Discrete Optimization Structures with Risks

The results of discrete optimization structures developed for decision-making with consideration of emerging risks in various decisions are presented in this work.

For each of the models discussed in this book, a numerical example is presented to illustrate some of the model's capabilities. The computational procedures used to solve the optimization problems are of polynomial computational complexity.

The numbering of the formulae, figures, and tables is for convenience, compiled separately for each of the seven chapters, and consists of two elements - the chapter number and the sequential number of the relevant table, figure, and formula. At the end of each chapter, a summary of the results in that chapter is given, as well as the references used in that chapter.

The proposed book also draws on the authors' many years of research in network flows, Markov decision processes, and discrete optimization.

АИ Проф. Марин Дринов
София 1113
ул. Академик Георги Бончев, блок 6
sales@aph.bas.bg

Introduction
Risk-aware network-flow optimization

• General requirements
• Notations
• Model M1 - Flowability of resources
• Model M2 - Flowability of risks
• Model M3 - Flowability of resource and risk flows at p_ij = const for the whole network
• Model M4 - Flowability of resources and risks
• Model M5 - Pseudo-optimal solutions for resource and risk flows
• Conclusion to chapter 1

Network-flow circulation with risks

• Theoretical and methodological prerequisites
• Numerical example
• Conclusions

The transportation task with risks and upper bounded capacities

• General theoretical setting of the transportation problem
• Numerical example
• Conclusions

Optimal allocation of resources among consumers under linear constraints and risks

• Model L₁ for resource allocation with risks and linear constraints
• Model L₂ for optimal resource allocation with risks and linear constraints
• Network-flow interpretation of resource allocation tasks and emerging risks
• Conclusions

Linear programming and risks

• Theoretical background and formal problem statement
• Numerical example
• Conclusions

Markov decision flows with risks

• Network-flow interpretation of Markov Decision Processes
• Numerical example
• Conclusion

Artificial network-flow neural networks with capacities and risks

• Preliminary remarks
• Theoretical setting
• Risk at signals' transmission
• Numerical example
• Conclusion

Concluding remarks