on multilevel rule, is unique.